Subgroups — C₂₃×#17505 #19165131

Order 5888.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1490	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#544	C₄	1	1	yes	characteristic
17	C₂₃×#542	—	2	1	no	—
18	C₂₃×#542	C₄	1	1	yes	characteristic
19	C₂₃×#542	C₄	1	1	yes	characteristic
20	C₂₃×#540	—	2	1	no	—
21	C₂₃×#540	C₄	1	1	yes	characteristic
22	C₂₃×#540	C₄	1	1	yes	characteristic
23	C₂₃×#538	—	2	1	no	—
24	C₂₃×#538	—	2	1	no	—
25	C₂₃×#537	C₄	1	1	yes	characteristic
26	C₂₃×#535	C₄	1	1	yes	characteristic
27	C₂₃×#535	C₄	1	1	yes	characteristic
28	C₂₃×#532	—	2	1	no	—
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	C₂²	1	1	yes	characteristic
33	C₂₃×#529	C₂²	1	1	yes	characteristic
34	C₂₃×#525	—	2	1	no	—
35	C₂₃×#525	—	2	1	no	—
36	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#446	—	2	1	no	—
40	C₂₃×#446	—	2	1	no	—
41	C₂₃×#436	—	2	1	no	—
42	C₂₃×#436	—	2	1	no	—
43	C₂₃×#435	—	2	1	no	—
44	C₂₃×#435	—	2	1	no	—
45	C₂₃×#435	—	2	1	no	—
46	C₂₃×#435	—	2	1	no	—
47	C₂₃×#432	C₂²	1	1	yes	characteristic
48	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#431	C₂²	1	1	yes	characteristic
50	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#423	C₂²	1	1	yes	characteristic
54	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₂₃	—	2	1	no	—
76	C₂×#41×C₂₃	—	2	1	no	—
77	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	—	2	1	no	—
81	C₂×M₁₆×C₂₃	—	2	1	no	—
82	C₂×M₁₆×C₂₃	—	2	1	no	—
83	C₂×M₁₆×C₂₃	—	2	1	no	—
84	C₂×M₁₆×C₂₃	—	2	1	no	—
85	C₂²×C₈×C₂₃	—	2	1	no	—
86	C₂²×C₈×C₂₃	—	2	1	no	—
87	C₂₃×C₄⋊Q₈	—	2	1	no	—
88	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
90	C₂₃×#127	—	2	1	no	—
91	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
92	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
93	C₂₃×#126	—	2	1	no	—
94	C₂₃×#126	—	2	1	no	—
95	C₂₃×#126	—	2	1	no	—
96	C₂₃×#126	—	2	1	no	—
97	C₂₃×#125	—	2	1	no	—
98	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
99	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
100	C₂₃×#124	—	2	1	no	—
101	C₂₃×#124	—	2	1	no	—
102	C₂₃×#124	—	2	1	no	—
103	C₂₃×#124	—	2	1	no	—
104	C₂₃×#124	—	2	1	no	—
105	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
106	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
107	C₂₃×#123	—	2	1	no	—
108	C₂₃×#123	—	2	1	no	—
109	C₂₃×#123	—	2	1	no	—
110	C₂₃×#123	—	2	1	no	—
111	C₂₃×#123	—	2	1	no	—
112	C₂₃×#123	—	2	1	no	—
113	C₂₃×#123	—	2	1	no	—
114	C₂₃×#123	—	2	1	no	—
115	C₂₃×C₂²⋊Q₈	—	2	1	no	—
116	C₂₃×C₂²⋊Q₈	—	2	1	no	—
117	C₂₃×C₂²⋊Q₈	—	2	1	no	—
118	C₂₃×C₂²⋊Q₈	—	2	1	no	—
119	C₂₃×C₂²⋊Q₈	—	2	1	no	—
120	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
121	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
122	C₂₃×#121	—	2	1	no	—
123	C₂₃×#121	—	2	1	no	—
124	C₂₃×#121	—	2	1	no	—
125	C₂₃×#121	—	2	1	no	—
126	C₂₃×#121	—	2	1	no	—
127	C₂₃×#121	—	2	1	no	—
128	C₂₃×#121	—	2	1	no	—
129	C₂₃×#121	—	2	1	no	—
130	C₂₃×#121	—	2	1	no	—
131	C₂₃×#121	—	2	1	no	—
132	C₂₃×#121	—	2	1	no	—
133	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
134	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
135	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
136	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
137	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
138	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
139	C₂₃×#120	—	2	1	no	—
140	C₂₃×#120	—	2	1	no	—
141	C₂₃×#120	—	2	1	no	—
142	C₂₃×#120	—	2	1	no	—
143	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
144	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
145	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
146	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
