Subgroups — C₂₃×#61253 #19208879

Order 5888.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3344	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#556	C₂²	1	1	yes	characteristic
28	C₂₃×#555	C₂²	1	1	yes	characteristic
29	C₂₃×#554	C₂²	1	1	yes	characteristic
30	C₂₃×#553	C₂²	1	1	yes	characteristic
31	C₂₃×#553	C₂²	1	1	yes	characteristic
32	C₂₃×#552	—	2	1	no	—
33	C₂₃×#552	—	2	1	no	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#552	—	2	1	no	—
37	C₂₃×#552	C₂²	1	2	yes	—
38	C₂₃×#552	C₂²	1	2	yes	—
39	C₂₃×#552	C₂²	1	2	yes	—
40	C₂₃×#552	C₂²	1	2	yes	—
41	C₂₃×#552	C₂²	1	1	yes	characteristic
42	C₂₃×#552	C₂²	1	1	yes	characteristic
43	C₂₃×#551	—	2	1	no	—
44	C₂₃×#551	—	2	1	no	—
45	C₂₃×#547	C₂²	1	1	yes	characteristic
46	C₂₃×#546	—	2	1	no	—
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#529	—	2	1	no	—
51	C₂×C₂₃×#126	—	2	1	no	—
52	C₂×C₂₃×#125	—	2	1	no	—
53	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂₃×#525	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#123	—	2	1	no	—
57	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₄×#41×C₂₃	—	2	1	no	—
60	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#117	—	2	1	no	—
64	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
67	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
68	C₂₃×#501	C₂²	1	2	yes	complemented
69	C₂₃×#501	C₂²	1	2	yes	complemented
70	C₂₃×#499	C₂²	1	2	yes	complemented
71	C₂₃×#499	C₂²	1	2	yes	complemented
72	C₂₃×#485	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	complemented
74	C₂₃×#485	C₂²	1	2	yes	complemented
75	C₂₃×#485	C₂²	1	2	yes	complemented
76	C₂₃×#485	C₂²	1	2	yes	complemented
77	C₂₃×#485	C₂²	1	2	yes	complemented
78	C₂₃×#484	C₂²	1	2	yes	complemented
79	C₂₃×#484	C₂²	1	2	yes	complemented
80	C₂₃×#484	C₂²	1	2	yes	complemented
81	C₂₃×#483	C₂²	1	2	yes	complemented
82	C₂₃×#483	C₂²	1	2	yes	complemented
83	C₂₃×#483	C₂²	1	2	yes	complemented
84	C₂₃×#482	C₂²	1	2	yes	complemented
85	C₂₃×#482	C₂²	1	2	yes	complemented
86	C₂₃×#481	C₂²	1	2	yes	complemented
87	C₂₃×#480	C₂²	1	2	yes	complemented
88	C₂₃×#479	C₂²	1	2	yes	complemented
89	C₂₃×#479	C₂²	1	2	yes	complemented
90	C₂₃×#479	C₂²	1	2	yes	complemented
91	C₂₃×#479	C₂²	1	2	yes	complemented
92	C₂₃×#478	C₂²	1	2	yes	complemented
93	C₂₃×#478	C₂²	1	2	yes	complemented
94	C₂₃×#477	C₂²	1	2	yes	complemented
95	C₂₃×#475	C₂²	1	2	yes	complemented
96	C₂₃×#470	C₂²	1	2	yes	complemented
97	C₂₃×#470	C₂²	1	2	yes	complemented
98	C₂₃×#468	C₂²	1	2	yes	complemented
99	C₂₃×#468	C₂²	1	2	yes	complemented
100	C₂₃×#467	C₂²	1	2	yes	complemented
101	C₂₃×#467	C₂²	1	2	yes	complemented
102	C₂₃×#465	C₂²	1	2	yes	complemented
103	C₂₃×#465	C₂²	1	2	yes	complemented
104	C₂₃×#441	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
108	C₂₃×#436	C₂²	1	2	yes	—
109	C₂₃×#435	C₂²	1	2	yes	—
110	C₂₃×#435	C₂²	1	2	yes	—
111	C₈×D₄×C₂₃	C₂²	1	2	yes	—
112	C₂₃×#428	C₂²	1	1	yes	characteristic
113	C₂₃×#428	C₂²	1	1	yes	characteristic
114	C₂₃×#428	C₂²	1	1	yes	characteristic
115	C₂₃×#428	C₂²	1	1	yes	characteristic
116	C₂₃×#428	C₂²	1	1	yes	characteristic
117	C₂₃×#428	C₂²	1	1	yes	characteristic
118	C₂₃×#428	C₂²	1	1	yes	characteristic
119	C₂₃×#428	C₂²	1	1	yes	characteristic
120	C₂₃×#428	C₂²	1	1	yes	characteristic
121	C₂₃×#428	C₂²	1	2	yes	complemented
122	C₂₃×#428	C₂²	1	2	yes	complemented
123	C₂₃×#428	C₂²	1	2	yes	complemented
124	C₂₃×#428	C₂²	1	2	yes	complemented
125	C₂₃×#427	C₂²	1	2	yes	complemented
126	C₂₃×#427	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
129	C₂₃×#423	C₂²	1	1	yes	characteristic
130	C₂₃×#419	C₂²	1	1	yes	characteristic
131	C₂₃×#419	C₂²	1	1	yes	characteristic
132	C₂₃×#419	C₂²	1	1	yes	characteristic
133	C₂₃×#417	C₂²	1	1	yes	characteristic
134	C₂₃×#417	C₂²	1	1	yes	characteristic
135	C₂₃×#417	C₂²	1	1	yes	characteristic
136	C₂₃×#407	C₂²	1	1	yes	characteristic
137	C₂₃×#407	C₂²	1	1	yes	characteristic
138	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	—	2	1	no	—
144	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂₃×#137	—	2	4	no	—
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	—	2	4	no	—
150	C₂×M₁₆×C₂₃	—	2	4	no	—
