Subgroups — C₂₃×#61737 #19209363

Order 5888.

2012 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3353	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3343	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3334	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3330	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3298	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3193	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#484	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	—	2	1	no	—
19	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#554	—	2	1	no	—
21	C₂₃×#552	C₂²	1	2	yes	complemented
22	C₂₃×#551	—	2	2	no	—
23	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#548	C₂²	1	2	yes	complemented
25	C₂₃×#547	—	2	1	no	—
26	C₂₃×#547	—	2	2	no	—
27	C₂₃×#547	—	2	1	no	—
28	C₂₃×#547	C₂²	1	2	yes	—
29	C₂₃×#547	C₂²	1	4	yes	—
30	C₂₃×#547	C₂²	1	2	yes	—
31	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#546	—	2	1	no	—
34	C₂₃×#542	—	2	1	no	—
35	C₂₃×#539	—	2	2	no	—
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂₃×#529	C₂²	1	1	yes	characteristic
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×#123	—	2	2	no	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₂₃×#121	C₂²	1	2	yes	—
44	C₂₃×#520	—	2	1	no	—
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#500	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#487	C₂²	1	2	yes	complemented
52	C₂₃×#484	C₂²	1	2	yes	—
53	C₂₃×#484	C₂²	1	2	yes	—
54	C₂₃×#484	C₂²	1	2	yes	—
55	C₂₃×#484	C₂²	1	1	yes	characteristic
56	C₂₃×#484	C₂²	1	2	yes	—
57	C₂₃×#484	C₂²	1	4	yes	complemented
58	C₂₃×#484	C₂²	1	4	yes	complemented
59	C₂₃×#483	C₂²	1	4	yes	complemented
60	C₂₃×#482	C₂²	1	4	yes	complemented
61	C₂₃×#481	C₂²	1	2	yes	—
62	C₂₃×#481	C₂²	1	1	yes	characteristic
63	C₂₃×#480	C₂²	1	4	yes	complemented
64	C₂₃×#480	C₂²	1	4	yes	complemented
65	C₂₃×#478	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	4	yes	complemented
67	C₂₃×#475	C₂²	1	2	yes	complemented
68	C₂₃×#474	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	2	yes	complemented
70	C₂₃×#468	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#466	C₂²	1	4	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	complemented
74	C₂₃×#463	C₂²	1	2	yes	complemented
75	C₂₃×#461	C₂²	1	2	yes	complemented
76	C₂₃×#450	C₂²	1	2	yes	—
77	C₂₃×#450	C₂²	1	1	yes	characteristic
78	C₂₃×#449	C₂²	1	4	yes	complemented
79	C₂₃×#448	C₂²	1	4	yes	complemented
80	C₂₃×#447	C₂²	1	1	yes	characteristic
81	C₂₃×#440	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#432	C₂²	1	1	yes	characteristic
88	C₂₃×#431	C₂²	1	1	yes	characteristic
89	C₂₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₂₃×#107	C₂²	1	4	yes	complemented
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	—
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	4	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	1	no	—
99	C₂×#41×C₂₃	—	4	8	no	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₂₃	—	2	1	no	—
102	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	—	2	2	no	—
107	C₂³×C₄×C₂₃	—	2	1	no	—
108	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×D₈×C₂₃	C₂³	1	2	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	—	2	1	no	—
116	C₂₃×C₄⋊Q₈	—	2	1	no	—