147	C₄×D₄×C₂₃	—	2	1	no	—
148	C₄×D₄×C₂₃	—	2	1	no	—
149	C₄×D₄×C₂₃	—	2	1	no	—
150	C₄×D₄×C₂₃	—	2	1	no	—
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	—	2	1	no	—
153	C₄×D₄×C₂₃	—	2	1	no	—
154	C₄×D₄×C₂₃	—	2	1	no	—
155	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
157	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
158	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
159	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
161	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
162	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
163	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
164	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₂₃×#117	—	2	1	no	—
168	C₂₃×#117	—	2	1	no	—
169	C₂₃×#117	—	2	1	no	—
170	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
171	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
172	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
173	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₄²×C₂₃	—	2	1	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
180	C₂₃×C₄⋊C₈	—	2	1	no	—
181	C₂₃×C₄⋊C₈	—	2	1	no	—
182	C₂₃×C₄⋊C₈	—	2	1	no	—
183	C₂₃×C₄⋊C₈	—	2	1	no	—
184	C₂₃×C₄⋊C₈	—	2	1	no	—
185	C₂₃×C₄⋊C₈	—	2	1	no	—
186	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
187	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
189	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₂₃×C₂²⋊C₈	—	2	1	no	—
191	C₂₃×C₂²⋊C₈	—	2	1	no	—
192	C₂₃×C₂²⋊C₈	—	2	1	no	—
193	C₂₃×C₂²⋊C₈	—	2	1	no	—
194	C₂₃×C₂²⋊C₈	—	2	1	no	—
195	C₂₃×C₂²⋊C₈	—	2	1	no	—
196	C₂₃×#97	—	2	1	no	—
197	C₂₃×#97	—	2	1	no	—
198	C₂₃×#97	—	2	1	no	—
199	C₂₃×#97	—	2	1	no	—
200	C₄×C₈×C₂₃	—	2	1	no	—
201	C₄×C₈×C₂₃	—	2	1	no	—
202	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
206	C₂⁴×C₂₃	—	2	1	no	—
207	#41×C₂₃	—	4	2	no	—
208	#41×C₂₃	—	4	2	no	—
209	#41×C₂₃	—	8	1	no	—
210	#41×C₂₃	—	8	1	no	—
211	#41×C₂₃	—	8	1	no	—
212	#41×C₂₃	—	8	1	no	—
213	C₂×Q₈×C₂₃	—	2	1	no	—
214	C₂×Q₈×C₂₃	—	2	1	no	—
215	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
216	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₂₃	—	2	1	no	—
218	C₂×D₄×C₂₃	—	2	1	no	—
219	C₂×D₄×C₂₃	—	2	1	no	—
220	C₂×D₄×C₂₃	—	2	1	no	—
221	C₂×D₄×C₂₃	—	2	1	no	—
222	C₂×D₄×C₂₃	—	2	1	no	—
223	C₂×D₄×C₂₃	—	2	1	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	4	2	no	—
230	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
231	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	1	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	8	1	no	—
245	C₂²×C₄×C₂₃	—	8	1	no	—
246	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	M₁₆×C₂₃	—	4	2	no	—
256	M₁₆×C₂₃	—	4	2	no	—
257	M₁₆×C₂₃	—	8	1	no	—
258	M₁₆×C₂₃	—	8	1	no	—
259	C₂×C₈×C₂₃	—	2	1	no	—
260	C₂×C₈×C₂₃	—	2	1	no	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	2	1	no	—
263	C₂×C₈×C₂₃	—	2	1	no	—
264	C₂×C₈×C₂₃	—	2	1	no	—
265	C₂×C₈×C₂₃	—	2	1	no	—
266	C₂×C₈×C₂₃	—	2	1	no	—
267	C₂×C₈×C₂₃	—	4	2	no	—
268	C₂×C₈×C₂₃	—	8	1	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
281	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
282	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
283	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
284	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
285	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
286	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
287	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
288	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
289	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
290	C₂²⋊C₄×C₂₃	—	2	1	no	—
291	C₂²⋊C₄×C₂₃	—	2	1	no	—