151	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×#126	—	2	1	no	—
162	C₂₃×#126	—	2	1	no	—
163	C₂₃×#126	—	2	1	no	—
164	C₂₃×#126	—	2	1	no	—
165	C₂₃×#126	—	2	1	no	—
166	C₂₃×#126	—	2	1	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	2	no	—
174	C₂₃×#125	—	2	2	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	1	no	—
177	C₂₃×#125	—	2	1	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	—	2	1	no	—
180	C₂₃×#125	C₂³	1	2	yes	—
181	C₂₃×#125	C₂³	1	2	yes	—
182	C₂₃×#125	C₂³	1	1	yes	characteristic
183	C₂₃×#125	C₂³	1	1	yes	characteristic
184	C₂₃×#124	—	2	1	no	—
185	C₂₃×#124	—	2	1	no	—
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	2	no	—
191	C₂₃×#123	—	2	1	no	—
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	1	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
197	C₂₃×#123	—	2	1	no	—
198	C₂₃×#123	—	2	1	no	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	1	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	C₂³	1	1	yes	characteristic
220	C₂₃×#121	C₂³	1	1	yes	characteristic
221	C₂₃×#121	C₂³	1	1	yes	characteristic
222	C₂₃×#121	C₂³	1	1	yes	characteristic
223	C₂₃×#120	—	2	1	no	—
224	C₂₃×#120	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	1	no	—
226	C₄×Q₈×C₂₃	—	2	1	no	—
227	C₄×Q₈×C₂₃	—	2	1	no	—
228	C₄×Q₈×C₂₃	—	2	1	no	—
229	C₄×Q₈×C₂₃	—	2	1	no	—
230	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	1	no	—
237	C₄×D₄×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	1	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
244	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
245	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
246	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	1	no	—
255	C₂₃×#117	—	2	1	no	—
256	C₂₃×#117	—	2	1	no	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	—	2	1	no	—
259	C₂₃×#117	—	2	1	no	—
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	2	no	—
263	C₂₃×#117	—	2	2	no	—
264	C₂₃×#117	—	2	2	no	—
265	C₂₃×#117	—	2	2	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	C₂³	1	2	yes	—
268	C₂₃×#117	C₂³	1	2	yes	—
269	C₂₃×#117	C₂³	1	1	yes	characteristic
270	C₂₃×#117	C₂³	1	1	yes	characteristic
271	C₂₃×#117	C₂³	1	1	yes	characteristic
272	C₂₃×#117	C₂³	1	1	yes	characteristic
273	C₂₃×#117	C₂³	1	1	yes	characteristic
274	C₂₃×#117	C₂³	1	1	yes	characteristic
275	C₂₃×#117	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	—	2	1	no	—
302	C₂×C₄²×C₂₃	—	2	1	no	—
303	C₂×C₄²×C₂₃	—	2	1	no	—
304	C₂×C₄²×C₂₃	—	2	1	no	—
305	C₂×C₄²×C₂₃	—	2	1	no	—
306	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
307	C₂₃×#107	C₂³	1	2	yes	—
308	C₂₃×#107	C₂³	1	2	yes	—
309	C₂₃×#107	C₂³	1	2	yes	—
310	C₂₃×#107	C₂³	1	2	yes	—
311	C₂₃×#107	C₂³	1	2	yes	—
312	C₂₃×#107	C₂³	1	2	yes	—
313	C₂₃×#107	C₂³	1	2	yes	—
314	C₂₃×#107	C₂³	1	2	yes	—
315	C₂₃×#107	C₂³	1	2	yes	—
316	C₂₃×#106	C₂³	1	2	yes	—
317	C₂₃×#106	C₂³	1	2	yes	—
318	C₂₃×#106	C₂³	1	2	yes	—
319	C₂₃×#106	C₂³	1	2	yes	—
320	C₂₃×#106	C₂³	1	2	yes	—
321	C₂₃×#106	C₂³	1	2	yes	—
322	C₂₃×#106	C₂³	1	2	yes	—
323	C₂₃×#106	C₂³	1	2	yes	—
324	C₂₃×#106	C₂³	1	2	yes	—
325	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
326	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
327	C₂₃×#103	C₂³	1	2	yes	—
328	C₂₃×#103	C₂³	1	2	yes	—
329	C₂₃×#103	C₂³	1	2	yes	—
330	C₂₃×#103	C₂³	1	2	yes	—
331	C₂₃×#103	C₂³	1	2	yes	—
332	C₂₃×#103	C₂³	1	2	yes	—
333	C₂₃×#103	C₂³	1	2	yes	—
334	C₂₃×#103	C₂³	1	2	yes	—
335	C₂₃×#103	C₂³	1	2	yes	—
336	C₂₃×#102	C₂³	1	2	yes	—
337	C₂₃×#102	C₂³	1	2	yes	—
338	C₂₃×#102	C₂³	1	2	yes	—
339	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₂₃×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₂₃	C₂³	1	2	yes	—
345	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
347	#41×C₂₃	—	2	2	no	—
348	#41×C₂₃	—	2	2	no	—
349	#41×C₂₃	—	4	4	no	—
350	C₂×Q₈×C₂₃	—	2	1	no	—
351	C₂×Q₈×C₂₃	—	2	1	no	—
352	C₂×Q₈×C₂₃	—	2	1	no	—
353	C₂×Q₈×C₂₃	—	2	2	no	—
354	C₂×Q₈×C₂₃	—	2	2	no	—
355	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	4	2	no	—
363	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₂₃	—	2	2	no	—
369	C₂²×C₄×C₂₃	—	2	2	no	—
370	C₂²×C₄×C₂₃	—	2	2	no	—
371	C₂²×C₄×C₂₃	—	2	2	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	1	no	—
