Subgroups — C₂₃×#61730 #19209356

Order 5888.

1752 conjugacy classes of subgroups.

The subgroup lattice has 856 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
2	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3353	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3349	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3342	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3313	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3302	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×#3196	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3189	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3095	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#556	—	2	1	no	—
19	C₂₃×#556	—	2	2	no	—
20	C₂₃×#556	—	2	1	no	—
21	C₂₃×#556	C₂²	1	2	yes	—
22	C₂₃×#556	C₂²	1	4	yes	—
23	C₂₃×#556	C₂²	1	2	yes	—
24	C₂₃×#556	C₂²	1	1	yes	characteristic
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#552	C₂²	1	2	yes	—
27	C₂₃×#551	—	2	2	no	—
28	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#548	C₂²	1	2	yes	—
30	C₂₃×#547	C₂²	1	1	yes	characteristic
31	C₂₃×#547	C₂²	1	1	yes	characteristic
32	C₂₃×#546	—	2	1	no	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#539	—	2	2	no	—
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#126	—	2	2	no	—
39	C₂×C₂₃×#124	—	2	1	no	—
40	C₂₃×#525	C₂²	1	2	yes	—
41	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#117	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×#485	C₂²	1	4	yes	complemented
53	C₂₃×#485	C₂²	1	4	yes	complemented
54	C₂₃×#485	C₂²	1	4	yes	complemented
55	C₂₃×#485	C₂²	1	4	yes	complemented
56	C₂₃×#484	C₂²	1	2	yes	—
57	C₂₃×#484	C₂²	1	2	yes	—
58	C₂₃×#484	C₂²	1	2	yes	—
59	C₂₃×#484	C₂²	1	4	yes	complemented
60	C₂₃×#483	C₂²	1	2	yes	—
61	C₂₃×#483	C₂²	1	1	yes	characteristic
62	C₂₃×#482	C₂²	1	4	yes	complemented
63	C₂₃×#481	C₂²	1	2	yes	—
64	C₂₃×#480	C₂²	1	1	yes	characteristic
65	C₂₃×#479	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	4	yes	complemented
67	C₂₃×#475	C₂²	1	2	yes	complemented
68	C₂₃×#475	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	2	yes	complemented
70	C₂₃×#470	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#467	C₂²	1	4	yes	complemented
73	C₂₃×#467	C₂²	1	4	yes	complemented
74	C₂₃×#464	C₂²	1	2	yes	complemented
75	C₂₃×#462	C₂²	1	2	yes	complemented
76	C₂₃×#452	C₂²	1	4	yes	complemented
77	C₂₃×#451	C₂²	1	1	yes	characteristic
78	C₂₃×#451	C₂²	1	2	yes	—
79	C₂₃×#451	C₂²	1	4	yes	complemented
80	C₂₃×#448	C₂²	1	1	yes	characteristic
81	C₂₃×#441	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	—
85	C₂₃×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₂₃	C₂²	1	2	yes	—
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	C₂₃×#427	C₂²	1	4	yes	complemented
91	C₂₃×#419	C₂²	1	4	yes	complemented
92	C₂₃×#416	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	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
107	C₂₃×C₄⋊Q₈	—	2	1	no	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×#126	—	2	2	no	—
115	C₂₃×#126	—	2	2	no	—
116	C₂₃×#126	—	2	4	no	—
117	C₂₃×#126	—	2	4	no	—
118	C₂₃×#126	—	2	4	no	—
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#126	—	2	1	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#125	C₂³	1	1	yes	characteristic
124	C₂₃×#124	—	2	2	no	—
125	C₂₃×#124	—	2	2	no	—
126	C₂₃×#124	—	2	4	no	—
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	2	no	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	2	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	—	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	C₂³	1	2	yes	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