117	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	1	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	—	2	1	no	—
126	C₂₃×#125	C₂³	1	1	yes	characteristic
127	C₂₃×#124	—	2	1	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	C₂³	1	1	yes	characteristic
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	1	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	4	no	—
134	C₂₃×#123	—	2	4	no	—
135	C₂₃×#123	—	2	4	no	—
136	C₂₃×#123	—	2	4	no	—
137	C₂₃×#123	—	2	2	no	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	C₂³	1	4	yes	—
158	C₂₃×#121	C₂³	1	4	yes	—
159	C₂₃×#121	C₂³	1	2	yes	—
160	C₂₃×#121	C₂³	1	1	yes	characteristic
161	C₂₃×#120	—	2	2	no	—
162	C₄×Q₈×C₂₃	—	2	1	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	D₄	1	2	yes	—
175	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	1	no	—
185	C₂₃×#117	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#107	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#107	C₂³	1	4	yes	—
207	C₂₃×#107	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	2	yes	—
209	C₂₃×#106	C₂³	1	4	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	2	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	2	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₂₃×#97	C₂³	1	2	yes	—
228	C₄×C₈×C₂₃	C₂³	1	2	yes	—
229	C₂⁴×C₂₃	—	2	1	no	—
230	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
231	#41×C₂₃	—	4	4	no	—
232	#41×C₂₃	—	4	16	no	—
233	#41×C₂₃	—	4	8	no	—
234	#41×C₂₃	—	4	4	no	—
235	#41×C₂₃	—	4	8	no	—
236	C₂×Q₈×C₂₃	—	2	1	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	2	2	no	—
240	C₂×Q₈×C₂₃	—	4	4	no	—
241	C₂×Q₈×C₂₃	—	4	4	no	—
242	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	4	2	no	—
252	C₂×D₄×C₂₃	—	4	8	no	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	4	no	—
262	C₂²×C₄×C₂₃	—	2	4	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	4	4	no	—
269	C₂²×C₄×C₂₃	—	4	4	no	—
270	C₂²×C₄×C₂₃	—	4	8	no	—
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	SD₁₆×C₂₃	—	4	4	no	—
280	SD₁₆×C₂₃	—	4	2	no	—
281	D₈×C₂₃	—	4	2	no	—
282	M₁₆×C₂₃	—	4	4	no	—
283	C₂×C₈×C₂₃	—	4	4	no	—
284	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	4	no	—
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	1	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
314	C₂²⋊C₄×C₂₃	—	2	1	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	—	2	1	no	—
325	C₂²⋊C₄×C₂₃	—	2	1	no	—
326	C₂²⋊C₄×C₂₃	—	2	1	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	1	no	—
329	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	2	no	—
335	C₄²×C₂₃	—	2	1	no	—
336	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
340	#61737	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂³×C₂₃	—	2	4	no	—
342	C₂³×C₂₃	—	2	4	no	—
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	4	2	no	—
346	C₂³×C₂₃	—	4	2	no	—
347	C₂³×C₂₃	—	4	2	no	—
348	C₂³×C₂₃	—	4	2	no	—
349	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
350	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
351	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₂₃	—	2	2	no	—
353	Q₈×C₂₃	—	2	4	no	—
354	Q₈×C₂₃	—	4	4	no	—
355	Q₈×C₂₃	—	4	4	no	—
356	Q₈×C₂₃	—	4	2	no	—
357	Q₈×C₂₃	—	8	2	no	—
358	D₄×C₂₃	—	2	4	no	—
359	D₄×C₂₃	—	2	2	no	—
360	D₄×C₂₃	—	2	2	no	—
361	D₄×C₂₃	—	2	2	no	—
362	D₄×C₂₃	—	2	2	no	—
363	D₄×C₂₃	—	4	2	no	—