376	C₂²×C₄×C₂₃	—	2	1	no	—
377	C₂²×C₄×C₂₃	—	2	1	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	1	no	—
385	C₂²×C₄×C₂₃	—	4	4	no	—
386	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₂₃	—	2	4	no	—
400	SD₁₆×C₂₃	—	2	4	no	—
401	M₁₆×C₂₃	—	2	2	no	—
402	M₁₆×C₂₃	—	2	2	no	—
403	M₁₆×C₂₃	—	2	2	no	—
404	M₁₆×C₂₃	—	2	4	no	—
405	M₁₆×C₂₃	—	2	4	no	—
406	M₁₆×C₂₃	#41	1	4	yes	complemented
407	C₂×C₈×C₂₃	—	2	4	no	—
408	C₂×C₈×C₂₃	—	2	4	no	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
412	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	—	2	1	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	—	2	2	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	2	no	—
424	C₄⋊C₄×C₂₃	—	2	2	no	—
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	1	no	—
435	C₄⋊C₄×C₂₃	—	2	1	no	—
436	C₄⋊C₄×C₂₃	—	2	1	no	—
437	C₄⋊C₄×C₂₃	—	2	1	no	—
438	C₄⋊C₄×C₂₃	—	2	1	no	—
439	C₄⋊C₄×C₂₃	—	2	1	no	—
440	C₄⋊C₄×C₂₃	—	2	1	no	—
441	C₄⋊C₄×C₂₃	—	2	1	no	—
442	C₄⋊C₄×C₂₃	—	2	1	no	—
443	C₄⋊C₄×C₂₃	—	2	1	no	—
444	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	1	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	1	no	—
463	C₂²⋊C₄×C₂₃	—	2	1	no	—
464	C₂²⋊C₄×C₂₃	—	2	1	no	—
465	C₂²⋊C₄×C₂₃	—	2	1	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	—	2	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	1	no	—
474	C₂²⋊C₄×C₂₃	—	2	1	no	—
475	C₂²⋊C₄×C₂₃	—	2	1	no	—
476	C₂²⋊C₄×C₂₃	—	2	1	no	—
477	C₂²⋊C₄×C₂₃	—	2	1	no	—
478	C₂²⋊C₄×C₂₃	—	2	1	no	—
479	C₂²⋊C₄×C₂₃	—	2	1	no	—
480	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₂₃	—	2	1	no	—
489	C₄²×C₂₃	—	2	1	no	—
490	C₄²×C₂₃	—	2	1	no	—
491	C₄²×C₂₃	—	2	2	no	—
492	C₄²×C₂₃	—	2	2	no	—
493	C₄²×C₂₃	—	2	1	no	—
494	C₄²×C₂₃	—	2	2	no	—
495	C₄²×C₂₃	—	2	2	no	—
496	C₄²×C₂₃	—	2	1	no	—
497	C₄²×C₂₃	—	2	1	no	—
498	C₄²×C₂₃	—	2	1	no	—
499	C₄²×C₂₃	—	2	1	no	—
500	C₄²×C₂₃	—	2	1	no	—
501	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
502	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
503	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
504	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
505	#61253	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂³×C₂₃	—	2	2	no	—
507	C₂³×C₂₃	—	2	2	no	—
508	C₂³×C₂₃	—	2	2	no	—
509	C₂³×C₂₃	—	2	1	no	—
510	C₂³×C₂₃	—	4	1	no	—
511	C₂³×C₂₃	—	4	1	no	—
512	C₂³×C₂₃	—	4	1	no	—
513	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₂₃	—	2	2	no	—
519	Q₈×C₂₃	—	2	1	no	—
520	Q₈×C₂₃	—	2	2	no	—
521	Q₈×C₂₃	—	2	1	no	—
522	Q₈×C₂₃	—	4	2	no	—
523	Q₈×C₂₃	—	4	2	no	—
524	Q₈×C₂₃	—	8	1	no	—
525	D₄×C₂₃	—	2	2	no	—
526	D₄×C₂₃	—	2	2	no	—
527	D₄×C₂₃	—	2	1	no	—
528	D₄×C₂₃	—	2	1	no	—
529	D₄×C₂₃	—	4	1	no	—
530	D₄×C₂₃	—	4	1	no	—
531	D₄×C₂₃	—	4	2	no	—
532	D₄×C₂₃	—	4	2	no	—
533	D₄×C₂₃	—	4	2	no	—
534	D₄×C₂₃	—	8	1	no	—
535	D₄×C₂₃	—	8	1	no	—
536	C₂×C₄×C₂₃	—	2	2	no	—
537	C₂×C₄×C₂₃	—	2	2	no	—
538	C₂×C₄×C₂₃	—	2	2	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	2	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	1	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	1	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	2	2	no	—
553	C₂×C₄×C₂₃	—	2	2	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	2	2	no	—
556	C₂×C₄×C₂₃	—	2	1	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	1	no	—
559	C₂×C₄×C₂₃	—	2	1	no	—
560	C₂×C₄×C₂₃	—	2	2	no	—
561	C₂×C₄×C₂₃	—	4	1	no	—
562	C₂×C₄×C₂₃	—	4	1	no	—
563	C₂×C₄×C₂₃	—	4	2	no	—
564	C₂×C₄×C₂₃	—	4	2	no	—
565	C₂×C₄×C₂₃	—	4	2	no	—
566	C₂×C₄×C₂₃	—	4	2	no	—
567	C₂×C₄×C₂₃	—	4	4	no	—
568	C₂×C₄×C₂₃	—	4	2	no	—
569	C₂×C₄×C₂₃	—	4	2	no	—
570	C₂×C₄×C₂₃	—	4	4	no	—
571	C₂×C₄×C₂₃	—	4	2	no	—
572	C₂×C₄×C₂₃	—	4	2	no	—
573	C₂×C₄×C₂₃	—	8	1	no	—
574	C₂×C₄×C₂₃	—	8	1	no	—
575	C₂×C₄×C₂₃	—	8	1	no	—
576	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
586	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
587	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
588	C₈×C₂₃	—	2	2	no	—
589	C₈×C₂₃	—	2	2	no	—
590	C₈×C₂₃	—	2	2	no	—
591	C₈×C₂₃	C₂×#41	1	4	yes	—
592	#3475	C₂×C₂₃	1	1	yes	characteristic
593	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3352	C₂×C₂₃	1	2	yes	complemented
595	#3351	C₂×C₂₃	1	2	yes	complemented
