Subgroups — C₂₃×#62816 #19210442

Order 5888.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3524	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3521	C₂	1	6	yes	maximal, complemented
5	C₂₃×#3520	C₂	1	3	yes	maximal, complemented
6	C₂₃×#3519	C₂	1	3	yes	maximal, complemented
7	C₂₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3516	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3515	C₂	1	3	yes	maximal, complemented
11	C₂₃×#3514	C₂	1	3	yes	maximal, complemented
12	C₂₃×#3513	C₂	1	6	yes	maximal, complemented
13	C₂₃×#3480	C₂	1	3	yes	maximal, complemented
14	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3475	C₂	1	6	yes	maximal, complemented
16	C₂₃×#3475	C₂	1	3	yes	maximal, complemented
17	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×#41×C₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3455	C₂	1	6	yes	maximal, complemented
20	C₂₃×#3444	C₂	1	3	yes	maximal, complemented
21	C₂×C₂₃×#529	C₂	1	3	yes	maximal, complemented
22	C₂₃×#3428	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#559	C₂²	1	6	yes	complemented
27	C₂₃×#559	C₂²	1	3	yes	complemented
28	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#557	C₂²	1	2	yes	complemented
30	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#557	C₂²	1	3	yes	complemented
32	C₂₃×#556	C₂²	1	3	yes	complemented
33	C₂₃×#556	C₂²	1	6	yes	complemented
34	C₂₃×#556	C₂²	1	6	yes	complemented
35	C₂₃×#556	C₂²	1	3	yes	complemented
36	C₂₃×#555	C₂²	1	6	yes	complemented
37	C₂₃×#555	C₂²	1	3	yes	complemented
38	C₂₃×#554	C₂²	1	3	yes	complemented
39	C₂₃×#554	C₂²	1	6	yes	complemented
40	C₂₃×#554	C₂²	1	6	yes	complemented
41	C₂₃×#554	C₂²	1	3	yes	complemented
42	C₂₃×#553	C₂²	1	6	yes	complemented
43	C₂₃×#553	C₂²	1	6	yes	complemented
44	C₂₃×#553	C₂²	1	6	yes	complemented
45	C₂₃×#553	C₂²	1	12	yes	complemented
46	C₂₃×#553	C₂²	1	6	yes	complemented
47	C₂₃×#552	C₂²	1	6	yes	complemented
48	C₂₃×#552	C₂²	1	6	yes	complemented
49	C₂₃×#552	C₂²	1	12	yes	complemented
50	C₂₃×#552	C₂²	1	6	yes	complemented
51	C₂₃×#552	C₂²	1	6	yes	complemented
52	C₂₃×#551	C₂²	1	12	yes	complemented
53	C₂₃×#551	C₂²	1	12	yes	complemented
54	C₂₃×#551	C₂²	1	12	yes	complemented
55	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#550	C₂²	1	2	yes	complemented
57	C₂₃×#550	C₂²	1	3	yes	complemented
58	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
59	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
60	D₄×Q₈×C₂₃	C₂²	1	3	yes	complemented
61	C₂₃×#548	C₂²	1	2	yes	complemented
62	C₂₃×#548	C₂²	1	2	yes	complemented
63	C₂₃×#548	C₂²	1	2	yes	complemented
64	C₂₃×#548	C₂²	1	6	yes	complemented
65	C₂₃×#547	C₂²	1	3	yes	complemented
66	C₂₃×#547	C₂²	1	6	yes	complemented
67	C₂₃×#547	C₂²	1	6	yes	complemented
68	C₂₃×#547	C₂²	1	3	yes	complemented
69	C₂₃×#546	C₂²	1	6	yes	complemented
70	C₂₃×#546	C₂²	1	6	yes	complemented
71	C₂₃×#546	C₂²	1	6	yes	complemented
72	C₂₃×#546	C₂²	1	12	yes	complemented
73	C₂₃×#546	C₂²	1	6	yes	complemented
74	D₄²×C₂₃	C₂²	1	6	yes	complemented
75	D₄²×C₂₃	C₂²	1	3	yes	complemented
76	C₂₃×#542	C₂²	1	6	yes	complemented
77	C₂₃×#542	C₂²	1	6	yes	complemented
78	C₂₃×#542	C₂²	1	6	yes	complemented
79	C₂₃×#542	C₂²	1	6	yes	complemented
80	C₂₃×#541	C₂²	1	6	yes	complemented
81	C₂₃×#541	C₂²	1	6	yes	complemented
82	C₂₃×#540	C₂²	1	6	yes	complemented
83	C₂₃×#540	C₂²	1	6	yes	complemented
84	C₂₃×#539	C₂²	1	12	yes	complemented
85	C₂₃×#539	C₂²	1	12	yes	complemented
86	C₂₃×#538	C₂²	1	12	yes	complemented
87	C₂₃×#538	C₂²	1	12	yes	complemented
88	C₂₃×#533	C₂²	1	3	yes	complemented
89	C₂₃×#533	C₂²	1	3	yes	complemented
90	C₂₃×#533	C₂²	1	3	yes	complemented
91	C₂₃×#533	C₂²	1	6	yes	complemented
92	C₂₃×#532	C₂²	1	3	yes	complemented
93	C₂₃×#532	C₂²	1	3	yes	complemented
94	C₂₃×#532	C₂²	1	3	yes	complemented
95	C₂₃×#532	C₂²	1	6	yes	complemented
96	C₂₃×#529	C₂²	1	1	yes	characteristic
97	C₂₃×#529	C₂²	1	3	yes	—
98	C₂₃×#529	C₂²	1	3	yes	complemented
99	C₂₃×#529	C₂²	1	6	yes	complemented
100	C₂₃×#529	C₂²	1	6	yes	complemented
101	C₂₃×#529	C₂²	1	3	yes	complemented
102	C₂₃×#529	C₂²	1	3	yes	complemented
103	C₂₃×#529	C₂²	1	6	yes	complemented
104	C₂₃×#529	C₂²	1	3	yes	complemented
105	C₂₃×#529	C₂²	1	3	yes	complemented
106	C₂₃×#529	C₂²	1	3	yes	complemented
107	C₂₃×#529	C₂²	1	6	yes	complemented
108	C₂₃×#529	C₂²	1	6	yes	complemented
109	C₂₃×#529	C₂²	1	6	yes	complemented
110	C₂₃×#529	C₂²	1	6	yes	complemented
111	C₂₃×#529	C₂²	1	6	yes	complemented
112	C₂₃×#529	C₂²	1	6	yes	complemented
113	C₂₃×#529	C₂²	1	12	yes	complemented
114	C₂₃×#529	C₂²	1	12	yes	complemented
115	C₂×C₂₃×#126	C₂²	1	6	yes	complemented
116	C₂×C₂₃×#125	C₂²	1	3	yes	complemented
117	C₂×C₂₃×#124	C₂²	1	3	yes	complemented
118	C₂₃×#525	C₂²	1	6	yes	complemented
119	C₂₃×#525	C₂²	1	6	yes	complemented
120	C₂₃×#525	C₂²	1	6	yes	complemented
121	C₂₃×#525	C₂²	1	6	yes	complemented
122	C₂₃×#525	C₂²	1	6	yes	complemented
123	C₂×C₂₃×#123	C₂²	1	6	yes	complemented
124	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
125	C₂×C₂₃×#121	C₂²	1	3	yes	—
126	C₂₃×#520	C₂²	1	6	yes	complemented
127	C₂₃×#520	C₂²	1	2	yes	complemented
128	C₂₃×#520	C₂²	1	6	yes	complemented
129	C₂₃×#520	C₂²	1	2	yes	complemented
130	C₂₃×#519	C₂²	1	2	yes	complemented
131	C₂₃×#519	C₂²	1	2	yes	complemented
132	C₂₃×#518	C₂²	1	6	yes	complemented
133	C₂₃×#518	C₂²	1	6	yes	complemented
134	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
135	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
136	C₄×#41×C₂₃	C₂²	1	2	yes	—
137	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
138	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
139	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
140	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
141	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
142	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
143	C₄×#41×C₂₃	C₂²	1	6	yes	complemented
144	C₄×#41×C₂₃	C₂²	1	6	yes	complemented
145	C₄×#41×C₂₃	C₂²	1	6	yes	complemented
146	C₄×#41×C₂₃	C₂²	1	6	yes	complemented
147	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
148	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
149	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	complemented
150	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	complemented
151	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	complemented
152	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	complemented
153	C₂×C₄×D₄×C₂₃	C₂²	1	6	yes	complemented
154	C₂×C₂₃×#117	C₂²	1	3	yes	complemented
155	C₂×C₂₃×#117	C₂²	1	6	yes	complemented
156	C₂×C₂₃×#117	C₂²	1	6	yes	complemented
157	C₂²×C₄²×C₂₃	C₂²	1	3	yes	complemented
158	C₂×#41×C₂₃	—	2	8	no	—
159	C₂×#41×C₂₃	—	2	16	no	—
160	C₂×#41×C₂₃	C₂³	1	3	yes	—
161	C₂×#41×C₂₃	C₂³	1	6	yes	—
162	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×#41×C₂₃	C₂³	1	2	yes	—
164	C₂×#41×C₂₃	C₂³	1	3	yes	—
165	C₂×#41×C₂₃	C₂³	1	6	yes	—
166	C₂×#41×C₂₃	C₂³	1	6	yes	—
167	C₂×#41×C₂₃	C₂³	1	6	yes	—
168	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
169	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
170	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
171	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
172	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
173	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
174	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
175	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
176	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
177	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
178	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
179	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
180	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
181	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
182	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
183	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
184	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
185	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
186	C₂₃×#127	C₂³	1	3	yes	—
187	C₂₃×#127	C₂³	1	6	yes	—
188	C₂₃×#126	C₂³	1	6	yes	—
189	C₂₃×#126	C₂³	1	12	yes	—
190	C₂₃×#126	C₂³	1	6	yes	—
191	C₂₃×#126	C₂³	1	12	yes	—
192	C₂₃×#126	C₂³	1	12	yes	—
