Subgroups — C₂₃×#62582 #19210208

Order 5888.

1770 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3316	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3314	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3239	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3215	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3181	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#489	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#559	C₂²	1	1	yes	characteristic
19	Q₈²×C₂₃	C₂²	1	2	yes	complemented
20	C₂₃×#557	—	2	1	no	—
21	C₂₃×#556	C₂²	1	1	yes	characteristic
22	C₂₃×#555	—	2	1	no	—
23	C₂₃×#554	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	4	yes	complemented
25	C₂₃×#551	—	2	2	no	—
26	D₄×Q₈×C₂₃	—	2	1	no	—
27	D₄×Q₈×C₂₃	—	2	2	no	—
28	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#548	C₂²	1	2	yes	—
30	C₂₃×#546	—	2	1	no	—
31	C₂₃×#546	C₂²	1	2	yes	—
32	D₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#544	—	2	2	no	—
34	C₂₃×#544	—	2	1	no	—
35	C₂₃×#542	—	2	1	no	—
36	C₂₃×#538	—	2	2	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#533	C₂²	1	2	yes	complemented
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂₃×#529	C₂²	1	1	yes	characteristic
43	C₂₃×#529	C₂²	1	2	yes	—
44	C₂×C₂₃×#124	C₂²	1	2	yes	—
45	C₂₃×#520	—	2	1	no	—
46	C₂₃×#518	—	2	1	no	—
47	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#501	C₂²	1	2	yes	complemented
50	C₂₃×#497	C₂²	1	1	yes	characteristic
51	C₂₃×#497	C₂²	1	2	yes	complemented
52	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#489	C₂²	1	1	yes	characteristic
54	C₂₃×#489	C₂²	1	2	yes	—
55	C₂₃×#489	C₂²	1	4	yes	—
56	C₂₃×#489	C₂²	1	2	yes	complemented
57	C₂₃×#489	C₂²	1	2	yes	complemented
58	C₂₃×#489	C₂²	1	2	yes	complemented
59	C₂₃×#489	C₂²	1	4	yes	complemented
60	C₂₃×#487	C₂²	1	2	yes	complemented
61	C₂₃×#486	C₂²	1	2	yes	—
62	C₂₃×#484	C₂²	1	4	yes	complemented
63	C₂₃×#483	C₂²	1	2	yes	complemented
64	C₂₃×#481	C₂²	1	4	yes	—
65	C₂₃×#480	C₂²	1	2	yes	—
66	C₂₃×#477	C₂²	1	2	yes	complemented
67	C₂₃×#476	C₂²	1	2	yes	—
68	C₂₃×#475	C₂²	1	4	yes	complemented
69	C₂₃×#474	C₂²	1	4	yes	complemented
70	C₂₃×#470	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	—
72	C₂₃×#467	C₂²	1	4	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	—
74	C₂₃×#464	C₂²	1	4	yes	—
75	C₂₃×#464	C₂²	1	4	yes	complemented
76	C₂₃×#462	C₂²	1	2	yes	complemented
77	C₂₃×#460	C₂²	1	2	yes	—
78	C₂₃×#452	C₂²	1	4	yes	complemented
79	C₂₃×#451	C₂²	1	4	yes	complemented
80	C₂₃×#450	C₂²	1	4	yes	—
81	C₂₃×#446	C₂²	1	2	yes	complemented
82	C₂₃×#441	C₂²	1	4	yes	complemented
83	C₂₃×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
86	C₂₃×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₂₃	C₂²	1	2	yes	—
88	C₂₃×#432	C₂²	1	2	yes	complemented
89	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#417	C₂²	1	4	yes	complemented
91	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#102	C₂²	1	4	yes	—
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
95	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	2	no	—
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×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×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	4	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	2	no	—
113	C₂₃×C₄⋊Q₈	—	2	2	no	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₂₃×#127	C₂³	1	1	yes	characteristic
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	1	no	—
124	C₂₃×#126	—	2	2	no	—
125	C₂₃×#125	—	2	2	no	—
126	C₂₃×#125	—	2	4	no	—
127	C₂₃×#125	—	2	2	no	—
128	C₂₃×#125	—	2	1	no	—
129	C₂₃×#125	C₂³	1	1	yes	characteristic
130	C₂₃×#124	—	2	1	no	—
131	C₂₃×#124	—	2	2	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	2	no	—
134	C₂₃×#124	C₂³	1	2	yes	—
135	C₂₃×#124	C₂³	1	2	yes	—
136	C₂₃×#124	C₂³	1	1	yes	characteristic