596	#3349	C₂×C₂₃	1	2	yes	complemented
597	#3348	C₂×C₂₃	1	2	yes	complemented
598	#3344	C₂×C₂₃	1	2	yes	complemented
599	#3343	C₂×C₂₃	1	2	yes	complemented
600	#3337	C₂×C₂₃	1	2	yes	complemented
601	#3336	C₂×C₂₃	1	2	yes	complemented
602	#3166	C₂×C₂₃	1	1	yes	characteristic, complemented
603	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
604	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
605	#3093	C₂×C₂₃	1	1	yes	characteristic, complemented
606	#3092	C₂×C₂₃	1	1	yes	characteristic, complemented
607	#3080	C₂×C₂₃	1	1	yes	characteristic, complemented
608	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
609	#3056	C₂×C₂₃	1	1	yes	characteristic, complemented
610	#3056	C₂×C₂₃	1	1	yes	characteristic, complemented
611	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
612	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
613	#2911	C₂×C₂₃	1	1	yes	characteristic, complemented
614	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
615	C₂²×C₂₃	—	2	1	no	—
616	C₂²×C₂₃	—	2	1	no	—
617	C₂²×C₂₃	—	2	1	no	—
618	C₂²×C₂₃	—	2	1	no	—
619	C₂²×C₂₃	—	2	1	no	—
620	C₂²×C₂₃	—	2	1	no	—
621	C₂²×C₂₃	—	2	1	no	—
622	C₂²×C₂₃	—	2	1	no	—
623	C₂²×C₂₃	—	2	1	no	—
624	C₂²×C₂₃	—	2	1	no	—
625	C₂²×C₂₃	—	2	1	no	—
626	C₂²×C₂₃	—	2	1	no	—
627	C₂²×C₂₃	—	2	1	no	—
628	C₂²×C₂₃	—	4	4	no	—
629	C₂²×C₂₃	—	4	1	no	—
630	C₂²×C₂₃	—	4	1	no	—
631	C₂²×C₂₃	—	4	1	no	—
632	C₂²×C₂₃	—	8	2	no	—
633	C₂²×C₂₃	#547	1	2	yes	—
634	C₂²×C₂₃	#575	1	2	yes	—
635	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
636	C₄×C₂₃	—	2	1	no	—
637	C₄×C₂₃	—	2	1	no	—
638	C₄×C₂₃	—	2	1	no	—
639	C₄×C₂₃	—	2	1	no	—
640	C₄×C₂₃	—	2	1	no	—
641	C₄×C₂₃	—	2	1	no	—
642	C₄×C₂₃	—	2	1	no	—
643	C₄×C₂₃	—	2	1	no	—
644	C₄×C₂₃	—	4	2	no	—
645	C₄×C₂₃	—	4	1	no	—
646	C₄×C₂₃	—	4	1	no	—
647	C₄×C₂₃	—	4	1	no	—
648	C₄×C₂₃	—	4	1	no	—
649	C₄×C₂₃	—	4	2	no	—
650	C₄×C₂₃	—	4	1	no	—
651	C₄×C₂₃	—	4	2	no	—
652	C₄×C₂₃	—	4	2	no	—
653	C₄×C₂₃	—	4	1	no	—
654	C₄×C₂₃	—	4	1	no	—
655	C₄×C₂₃	#547	1	2	yes	—
656	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
657	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
659	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
660	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
661	#556	C₂²×C₂₃	1	1	yes	characteristic
662	#555	C₂²×C₂₃	1	1	yes	characteristic
663	#554	C₂²×C₂₃	1	1	yes	characteristic
664	#553	C₂²×C₂₃	1	1	yes	characteristic
665	#553	C₂²×C₂₃	1	1	yes	characteristic
666	#552	—	2	1	no	—
667	#552	—	2	1	no	—
668	#552	—	2	1	no	—
669	#552	—	2	1	no	—
670	#552	—	2	1	no	—
671	#552	C₂²×C₂₃	1	1	yes	characteristic
672	#552	C₂²×C₂₃	1	2	yes	—
673	#552	C₂²×C₂₃	1	2	yes	—
674	#552	C₂²×C₂₃	1	2	yes	—
675	#552	C₂²×C₂₃	1	2	yes	—
676	#552	C₂²×C₂₃	1	1	yes	characteristic
677	#551	—	2	1	no	—
678	#551	—	2	1	no	—
679	#547	C₂²×C₂₃	1	1	yes	characteristic
680	#546	—	2	1	no	—
681	#533	C₂²×C₂₃	1	1	yes	characteristic
682	#529	—	2	1	no	—
683	#529	—	2	1	no	—
684	#529	—	2	1	no	—
685	C₂×#126	—	2	1	no	—
686	C₂×#125	—	2	1	no	—
687	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
688	#525	C₂²×C₂₃	1	1	yes	characteristic
689	#525	C₂²×C₂₃	1	1	yes	characteristic
690	C₂×#123	—	2	1	no	—
691	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
692	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
693	C₄×#41	—	2	1	no	—
694	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
695	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
696	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
697	C₂×#117	—	2	1	no	—
698	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
699	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
700	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
701	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
702	#501	C₂²×C₂₃	1	2	yes	complemented
703	#501	C₂²×C₂₃	1	2	yes	complemented
704	#499	C₂²×C₂₃	1	2	yes	complemented
705	#499	C₂²×C₂₃	1	2	yes	complemented
706	#485	C₂²×C₂₃	1	2	yes	complemented
707	#485	C₂²×C₂₃	1	2	yes	complemented
708	#485	C₂²×C₂₃	1	2	yes	complemented
709	#485	C₂²×C₂₃	1	2	yes	complemented
710	#485	C₂²×C₂₃	1	2	yes	complemented
711	#485	C₂²×C₂₃	1	2	yes	complemented