193	C₂₃×#126	C₂³	1	6	yes	—
194	C₂₃×#126	C₂³	1	12	yes	—
195	C₂₃×#126	C₂³	1	6	yes	—
196	C₂₃×#126	C₂³	1	2	yes	—
197	C₂₃×#126	C₂³	1	6	yes	—
198	C₂₃×#126	C₂³	1	6	yes	—
199	C₂₃×#126	C₂³	1	6	yes	—
200	C₂₃×#126	C₂³	1	12	yes	—
201	C₂₃×#125	C₂³	1	6	yes	—
202	C₂₃×#125	C₂³	1	12	yes	—
203	C₂₃×#125	C₂³	1	12	yes	—
204	C₂₃×#125	C₂³	1	3	yes	—
205	C₂₃×#125	C₂³	1	6	yes	—
206	C₂₃×#125	C₂³	1	6	yes	—
207	C₂₃×#125	C₂³	1	6	yes	—
208	C₂₃×#125	C₂³	1	3	yes	—
209	C₂₃×#125	C₂³	1	1	yes	characteristic
210	C₂₃×#125	C₂³	1	3	yes	—
211	C₂₃×#125	C₂³	1	6	yes	—
212	C₂₃×#125	C₂³	1	6	yes	—
213	C₂₃×#124	C₂³	1	3	yes	—
214	C₂₃×#124	C₂³	1	12	yes	—
215	C₂₃×#124	C₂³	1	6	yes	—
216	C₂₃×#124	C₂³	1	6	yes	—
217	C₂₃×#124	C₂³	1	6	yes	—
218	C₂₃×#124	C₂³	1	6	yes	—
219	C₂₃×#124	C₂³	1	12	yes	—
220	C₂₃×#124	C₂³	1	3	yes	—
221	C₂₃×#124	C₂³	1	1	yes	characteristic
222	C₂₃×#124	C₂³	1	3	yes	—
223	C₂₃×#124	C₂³	1	6	yes	—
224	C₂₃×#124	C₂³	1	6	yes	—
225	C₂₃×#123	C₂³	1	6	yes	—
226	C₂₃×#123	C₂³	1	12	yes	—
227	C₂₃×#123	C₂³	1	12	yes	—
228	C₂₃×#123	C₂³	1	12	yes	—
229	C₂₃×#123	C₂³	1	12	yes	—
230	C₂₃×#123	C₂³	1	12	yes	—
231	C₂₃×#123	C₂³	1	6	yes	—
232	C₂₃×#123	C₂³	1	12	yes	—
233	C₂₃×#123	C₂³	1	6	yes	—
234	C₂₃×#123	C₂³	1	12	yes	—
235	C₂₃×#123	C₂³	1	6	yes	—
236	C₂₃×#123	C₂³	1	2	yes	—
237	C₂₃×#123	C₂³	1	6	yes	—
238	C₂₃×#123	C₂³	1	6	yes	—
239	C₂₃×#123	C₂³	1	6	yes	—
240	C₂₃×#123	C₂³	1	12	yes	—
241	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
242	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
243	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
244	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
245	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
246	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
247	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
248	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
249	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
250	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
251	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
252	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
253	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
254	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
255	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
256	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
257	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	—
258	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
259	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
260	C₂₃×#121	C₂³	1	6	yes	—
261	C₂₃×#121	C₂³	1	6	yes	—
262	C₂₃×#121	C₂³	1	6	yes	—
263	C₂₃×#121	C₂³	1	6	yes	—
264	C₂₃×#121	C₂³	1	12	yes	—
265	C₂₃×#121	C₂³	1	6	yes	—
266	C₂₃×#121	C₂³	1	6	yes	—
267	C₂₃×#121	C₂³	1	12	yes	—
268	C₂₃×#121	C₂³	1	3	yes	—
269	C₂₃×#121	C₂³	1	12	yes	—
270	C₂₃×#121	C₂³	1	6	yes	—
271	C₂₃×#121	C₂³	1	6	yes	—
272	C₂₃×#121	C₂³	1	6	yes	—
273	C₂₃×#121	C₂³	1	12	yes	—
274	C₂₃×#121	C₂³	1	3	yes	—
275	C₂₃×#121	C₂³	1	1	yes	characteristic
276	C₂₃×#121	C₂³	1	3	yes	—
277	C₂₃×#121	C₂³	1	6	yes	—
278	C₂₃×#121	C₂³	1	6	yes	—
279	C₂₃×#120	C₂³	1	12	yes	—
280	C₂₃×#120	C₂³	1	12	yes	—
281	C₂₃×#120	C₂³	1	12	yes	—
282	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
284	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
285	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
286	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
288	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
289	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
290	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
291	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
292	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
293	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
294	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
295	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
296	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
297	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
299	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
300	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
301	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
302	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
303	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
304	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
305	C₄×D₄×C₂₃	C₂³	1	3	yes	—
306	C₄×D₄×C₂₃	C₂³	1	6	yes	—
307	C₄×D₄×C₂₃	C₂³	1	3	yes	—
308	C₄×D₄×C₂₃	C₂³	1	6	yes	—
309	C₄×D₄×C₂₃	C₂³	1	3	yes	—
310	C₄×D₄×C₂₃	C₂³	1	6	yes	—
311	C₄×D₄×C₂₃	C₂³	1	6	yes	—
312	C₄×D₄×C₂₃	C₂³	1	12	yes	—
313	C₄×D₄×C₂₃	C₂³	1	6	yes	—
314	C₄×D₄×C₂₃	C₂³	1	6	yes	—
315	C₄×D₄×C₂₃	C₂³	1	6	yes	—
316	C₄×D₄×C₂₃	C₂³	1	6	yes	—
317	C₄×D₄×C₂₃	C₂³	1	6	yes	—
318	C₄×D₄×C₂₃	C₂³	1	3	yes	—
319	C₄×D₄×C₂₃	C₂³	1	6	yes	—
320	C₄×D₄×C₂₃	C₂³	1	6	yes	—
321	C₄×D₄×C₂₃	C₂³	1	6	yes	—
322	C₄×D₄×C₂₃	C₂³	1	12	yes	—
323	C₄×D₄×C₂₃	C₂³	1	12	yes	—
324	C₄×D₄×C₂₃	C₂³	1	12	yes	—
325	C₄×D₄×C₂₃	C₂³	1	3	yes	—
326	C₄×D₄×C₂₃	C₂³	1	6	yes	—
327	C₄×D₄×C₂₃	C₂³	1	3	yes	—
328	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
329	C₄×D₄×C₂₃	C₂³	1	2	yes	—
330	C₄×D₄×C₂₃	C₂³	1	3	yes	—
331	C₄×D₄×C₂₃	C₂³	1	3	yes	—
332	C₄×D₄×C₂₃	C₂³	1	6	yes	—
333	C₄×D₄×C₂₃	C₂³	1	3	yes	—
334	C₄×D₄×C₂₃	C₂³	1	6	yes	—
335	C₄×D₄×C₂₃	C₂³	1	6	yes	—
336	C₄×D₄×C₂₃	C₂³	1	3	yes	—
337	C₄×D₄×C₂₃	C₂³	1	3	yes	—
338	C₄×D₄×C₂₃	C₂³	1	6	yes	—
339	C₄×D₄×C₂₃	C₂³	1	6	yes	—
340	C₄×D₄×C₂₃	C₂³	1	6	yes	—
341	C₄×D₄×C₂₃	C₂³	1	12	yes	—
342	C₄×D₄×C₂₃	C₂³	1	12	yes	—
343	C₄×D₄×C₂₃	C₂³	1	6	yes	—
344	C₄×D₄×C₂₃	C₂³	1	6	yes	—
345	C₄×D₄×C₂₃	C₂³	1	6	yes	—
346	C₄×D₄×C₂₃	C₂³	1	12	yes	—
347	C₂₃×#117	C₂³	1	6	yes	—
348	C₂₃×#117	C₂³	1	12	yes	—
349	C₂₃×#117	C₂³	1	6	yes	—
350	C₂₃×#117	C₂³	1	12	yes	—
351	C₂₃×#117	C₂³	1	12	yes	—
352	C₂₃×#117	C₂³	1	3	yes	—
353	C₂₃×#117	C₂³	1	6	yes	—
354	C₂₃×#117	C₂³	1	6	yes	—
355	C₂₃×#117	C₂³	1	6	yes	—
356	C₂₃×#117	C₂³	1	3	yes	—
357	C₂₃×#117	C₂³	1	3	yes	—
358	C₂₃×#117	C₂³	1	2	yes	—
359	C₂₃×#117	C₂³	1	6	yes	—
360	C₂₃×#117	C₂³	1	3	yes	—
361	C₂₃×#117	C₂³	1	6	yes	—
362	C₂₃×#117	C₂³	1	6	yes	—
363	C₂₃×#117	C₂³	1	6	yes	—
364	C₂₃×#117	C₂³	1	6	yes	—
365	C₂₃×#117	C₂³	1	6	yes	—
366	C₂₃×#117	C₂³	1	6	yes	—
367	C₂₃×#117	C₂³	1	6	yes	—
368	C₂₃×#117	C₂³	1	6	yes	—
369	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
370	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
371	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
372	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
373	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
374	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
375	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
376	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
377	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
378	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
379	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
380	C₂×C₂²⋊C₄×C₂₃	C₂³	1	12	yes	—
381	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
382	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
383	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
384	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
385	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
386	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
387	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
388	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
389	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
390	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
391	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
392	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
393	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
394	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
395	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
396	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
397	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
398	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
399	C₂×C₄²×C₂₃	C₂³	1	12	yes	—
400	C₂⁴×C₂₃	C₂⁴	1	3	yes	—
401	C₂⁴×C₂₃	C₂⁴	1	6	yes	—
402	#41×C₂₃	—	2	4	no	—
403	#41×C₂₃	—	2	8	no	—
404	#41×C₂₃	—	2	12	no	—
405	#41×C₂₃	—	2	24	no	—
406	#41×C₂₃	—	2	12	no	—
407	#41×C₂₃	—	2	24	no	—
408	#41×C₂₃	—	4	12	no	—