149	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	1	yes	characteristic
154	C₂₃×#120	—	2	2	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	4	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	—	2	1	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
172	C₄×D₄×C₂₃	D₄	1	2	yes	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₂₃×#117	—	2	1	no	—
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	C₂³	1	2	yes	—
184	C₂₃×#117	C₂³	1	4	yes	—
185	C₂₃×#117	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
199	C₂×C₄²×C₂₃	—	2	2	no	—
200	C₂×C₄²×C₂₃	—	2	1	no	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	2	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
229	#41×C₂₃	—	4	4	no	—
230	#41×C₂₃	—	4	4	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	4	2	no	—
237	C₂×Q₈×C₂₃	—	4	4	no	—
238	C₂×Q₈×C₂₃	—	4	4	no	—
239	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	4	2	no	—
246	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	—	2	1	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	4	4	no	—
258	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	Q₁₆×C₂₃	—	4	2	no	—
267	Q₁₆×C₂₃	—	4	4	no	—
268	SD₁₆×C₂₃	—	4	2	no	—
269	M₁₆×C₂₃	—	4	4	no	—
270	C₂×C₈×C₂₃	—	4	4	no	—
271	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
272	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	2	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	1	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
322	C₄²×C₂₃	—	2	4	no	—
323	C₄²×C₂₃	—	2	4	no	—
324	C₄²×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	#61730	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	4	no	—
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	4	2	no	—
337	C₂³×C₂₃	—	4	2	no	—
338	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
340	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₂₃	—	2	2	no	—
342	Q₈×C₂₃	—	2	2	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	4	no	—
345	Q₈×C₂₃	—	4	2	no	—
346	Q₈×C₂₃	—	4	4	no	—
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	2	no	—
349	Q₈×C₂₃	—	8	2	no	—
350	D₄×C₂₃	—	2	2	no	—
351	D₄×C₂₃	—	2	2	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	4	2	no	—
354	D₄×C₂₃	—	4	4	no	—
355	D₄×C₂₃	—	4	2	no	—
356	D₄×C₂₃	—	8	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	4	no	—
360	C₂×C₄×C₂₃	—	2	4	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	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	4	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	4	2	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	4	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	8	2	no	—
379	C₂×C₄×C₂₃	—	8	2	no	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
388	C₈×C₂₃	—	2	2	no	—
389	C₈×C₂₃	—	2	4	no	—
390	C₈×C₂₃	—	2	2	no	—
391	#3520	C₂×C₂₃	1	1	yes	characteristic
392	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#3353	C₂×C₂₃	1	2	yes	complemented
394	#3349	C₂×C₂₃	1	4	yes	complemented
395	#3342	C₂×C₂₃	1	2	yes	complemented
396	#3328	C₂×C₂₃	1	2	yes	complemented
397	#3313	C₂×C₂₃	1	4	yes	complemented
398	#3302	C₂×C₂₃	1	2	yes	complemented
399	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3230	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3196	C₂×C₂₃	1	2	yes	complemented
402	#3189	C₂×C₂₃	1	2	yes	complemented
403	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#3095	C₂×C₂₃	1	2	yes	complemented
406	#3091	C₂×C₂₃	1	2	yes	complemented
407	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	2	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	1	no	—
418	C₂²×C₂₃	—	4	1	no	—