364	D₄×C₂₃	—	4	8	no	—
365	D₄×C₂₃	—	4	8	no	—
366	D₄×C₂₃	—	4	4	no	—
367	D₄×C₂₃	—	4	2	no	—
368	D₄×C₂₃	—	8	2	no	—
369	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	4	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	4	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	2	no	—
385	C₂×C₄×C₂₃	—	4	4	no	—
386	C₂×C₄×C₂₃	—	4	2	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	4	8	no	—
389	C₂×C₄×C₂₃	—	4	8	no	—
390	C₂×C₄×C₂₃	—	4	4	no	—
391	C₂×C₄×C₂₃	—	4	4	no	—
392	C₂×C₄×C₂₃	—	4	2	no	—
393	C₂×C₄×C₂₃	—	8	2	no	—
394	C₂×C₄×C₂₃	—	8	2	no	—
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₂₃	C₂²×D₄	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	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₂₃	—	2	2	no	—
404	C₈×C₂₃	—	2	4	no	—
405	C₈×C₂₃	—	2	2	no	—
406	#3520	C₂×C₂₃	1	1	yes	characteristic, complemented
407	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3353	C₂×C₂₃	1	2	yes	complemented
409	#3343	C₂×C₂₃	1	4	yes	complemented
410	#3334	C₂×C₂₃	1	2	yes	complemented
411	#3330	C₂×C₂₃	1	2	yes	complemented
412	#3308	C₂×C₂₃	1	4	yes	complemented
413	#3298	C₂×C₂₃	1	2	yes	complemented
414	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#3230	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3193	C₂×C₂₃	1	2	yes	complemented
417	#3188	C₂×C₂₃	1	2	yes	complemented
418	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#3092	C₂×C₂₃	1	2	yes	complemented
421	C₂×#484	C₂×C₂₃	1	2	yes	complemented
422	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	2	no	—
425	C₂²×C₂₃	—	2	1	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	2	2	no	—
428	C₂²×C₂₃	—	2	2	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	4	8	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	2	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	4	1	no	—
436	C₂²×C₂₃	—	4	2	no	—
437	C₂²×C₂₃	—	8	4	no	—
438	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
439	C₂²×C₂₃	#578	1	2	yes	—
440	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₂₃	—	2	1	no	—
442	C₄×C₂₃	—	2	2	no	—
443	C₄×C₂₃	—	2	2	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	2	1	no	—
446	C₄×C₂₃	—	2	1	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	4	1	no	—
449	C₄×C₂₃	—	4	1	no	—
450	C₄×C₂₃	—	4	2	no	—
451	C₄×C₂₃	—	4	4	no	—
452	C₄×C₂₃	—	4	2	no	—
453	C₄×C₂₃	—	4	1	no	—
454	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
455	C₄×C₂₃	#585	1	2	yes	—
456	C₂²×#41	—	2	1	no	—
457	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#554	—	2	1	no	—
459	#552	C₂²×C₂₃	1	2	yes	complemented
460	#551	—	2	2	no	—
461	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#548	C₂²×C₂₃	1	2	yes	complemented
463	#547	—	2	1	no	—
464	#547	—	2	2	no	—
465	#547	—	2	1	no	—
466	#547	C₂²×C₂₃	1	2	yes	—
467	#547	C₂²×C₂₃	1	2	yes	—
468	#547	C₂²×C₂₃	1	4	yes	—
469	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
470	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#546	—	2	1	no	—
472	#542	—	2	1	no	—
473	#539	—	2	2	no	—
474	#533	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
476	#529	C₂²×C₂₃	1	1	yes	characteristic
477	#525	C₂²×C₂₃	1	2	yes	—
478	C₂×#123	—	2	2	no	—
479	C₂×C₂²⋊Q₈	—	2	1	no	—
480	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
481	C₂×#121	C₂²×C₂₃	1	2	yes	—
482	#520	—	2	1	no	—