409	#41×C₂₃	—	4	12	no	—
410	#41×C₂₃	#41	1	8	yes	complemented
411	C₂×Q₈×C₂₃	—	2	4	no	—
412	C₂×Q₈×C₂₃	—	2	8	no	—
413	C₂×Q₈×C₂₃	—	4	6	no	—
414	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
416	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
417	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
418	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
419	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
420	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₂₃	—	2	12	no	—
422	C₂×D₄×C₂₃	—	2	24	no	—
423	C₂×D₄×C₂₃	—	4	6	no	—
424	C₂×D₄×C₂₃	—	4	12	no	—
425	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
426	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
427	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
428	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
429	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
430	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
431	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
432	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
433	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
434	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
435	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
436	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
437	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
438	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
439	C₂²×C₄×C₂₃	—	2	12	no	—
440	C₂²×C₄×C₂₃	—	2	24	no	—
441	C₂²×C₄×C₂₃	—	4	6	no	—
442	C₂²×C₄×C₂₃	—	4	6	no	—
443	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
446	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
447	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
448	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
449	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
450	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
451	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
452	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
453	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
454	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
456	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
457	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
458	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
459	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
460	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
461	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
462	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
463	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
464	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
465	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
466	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
467	C₂²×C₄×C₂₃	C₂⁴	1	12	yes	—
468	C₂²×C₄×C₂₃	C₂⁴	1	12	yes	—
469	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
470	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
471	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
472	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
473	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
474	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
475	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
476	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
477	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
478	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
479	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
480	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
481	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
482	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
483	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
484	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
485	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
486	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
487	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
488	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
489	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
490	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
491	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
492	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
493	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
494	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
495	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
496	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
497	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
498	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
499	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
500	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
501	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
502	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
503	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
504	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
505	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
506	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
507	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
508	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
509	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
510	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
511	C₂²⋊C₄×C₂₃	C₂⁴	1	2	yes	—
512	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
513	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
514	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
515	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
516	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
517	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
518	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
519	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
520	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
521	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
522	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
523	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
524	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
525	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
526	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
527	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
528	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
529	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
530	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
531	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
532	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
533	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
534	C₄²×C₂₃	C₂⁴	1	3	yes	—
535	C₄²×C₂₃	C₂⁴	1	3	yes	—
536	C₄²×C₂₃	C₂⁴	1	3	yes	—
537	C₄²×C₂₃	C₂⁴	1	3	yes	—
538	C₄²×C₂₃	C₂⁴	1	3	yes	—
539	C₄²×C₂₃	C₂⁴	1	3	yes	—
540	C₄²×C₂₃	C₂⁴	1	3	yes	—
541	C₄²×C₂₃	C₂⁴	1	3	yes	—
542	C₄²×C₂₃	C₂⁴	1	3	yes	—
543	C₄²×C₂₃	C₂⁴	1	3	yes	—
544	C₄²×C₂₃	C₂⁴	1	12	yes	—
545	C₄²×C₂₃	C₂⁴	1	12	yes	—
546	C₄²×C₂₃	C₂⁴	1	6	yes	—
547	C₄²×C₂₃	C₂⁴	1	6	yes	—
548	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
549	C₄²×C₂₃	C₂⁴	1	3	yes	—
550	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
551	C₄²×C₂₃	C₂⁴	1	2	yes	—
552	C₄²×C₂₃	C₂⁴	1	3	yes	—
553	C₄²×C₂₃	C₂⁴	1	6	yes	—
554	#62816	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂³×C₂₃	—	2	6	no	—
556	C₂³×C₂₃	—	2	6	no	—
557	C₂³×C₂₃	—	2	12	no	—
558	C₂³×C₂₃	—	4	3	no	—
559	C₂³×C₂₃	—	4	6	no	—
560	C₂³×C₂₃	—	4	6	no	—
561	C₂³×C₂₃	C₂⁵	1	2	yes	—
562	C₂³×C₂₃	C₂⁵	1	3	yes	—
563	C₂³×C₂₃	C₂⁵	1	6	yes	—
564	C₂³×C₂₃	C₂⁵	1	3	yes	—
565	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
566	Q₈×C₂₃	—	2	6	no	—
567	Q₈×C₂₃	—	2	12	no	—
568	Q₈×C₂₃	—	2	2	no	—
569	Q₈×C₂₃	—	2	6	no	—
570	Q₈×C₂₃	—	4	6	no	—
571	Q₈×C₂₃	—	4	6	no	—
572	Q₈×C₂₃	C₂×#41	1	4	yes	—
573	D₄×C₂₃	—	2	12	no	—
574	D₄×C₂₃	—	2	24	no	—
575	D₄×C₂₃	—	2	4	no	—
576	D₄×C₂₃	—	2	12	no	—
577	D₄×C₂₃	—	2	6	no	—
578	D₄×C₂₃	—	2	12	no	—
579	D₄×C₂₃	—	2	2	no	—
580	D₄×C₂₃	—	2	6	no	—
581	D₄×C₂₃	—	4	6	no	—
582	D₄×C₂₃	—	4	6	no	—
583	D₄×C₂₃	—	4	6	no	—
584	D₄×C₂₃	—	4	6	no	—
585	D₄×C₂₃	—	4	12	no	—
586	D₄×C₂₃	C₂×#41	1	12	yes	—
587	C₂×C₄×C₂₃	—	2	6	no	—