419	C₂²×C₂₃	—	8	4	no	—
420	C₂²×C₂₃	#578	1	2	yes	—
421	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	2	no	—
424	C₄×C₂₃	—	2	2	no	—
425	C₄×C₂₃	—	2	1	no	—
426	C₄×C₂₃	—	2	1	no	—
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	—	4	2	no	—
433	C₄×C₂₃	—	4	4	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	1	no	—
436	C₄×C₂₃	#575	1	2	yes	—
437	C₄×C₂₃	#585	1	2	yes	—
438	#556	—	2	1	no	—
439	#556	—	2	2	no	—
440	#556	—	2	1	no	—
441	#556	C₂²×C₂₃	1	2	yes	—
442	#556	C₂²×C₂₃	1	1	yes	characteristic
443	#556	C₂²×C₂₃	1	2	yes	—
444	#556	C₂²×C₂₃	1	4	yes	—
445	#554	—	2	1	no	—
446	#552	C₂²×C₂₃	1	2	yes	—
447	#551	—	2	2	no	—
448	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
449	#548	C₂²×C₂₃	1	2	yes	—
450	#547	C₂²×C₂₃	1	1	yes	characteristic
451	#547	C₂²×C₂₃	1	1	yes	characteristic
452	#546	—	2	1	no	—
453	#542	—	2	1	no	—
454	#539	—	2	2	no	—
455	#533	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
457	#529	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#126	—	2	2	no	—
459	C₂×#124	—	2	1	no	—
460	#525	C₂²×C₂₃	1	2	yes	—
461	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
463	#520	—	2	1	no	—
464	C₂×C₄×Q₈	—	2	1	no	—
465	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×#117	C₂²×C₂₃	1	2	yes	—
468	#501	C₂²×C₂₃	1	2	yes	complemented
469	#500	C₂²×C₂₃	1	2	yes	complemented
470	#489	C₂²×C₂₃	1	2	yes	complemented
471	#487	C₂²×C₂₃	1	2	yes	complemented
472	#485	C₂²×C₂₃	1	4	yes	complemented
473	#485	C₂²×C₂₃	1	4	yes	complemented
474	#485	C₂²×C₂₃	1	4	yes	complemented
475	#485	C₂²×C₂₃	1	4	yes	complemented
476	#484	C₂²×C₂₃	1	2	yes	—
477	#484	C₂²×C₂₃	1	2	yes	—
478	#484	C₂²×C₂₃	1	2	yes	—
479	#484	C₂²×C₂₃	1	4	yes	complemented
480	#483	C₂²×C₂₃	1	2	yes	—
481	#483	C₂²×C₂₃	1	1	yes	characteristic
482	#482	C₂²×C₂₃	1	4	yes	complemented
483	#481	C₂²×C₂₃	1	2	yes	—
484	#480	C₂²×C₂₃	1	1	yes	characteristic
485	#479	C₂²×C₂₃	1	2	yes	complemented
486	#477	C₂²×C₂₃	1	4	yes	complemented
487	#475	C₂²×C₂₃	1	2	yes	complemented
488	#475	C₂²×C₂₃	1	2	yes	complemented
489	#474	C₂²×C₂₃	1	2	yes	complemented
490	#470	C₂²×C₂₃	1	4	yes	complemented
491	#468	C₂²×C₂₃	1	4	yes	complemented
492	#467	C₂²×C₂₃	1	4	yes	complemented
493	#467	C₂²×C₂₃	1	4	yes	complemented
494	#464	C₂²×C₂₃	1	2	yes	complemented
495	#462	C₂²×C₂₃	1	2	yes	complemented
496	#452	C₂²×C₂₃	1	4	yes	complemented
497	#451	C₂²×C₂₃	1	1	yes	characteristic
498	#451	C₂²×C₂₃	1	2	yes	—
499	#451	C₂²×C₂₃	1	4	yes	complemented
500	#448	C₂²×C₂₃	1	1	yes	characteristic
501	#441	C₂²×C₂₃	1	4	yes	complemented
502	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
503	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
504	#436	C₂²×C₂₃	1	2	yes	—
505	#435	C₂²×C₂₃	1	4	yes	—
506	C₈×D₄	C₂²×C₂₃	1	2	yes	—
507	#432	C₂²×C₂₃	1	1	yes	characteristic
508	#431	C₂²×C₂₃	1	1	yes	characteristic
509	#428	C₂²×C₂₃	1	4	yes	complemented
510	#427	C₂²×C₂₃	1	4	yes	complemented
511	#419	C₂²×C₂₃	1	4	yes	complemented
512	#416	C₂²×C₂₃	1	4	yes	complemented
513	#407	C₂²×C₂₃	1	2	yes	—
514	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
515	C₂×C₂₃	—	2	2	no	—
516	C₂×C₂₃	—	4	2	no	—
517	C₂×C₂₃	—	4	2	no	—
518	C₂×C₂₃	—	8	1	no	—
519	C₂×C₂₃	#3485	1	1	yes	characteristic
520	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
521	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
522	C₂×#41	—	2	1	no	—
523	C₂×#41	C₂³×C₂₃	1	2	yes	—
524	C₂²×Q₈	—	2	1	no	—
525	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
527	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
529	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
530	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