137	C₂₃×#124	C₂³	1	2	yes	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	1	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	1	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	—	2	4	no	—
148	C₂₃×C₂²⋊Q₈	—	2	4	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	1	no	—
158	C₂₃×#121	—	2	2	no	—
159	C₂₃×#121	C₂³	1	2	yes	—
160	C₂₃×#121	C₂³	1	1	yes	characteristic
161	C₂₃×#120	—	2	2	no	—
162	C₂₃×#120	—	2	2	no	—
163	C₄×Q₈×C₂₃	—	2	2	no	—
164	C₄×Q₈×C₂₃	—	2	1	no	—
165	C₄×Q₈×C₂₃	—	2	2	no	—
166	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
171	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	4	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	—	2	1	no	—
181	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₂₃	D₄	1	2	yes	—
183	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₂₃	C₂³	1	2	yes	—
185	C₄×D₄×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	—	2	1	no	—
189	C₂₃×#117	—	2	1	no	—
190	C₂₃×#117	—	2	2	no	—
191	C₂₃×#117	—	2	1	no	—
192	C₂₃×#117	D₄	1	2	yes	—
193	C₂₃×#117	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	C₂³	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×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₂₃×#103	C₂³	1	2	yes	—
210	C₂₃×#103	C₂³	1	4	yes	—
211	C₂₃×#103	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	2	yes	—
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×#97	C₂³	1	1	yes	characteristic
224	C₂₃×#97	C₂³	1	2	yes	—
225	C₂₃×#97	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	2	no	—
229	#41×C₂₃	—	2	4	no	—
230	#41×C₂₃	—	4	4	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	4	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	4	4	no	—
237	C₂×Q₈×C₂₃	—	8	4	no	—
238	C₂×Q₈×C₂₃	—	8	2	no	—
239	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	1	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	4	4	no	—
250	C₂×D₄×C₂₃	—	4	4	no	—
251	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
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	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₂₃	—	4	4	no	—
268	Q₁₆×C₂₃	—	4	2	no	—
269	SD₁₆×C₂₃	—	4	4	no	—
270	SD₁₆×C₂₃	—	4	2	no	—
271	M₁₆×C₂₃	—	4	2	no	—
272	C₂×C₈×C₂₃	—	4	4	no	—
273	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	4	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	2	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	1	no	—
310	C₂²⋊C₄×C₂₃	—	2	1	no	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	2	1	no	—
325	C₄²×C₂₃	—	2	4	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	C₂×D₄	1	2	yes	—
328	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	2	yes	—
331	C₄²×C₂₃	C₂⁴	1	2	yes	—
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	#62582	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	4	4	no	—
338	C₂³×C₂₃	—	8	2	no	—
339	C₂³×C₂₃	—	8	2	no	—
340	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
342	Q₈×C₂₃	—	2	2	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	2	no	—
346	Q₈×C₂₃	—	2	4	no	—
347	Q₈×C₂₃	—	4	2	no	—
348	Q₈×C₂₃	—	4	4	no	—
349	Q₈×C₂₃	—	8	2	no	—
350	Q₈×C₂₃	—	8	4	no	—
351	Q₈×C₂₃	—	8	2	no	—
352	D₄×C₂₃	—	2	4	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	4	4	no	—
356	D₄×C₂₃	—	4	2	no	—
357	D₄×C₂₃	—	8	1	no	—
358	D₄×C₂₃	—	8	2	no	—
359	D₄×C₂₃	—	8	1	no	—
360	D₄×C₂₃	—	8	2	no	—
361	D₄×C₂₃	#137	1	4	yes	—
362	C₂×C₄×C₂₃	—	2	4	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	4	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	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	2	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	2	no	—
376	C₂×C₄×C₂₃	—	8	2	no	—
377	C₂×C₄×C₂₃	—	8	2	no	—
378	C₂×C₄×C₂₃	—	8	2	no	—
379	C₂×C₄×C₂₃	—	8	4	no	—
380	C₂×C₄×C₂₃	—	8	2	no	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
390	C₈×C₂₃	—	2	2	no	—
391	C₈×C₂₃	—	2	4	no	—
392	C₈×C₂₃	—	2	2	no	—