588	C₂×C₄×C₂₃	—	2	12	no	—
589	C₂×C₄×C₂₃	—	2	2	no	—
590	C₂×C₄×C₂₃	—	2	6	no	—
591	C₂×C₄×C₂₃	—	2	2	no	—
592	C₂×C₄×C₂₃	—	2	4	no	—
593	C₂×C₄×C₂₃	—	2	6	no	—
594	C₂×C₄×C₂₃	—	2	12	no	—
595	C₂×C₄×C₂₃	—	2	6	no	—
596	C₂×C₄×C₂₃	—	2	12	no	—
597	C₂×C₄×C₂₃	—	2	6	no	—
598	C₂×C₄×C₂₃	—	2	12	no	—
599	C₂×C₄×C₂₃	—	2	2	no	—
600	C₂×C₄×C₂₃	—	2	6	no	—
601	C₂×C₄×C₂₃	—	2	6	no	—
602	C₂×C₄×C₂₃	—	4	3	no	—
603	C₂×C₄×C₂₃	—	4	3	no	—
604	C₂×C₄×C₂₃	—	4	3	no	—
605	C₂×C₄×C₂₃	—	4	3	no	—
606	C₂×C₄×C₂₃	—	4	3	no	—
607	C₂×C₄×C₂₃	—	4	3	no	—
608	C₂×C₄×C₂₃	—	4	3	no	—
609	C₂×C₄×C₂₃	—	4	6	no	—
610	C₂×C₄×C₂₃	—	4	6	no	—
611	C₂×C₄×C₂₃	—	4	12	no	—
612	C₂×C₄×C₂₃	—	4	12	no	—
613	C₂×C₄×C₂₃	C₂×#41	1	12	yes	—
614	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
615	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
616	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
617	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
618	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
619	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
620	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
621	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
622	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
623	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
624	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
625	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
626	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
627	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
628	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
629	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
630	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
631	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
632	#3524	C₂×C₂₃	1	2	yes	complemented
633	#3523	C₂×C₂₃	1	1	yes	characteristic, complemented
634	#3522	C₂×C₂₃	1	1	yes	characteristic, complemented
635	#3521	C₂×C₂₃	1	6	yes	complemented
636	#3520	C₂×C₂₃	1	3	yes	complemented
637	#3519	C₂×C₂₃	1	3	yes	complemented
638	#3518	C₂×C₂₃	1	1	yes	characteristic, complemented
639	#3517	C₂×C₂₃	1	1	yes	characteristic, complemented
640	#3516	C₂×C₂₃	1	2	yes	complemented
641	#3515	C₂×C₂₃	1	3	yes	complemented
642	#3514	C₂×C₂₃	1	3	yes	complemented
643	#3513	C₂×C₂₃	1	6	yes	complemented
644	#3480	C₂×C₂₃	1	3	yes	complemented
645	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
646	#3475	C₂×C₂₃	1	6	yes	complemented
647	#3475	C₂×C₂₃	1	3	yes	complemented
648	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
649	D₄×#41	C₂×C₂₃	1	2	yes	complemented
650	#3455	C₂×C₂₃	1	6	yes	complemented
651	#3444	C₂×C₂₃	1	3	yes	complemented
652	C₂×#529	C₂×C₂₃	1	3	yes	complemented
653	#3428	C₂×C₂₃	1	2	yes	complemented
654	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
655	C₂²×C₂₃	—	2	1	no	—
656	C₂²×C₂₃	—	2	1	no	—
657	C₂²×C₂₃	—	2	3	no	—
658	C₂²×C₂₃	—	2	3	no	—
659	C₂²×C₂₃	—	2	2	no	—
660	C₂²×C₂₃	—	2	3	no	—
661	C₂²×C₂₃	—	2	6	no	—
662	C₂²×C₂₃	—	2	3	no	—
663	C₂²×C₂₃	—	2	6	no	—
664	C₂²×C₂₃	—	2	6	no	—
665	C₂²×C₂₃	—	2	3	no	—
666	C₂²×C₂₃	—	2	2	no	—
667	C₂²×C₂₃	—	2	2	no	—
668	C₂²×C₂₃	—	4	12	no	—
669	C₂²×C₂₃	—	8	12	no	—
670	C₂²×C₂₃	C₂²×#41	1	6	yes	—
671	C₂²×C₂₃	#585	1	2	yes	—
672	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
673	C₄×C₂₃	—	2	1	no	—
674	C₄×C₂₃	—	2	2	no	—
675	C₄×C₂₃	—	2	3	no	—
676	C₄×C₂₃	—	2	6	no	—
677	C₄×C₂₃	—	2	1	no	—
678	C₄×C₂₃	—	2	1	no	—
679	C₄×C₂₃	—	2	3	no	—
680	C₄×C₂₃	—	2	1	no	—
681	C₄×C₂₃	—	2	3	no	—
682	C₄×C₂₃	—	2	3	no	—
683	C₄×C₂₃	—	2	3	no	—
684	C₄×C₂₃	—	2	2	no	—
685	C₄×C₂₃	—	2	6	no	—
686	C₄×C₂₃	—	2	6	no	—
687	C₄×C₂₃	—	2	2	no	—
688	C₄×C₂₃	C₂²×#41	1	2	yes	—
689	C₄×C₂₃	C₂²×#41	1	6	yes	—
690	C₄×C₂₃	#585	1	2	yes	—
691	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
692	C₂²×#41	C₂²×C₂₃	1	2	yes	—
693	#559	C₂²×C₂₃	1	6	yes	complemented
694	#559	C₂²×C₂₃	1	3	yes	complemented
695	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	#557	C₂²×C₂₃	1	2	yes	complemented
697	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#557	C₂²×C₂₃	1	3	yes	complemented
699	#556	C₂²×C₂₃	1	3	yes	complemented
700	#556	C₂²×C₂₃	1	6	yes	complemented
701	#556	C₂²×C₂₃	1	6	yes	complemented
702	#556	C₂²×C₂₃	1	3	yes	complemented
703	#555	C₂²×C₂₃	1	6	yes	complemented
704	#555	C₂²×C₂₃	1	3	yes	complemented
705	#554	C₂²×C₂₃	1	3	yes	complemented
706	#554	C₂²×C₂₃	1	6	yes	complemented
707	#554	C₂²×C₂₃	1	6	yes	complemented
708	#554	C₂²×C₂₃	1	3	yes	complemented
709	#553	C₂²×C₂₃	1	6	yes	complemented
710	#553	C₂²×C₂₃	1	6	yes	complemented
711	#553	C₂²×C₂₃	1	6	yes	complemented
712	#553	C₂²×C₂₃	1	12	yes	complemented
713	#553	C₂²×C₂₃	1	6	yes	complemented
714	#552	C₂²×C₂₃	1	6	yes	complemented
715	#552	C₂²×C₂₃	1	6	yes	complemented
716	#552	C₂²×C₂₃	1	12	yes	complemented
717	#552	C₂²×C₂₃	1	6	yes	complemented
718	#552	C₂²×C₂₃	1	6	yes	complemented
719	#551	C₂²×C₂₃	1	12	yes	complemented
720	#551	C₂²×C₂₃	1	12	yes	complemented
721	#551	C₂²×C₂₃	1	12	yes	complemented
722	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	#550	C₂²×C₂₃	1	2	yes	complemented
724	#550	C₂²×C₂₃	1	3	yes	complemented
725	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
726	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	D₄×Q₈	C₂²×C₂₃	1	3	yes	complemented
728	#548	C₂²×C₂₃	1	2	yes	complemented
729	#548	C₂²×C₂₃	1	2	yes	complemented
730	#548	C₂²×C₂₃	1	2	yes	complemented
731	#548	C₂²×C₂₃	1	6	yes	complemented
732	#547	C₂²×C₂₃	1	3	yes	complemented
733	#547	C₂²×C₂₃	1	6	yes	complemented
734	#547	C₂²×C₂₃	1	6	yes	complemented
735	#547	C₂²×C₂₃	1	3	yes	complemented
736	#546	C₂²×C₂₃	1	6	yes	complemented
737	#546	C₂²×C₂₃	1	6	yes	complemented
738	#546	C₂²×C₂₃	1	6	yes	complemented
739	#546	C₂²×C₂₃	1	12	yes	complemented
740	#546	C₂²×C₂₃	1	6	yes	complemented
741	D₄²	C₂²×C₂₃	1	6	yes	complemented
742	D₄²	C₂²×C₂₃	1	3	yes	complemented
743	#542	C₂²×C₂₃	1	6	yes	complemented
744	#542	C₂²×C₂₃	1	6	yes	complemented
745	#542	C₂²×C₂₃	1	6	yes	complemented
746	#542	C₂²×C₂₃	1	6	yes	complemented
747	#541	C₂²×C₂₃	1	6	yes	complemented
748	#541	C₂²×C₂₃	1	6	yes	complemented
749	#540	C₂²×C₂₃	1	6	yes	complemented
750	#540	C₂²×C₂₃	1	6	yes	complemented
751	#539	C₂²×C₂₃	1	12	yes	complemented
752	#539	C₂²×C₂₃	1	12	yes	complemented
753	#538	C₂²×C₂₃	1	12	yes	complemented
754	#538	C₂²×C₂₃	1	12	yes	complemented
755	#533	C₂²×C₂₃	1	3	yes	complemented
756	#533	C₂²×C₂₃	1	3	yes	complemented
757	#533	C₂²×C₂₃	1	3	yes	complemented
758	#533	C₂²×C₂₃	1	6	yes	complemented
759	#532	C₂²×C₂₃	1	3	yes	complemented
760	#532	C₂²×C₂₃	1	3	yes	complemented
761	#532	C₂²×C₂₃	1	3	yes	complemented
762	#532	C₂²×C₂₃	1	6	yes	complemented
763	#529	C₂²×C₂₃	1	1	yes	characteristic
764	#529	C₂²×C₂₃	1	3	yes	—
765	#529	C₂²×C₂₃	1	3	yes	complemented
766	#529	C₂²×C₂₃	1	6	yes	complemented
767	#529	C₂²×C₂₃	1	6	yes	complemented
768	#529	C₂²×C₂₃	1	3	yes	complemented
769	#529	C₂²×C₂₃	1	3	yes	complemented
770	#529	C₂²×C₂₃	1	6	yes	complemented
771	#529	C₂²×C₂₃	1	3	yes	complemented
772	#529	C₂²×C₂₃	1	3	yes	complemented
773	#529	C₂²×C₂₃	1	3	yes	complemented
774	#529	C₂²×C₂₃	1	6	yes	complemented
775	#529	C₂²×C₂₃	1	6	yes	complemented
776	#529	C₂²×C₂₃	1	6	yes	complemented
777	#529	C₂²×C₂₃	1	6	yes	complemented
778	#529	C₂²×C₂₃	1	6	yes	complemented
779	#529	C₂²×C₂₃	1	6	yes	complemented
780	#529	C₂²×C₂₃	1	12	yes	complemented
781	#529	C₂²×C₂₃	1	12	yes	complemented
782	C₂×#126	C₂²×C₂₃	1	6	yes	complemented
783	C₂×#125	C₂²×C₂₃	1	3	yes	complemented
784	C₂×#124	C₂²×C₂₃	1	3	yes	complemented
785	#525	C₂²×C₂₃	1	6	yes	complemented
786	#525	C₂²×C₂₃	1	6	yes	complemented
787	#525	C₂²×C₂₃	1	6	yes	complemented
788	#525	C₂²×C₂₃	1	6	yes	complemented
789	#525	C₂²×C₂₃	1	6	yes	complemented
790	C₂×#123	C₂²×C₂₃	1	6	yes	complemented
791	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	3	yes	complemented
792	C₂×#121	C₂²×C₂₃	1	3	yes	—
793	#520	C₂²×C₂₃	1	6	yes	complemented
794	#520	C₂²×C₂₃	1	2	yes	complemented
795	#520	C₂²×C₂₃	1	6	yes	complemented
796	#520	C₂²×C₂₃	1	2	yes	complemented
797	#519	C₂²×C₂₃	1	2	yes	complemented
798	#519	C₂²×C₂₃	1	2	yes	complemented
799	#518	C₂²×C₂₃	1	6	yes	complemented
800	#518	C₂²×C₂₃	1	6	yes	complemented
801	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