712	#484	C₂²×C₂₃	1	2	yes	complemented
713	#484	C₂²×C₂₃	1	2	yes	complemented
714	#484	C₂²×C₂₃	1	2	yes	complemented
715	#483	C₂²×C₂₃	1	2	yes	complemented
716	#483	C₂²×C₂₃	1	2	yes	complemented
717	#483	C₂²×C₂₃	1	2	yes	complemented
718	#482	C₂²×C₂₃	1	2	yes	complemented
719	#482	C₂²×C₂₃	1	2	yes	complemented
720	#481	C₂²×C₂₃	1	2	yes	complemented
721	#480	C₂²×C₂₃	1	2	yes	complemented
722	#479	C₂²×C₂₃	1	2	yes	complemented
723	#479	C₂²×C₂₃	1	2	yes	complemented
724	#479	C₂²×C₂₃	1	2	yes	complemented
725	#479	C₂²×C₂₃	1	2	yes	complemented
726	#478	C₂²×C₂₃	1	2	yes	complemented
727	#478	C₂²×C₂₃	1	2	yes	complemented
728	#477	C₂²×C₂₃	1	2	yes	complemented
729	#475	C₂²×C₂₃	1	2	yes	complemented
730	#470	C₂²×C₂₃	1	2	yes	complemented
731	#470	C₂²×C₂₃	1	2	yes	complemented
732	#468	C₂²×C₂₃	1	2	yes	complemented
733	#468	C₂²×C₂₃	1	2	yes	complemented
734	#467	C₂²×C₂₃	1	2	yes	complemented
735	#467	C₂²×C₂₃	1	2	yes	complemented
736	#465	C₂²×C₂₃	1	2	yes	complemented
737	#465	C₂²×C₂₃	1	2	yes	complemented
738	#441	C₂²×C₂₃	1	2	yes	complemented
739	#440	C₂²×C₂₃	1	2	yes	complemented
740	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
741	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
742	#436	C₂²×C₂₃	1	2	yes	—
743	#435	C₂²×C₂₃	1	2	yes	—
744	#435	C₂²×C₂₃	1	2	yes	—
745	C₈×D₄	C₂²×C₂₃	1	2	yes	—
746	#428	C₂²×C₂₃	1	1	yes	characteristic
747	#428	C₂²×C₂₃	1	1	yes	characteristic
748	#428	C₂²×C₂₃	1	1	yes	characteristic
749	#428	C₂²×C₂₃	1	1	yes	characteristic
750	#428	C₂²×C₂₃	1	1	yes	characteristic
751	#428	C₂²×C₂₃	1	1	yes	characteristic
752	#428	C₂²×C₂₃	1	1	yes	characteristic
753	#428	C₂²×C₂₃	1	1	yes	characteristic
754	#428	C₂²×C₂₃	1	1	yes	characteristic
755	#428	C₂²×C₂₃	1	2	yes	complemented
756	#428	C₂²×C₂₃	1	2	yes	complemented
757	#428	C₂²×C₂₃	1	2	yes	complemented
758	#428	C₂²×C₂₃	1	2	yes	complemented
759	#427	C₂²×C₂₃	1	2	yes	complemented
760	#427	C₂²×C₂₃	1	2	yes	complemented
761	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
762	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
763	#423	C₂²×C₂₃	1	1	yes	characteristic
764	#419	C₂²×C₂₃	1	1	yes	characteristic
765	#419	C₂²×C₂₃	1	1	yes	characteristic
766	#419	C₂²×C₂₃	1	1	yes	characteristic
767	#417	C₂²×C₂₃	1	1	yes	characteristic
768	#417	C₂²×C₂₃	1	1	yes	characteristic
769	#417	C₂²×C₂₃	1	1	yes	characteristic
770	#407	C₂²×C₂₃	1	1	yes	characteristic
771	#407	C₂²×C₂₃	1	1	yes	characteristic
772	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
773	C₂×C₂₃	—	2	2	no	—
774	C₂×C₂₃	—	2	2	no	—
775	C₂×C₂₃	—	4	1	no	—
776	C₂×C₂₃	—	4	1	no	—
777	C₂×C₂₃	—	4	1	no	—
778	C₂×C₂₃	—	8	1	no	—
779	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
780	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
781	C₂×C₂₃	#3586	1	1	yes	characteristic
782	C₂×#41	—	2	1	no	—
783	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
784	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
786	C₂³×C₄	—	2	1	no	—
787	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
788	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
789	#137	—	2	4	no	—
790	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
792	C₂×M₁₆	—	2	4	no	—
793	C₂×M₁₆	—	2	4	no	—
794	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
795	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
797	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
798	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
799	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
802	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
803	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
804	#126	—	2	1	no	—
805	#126	—	2	1	no	—
806	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	1	no	—
811	#126	—	2	1	no	—
812	#126	—	2	1	no	—
813	#126	—	2	1	no	—
814	#125	—	2	2	no	—
815	#125	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	1	no	—
819	#125	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	C₂³×C₂₃	1	2	yes	—
824	#125	C₂³×C₂₃	1	2	yes	—
825	#125	C₂³×C₂₃	1	1	yes	characteristic
826	#125	C₂³×C₂₃	1	1	yes	characteristic
827	#124	—	2	1	no	—
828	#124	—	2	1	no	—
829	#124	—	2	1	no	—