483	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
486	#501	C₂²×C₂₃	1	2	yes	complemented
487	#500	C₂²×C₂₃	1	2	yes	complemented
488	#489	C₂²×C₂₃	1	2	yes	complemented
489	#487	C₂²×C₂₃	1	2	yes	complemented
490	#484	C₂²×C₂₃	1	1	yes	characteristic
491	#484	C₂²×C₂₃	1	2	yes	—
492	#484	C₂²×C₂₃	1	2	yes	—
493	#484	C₂²×C₂₃	1	2	yes	—
494	#484	C₂²×C₂₃	1	2	yes	—
495	#484	C₂²×C₂₃	1	4	yes	complemented
496	#484	C₂²×C₂₃	1	4	yes	complemented
497	#483	C₂²×C₂₃	1	4	yes	complemented
498	#482	C₂²×C₂₃	1	4	yes	complemented
499	#481	C₂²×C₂₃	1	1	yes	characteristic
500	#481	C₂²×C₂₃	1	2	yes	—
501	#480	C₂²×C₂₃	1	4	yes	complemented
502	#480	C₂²×C₂₃	1	4	yes	complemented
503	#478	C₂²×C₂₃	1	2	yes	complemented
504	#477	C₂²×C₂₃	1	4	yes	complemented
505	#475	C₂²×C₂₃	1	2	yes	complemented
506	#474	C₂²×C₂₃	1	2	yes	complemented
507	#474	C₂²×C₂₃	1	2	yes	complemented
508	#468	C₂²×C₂₃	1	4	yes	complemented
509	#468	C₂²×C₂₃	1	4	yes	complemented
510	#466	C₂²×C₂₃	1	4	yes	complemented
511	#465	C₂²×C₂₃	1	4	yes	complemented
512	#463	C₂²×C₂₃	1	2	yes	complemented
513	#461	C₂²×C₂₃	1	2	yes	complemented
514	#450	C₂²×C₂₃	1	1	yes	characteristic
515	#450	C₂²×C₂₃	1	2	yes	—
516	#449	C₂²×C₂₃	1	4	yes	complemented
517	#448	C₂²×C₂₃	1	4	yes	complemented
518	#447	C₂²×C₂₃	1	1	yes	characteristic
519	#440	C₂²×C₂₃	1	4	yes	complemented
520	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
521	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
522	#436	C₂²×C₂₃	1	2	yes	complemented
523	#435	C₂²×C₂₃	1	4	yes	complemented
524	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
525	#432	C₂²×C₂₃	1	1	yes	characteristic
526	#431	C₂²×C₂₃	1	1	yes	characteristic
527	#428	C₂²×C₂₃	1	4	yes	complemented
528	C₂×#107	C₂²×C₂₃	1	4	yes	complemented
529	#417	C₂²×C₂₃	1	4	yes	complemented
530	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
531	#407	C₂²×C₂₃	1	2	yes	—
532	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
533	C₂×C₂₃	—	2	2	no	—
534	C₂×C₂₃	—	2	4	no	—
535	C₂×C₂₃	—	4	2	no	—
536	C₂×C₂₃	—	8	1	no	—
537	C₂×C₂₃	—	8	2	no	—
538	C₂×C₂₃	#3485	1	1	yes	characteristic
539	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
540	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	4	8	no	—
546	C₂×#41	C₂³×C₂₃	1	2	yes	—
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
552	C₂³×C₄	—	2	2	no	—
553	C₂³×C₄	—	2	1	no	—
554	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
557	C₂×D₈	C₂³×C₂₃	1	2	yes	—
558	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
559	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#126	—	2	1	no	—
570	#125	—	2	2	no	—
571	#125	—	2	1	no	—
572	#125	C₂³×C₂₃	1	1	yes	characteristic
573	#124	—	2	1	no	—
574	#124	—	2	2	no	—
575	#124	C₂³×C₂₃	1	1	yes	characteristic
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	1	no	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
595	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
599	#121	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	C₂³×C₂₃	1	4	yes	—
604	#121	C₂³×C₂₃	1	4	yes	—
605	#121	C₂³×C₂₃	1	1	yes	characteristic
606	#121	C₂³×C₂₃	1	2	yes	—
607	#120	—	2	2	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
620	C₄×D₄	D₄×C₂₃	1	2	yes	—
621	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₂₃	1	2	yes	—
623	C₄×D₄	C₂³×C₂₃	1	2	yes	—