532	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
533	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
541	#126	—	2	4	no	—
542	#126	—	2	4	no	—
543	#126	—	2	4	no	—
544	#126	—	2	4	no	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	C₂³×C₂₃	1	1	yes	characteristic
551	#124	—	2	2	no	—
552	#124	—	2	2	no	—
553	#124	—	2	4	no	—
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₂₃	1	1	yes	characteristic
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	#123	—	2	1	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
571	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
575	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
576	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
577	#121	—	2	2	no	—
578	#121	—	2	1	no	—
579	#121	C₂³×C₂₃	1	1	yes	characteristic
580	#121	C₂³×C₂₃	1	2	yes	—
581	#120	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	4	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
599	C₄×D₄	D₄×C₂₃	1	2	yes	—
600	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₂₃	1	2	yes	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	1	no	—
610	#117	C₂³×C₂₃	1	4	yes	—
611	#117	C₂³×C₂₃	1	4	yes	—
612	#117	C₂³×C₂₃	1	2	yes	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
626	C₂×C₄²	—	2	2	no	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
629	#107	C₂³×C₂₃	1	2	yes	—
630	#107	C₂³×C₂₃	1	4	yes	—
631	#107	C₂³×C₂₃	1	4	yes	—
632	#107	C₂³×C₂₃	1	4	yes	—
633	#106	C₂³×C₂₃	1	4	yes	—
634	#106	C₂³×C₂₃	1	4	yes	—
635	#106	C₂³×C₂₃	1	2	yes	—
636	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
638	#103	C₂³×C₂₃	1	4	yes	—
639	#103	C₂³×C₂₃	1	4	yes	—
640	#103	C₂³×C₂₃	1	2	yes	—
641	#103	C₂³×C₂₃	1	4	yes	—
642	#103	C₂³×C₂₃	1	4	yes	—
643	#103	C₂³×C₂₃	1	2	yes	—
644	#103	C₂³×C₂₃	1	2	yes	—
645	#103	C₂³×C₂₃	1	4	yes	—
646	#102	C₂³×C₂₃	1	2	yes	—
647	#102	C₂³×C₂₃	1	4	yes	—
648	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
649	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
652	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
653	#97	C₂³×C₂₃	1	2	yes	—
654	C₄×C₈	C₂³×C₂₃	1	2	yes	—
655	C₂₃	#61730	1	1	yes	characteristic, direct product factor, Sylow
656	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
657	#41	—	4	4	no	—
658	#41	—	4	4	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	—	4	4	no	—
667	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
669	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	4	4	no	—
686	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
689	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
694	Q₁₆	—	4	2	no	—
695	Q₁₆	—	4	4	no	—
696	SD₁₆	—	4	2	no	—
697	M₁₆	—	4	4	no	—
698	C₂×C₈	—	4	4	no	—
699	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
700	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
701	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
748	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
749	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	1	no	—
757	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
759	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
760	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂³	—	2	4	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
766	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	4	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	8	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
814	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
815	C₈	—	2	2	no	—
816	C₈	—	2	4	no	—
817	C₈	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	8	4	no	—
830	C₂²	C₂₃×#578	1	2	yes	—