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	#123	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
853	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
854	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	C₂³×C₂₃	1	1	yes	characteristic
863	#121	C₂³×C₂₃	1	1	yes	characteristic
864	#121	C₂³×C₂₃	1	1	yes	characteristic
865	#121	C₂³×C₂₃	1	1	yes	characteristic
866	#120	—	2	1	no	—
867	#120	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
874	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
875	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
887	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
888	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
889	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
892	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
893	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
894	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	—	2	1	no	—
902	#117	—	2	1	no	—
903	#117	—	2	2	no	—
904	#117	—	2	2	no	—
905	#117	—	2	2	no	—
906	#117	—	2	2	no	—
907	#117	—	2	1	no	—
908	#117	—	2	1	no	—
909	#117	—	2	1	no	—
910	#117	C₂³×C₂₃	1	1	yes	characteristic
911	#117	C₂³×C₂₃	1	1	yes	characteristic
912	#117	C₂³×C₂₃	1	1	yes	characteristic
913	#117	C₂³×C₂₃	1	2	yes	—
914	#117	C₂³×C₂₃	1	2	yes	—
915	#117	C₂³×C₂₃	1	1	yes	characteristic
916	#117	C₂³×C₂₃	1	1	yes	characteristic
917	#117	C₂³×C₂₃	1	1	yes	characteristic
918	#117	C₂³×C₂₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	—	2	1	no	—
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	—	2	1	no	—
922	C₂×C₄⋊C₄	—	2	1	no	—
923	C₂×C₄⋊C₄	—	2	1	no	—
924	C₂×C₄⋊C₄	—	2	1	no	—
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	—	2	1	no	—
927	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
931	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
932	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
937	C₂×C₂²⋊C₄	—	2	1	no	—
938	C₂×C₂²⋊C₄	—	2	1	no	—
939	C₂×C₂²⋊C₄	—	2	1	no	—
940	C₂×C₂²⋊C₄	—	2	1	no	—
941	C₂×C₂²⋊C₄	—	2	1	no	—
942	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
943	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
944	C₂×C₄²	—	2	1	no	—
945	C₂×C₄²	—	2	1	no	—
946	C₂×C₄²	—	2	1	no	—
947	C₂×C₄²	—	2	1	no	—
948	C₂×C₄²	—	2	1	no	—
949	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
950	#107	C₂³×C₂₃	1	2	yes	—
951	#107	C₂³×C₂₃	1	2	yes	—
952	#107	C₂³×C₂₃	1	2	yes	—
953	#107	C₂³×C₂₃	1	2	yes	—
954	#107	C₂³×C₂₃	1	2	yes	—
955	#107	C₂³×C₂₃	1	2	yes	—
956	#107	C₂³×C₂₃	1	2	yes	—
957	#107	C₂³×C₂₃	1	2	yes	—
958	#107	C₂³×C₂₃	1	2	yes	—
959	#106	C₂³×C₂₃	1	2	yes	—
960	#106	C₂³×C₂₃	1	2	yes	—
961	#106	C₂³×C₂₃	1	2	yes	—
962	#106	C₂³×C₂₃	1	2	yes	—
963	#106	C₂³×C₂₃	1	2	yes	—
964	#106	C₂³×C₂₃	1	2	yes	—
965	#106	C₂³×C₂₃	1	2	yes	—
966	#106	C₂³×C₂₃	1	2	yes	—
967	#106	C₂³×C₂₃	1	2	yes	—
968	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
969	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
970	#103	C₂³×C₂₃	1	2	yes	—
971	#103	C₂³×C₂₃	1	2	yes	—
972	#103	C₂³×C₂₃	1	2	yes	—
973	#103	C₂³×C₂₃	1	2	yes	—
974	#103	C₂³×C₂₃	1	2	yes	—
975	#103	C₂³×C₂₃	1	2	yes	—
976	#103	C₂³×C₂₃	1	2	yes	—
977	#103	C₂³×C₂₃	1	2	yes	—
978	#103	C₂³×C₂₃	1	2	yes	—
979	#102	C₂³×C₂₃	1	2	yes	—
980	#102	C₂³×C₂₃	1	2	yes	—
981	#102	C₂³×C₂₃	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
984	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
985	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
986	#97	C₂³×C₂₃	1	2	yes	—
987	C₄×C₈	C₂³×C₂₃	1	2	yes	—
988	C₂₃	#61253	1	1	yes	characteristic, direct product factor, Sylow
989	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
990	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	4	4	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	2	1	no	—
996	C₂×Q₈	—	2	1	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1000	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1010	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1011	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	4	4	no	—
1030	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1031	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1043	Q₁₆	—	2	4	no	—
1044	SD₁₆	—	2	4	no	—