393	#3514	C₂×C₂₃	1	1	yes	characteristic
394	#3503	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#3375	C₂×C₂₃	1	2	yes	complemented
396	#3369	C₂×C₂₃	1	2	yes	complemented
397	#3316	C₂×C₂₃	1	4	yes	complemented
398	#3314	C₂×C₂₃	1	4	yes	complemented
399	#3299	C₂×C₂₃	1	2	yes	complemented
400	#3295	C₂×C₂₃	1	2	yes	complemented
401	#3239	C₂×C₂₃	1	2	yes	complemented
402	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3215	C₂×C₂₃	1	2	yes	complemented
405	#3181	C₂×C₂₃	1	2	yes	complemented
406	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
408	C₂×#489	C₂×C₂₃	1	2	yes	complemented
409	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	1	no	—
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	1	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	4	2	no	—
421	C₂²×C₂₃	—	16	4	no	—
422	C₂²×C₂₃	C₂×#137	1	4	yes	—
423	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₂₃	—	2	1	no	—
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	1	no	—
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	2	no	—
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	2	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	—	4	2	no	—
437	C₄×C₂₃	—	4	1	no	—
438	C₄×C₂₃	C₂×#137	1	2	yes	—
439	C₄×C₂₃	#585	1	2	yes	—
440	#559	C₂²×C₂₃	1	1	yes	characteristic
441	Q₈²	C₂²×C₂₃	1	2	yes	complemented
442	#557	—	2	1	no	—
443	#556	C₂²×C₂₃	1	1	yes	characteristic
444	#555	—	2	1	no	—
445	#554	C₂²×C₂₃	1	2	yes	—
446	#554	C₂²×C₂₃	1	4	yes	complemented
447	#551	—	2	2	no	—
448	D₄×Q₈	—	2	1	no	—
449	D₄×Q₈	—	2	2	no	—
450	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
451	#548	C₂²×C₂₃	1	2	yes	—
452	#546	—	2	1	no	—
453	#546	C₂²×C₂₃	1	2	yes	—
454	D₄²	C₂²×C₂₃	1	1	yes	characteristic
455	#544	—	2	2	no	—
456	#544	—	2	1	no	—
457	#542	—	2	1	no	—
458	#538	—	2	2	no	—
459	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#533	C₂²×C₂₃	1	2	yes	complemented
461	#532	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
463	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	#529	C₂²×C₂₃	1	1	yes	characteristic
465	#529	C₂²×C₂₃	1	2	yes	—
466	C₂×#124	C₂²×C₂₃	1	2	yes	—
467	#520	—	2	1	no	—
468	#518	—	2	1	no	—
469	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
470	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#501	C₂²×C₂₃	1	2	yes	complemented
472	#497	C₂²×C₂₃	1	1	yes	characteristic
473	#497	C₂²×C₂₃	1	2	yes	complemented
474	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#489	C₂²×C₂₃	1	4	yes	—
476	#489	C₂²×C₂₃	1	1	yes	characteristic
477	#489	C₂²×C₂₃	1	2	yes	—
478	#489	C₂²×C₂₃	1	4	yes	complemented
479	#489	C₂²×C₂₃	1	2	yes	complemented
480	#489	C₂²×C₂₃	1	2	yes	complemented
481	#489	C₂²×C₂₃	1	2	yes	complemented
482	#487	C₂²×C₂₃	1	2	yes	complemented
483	#486	C₂²×C₂₃	1	2	yes	—
484	#484	C₂²×C₂₃	1	4	yes	complemented
485	#483	C₂²×C₂₃	1	2	yes	complemented
486	#481	C₂²×C₂₃	1	4	yes	—
487	#480	C₂²×C₂₃	1	2	yes	—
488	#477	C₂²×C₂₃	1	2	yes	complemented
489	#476	C₂²×C₂₃	1	2	yes	—
490	#475	C₂²×C₂₃	1	4	yes	complemented
491	#474	C₂²×C₂₃	1	4	yes	complemented
492	#470	C₂²×C₂₃	1	2	yes	complemented
493	#468	C₂²×C₂₃	1	2	yes	—
494	#467	C₂²×C₂₃	1	4	yes	complemented
495	#465	C₂²×C₂₃	1	4	yes	—
496	#464	C₂²×C₂₃	1	4	yes	—
497	#464	C₂²×C₂₃	1	4	yes	complemented
498	#462	C₂²×C₂₃	1	2	yes	complemented
499	#460	C₂²×C₂₃	1	2	yes	—
500	#452	C₂²×C₂₃	1	4	yes	complemented
501	#451	C₂²×C₂₃	1	4	yes	complemented
502	#450	C₂²×C₂₃	1	4	yes	—
503	#446	C₂²×C₂₃	1	2	yes	complemented
504	#441	C₂²×C₂₃	1	4	yes	complemented
505	#440	C₂²×C₂₃	1	4	yes	complemented
506	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
508	#435	C₂²×C₂₃	1	4	yes	complemented
509	C₈×D₄	C₂²×C₂₃	1	2	yes	—
510	#432	C₂²×C₂₃	1	2	yes	complemented
511	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	#417	C₂²×C₂₃	1	4	yes	complemented
513	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