292	C₂²⋊C₄×C₂₃	—	2	1	no	—
293	C₂²⋊C₄×C₂₃	—	2	1	no	—
294	C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂²⋊C₄×C₂₃	—	2	1	no	—
301	C₂²⋊C₄×C₂₃	—	2	1	no	—
302	C₂²⋊C₄×C₂₃	—	2	1	no	—
303	C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
310	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
311	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
312	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
313	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
314	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
315	C₄²×C₂₃	—	2	1	no	—
316	C₄²×C₂₃	—	2	1	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
320	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
321	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#17505	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	—	2	1	no	—
331	C₂³×C₂₃	—	2	1	no	—
332	C₂³×C₂₃	—	4	2	no	—
333	C₂³×C₂₃	—	8	1	no	—
334	C₂³×C₂₃	—	8	1	no	—
335	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	Q₈×C₂₃	—	2	2	no	—
339	Q₈×C₂₃	—	4	1	no	—
340	Q₈×C₂₃	—	8	1	no	—
341	Q₈×C₂₃	—	8	1	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	2	no	—
344	D₄×C₂₃	—	2	2	no	—
345	D₄×C₂₃	—	4	1	no	—
346	D₄×C₂₃	—	4	1	no	—
347	D₄×C₂₃	—	4	1	no	—
348	D₄×C₂₃	—	4	2	no	—
349	D₄×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	8	1	no	—
351	D₄×C₂₃	—	8	1	no	—
352	D₄×C₂₃	—	8	1	no	—
353	D₄×C₂₃	—	8	1	no	—
354	D₄×C₂₃	—	8	1	no	—
355	D₄×C₂₃	—	8	1	no	—
356	D₄×C₂₃	—	8	1	no	—
357	D₄×C₂₃	—	8	1	no	—
358	D₄×C₂₃	—	8	1	no	—
359	D₄×C₂₃	—	8	1	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	1	no	—
379	C₂×C₄×C₂₃	—	4	1	no	—
380	C₂×C₄×C₂₃	—	4	1	no	—
381	C₂×C₄×C₂₃	—	4	1	no	—
382	C₂×C₄×C₂₃	—	4	1	no	—
383	C₂×C₄×C₂₃	—	4	1	no	—
384	C₂×C₄×C₂₃	—	8	1	no	—
385	C₂×C₄×C₂₃	—	8	1	no	—
386	C₂×C₄×C₂₃	—	8	1	no	—
387	C₂×C₄×C₂₃	—	8	1	no	—
388	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₈×C₂₃	—	2	2	no	—
401	C₈×C₂₃	—	4	1	no	—
402	C₈×C₂₃	—	4	1	no	—
403	C₈×C₂₃	—	4	1	no	—
404	C₈×C₂₃	—	4	1	no	—
405	C₈×C₂₃	—	4	1	no	—
406	C₈×C₂₃	—	4	1	no	—
407	C₈×C₂₃	—	4	1	no	—
408	#3460	C₂×C₂₃	1	1	yes	characteristic
409	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#1496	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#1495	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#1492	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#1490	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#1489	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#1488	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#1486	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#1484	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#1483	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#1482	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#1480	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	1	no	—
426	C₂²×C₂₃	—	2	1	no	—
427	C₂²×C₂₃	—	2	1	no	—
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	2	1	no	—
430	C₂²×C₂₃	—	2	1	no	—
431	C₂²×C₂₃	—	2	1	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	1	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	4	1	no	—
436	C₂²×C₂₃	—	4	1	no	—
437	C₂²×C₂₃	—	4	1	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	—	4	1	no	—
440	C₂²×C₂₃	—	4	1	no	—
441	C₂²×C₂₃	—	8	4	no	—
442	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	2	1	no	—
446	C₄×C₂₃	—	2	1	no	—
447	C₄×C₂₃	—	2	1	no	—
448	C₄×C₂₃	—	2	1	no	—
449	C₄×C₂₃	—	2	1	no	—
450	C₄×C₂₃	—	2	1	no	—
451	C₄×C₂₃	—	2	1	no	—
452	C₄×C₂₃	—	2	1	no	—
453	C₄×C₂₃	—	4	1	no	—
454	C₄×C₂₃	—	4	1	no	—
455	C₄×C₂₃	—	4	1	no	—
456	C₄×C₂₃	—	4	1	no	—
457	C₄×C₂₃	—	4	1	no	—
458	C₄×C₂₃	#568	1	2	yes	—
459	C₄×C₂₃	#576	1	1	yes	characteristic