1045	M₁₆	—	2	2	no	—
1046	M₁₆	—	2	2	no	—
1047	M₁₆	—	2	2	no	—
1048	M₁₆	—	2	4	no	—
1049	M₁₆	—	2	4	no	—
1050	M₁₆	#41×C₂₃	1	4	yes	complemented
1051	C₂×C₈	—	2	4	no	—
1052	C₂×C₈	—	2	4	no	—
1053	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1054	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1055	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1089	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1090	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1091	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1093	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1094	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1096	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1127	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1129	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1132	C₄²	—	2	1	no	—
1133	C₄²	—	2	1	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	2	no	—
1137	C₄²	—	2	1	no	—
1138	C₄²	—	2	2	no	—
1139	C₄²	—	2	2	no	—
1140	C₄²	—	2	1	no	—
1141	C₄²	—	2	1	no	—
1142	C₄²	—	2	1	no	—
1143	C₄²	—	2	1	no	—
1144	C₄²	—	2	1	no	—
1145	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1146	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1147	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1148	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	1	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	1	no	—
1155	C₂³	—	4	1	no	—
1156	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1157	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1158	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1159	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1160	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1161	Q₈	—	2	2	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	2	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	4	2	no	—
1166	Q₈	—	4	2	no	—
1167	Q₈	—	8	1	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	4	1	no	—
1173	D₄	—	4	1	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	8	1	no	—
1178	D₄	—	8	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	4	1	no	—
1205	C₂×C₄	—	4	1	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	4	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	8	1	no	—
1217	C₂×C₄	—	8	1	no	—
1218	C₂×C₄	—	8	1	no	—
1219	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1223	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1228	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1229	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1230	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₈	—	2	2	no	—
1234	C₈	C₂×#41×C₂₃	1	4	yes	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	4	4	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	8	2	no	—
1253	C₂²	C₂₃×#547	1	2	yes	—
1254	C₂²	C₂₃×#575	1	2	yes	—
1255	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	2	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	4	2	no	—
1268	C₄	—	4	2	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	2	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	C₂₃×#547	1	2	yes	—
1276	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1277	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1278	C₂	—	2	2	no	—
1279	C₂	—	2	2	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	1	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	8	1	no	—
1284	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1285	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1286	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#552	C₂	semidirect
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3351	C₂	semidirect
5. C₂₃×#3349	C₂	semidirect
6. C₂₃×#3348	C₂	semidirect
7. C₂₃×#3344	C₂	semidirect
8. C₂₃×#3343	C₂	semidirect
9. C₂₃×#3337	C₂	semidirect
10. C₂₃×#3336	C₂	semidirect
11. C₂₃×#3166	C₂	semidirect
12. C₂₃×#3095	C₂	semidirect
13. C₂₃×#3095	C₂	semidirect
14. C₂₃×#3093	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂₃×#3080	C₂	semidirect
17. C₂₃×#3078	C₂	semidirect
18. C₂₃×#3056	C₂	semidirect
19. C₂₃×#3056	C₂	semidirect
20. C₄×C₂₃×#137	C₂	semidirect
21. D₄×M₁₆×C₂₃	C₂	semidirect