624	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₂₃	1	2	yes	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	#117	C₂³×C₂₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₂²⋊C₄	—	2	2	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	2	no	—
647	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
649	#107	C₂³×C₂₃	1	2	yes	—
650	#107	C₂³×C₂₃	1	4	yes	—
651	#107	C₂³×C₂₃	1	4	yes	—
652	#107	C₂³×C₂₃	1	4	yes	—
653	#107	C₂³×C₂₃	1	4	yes	—
654	#106	C₂³×C₂₃	1	2	yes	—
655	#106	C₂³×C₂₃	1	4	yes	—
656	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
657	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
658	#103	C₂³×C₂₃	1	2	yes	—
659	#103	C₂³×C₂₃	1	4	yes	—
660	#103	C₂³×C₂₃	1	4	yes	—
661	#103	C₂³×C₂₃	1	4	yes	—
662	#103	C₂³×C₂₃	1	4	yes	—
663	#102	C₂³×C₂₃	1	2	yes	—
664	#102	C₂³×C₂₃	1	4	yes	—
665	#102	C₂³×C₂₃	1	2	yes	—
666	#102	C₂³×C₂₃	1	2	yes	—
667	#102	C₂³×C₂₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
669	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
671	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
672	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
673	#97	C₂³×C₂₃	1	2	yes	—
674	C₄×C₈	C₂³×C₂₃	1	2	yes	—
675	C₂₃	#61737	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	—	2	1	no	—
677	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
678	#41	—	4	4	no	—
679	#41	—	4	16	no	—
680	#41	—	4	8	no	—
681	#41	—	4	8	no	—
682	#41	—	4	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
701	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	4	4	no	—
717	C₂²×C₄	—	4	8	no	—
718	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	2	no	—
728	D₈	—	4	2	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
733	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	1	no	—
783	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
796	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
797	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	Q₈	—	2	2	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	4	4	no	—
801	Q₈	—	4	4	no	—
802	Q₈	—	4	2	no	—
803	Q₈	—	8	2	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	2	no	—
815	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
848	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
849	C₈	—	2	2	no	—
850	C₈	—	2	4	no	—
851	C₈	—	2	2	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	8	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	8	4	no	—
867	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
868	C₂²	C₂₃×#578	1	2	yes	—
869	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	4	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
884	C₄	C₂₃×#585	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	8	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₂₃×#3485	1	1	yes	characteristic
891	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
892	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
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
1. C₂₃×#3520	C₂	semidirect
2. C₂×C₂₃×#547	C₂	semidirect
3. C₂₃×#3353	C₂	semidirect
4. C₂₃×#3343	C₂	semidirect
5. C₂₃×#3334	C₂	semidirect
6. C₂₃×#3330	C₂	semidirect
7. C₂₃×#3308	C₂	semidirect
8. C₂₃×#3298	C₂	semidirect
9. C₂₃×#3239	C₂	semidirect
10. C₂₃×#3230	C₂	semidirect
11. C₂₃×#3193	C₂	semidirect
12. C₂₃×#3188	C₂	semidirect