460	C₄×C₂₃	#577	1	1	yes	characteristic
461	#544	C₄×C₂₃	1	1	yes	characteristic
462	#542	—	2	1	no	—
463	#542	C₄×C₂₃	1	1	yes	characteristic
464	#542	C₄×C₂₃	1	1	yes	characteristic
465	#540	—	2	1	no	—
466	#540	C₄×C₂₃	1	1	yes	characteristic
467	#540	C₄×C₂₃	1	1	yes	characteristic
468	#538	—	2	1	no	—
469	#538	—	2	1	no	—
470	#537	C₄×C₂₃	1	1	yes	characteristic
471	#535	C₄×C₂₃	1	1	yes	characteristic
472	#535	C₄×C₂₃	1	1	yes	characteristic
473	#532	—	2	1	no	—
474	#532	C₂²×C₂₃	1	1	yes	characteristic
475	#532	C₂²×C₂₃	1	1	yes	characteristic
476	#529	—	2	1	no	—
477	#529	C₂²×C₂₃	1	1	yes	characteristic
478	#529	C₂²×C₂₃	1	1	yes	characteristic
479	#525	—	2	1	no	—
480	#525	—	2	1	no	—
481	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
482	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
484	#446	—	2	1	no	—
485	#446	—	2	1	no	—
486	#436	—	2	1	no	—
487	#436	—	2	1	no	—
488	#435	—	2	1	no	—
489	#435	—	2	1	no	—
490	#435	—	2	1	no	—
491	#435	—	2	1	no	—
492	#432	C₂²×C₂₃	1	1	yes	characteristic
493	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	#431	C₂²×C₂₃	1	1	yes	characteristic
495	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
497	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
498	#423	C₂²×C₂₃	1	1	yes	characteristic
499	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
502	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
509	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
510	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
511	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
512	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
513	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
514	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
515	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
516	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
520	C₂×C₂₃	—	4	1	no	—
521	C₂×C₂₃	—	4	1	no	—
522	C₂×C₂₃	—	4	1	no	—
523	C₂×C₂₃	—	8	1	no	—
524	C₂×C₂₃	—	8	1	no	—
525	C₂×C₂₃	—	8	1	no	—
526	C₂×C₂₃	#2879	1	1	yes	characteristic
527	C₂×C₂₃	#2897	1	1	yes	characteristic
528	C₂×C₂₃	#2901	1	1	yes	characteristic
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
532	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
533	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	1	no	—
538	C₂×M₁₆	—	2	1	no	—
539	C₂²×C₈	—	2	1	no	—
540	C₂²×C₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
544	#127	—	2	1	no	—
545	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
546	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
547	#126	—	2	1	no	—
548	#126	—	2	1	no	—
549	#126	—	2	1	no	—
550	#126	—	2	1	no	—
551	#125	—	2	1	no	—
552	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
553	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
554	#124	—	2	1	no	—
555	#124	—	2	1	no	—
556	#124	—	2	1	no	—
557	#124	—	2	1	no	—
558	#124	—	2	1	no	—
559	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
560	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
561	#123	—	2	1	no	—
562	#123	—	2	1	no	—
563	#123	—	2	1	no	—
564	#123	—	2	1	no	—
565	#123	—	2	1	no	—
566	#123	—	2	1	no	—
567	#123	—	2	1	no	—
568	#123	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
575	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	1	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
588	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
589	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
590	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
591	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
592	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