22. C₂₃×#2911	C₂	semidirect
23. C₂×C₂₃×#428	C₂	semidirect
68. C₂₃×#501	C₂²	semidirect
69. C₂₃×#501	C₂²	semidirect
70. C₂₃×#499	C₂²	semidirect
71. C₂₃×#499	C₂²	semidirect
72. C₂₃×#485	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
74. C₂₃×#485	C₂²	semidirect
75. C₂₃×#485	C₂²	semidirect
76. C₂₃×#485	C₂²	semidirect
77. C₂₃×#485	C₂²	semidirect
78. C₂₃×#484	C₂²	semidirect
79. C₂₃×#484	C₂²	semidirect
80. C₂₃×#484	C₂²	semidirect
81. C₂₃×#483	C₂²	semidirect
82. C₂₃×#483	C₂²	semidirect
83. C₂₃×#483	C₂²	semidirect
84. C₂₃×#482	C₂²	semidirect
85. C₂₃×#482	C₂²	semidirect
86. C₂₃×#481	C₂²	semidirect
87. C₂₃×#480	C₂²	semidirect
88. C₂₃×#479	C₂²	semidirect
89. C₂₃×#479	C₂²	semidirect
90. C₂₃×#479	C₂²	semidirect
91. C₂₃×#479	C₂²	semidirect
92. C₂₃×#478	C₂²	semidirect
93. C₂₃×#478	C₂²	semidirect
94. C₂₃×#477	C₂²	semidirect
95. C₂₃×#475	C₂²	semidirect
96. C₂₃×#470	C₂²	semidirect
97. C₂₃×#470	C₂²	semidirect
98. C₂₃×#468	C₂²	semidirect
99. C₂₃×#468	C₂²	semidirect
100. C₂₃×#467	C₂²	semidirect
101. C₂₃×#467	C₂²	semidirect
102. C₂₃×#465	C₂²	semidirect
103. C₂₃×#465	C₂²	semidirect
104. C₂₃×#441	C₂²	semidirect
105. C₂₃×#440	C₂²	semidirect
106. C₄×Q₁₆×C₂₃	C₂²	semidirect
107. C₄×SD₁₆×C₂₃	C₂²	semidirect
121. C₂₃×#428	C₂²	semidirect
122. C₂₃×#428	C₂²	semidirect
123. C₂₃×#428	C₂²	semidirect
124. C₂₃×#428	C₂²	semidirect
125. C₂₃×#427	C₂²	semidirect
126. C₂₃×#427	C₂²	semidirect
127. C₂×C₂₃×#107	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
406. M₁₆×C₂₃	#41	semidirect
505. #61253	C₂₃	direct (N × H)
593. C₂×#552	C₂×C₂₃	semidirect
594. #3352	C₂×C₂₃	semidirect
595. #3351	C₂×C₂₃	semidirect
596. #3349	C₂×C₂₃	semidirect
597. #3348	C₂×C₂₃	semidirect
598. #3344	C₂×C₂₃	semidirect
599. #3343	C₂×C₂₃	semidirect
600. #3337	C₂×C₂₃	semidirect
601. #3336	C₂×C₂₃	semidirect
602. #3166	C₂×C₂₃	semidirect
603. #3095	C₂×C₂₃	semidirect
604. #3095	C₂×C₂₃	semidirect
605. #3093	C₂×C₂₃	semidirect
606. #3092	C₂×C₂₃	semidirect
607. #3080	C₂×C₂₃	semidirect
608. #3078	C₂×C₂₃	semidirect
609. #3056	C₂×C₂₃	semidirect
610. #3056	C₂×C₂₃	semidirect
611. C₄×#137	C₂×C₂₃	semidirect
612. D₄×M₁₆	C₂×C₂₃	semidirect
613. #2911	C₂×C₂₃	semidirect
614. C₂×#428	C₂×C₂₃	semidirect
702. #501	C₂²×C₂₃	semidirect
703. #501	C₂²×C₂₃	semidirect
704. #499	C₂²×C₂₃	semidirect
705. #499	C₂²×C₂₃	semidirect
706. #485	C₂²×C₂₃	semidirect
707. #485	C₂²×C₂₃	semidirect
708. #485	C₂²×C₂₃	semidirect
709. #485	C₂²×C₂₃	semidirect
710. #485	C₂²×C₂₃	semidirect
711. #485	C₂²×C₂₃	semidirect
712. #484	C₂²×C₂₃	semidirect
713. #484	C₂²×C₂₃	semidirect
714. #484	C₂²×C₂₃	semidirect
715. #483	C₂²×C₂₃	semidirect
716. #483	C₂²×C₂₃	semidirect
717. #483	C₂²×C₂₃	semidirect
718. #482	C₂²×C₂₃	semidirect
719. #482	C₂²×C₂₃	semidirect
720. #481	C₂²×C₂₃	semidirect
721. #480	C₂²×C₂₃	semidirect
722. #479	C₂²×C₂₃	semidirect
723. #479	C₂²×C₂₃	semidirect
724. #479	C₂²×C₂₃	semidirect
725. #479	C₂²×C₂₃	semidirect
726. #478	C₂²×C₂₃	semidirect
727. #478	C₂²×C₂₃	semidirect
728. #477	C₂²×C₂₃	semidirect
729. #475	C₂²×C₂₃	semidirect
730. #470	C₂²×C₂₃	semidirect
731. #470	C₂²×C₂₃	semidirect
732. #468	C₂²×C₂₃	semidirect
733. #468	C₂²×C₂₃	semidirect
734. #467	C₂²×C₂₃	semidirect
735. #467	C₂²×C₂₃	semidirect
736. #465	C₂²×C₂₃	semidirect
737. #465	C₂²×C₂₃	semidirect
738. #441	C₂²×C₂₃	semidirect
739. #440	C₂²×C₂₃	semidirect
740. C₄×Q₁₆	C₂²×C₂₃	semidirect
741. C₄×SD₁₆	C₂²×C₂₃	semidirect
755. #428	C₂²×C₂₃	semidirect
756. #428	C₂²×C₂₃	semidirect
757. #428	C₂²×C₂₃	semidirect
758. #428	C₂²×C₂₃	semidirect
759. #427	C₂²×C₂₃	semidirect
760. #427	C₂²×C₂₃	semidirect
761. C₂×#107	C₂²×C₂₃	semidirect
762. C₂×#106	C₂²×C₂₃	semidirect
988. C₂₃	#61253	direct (N × H)
1050. M₁₆	#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×#3475	2
C₂×C₂₃×#552	2
C₂₃×#3352	2
C₂₃×#3351	2
C₂₃×#3349	2
C₂₃×#3348	2
C₂₃×#3344	2
C₂₃×#3343	2
C₂₃×#3337	2
C₂₃×#3336	2
C₂₃×#3166	2
C₂₃×#3095	2
C₂₃×#3093	2
C₂₃×#3092	2
C₂₃×#3080	2
C₂₃×#3078	2
C₂₃×#3056	2
C₄×C₂₃×#137	2
D₄×M₁₆×C₂₃	2
C₂₃×#2911	2
C₂×C₂₃×#428	2
#61253	23

Subgroups — C23×#61253 #19208879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61253 #19208879