802	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
803	C₄×#41	C₂²×C₂₃	1	2	yes	—
804	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
805	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
806	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
807	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
808	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
809	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
810	C₄×#41	C₂²×C₂₃	1	6	yes	complemented
811	C₄×#41	C₂²×C₂₃	1	6	yes	complemented
812	C₄×#41	C₂²×C₂₃	1	6	yes	complemented
813	C₄×#41	C₂²×C₂₃	1	6	yes	complemented
814	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
815	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
816	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	complemented
817	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	complemented
818	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	complemented
819	C₂×C₄×D₄	C₂²×C₂₃	1	6	yes	complemented
820	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	complemented
821	C₂×#117	C₂²×C₂₃	1	3	yes	complemented
822	C₂×#117	C₂²×C₂₃	1	6	yes	complemented
823	C₂×#117	C₂²×C₂₃	1	6	yes	complemented
824	C₂²×C₄²	C₂²×C₂₃	1	3	yes	complemented
825	C₂×C₂₃	—	2	2	no	—
826	C₂×C₂₃	—	2	6	no	—
827	C₂×C₂₃	—	4	3	no	—
828	C₂×C₂₃	—	4	6	no	—
829	C₂×C₂₃	—	4	2	no	—
830	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
831	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
832	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
833	C₂×#41	—	2	8	no	—
834	C₂×#41	—	2	16	no	—
835	C₂×#41	C₂³×C₂₃	1	3	yes	—
836	C₂×#41	C₂³×C₂₃	1	6	yes	—
837	C₂×#41	C₂³×C₂₃	1	3	yes	—
838	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
839	C₂×#41	C₂³×C₂₃	1	6	yes	—
840	C₂×#41	C₂³×C₂₃	1	2	yes	—
841	C₂×#41	C₂³×C₂₃	1	6	yes	—
842	C₂×#41	C₂³×C₂₃	1	6	yes	—
843	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
844	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
846	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
847	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
848	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
849	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
850	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
851	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
852	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
853	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
854	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
855	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
856	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
857	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
858	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
859	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
860	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
861	#127	C₂³×C₂₃	1	3	yes	—
862	#127	C₂³×C₂₃	1	6	yes	—
863	#126	C₂³×C₂₃	1	2	yes	—
864	#126	C₂³×C₂₃	1	6	yes	—
865	#126	C₂³×C₂₃	1	6	yes	—
866	#126	C₂³×C₂₃	1	6	yes	—
867	#126	C₂³×C₂₃	1	6	yes	—
868	#126	C₂³×C₂₃	1	6	yes	—
869	#126	C₂³×C₂₃	1	6	yes	—
870	#126	C₂³×C₂₃	1	6	yes	—
871	#126	C₂³×C₂₃	1	12	yes	—
872	#126	C₂³×C₂₃	1	12	yes	—
873	#126	C₂³×C₂₃	1	12	yes	—
874	#126	C₂³×C₂₃	1	12	yes	—
875	#126	C₂³×C₂₃	1	12	yes	—
876	#125	C₂³×C₂₃	1	1	yes	characteristic
877	#125	C₂³×C₂₃	1	3	yes	—
878	#125	C₂³×C₂₃	1	3	yes	—
879	#125	C₂³×C₂₃	1	6	yes	—
880	#125	C₂³×C₂₃	1	6	yes	—
881	#125	C₂³×C₂₃	1	3	yes	—
882	#125	C₂³×C₂₃	1	6	yes	—
883	#125	C₂³×C₂₃	1	6	yes	—
884	#125	C₂³×C₂₃	1	12	yes	—
885	#125	C₂³×C₂₃	1	12	yes	—
886	#125	C₂³×C₂₃	1	6	yes	—
887	#125	C₂³×C₂₃	1	6	yes	—
888	#124	C₂³×C₂₃	1	1	yes	characteristic
889	#124	C₂³×C₂₃	1	3	yes	—
890	#124	C₂³×C₂₃	1	3	yes	—
891	#124	C₂³×C₂₃	1	6	yes	—
892	#124	C₂³×C₂₃	1	3	yes	—
893	#124	C₂³×C₂₃	1	6	yes	—
894	#124	C₂³×C₂₃	1	6	yes	—
895	#124	C₂³×C₂₃	1	6	yes	—
896	#124	C₂³×C₂₃	1	12	yes	—
897	#124	C₂³×C₂₃	1	12	yes	—
898	#124	C₂³×C₂₃	1	6	yes	—
899	#124	C₂³×C₂₃	1	6	yes	—
900	#123	C₂³×C₂₃	1	2	yes	—
901	#123	C₂³×C₂₃	1	6	yes	—
902	#123	C₂³×C₂₃	1	6	yes	—
903	#123	C₂³×C₂₃	1	6	yes	—
904	#123	C₂³×C₂₃	1	6	yes	—
905	#123	C₂³×C₂₃	1	6	yes	—
906	#123	C₂³×C₂₃	1	6	yes	—
907	#123	C₂³×C₂₃	1	6	yes	—
908	#123	C₂³×C₂₃	1	12	yes	—
909	#123	C₂³×C₂₃	1	12	yes	—
910	#123	C₂³×C₂₃	1	12	yes	—
911	#123	C₂³×C₂₃	1	12	yes	—
912	#123	C₂³×C₂₃	1	12	yes	—
913	#123	C₂³×C₂₃	1	12	yes	—
914	#123	C₂³×C₂₃	1	12	yes	—
915	#123	C₂³×C₂₃	1	12	yes	—
916	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
917	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
918	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
919	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
920	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	—
921	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
922	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
923	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
924	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
925	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
926	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
927	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
928	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
929	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
930	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
931	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
932	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
933	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
934	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
935	#121	C₂³×C₂₃	1	1	yes	characteristic
936	#121	C₂³×C₂₃	1	3	yes	—
937	#121	C₂³×C₂₃	1	6	yes	—
938	#121	C₂³×C₂₃	1	6	yes	—
939	#121	C₂³×C₂₃	1	3	yes	—
940	#121	C₂³×C₂₃	1	3	yes	—
941	#121	C₂³×C₂₃	1	6	yes	—
942	#121	C₂³×C₂₃	1	6	yes	—
943	#121	C₂³×C₂₃	1	6	yes	—
944	#121	C₂³×C₂₃	1	6	yes	—
945	#121	C₂³×C₂₃	1	6	yes	—
946	#121	C₂³×C₂₃	1	6	yes	—
947	#121	C₂³×C₂₃	1	6	yes	—
948	#121	C₂³×C₂₃	1	6	yes	—
949	#121	C₂³×C₂₃	1	6	yes	—
950	#121	C₂³×C₂₃	1	12	yes	—
951	#121	C₂³×C₂₃	1	12	yes	—
952	#121	C₂³×C₂₃	1	12	yes	—
953	#121	C₂³×C₂₃	1	12	yes	—
954	#120	C₂³×C₂₃	1	12	yes	—
955	#120	C₂³×C₂₃	1	12	yes	—
956	#120	C₂³×C₂₃	1	12	yes	—
957	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
958	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
959	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
960	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
961	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
962	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
963	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
964	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
965	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
966	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
967	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
968	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
969	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
970	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
971	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
972	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
973	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
974	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
975	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
976	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
977	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
978	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
979	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
980	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
981	C₄×D₄	C₂³×C₂₃	1	2	yes	—
982	C₄×D₄	C₂³×C₂₃	1	3	yes	—
983	C₄×D₄	C₂³×C₂₃	1	3	yes	—
984	C₄×D₄	C₂³×C₂₃	1	3	yes	—
985	C₄×D₄	C₂³×C₂₃	1	3	yes	—
986	C₄×D₄	C₂³×C₂₃	1	6	yes	—
987	C₄×D₄	C₂³×C₂₃	1	3	yes	—
988	C₄×D₄	C₂³×C₂₃	1	6	yes	—
989	C₄×D₄	C₂³×C₂₃	1	6	yes	—
990	C₄×D₄	C₂³×C₂₃	1	3	yes	—
991	C₄×D₄	C₂³×C₂₃	1	3	yes	—
992	C₄×D₄	C₂³×C₂₃	1	6	yes	—
993	C₄×D₄	C₂³×C₂₃	1	3	yes	—
994	C₄×D₄	C₂³×C₂₃	1	6	yes	—
995	C₄×D₄	C₂³×C₂₃	1	3	yes	—
996	C₄×D₄	C₂³×C₂₃	1	6	yes	—
997	C₄×D₄	C₂³×C₂₃	1	6	yes	—
998	C₄×D₄	C₂³×C₂₃	1	6	yes	—
999	C₄×D₄	C₂³×C₂₃	1	3	yes	—