593	#120	—	2	1	no	—
594	#120	—	2	1	no	—
595	#120	—	2	1	no	—
596	#120	—	2	1	no	—
597	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
598	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
610	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
611	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
612	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
613	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
614	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
615	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
616	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
617	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
625	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
626	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
627	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
634	C₄⋊C₈	—	2	1	no	—
635	C₄⋊C₈	—	2	1	no	—
636	C₄⋊C₈	—	2	1	no	—
637	C₄⋊C₈	—	2	1	no	—
638	C₄⋊C₈	—	2	1	no	—
639	C₄⋊C₈	—	2	1	no	—
640	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
641	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
642	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
643	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
644	C₂²⋊C₈	—	2	1	no	—
645	C₂²⋊C₈	—	2	1	no	—
646	C₂²⋊C₈	—	2	1	no	—
647	C₂²⋊C₈	—	2	1	no	—
648	C₂²⋊C₈	—	2	1	no	—
649	C₂²⋊C₈	—	2	1	no	—
650	#97	—	2	1	no	—
651	#97	—	2	1	no	—
652	#97	—	2	1	no	—
653	#97	—	2	1	no	—
654	C₄×C₈	—	2	1	no	—
655	C₄×C₈	—	2	1	no	—
656	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
657	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
658	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
659	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₂₃	#17505	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	#41	—	4	2	no	—
663	#41	—	4	2	no	—
664	#41	—	8	1	no	—
665	#41	—	8	1	no	—
666	#41	—	8	1	no	—
667	#41	—	8	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
671	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
686	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
687	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
688	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
689	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
690	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	8	1	no	—
700	C₂²×C₄	—	8	1	no	—
701	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
702	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
703	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
710	M₁₆	—	4	2	no	—
711	M₁₆	—	4	2	no	—
712	M₁₆	—	8	1	no	—
713	M₁₆	—	8	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	4	2	no	—
723	C₂×C₈	—	8	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
765	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
766	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
767	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
768	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
769	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
770	C₄²	—	2	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	1	no	—
773	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
774	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
775	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	8	1	no	—
788	C₂³	—	8	1	no	—
789	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
790	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
791	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	4	1	no	—
794	Q₈	—	8	1	no	—
795	Q₈	—	8	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	—	4	1	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	2	no	—