831	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
832	C₄	—	2	1	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	1	no	—
837	C₄	—	2	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	4	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	C₂₃×#575	1	2	yes	—
847	C₄	C₂₃×#585	1	2	yes	—
848	C₂	—	2	2	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	2	no	—
851	C₂	—	8	1	no	—
852	C₂	C₂₃×#3485	1	1	yes	characteristic
853	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
854	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3520	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×#556	C₂	semidirect
3. C₂₃×#3353	C₂	semidirect
4. C₂₃×#3349	C₂	semidirect
5. C₂₃×#3342	C₂	semidirect
6. C₂₃×#3328	C₂	semidirect
7. C₂₃×#3313	C₂	semidirect
8. C₂₃×#3302	C₂	semidirect
9. C₂₃×#3239	C₂	semidirect
10. C₂₃×#3230	C₂	semidirect
11. C₂₃×#3196	C₂	semidirect
12. C₂₃×#3189	C₂	semidirect
13. C₂₃×#3113	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3095	C₂	semidirect
16. C₂₃×#3091	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#500	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#485	C₂²	semidirect
54. C₂₃×#485	C₂²	semidirect
55. C₂₃×#485	C₂²	semidirect
59. C₂₃×#484	C₂²	semidirect
62. C₂₃×#482	C₂²	semidirect
65. C₂₃×#479	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#475	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#470	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
73. C₂₃×#467	C₂²	semidirect
74. C₂₃×#464	C₂²	semidirect
75. C₂₃×#462	C₂²	semidirect
76. C₂₃×#452	C₂²	semidirect
79. C₂₃×#451	C₂²	semidirect
81. C₂₃×#441	C₂²	semidirect
82. C₄×Q₁₆×C₂₃	C₂²	semidirect
83. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂₃×#427	C₂²	semidirect
91. C₂₃×#419	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
333. #61730	C₂₃	direct (N × H)
392. C₂×#556	C₂×C₂₃	semidirect
393. #3353	C₂×C₂₃	semidirect
394. #3349	C₂×C₂₃	semidirect
395. #3342	C₂×C₂₃	semidirect
396. #3328	C₂×C₂₃	semidirect
397. #3313	C₂×C₂₃	semidirect
398. #3302	C₂×C₂₃	semidirect
399. #3239	C₂×C₂₃	semidirect
400. #3230	C₂×C₂₃	semidirect
401. #3196	C₂×C₂₃	semidirect
402. #3189	C₂×C₂₃	semidirect
403. #3113	C₂×C₂₃	semidirect
404. #3108	C₂×C₂₃	semidirect
405. #3095	C₂×C₂₃	semidirect
406. #3091	C₂×C₂₃	semidirect
407. #2974	C₂×C₂₃	semidirect
468. #501	C₂²×C₂₃	semidirect
469. #500	C₂²×C₂₃	semidirect
470. #489	C₂²×C₂₃	semidirect
471. #487	C₂²×C₂₃	semidirect
472. #485	C₂²×C₂₃	semidirect
473. #485	C₂²×C₂₃	semidirect
474. #485	C₂²×C₂₃	semidirect
475. #485	C₂²×C₂₃	semidirect
479. #484	C₂²×C₂₃	semidirect
482. #482	C₂²×C₂₃	semidirect
485. #479	C₂²×C₂₃	semidirect
486. #477	C₂²×C₂₃	semidirect
487. #475	C₂²×C₂₃	semidirect
488. #475	C₂²×C₂₃	semidirect
489. #474	C₂²×C₂₃	semidirect
490. #470	C₂²×C₂₃	semidirect
491. #468	C₂²×C₂₃	semidirect
492. #467	C₂²×C₂₃	semidirect
493. #467	C₂²×C₂₃	semidirect
494. #464	C₂²×C₂₃	semidirect
495. #462	C₂²×C₂₃	semidirect
496. #452	C₂²×C₂₃	semidirect
499. #451	C₂²×C₂₃	semidirect
501. #441	C₂²×C₂₃	semidirect
502. C₄×Q₁₆	C₂²×C₂₃	semidirect
503. C₄×SD₁₆	C₂²×C₂₃	semidirect
509. #428	C₂²×C₂₃	semidirect
510. #427	C₂²×C₂₃	semidirect
511. #419	C₂²×C₂₃	semidirect
512. #416	C₂²×C₂₃	semidirect
655. C₂₃	#61730	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×#556	2
C₂₃×#3353	2
C₂₃×#3349	2
C₂₃×#3342	2
C₂₃×#3328	2
C₂₃×#3313	2
C₂₃×#3302	2
C₂₃×#3239	2
C₂₃×#3230	2
C₂₃×#3196	2
C₂₃×#3189	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3095	2
C₂₃×#3091	2
C₂₃×#2974	2
#61730	23

Subgroups — C23×#61730 #19209356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61730 #19209356