1000	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1001	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1002	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1003	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1004	C₄×D₄	C₂³×C₂₃	1	3	yes	—
1005	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1006	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1007	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1008	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1009	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1010	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1011	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1012	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1013	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1014	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1015	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1016	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1017	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1018	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1019	C₄×D₄	C₂³×C₂₃	1	12	yes	—
1020	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1021	C₄×D₄	C₂³×C₂₃	1	6	yes	—
1022	#117	C₂³×C₂₃	1	3	yes	—
1023	#117	C₂³×C₂₃	1	2	yes	—
1024	#117	C₂³×C₂₃	1	6	yes	—
1025	#117	C₂³×C₂₃	1	3	yes	—
1026	#117	C₂³×C₂₃	1	6	yes	—
1027	#117	C₂³×C₂₃	1	6	yes	—
1028	#117	C₂³×C₂₃	1	6	yes	—
1029	#117	C₂³×C₂₃	1	6	yes	—
1030	#117	C₂³×C₂₃	1	6	yes	—
1031	#117	C₂³×C₂₃	1	3	yes	—
1032	#117	C₂³×C₂₃	1	3	yes	—
1033	#117	C₂³×C₂₃	1	6	yes	—
1034	#117	C₂³×C₂₃	1	6	yes	—
1035	#117	C₂³×C₂₃	1	6	yes	—
1036	#117	C₂³×C₂₃	1	6	yes	—
1037	#117	C₂³×C₂₃	1	6	yes	—
1038	#117	C₂³×C₂₃	1	6	yes	—
1039	#117	C₂³×C₂₃	1	12	yes	—
1040	#117	C₂³×C₂₃	1	6	yes	—
1041	#117	C₂³×C₂₃	1	6	yes	—
1042	#117	C₂³×C₂₃	1	12	yes	—
1043	#117	C₂³×C₂₃	1	12	yes	—
1044	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
1045	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
1046	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1047	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1048	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1049	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1050	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
1051	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1052	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
1053	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
1054	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1055	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1056	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1057	C₂×C₂²⋊C₄	C₂³×C₂₃	1	12	yes	—
1058	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1059	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1060	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
1061	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1062	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1063	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
1064	C₂×C₄²	C₂³×C₂₃	1	12	yes	—
1065	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1066	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1067	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1068	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1069	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1070	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1071	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1072	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1073	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
1074	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1075	C₂₃	#62816	1	1	yes	characteristic, direct product factor, Sylow
1076	C₂⁴	C₂⁴×C₂₃	1	3	yes	—
1077	C₂⁴	C₂⁴×C₂₃	1	6	yes	—
1078	#41	—	2	4	no	—
1079	#41	—	2	8	no	—
1080	#41	—	2	12	no	—
1081	#41	—	2	24	no	—
1082	#41	—	2	12	no	—
1083	#41	—	2	24	no	—
1084	#41	—	4	12	no	—
1085	#41	—	4	12	no	—
1086	#41	#41×C₂₃	1	8	yes	complemented
1087	C₂×Q₈	—	2	4	no	—
1088	C₂×Q₈	—	2	8	no	—
1089	C₂×Q₈	—	4	6	no	—
1090	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1091	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
1092	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
1093	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
1094	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
1095	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
1096	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1097	C₂×D₄	—	2	12	no	—
1098	C₂×D₄	—	2	24	no	—
1099	C₂×D₄	—	4	6	no	—
1100	C₂×D₄	—	4	12	no	—
1101	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1102	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
1103	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1104	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1105	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1106	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
1107	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1108	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
1109	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1110	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1111	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
1112	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1113	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
1114	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
1115	C₂²×C₄	—	2	12	no	—
1116	C₂²×C₄	—	2	24	no	—
1117	C₂²×C₄	—	4	6	no	—
1118	C₂²×C₄	—	4	6	no	—
1119	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1123	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1124	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1125	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1126	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1127	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1128	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1129	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1130	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1131	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1132	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1133	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1134	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1135	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1136	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1137	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1138	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1139	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1140	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1141	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1142	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
1143	C₂²×C₄	C₂⁴×C₂₃	1	12	yes	—
1144	C₂²×C₄	C₂⁴×C₂₃	1	12	yes	—
1145	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
1146	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1147	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1148	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1149	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1150	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1151	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1152	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1153	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1154	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1155	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1156	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1157	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1158	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1159	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1160	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1161	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