804	D₄	—	8	1	no	—
805	D₄	—	8	1	no	—
806	D₄	—	8	1	no	—
807	D₄	—	8	1	no	—
808	D₄	—	8	1	no	—
809	D₄	—	8	1	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	1	no	—
812	D₄	—	8	1	no	—
813	D₄	—	8	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	8	1	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	1	no	—
841	C₂×C₄	—	8	1	no	—
842	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
843	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
848	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
849	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
850	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
851	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
854	C₈	—	2	2	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₈	—	4	1	no	—
859	C₈	—	4	1	no	—
860	C₈	—	4	1	no	—
861	C₈	—	4	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	8	4	no	—
881	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	C₂₃×#568	1	2	yes	—
898	C₄	C₂₃×#576	1	1	yes	characteristic
899	C₄	C₂₃×#577	1	1	yes	characteristic
900	C₂	—	4	1	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	1	no	—
903	C₂	—	8	1	no	—
904	C₂	—	8	1	no	—
905	C₂	—	8	1	no	—
906	C₂	C₂₃×#2879	1	1	yes	characteristic
907	C₂	C₂₃×#2897	1	1	yes	characteristic
908	C₂	C₂₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂₃×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2989	C₂	semidirect
3. C₂₃×#2965	C₂	semidirect
4. C₂₃×#1496	C₂	semidirect
5. C₂₃×#1495	C₂	semidirect
6. C₂₃×#1494	C₂	semidirect
7. C₂₃×#1492	C₂	semidirect
8. C₂₃×#1490	C₂	semidirect
9. C₂₃×#1489	C₂	semidirect
10. C₂₃×#1488	C₂	semidirect
11. C₂₃×#1486	C₂	semidirect
12. C₂₃×#1484	C₂	semidirect
13. C₂₃×#1483	C₂	semidirect
14. C₂₃×#1482	C₂	semidirect
15. C₂₃×#1480	C₂	semidirect
48. C₂₃×#432	C₂²	semidirect
50. C₂₃×#431	C₂²	semidirect
51. C₂₃×#431	C₂²	semidirect
52. C₂₃×#431	C₂²	semidirect
54. C₂₃×#423	C₂²	semidirect
55. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
57. C₄×M₁₆×C₂₃	C₂²	semidirect
58. C₂×C₄×C₈×C₂₃	C₂²	semidirect
59. C₂₃×Q₈⋊C₈	C₂²	semidirect
60. C₂₃×Q₈⋊C₈	C₂²	semidirect
61. C₂₃×Q₈⋊C₈	C₂²	semidirect
62. C₂₃×Q₈⋊C₈	C₂²	semidirect
71. C₂₃×D₄⋊C₈	C₂²	semidirect
72. C₂₃×D₄⋊C₈	C₂²	semidirect
73. C₂₃×D₄⋊C₈	C₂²	semidirect
74. C₂₃×D₄⋊C₈	C₂²	semidirect
328. #17505	C₂₃	direct (N × H)
409. #2989	C₂×C₂₃	semidirect
410. #2965	C₂×C₂₃	semidirect
411. #1496	C₂×C₂₃	semidirect
412. #1495	C₂×C₂₃	semidirect
413. #1494	C₂×C₂₃	semidirect
414. #1492	C₂×C₂₃	semidirect
415. #1490	C₂×C₂₃	semidirect
416. #1489	C₂×C₂₃	semidirect
417. #1488	C₂×C₂₃	semidirect
418. #1486	C₂×C₂₃	semidirect
419. #1484	C₂×C₂₃	semidirect
420. #1483	C₂×C₂₃	semidirect
421. #1482	C₂×C₂₃	semidirect
422. #1480	C₂×C₂₃	semidirect
493. #432	C₂²×C₂₃	semidirect
495. #431	C₂²×C₂₃	semidirect
496. #431	C₂²×C₂₃	semidirect
497. #431	C₂²×C₂₃	semidirect
499. #423	C₂²×C₂₃	semidirect
500. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
502. C₄×M₁₆	C₂²×C₂₃	semidirect
503. C₂×C₄×C₈	C₂²×C₂₃	semidirect
504. Q₈⋊C₈	C₂²×C₂₃	semidirect
505. Q₈⋊C₈	C₂²×C₂₃	semidirect
506. Q₈⋊C₈	C₂²×C₂₃	semidirect
507. Q₈⋊C₈	C₂²×C₂₃	semidirect
516. D₄⋊C₈	C₂²×C₂₃	semidirect
517. D₄⋊C₈	C₂²×C₂₃	semidirect
518. D₄⋊C₈	C₂²×C₂₃	semidirect
519. D₄⋊C₈	C₂²×C₂₃	semidirect
660. C₂₃	#17505	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3460	2
C₂₃×#2989	2
C₂₃×#2965	2
C₂₃×#1496	2
C₂₃×#1495	2
C₂₃×#1494	2
C₂₃×#1492	2
C₂₃×#1490	2
C₂₃×#1489	2
C₂₃×#1488	2
C₂₃×#1486	2
C₂₃×#1484	2
C₂₃×#1483	2
C₂₃×#1482	2
C₂₃×#1480	2
#17505	23

Subgroups — C23×#17505 #19165131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17505 #19165131