13. C₂₃×#3110	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂×C₂₃×#484	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
19. C₂₃×#556	C₂²	semidirect
21. C₂₃×#552	C₂²	semidirect
23. D₄×Q₈×C₂₃	C₂²	semidirect
24. C₂₃×#548	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
32. C₂₃×#547	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#500	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
57. C₂₃×#484	C₂²	semidirect
58. C₂₃×#484	C₂²	semidirect
59. C₂₃×#483	C₂²	semidirect
60. C₂₃×#482	C₂²	semidirect
63. C₂₃×#480	C₂²	semidirect
64. C₂₃×#480	C₂²	semidirect
65. C₂₃×#478	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#475	C₂²	semidirect
68. C₂₃×#474	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#466	C₂²	semidirect
73. C₂₃×#465	C₂²	semidirect
74. C₂₃×#463	C₂²	semidirect
75. C₂₃×#461	C₂²	semidirect
78. C₂₃×#449	C₂²	semidirect
79. C₂₃×#448	C₂²	semidirect
81. C₂₃×#440	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×D₈×C₂₃	C₂²	semidirect
84. C₂₃×#436	C₂²	semidirect
85. C₂₃×#435	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂×C₂₃×#107	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂×C₂₃×#103	C₂²	semidirect
340. #61737	C₂₃	direct (N × H)
406. #3520	C₂×C₂₃	semidirect
407. C₂×#547	C₂×C₂₃	semidirect
408. #3353	C₂×C₂₃	semidirect
409. #3343	C₂×C₂₃	semidirect
410. #3334	C₂×C₂₃	semidirect
411. #3330	C₂×C₂₃	semidirect
412. #3308	C₂×C₂₃	semidirect
413. #3298	C₂×C₂₃	semidirect
414. #3239	C₂×C₂₃	semidirect
415. #3230	C₂×C₂₃	semidirect
416. #3193	C₂×C₂₃	semidirect
417. #3188	C₂×C₂₃	semidirect
418. #3110	C₂×C₂₃	semidirect
419. #3105	C₂×C₂₃	semidirect
420. #3092	C₂×C₂₃	semidirect
421. C₂×#484	C₂×C₂₃	semidirect
422. #2974	C₂×C₂₃	semidirect
457. #556	C₂²×C₂₃	semidirect
459. #552	C₂²×C₂₃	semidirect
461. D₄×Q₈	C₂²×C₂₃	semidirect
462. #548	C₂²×C₂₃	semidirect
469. #547	C₂²×C₂₃	semidirect
470. #547	C₂²×C₂₃	semidirect
486. #501	C₂²×C₂₃	semidirect
487. #500	C₂²×C₂₃	semidirect
488. #489	C₂²×C₂₃	semidirect
489. #487	C₂²×C₂₃	semidirect
495. #484	C₂²×C₂₃	semidirect
496. #484	C₂²×C₂₃	semidirect
497. #483	C₂²×C₂₃	semidirect
498. #482	C₂²×C₂₃	semidirect
501. #480	C₂²×C₂₃	semidirect
502. #480	C₂²×C₂₃	semidirect
503. #478	C₂²×C₂₃	semidirect
504. #477	C₂²×C₂₃	semidirect
505. #475	C₂²×C₂₃	semidirect
506. #474	C₂²×C₂₃	semidirect
507. #474	C₂²×C₂₃	semidirect
508. #468	C₂²×C₂₃	semidirect
509. #468	C₂²×C₂₃	semidirect
510. #466	C₂²×C₂₃	semidirect
511. #465	C₂²×C₂₃	semidirect
512. #463	C₂²×C₂₃	semidirect
513. #461	C₂²×C₂₃	semidirect
516. #449	C₂²×C₂₃	semidirect
517. #448	C₂²×C₂₃	semidirect
519. #440	C₂²×C₂₃	semidirect
520. C₄×SD₁₆	C₂²×C₂₃	semidirect
521. C₄×D₈	C₂²×C₂₃	semidirect
522. #436	C₂²×C₂₃	semidirect
523. #435	C₂²×C₂₃	semidirect
524. C₈×D₄	C₂²×C₂₃	semidirect
527. #428	C₂²×C₂₃	semidirect
528. C₂×#107	C₂²×C₂₃	semidirect
529. #417	C₂²×C₂₃	semidirect
530. C₂×#103	C₂²×C₂₃	semidirect
675. C₂₃	#61737	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×#3520	2
C₂×C₂₃×#547	2
C₂₃×#3353	2
C₂₃×#3343	2
C₂₃×#3334	2
C₂₃×#3330	2
C₂₃×#3308	2
C₂₃×#3298	2
C₂₃×#3239	2
C₂₃×#3230	2
C₂₃×#3193	2
C₂₃×#3188	2
C₂₃×#3110	2
C₂₃×#3105	2
C₂₃×#3092	2
C₂×C₂₃×#484	2
C₂₃×#2974	2
#61737	23

Subgroups — C23×#61737 #19209363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61737 #19209363