1162	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1163	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1164	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1165	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1166	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1167	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1168	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1169	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1170	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1171	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1172	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1173	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1174	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1175	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1176	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1177	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1178	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1179	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1180	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1181	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1182	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1183	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1184	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1185	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1186	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1187	C₂²⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1188	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1189	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1190	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1191	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1192	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1193	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1194	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1195	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1196	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1197	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1198	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1199	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1200	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1201	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1202	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1203	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1204	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
1205	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1206	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1207	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
1208	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1209	C₄²	C₂⁴×C₂₃	1	3	yes	—
1210	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1211	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1213	C₄²	C₂⁴×C₂₃	1	3	yes	—
1214	C₄²	C₂⁴×C₂₃	1	3	yes	—
1215	C₄²	C₂⁴×C₂₃	1	3	yes	—
1216	C₄²	C₂⁴×C₂₃	1	2	yes	—
1217	C₄²	C₂⁴×C₂₃	1	3	yes	—
1218	C₄²	C₂⁴×C₂₃	1	6	yes	—
1219	C₄²	C₂⁴×C₂₃	1	3	yes	—
1220	C₄²	C₂⁴×C₂₃	1	3	yes	—
1221	C₄²	C₂⁴×C₂₃	1	3	yes	—
1222	C₄²	C₂⁴×C₂₃	1	3	yes	—
1223	C₄²	C₂⁴×C₂₃	1	3	yes	—
1224	C₄²	C₂⁴×C₂₃	1	3	yes	—
1225	C₄²	C₂⁴×C₂₃	1	3	yes	—
1226	C₄²	C₂⁴×C₂₃	1	12	yes	—
1227	C₄²	C₂⁴×C₂₃	1	12	yes	—
1228	C₄²	C₂⁴×C₂₃	1	6	yes	—
1229	C₄²	C₂⁴×C₂₃	1	6	yes	—
1230	C₂³	—	2	6	no	—
1231	C₂³	—	2	6	no	—
1232	C₂³	—	2	12	no	—
1233	C₂³	—	4	3	no	—
1234	C₂³	—	4	6	no	—
1235	C₂³	—	4	6	no	—
1236	C₂³	C₂⁵×C₂₃	1	2	yes	—
1237	C₂³	C₂⁵×C₂₃	1	3	yes	—
1238	C₂³	C₂⁵×C₂₃	1	6	yes	—
1239	C₂³	C₂⁵×C₂₃	1	3	yes	—
1240	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1241	Q₈	—	2	6	no	—
1242	Q₈	—	2	12	no	—
1243	Q₈	—	2	2	no	—
1244	Q₈	—	2	6	no	—
1245	Q₈	—	4	6	no	—
1246	Q₈	—	4	6	no	—
1247	Q₈	C₂×#41×C₂₃	1	4	yes	—
1248	D₄	—	2	12	no	—
1249	D₄	—	2	24	no	—
1250	D₄	—	2	4	no	—
1251	D₄	—	2	12	no	—
1252	D₄	—	2	6	no	—
1253	D₄	—	2	12	no	—
1254	D₄	—	2	2	no	—
1255	D₄	—	2	6	no	—
1256	D₄	—	4	6	no	—
1257	D₄	—	4	6	no	—
1258	D₄	—	4	6	no	—
1259	D₄	—	4	6	no	—
1260	D₄	—	4	12	no	—
1261	D₄	C₂×#41×C₂₃	1	12	yes	—
1262	C₂×C₄	—	2	6	no	—
1263	C₂×C₄	—	2	12	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	6	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	4	no	—
1268	C₂×C₄	—	2	6	no	—
1269	C₂×C₄	—	2	12	no	—
1270	C₂×C₄	—	2	6	no	—
1271	C₂×C₄	—	2	12	no	—
1272	C₂×C₄	—	2	6	no	—
1273	C₂×C₄	—	2	12	no	—
1274	C₂×C₄	—	2	2	no	—
1275	C₂×C₄	—	2	6	no	—
1276	C₂×C₄	—	2	6	no	—
1277	C₂×C₄	—	4	3	no	—
1278	C₂×C₄	—	4	3	no	—
1279	C₂×C₄	—	4	3	no	—
1280	C₂×C₄	—	4	3	no	—
1281	C₂×C₄	—	4	3	no	—
1282	C₂×C₄	—	4	3	no	—
1283	C₂×C₄	—	4	3	no	—
1284	C₂×C₄	—	4	6	no	—
1285	C₂×C₄	—	4	6	no	—
1286	C₂×C₄	—	4	12	no	—
1287	C₂×C₄	—	4	12	no	—
1288	C₂×C₄	C₂×#41×C₂₃	1	12	yes	—
1289	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1290	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1291	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1292	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1293	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1294	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1295	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1296	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1297	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
1298	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1299	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1300	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
1301	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
1302	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1303	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1304	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1305	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
1306	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1307	C₂²	—	2	1	no	—
1308	C₂²	—	2	1	no	—
1309	C₂²	—	2	3	no	—
1310	C₂²	—	2	3	no	—
1311	C₂²	—	2	2	no	—
1312	C₂²	—	2	3	no	—
1313	C₂²	—	2	6	no	—
1314	C₂²	—	2	3	no	—
1315	C₂²	—	2	6	no	—
1316	C₂²	—	2	6	no	—
1317	C₂²	—	2	3	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	2	no	—
1320	C₂²	—	4	12	no	—
1321	C₂²	—	8	12	no	—
1322	C₂²	C₂²×#41×C₂₃	1	6	yes	—
1323	C₂²	C₂₃×#585	1	2	yes	—
1324	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1325	C₄	—	2	1	no	—
1326	C₄	—	2	2	no	—
1327	C₄	—	2	3	no	—
1328	C₄	—	2	6	no	—
1329	C₄	—	2	1	no	—
1330	C₄	—	2	1	no	—
1331	C₄	—	2	3	no	—
1332	C₄	—	2	1	no	—
1333	C₄	—	2	3	no	—
1334	C₄	—	2	3	no	—
1335	C₄	—	2	3	no	—
1336	C₄	—	2	2	no	—
1337	C₄	—	2	6	no	—
1338	C₄	—	2	6	no	—
1339	C₄	—	2	2	no	—
1340	C₄	C₂²×#41×C₂₃	1	2	yes	—
1341	C₄	C₂²×#41×C₂₃	1	6	yes	—
1342	C₄	C₂₃×#585	1	2	yes	—
1343	C₂	—	2	2	no	—
1344	C₂	—	2	6	no	—
1345	C₂	—	4	3	no	—
1346	C₂	—	4	2	no	—
1347	C₂	—	4	6	no	—
1348	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
1349	C₂	C₂×C₂₃×#585	1	1	yes	characteristic
1350	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
socle	C₂²×C₂₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3524	C₂	semidirect
2. C₂₃×#3523	C₂	semidirect
3. C₂₃×#3522	C₂	semidirect
4. C₂₃×#3521	C₂	semidirect
5. C₂₃×#3520	C₂	semidirect
6. C₂₃×#3519	C₂	semidirect
7. C₂₃×#3518	C₂	semidirect
8. C₂₃×#3517	C₂	semidirect
9. C₂₃×#3516	C₂	semidirect
10. C₂₃×#3515	C₂	semidirect
11. C₂₃×#3514	C₂	semidirect
12. C₂₃×#3513	C₂	semidirect
13. C₂₃×#3480	C₂	semidirect
14. Q₈×#41×C₂₃	C₂	semidirect
15. C₂₃×#3475	C₂	semidirect
16. C₂₃×#3475	C₂	semidirect
17. D₄×#41×C₂₃	C₂	semidirect
18. D₄×#41×C₂₃	C₂	semidirect
19. C₂₃×#3455	C₂	semidirect
20. C₂₃×#3444	C₂	semidirect
21. C₂×C₂₃×#529	C₂	semidirect
22. C₂₃×#3428	C₂	semidirect
23. C₂×C₄×#41×C₂₃	C₂	semidirect
26. C₂₃×#559	C₂²	semidirect
27. C₂₃×#559	C₂²	semidirect
28. Q₈²×C₂₃	C₂²	semidirect
29. C₂₃×#557	C₂²	semidirect
30. C₂₃×#557	C₂²	semidirect
31. C₂₃×#557	C₂²	semidirect
32. C₂₃×#556	C₂²	semidirect
33. C₂₃×#556	C₂²	semidirect
34. C₂₃×#556	C₂²	semidirect
35. C₂₃×#556	C₂²	semidirect
36. C₂₃×#555	C₂²	semidirect
37. C₂₃×#555	C₂²	semidirect
38. C₂₃×#554	C₂²	semidirect
39. C₂₃×#554	C₂²	semidirect
40. C₂₃×#554	C₂²	semidirect
41. C₂₃×#554	C₂²	semidirect
42. C₂₃×#553	C₂²	semidirect
43. C₂₃×#553	C₂²	semidirect
44. C₂₃×#553	C₂²	semidirect
45. C₂₃×#553	C₂²	semidirect
46. C₂₃×#553	C₂²	semidirect
47. C₂₃×#552	C₂²	semidirect
48. C₂₃×#552	C₂²	semidirect
49. C₂₃×#552	C₂²	semidirect
50. C₂₃×#552	C₂²	semidirect
51. C₂₃×#552	C₂²	semidirect
52. C₂₃×#551	C₂²	semidirect
53. C₂₃×#551	C₂²	semidirect
54. C₂₃×#551	C₂²	semidirect
55. C₂₃×#550	C₂²	semidirect
56. C₂₃×#550	C₂²	semidirect
57. C₂₃×#550	C₂²	semidirect
58. D₄×Q₈×C₂₃	C₂²	semidirect
59. D₄×Q₈×C₂₃	C₂²	semidirect
60. D₄×Q₈×C₂₃	C₂²	semidirect
61. C₂₃×#548	C₂²	semidirect
62. C₂₃×#548	C₂²	semidirect
63. C₂₃×#548	C₂²	semidirect
64. C₂₃×#548	C₂²	semidirect
65. C₂₃×#547	C₂²	semidirect
66. C₂₃×#547	C₂²	semidirect
67. C₂₃×#547	C₂²	semidirect
68. C₂₃×#547	C₂²	semidirect
69. C₂₃×#546	C₂²	semidirect
70. C₂₃×#546	C₂²	semidirect
71. C₂₃×#546	C₂²	semidirect
72. C₂₃×#546	C₂²	semidirect
73. C₂₃×#546	C₂²	semidirect
74. D₄²×C₂₃	C₂²	semidirect
75. D₄²×C₂₃	C₂²	semidirect
76. C₂₃×#542	C₂²	semidirect
77. C₂₃×#542	C₂²	semidirect
78. C₂₃×#542	C₂²	semidirect
79. C₂₃×#542	C₂²	semidirect
80. C₂₃×#541	C₂²	semidirect
81. C₂₃×#541	C₂²	semidirect
82. C₂₃×#540	C₂²	semidirect
83. C₂₃×#540	C₂²	semidirect
84. C₂₃×#539	C₂²	semidirect
85. C₂₃×#539	C₂²	semidirect
86. C₂₃×#538	C₂²	semidirect
87. C₂₃×#538	C₂²	semidirect
88. C₂₃×#533	C₂²	semidirect
89. C₂₃×#533	C₂²	semidirect
90. C₂₃×#533	C₂²	semidirect
91. C₂₃×#533	C₂²	semidirect
92. C₂₃×#532	C₂²	semidirect
93. C₂₃×#532	C₂²	semidirect
94. C₂₃×#532	C₂²	semidirect
95. C₂₃×#532	C₂²	semidirect
98. C₂₃×#529	C₂²	semidirect
99. C₂₃×#529	C₂²	semidirect
100. C₂₃×#529	C₂²	semidirect
101. C₂₃×#529	C₂²	semidirect
102. C₂₃×#529	C₂²	semidirect
103. C₂₃×#529	C₂²	semidirect
104. C₂₃×#529	C₂²	semidirect
105. C₂₃×#529	C₂²	semidirect
106. C₂₃×#529	C₂²	semidirect
107. C₂₃×#529	C₂²	semidirect
108. C₂₃×#529	C₂²	semidirect
109. C₂₃×#529	C₂²	semidirect
110. C₂₃×#529	C₂²	semidirect
111. C₂₃×#529	C₂²	semidirect
112. C₂₃×#529	C₂²	semidirect
113. C₂₃×#529	C₂²	semidirect
114. C₂₃×#529	C₂²	semidirect
115. C₂×C₂₃×#126	C₂²	semidirect
116. C₂×C₂₃×#125	C₂²	semidirect
117. C₂×C₂₃×#124	C₂²	semidirect
118. C₂₃×#525	C₂²	semidirect
119. C₂₃×#525	C₂²	semidirect
120. C₂₃×#525	C₂²	semidirect
121. C₂₃×#525	C₂²	semidirect
122. C₂₃×#525	C₂²	semidirect
123. C₂×C₂₃×#123	C₂²	semidirect
124. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
126. C₂₃×#520	C₂²	semidirect
127. C₂₃×#520	C₂²	semidirect
128. C₂₃×#520	C₂²	semidirect
129. C₂₃×#520	C₂²	semidirect
130. C₂₃×#519	C₂²	semidirect
131. C₂₃×#519	C₂²	semidirect
132. C₂₃×#518	C₂²	semidirect
133. C₂₃×#518	C₂²	semidirect
137. C₄×#41×C₂₃	C₂²	semidirect
138. C₄×#41×C₂₃	C₂²	semidirect
139. C₄×#41×C₂₃	C₂²	semidirect
140. C₄×#41×C₂₃	C₂²	semidirect
141. C₄×#41×C₂₃	C₂²	semidirect
142. C₄×#41×C₂₃	C₂²	semidirect
143. C₄×#41×C₂₃	C₂²	semidirect
144. C₄×#41×C₂₃	C₂²	semidirect
145. C₄×#41×C₂₃	C₂²	semidirect
146. C₄×#41×C₂₃	C₂²	semidirect
147. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
148. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
149. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
150. C₂×C₄×D₄×C₂₃	C₂²	semidirect
151. C₂×C₄×D₄×C₂₃	C₂²	semidirect
152. C₂×C₄×D₄×C₂₃	C₂²	semidirect
153. C₂×C₄×D₄×C₂₃	C₂²	semidirect
154. C₂×C₂₃×#117	C₂²	semidirect
155. C₂×C₂₃×#117	C₂²	semidirect
156. C₂×C₂₃×#117	C₂²	semidirect
157. C₂²×C₄²×C₂₃	C₂²	semidirect
410. #41×C₂₃	#41	semidirect
554. #62816	C₂₃	direct (N × H)
632. #3524	C₂×C₂₃	semidirect
633. #3523	C₂×C₂₃	semidirect
634. #3522	C₂×C₂₃	semidirect
635. #3521	C₂×C₂₃	semidirect
636. #3520	C₂×C₂₃	semidirect
637. #3519	C₂×C₂₃	semidirect
638. #3518	C₂×C₂₃	semidirect
639. #3517	C₂×C₂₃	semidirect
640. #3516	C₂×C₂₃	semidirect
641. #3515	C₂×C₂₃	semidirect
642. #3514	C₂×C₂₃	semidirect
643. #3513	C₂×C₂₃	semidirect
644. #3480	C₂×C₂₃	semidirect
645. Q₈×#41	C₂×C₂₃	semidirect
646. #3475	C₂×C₂₃	semidirect
647. #3475	C₂×C₂₃	semidirect
648. D₄×#41	C₂×C₂₃	semidirect
649. D₄×#41	C₂×C₂₃	semidirect
650. #3455	C₂×C₂₃	semidirect
651. #3444	C₂×C₂₃	semidirect
652. C₂×#529	C₂×C₂₃	semidirect
653. #3428	C₂×C₂₃	semidirect
654. C₂×C₄×#41	C₂×C₂₃	semidirect
693. #559	C₂²×C₂₃	semidirect
694. #559	C₂²×C₂₃	semidirect
695. Q₈²	C₂²×C₂₃	semidirect
696. #557	C₂²×C₂₃	semidirect
697. #557	C₂²×C₂₃	semidirect
698. #557	C₂²×C₂₃	semidirect
699. #556	C₂²×C₂₃	semidirect
700. #556	C₂²×C₂₃	semidirect
701. #556	C₂²×C₂₃	semidirect
702. #556	C₂²×C₂₃	semidirect
703. #555	C₂²×C₂₃	semidirect
704. #555	C₂²×C₂₃	semidirect
705. #554	C₂²×C₂₃	semidirect
706. #554	C₂²×C₂₃	semidirect
707. #554	C₂²×C₂₃	semidirect
708. #554	C₂²×C₂₃	semidirect
709. #553	C₂²×C₂₃	semidirect
710. #553	C₂²×C₂₃	semidirect
711. #553	C₂²×C₂₃	semidirect
712. #553	C₂²×C₂₃	semidirect
713. #553	C₂²×C₂₃	semidirect
714. #552	C₂²×C₂₃	semidirect
715. #552	C₂²×C₂₃	semidirect
716. #552	C₂²×C₂₃	semidirect
717. #552	C₂²×C₂₃	semidirect
718. #552	C₂²×C₂₃	semidirect
719. #551	C₂²×C₂₃	semidirect
720. #551	C₂²×C₂₃	semidirect
721. #551	C₂²×C₂₃	semidirect
722. #550	C₂²×C₂₃	semidirect
723. #550	C₂²×C₂₃	semidirect
724. #550	C₂²×C₂₃	semidirect
725. D₄×Q₈	C₂²×C₂₃	semidirect
726. D₄×Q₈	C₂²×C₂₃	semidirect
727. D₄×Q₈	C₂²×C₂₃	semidirect
728. #548	C₂²×C₂₃	semidirect
729. #548	C₂²×C₂₃	semidirect
730. #548	C₂²×C₂₃	semidirect
731. #548	C₂²×C₂₃	semidirect
732. #547	C₂²×C₂₃	semidirect
733. #547	C₂²×C₂₃	semidirect
734. #547	C₂²×C₂₃	semidirect
735. #547	C₂²×C₂₃	semidirect
736. #546	C₂²×C₂₃	semidirect
737. #546	C₂²×C₂₃	semidirect
738. #546	C₂²×C₂₃	semidirect
739. #546	C₂²×C₂₃	semidirect
740. #546	C₂²×C₂₃	semidirect
741. D₄²	C₂²×C₂₃	semidirect
742. D₄²	C₂²×C₂₃	semidirect
743. #542	C₂²×C₂₃	semidirect
744. #542	C₂²×C₂₃	semidirect
745. #542	C₂²×C₂₃	semidirect
746. #542	C₂²×C₂₃	semidirect
747. #541	C₂²×C₂₃	semidirect
748. #541	C₂²×C₂₃	semidirect
749. #540	C₂²×C₂₃	semidirect
750. #540	C₂²×C₂₃	semidirect
751. #539	C₂²×C₂₃	semidirect
752. #539	C₂²×C₂₃	semidirect
753. #538	C₂²×C₂₃	semidirect
754. #538	C₂²×C₂₃	semidirect
755. #533	C₂²×C₂₃	semidirect
756. #533	C₂²×C₂₃	semidirect
757. #533	C₂²×C₂₃	semidirect
758. #533	C₂²×C₂₃	semidirect
759. #532	C₂²×C₂₃	semidirect
760. #532	C₂²×C₂₃	semidirect
761. #532	C₂²×C₂₃	semidirect
762. #532	C₂²×C₂₃	semidirect
765. #529	C₂²×C₂₃	semidirect
766. #529	C₂²×C₂₃	semidirect
767. #529	C₂²×C₂₃	semidirect
768. #529	C₂²×C₂₃	semidirect
769. #529	C₂²×C₂₃	semidirect
770. #529	C₂²×C₂₃	semidirect
771. #529	C₂²×C₂₃	semidirect
772. #529	C₂²×C₂₃	semidirect
773. #529	C₂²×C₂₃	semidirect
774. #529	C₂²×C₂₃	semidirect
775. #529	C₂²×C₂₃	semidirect
776. #529	C₂²×C₂₃	semidirect
777. #529	C₂²×C₂₃	semidirect
778. #529	C₂²×C₂₃	semidirect
779. #529	C₂²×C₂₃	semidirect
780. #529	C₂²×C₂₃	semidirect
781. #529	C₂²×C₂₃	semidirect
782. C₂×#126	C₂²×C₂₃	semidirect
783. C₂×#125	C₂²×C₂₃	semidirect
784. C₂×#124	C₂²×C₂₃	semidirect
785. #525	C₂²×C₂₃	semidirect
786. #525	C₂²×C₂₃	semidirect
787. #525	C₂²×C₂₃	semidirect
788. #525	C₂²×C₂₃	semidirect
789. #525	C₂²×C₂₃	semidirect
790. C₂×#123	C₂²×C₂₃	semidirect
791. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
793. #520	C₂²×C₂₃	semidirect
794. #520	C₂²×C₂₃	semidirect
795. #520	C₂²×C₂₃	semidirect
796. #520	C₂²×C₂₃	semidirect
797. #519	C₂²×C₂₃	semidirect
798. #519	C₂²×C₂₃	semidirect
799. #518	C₂²×C₂₃	semidirect
800. #518	C₂²×C₂₃	semidirect
804. C₄×#41	C₂²×C₂₃	semidirect
805. C₄×#41	C₂²×C₂₃	semidirect
806. C₄×#41	C₂²×C₂₃	semidirect
807. C₄×#41	C₂²×C₂₃	semidirect
808. C₄×#41	C₂²×C₂₃	semidirect
809. C₄×#41	C₂²×C₂₃	semidirect
810. C₄×#41	C₂²×C₂₃	semidirect
811. C₄×#41	C₂²×C₂₃	semidirect
812. C₄×#41	C₂²×C₂₃	semidirect
813. C₄×#41	C₂²×C₂₃	semidirect
814. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
815. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
816. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
817. C₂×C₄×D₄	C₂²×C₂₃	semidirect
818. C₂×C₄×D₄	C₂²×C₂₃	semidirect
819. C₂×C₄×D₄	C₂²×C₂₃	semidirect
820. C₂×C₄×D₄	C₂²×C₂₃	semidirect
821. C₂×#117	C₂²×C₂₃	semidirect
822. C₂×#117	C₂²×C₂₃	semidirect
823. C₂×#117	C₂²×C₂₃	semidirect
824. C₂²×C₄²	C₂²×C₂₃	semidirect
1075. C₂₃	#62816	direct (N × H)
1086. #41	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3524	2
C₂₃×#3523	2
C₂₃×#3522	2
C₂₃×#3521	2
C₂₃×#3520	2
C₂₃×#3519	2
C₂₃×#3518	2
C₂₃×#3517	2
C₂₃×#3516	2
C₂₃×#3515	2
C₂₃×#3514	2
C₂₃×#3513	2
C₂₃×#3480	2
Q₈×#41×C₂₃	2
C₂₃×#3475	2
D₄×#41×C₂₃	2
C₂₃×#3455	2
C₂₃×#3444	2
C₂×C₂₃×#529	2
C₂₃×#3428	2
C₂×C₄×#41×C₂₃	2
#62816	23

Subgroups — C23×#62816 #19210442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62816 #19210442