514	C₂×#102	C₂²×C₂₃	1	4	yes	—
515	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
517	C₂×C₂₃	—	2	4	no	—
518	C₂×C₂₃	—	4	1	no	—
519	C₂×C₂₃	—	8	2	no	—
520	C₂×C₂₃	—	8	1	no	—
521	C₂×C₂₃	#3500	1	1	yes	characteristic
522	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
523	C₂×C₂₃	#3585	1	1	yes	characteristic
524	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
525	C₂×#41	C₂³×C₂₃	1	2	yes	—
526	C₂²×Q₈	—	2	2	no	—
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
531	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
532	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
535	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	4	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
550	#127	C₂³×C₂₃	1	1	yes	characteristic
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	1	no	—
554	#125	—	2	2	no	—
555	#125	—	2	4	no	—
556	#125	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	C₂³×C₂₃	1	1	yes	characteristic
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	C₂³×C₂₃	1	1	yes	characteristic
564	#124	C₂³×C₂₃	1	2	yes	—
565	#124	C₂³×C₂₃	1	2	yes	—
566	#124	C₂³×C₂₃	1	2	yes	—
567	#123	—	2	1	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	C₂³×C₂₃	1	2	yes	—
589	#121	C₂³×C₂₃	1	1	yes	characteristic
590	#120	—	2	2	no	—
591	#120	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
600	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
611	C₄×D₄	D₄×C₂₃	1	2	yes	—
612	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₂₃	1	2	yes	—
614	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₂₃	1	2	yes	—
616	#117	—	2	2	no	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	D₄×C₂₃	1	2	yes	—
622	#117	D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
632	#107	C₂³×C₂₃	1	2	yes	—
633	#107	C₂³×C₂₃	1	4	yes	—
634	#106	C₂³×C₂₃	1	2	yes	—
635	#106	C₂³×C₂₃	1	4	yes	—
636	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
638	#103	C₂³×C₂₃	1	2	yes	—
639	#103	C₂³×C₂₃	1	4	yes	—
640	#103	C₂³×C₂₃	1	4	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	#102	C₂³×C₂₃	1	2	yes	—
646	#102	C₂³×C₂₃	1	4	yes	—
647	#102	C₂³×C₂₃	1	4	yes	—
648	#102	C₂³×C₂₃	1	4	yes	—
649	#102	C₂³×C₂₃	1	4	yes	—
650	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
652	#97	C₂³×C₂₃	1	1	yes	characteristic
653	#97	C₂³×C₂₃	1	2	yes	—
654	#97	C₂³×C₂₃	1	4	yes	—
655	#97	C₂³×C₂₃	1	1	yes	characteristic
656	C₄×C₈	C₂³×C₂₃	1	2	yes	—
657	C₂₃	#62582	1	1	yes	characteristic, direct product factor, Sylow
658	C₂⁴	—	2	2	no	—
659	#41	—	2	4	no	—
660	#41	—	4	4	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	4	4	no	—
667	C₂×Q₈	—	8	4	no	—
668	C₂×Q₈	—	8	2	no	—
669	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
684	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
694	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
697	Q₁₆	—	4	4	no	—
698	Q₁₆	—	4	2	no	—
699	SD₁₆	—	4	4	no	—
700	SD₁₆	—	4	2	no	—
701	M₁₆	—	4	2	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
732	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	C₂×D₄×C₂₃	1	2	yes	—
758	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₂₃	1	2	yes	—
761	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₂₃	1	2	yes	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	8	2	no	—
779	Q₈	—	8	4	no	—
780	Q₈	—	8	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	1	no	—
788	D₄	—	8	2	no	—
789	D₄	—	8	1	no	—
790	D₄	C₂₃×#137	1	4	yes	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
819	C₈	—	2	2	no	—
820	C₈	—	2	4	no	—
821	C₈	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	16	4	no	—
834	C₂²	C₂×C₂₃×#137	1	4	yes	—
835	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	C₂×C₂₃×#137	1	2	yes	—
851	C₄	C₂₃×#585	1	2	yes	—
852	C₂	—	2	4	no	—
853	C₂	—	4	1	no	—
854	C₂	—	8	1	no	—
855	C₂	—	8	2	no	—
856	C₂	C₂₃×#3500	1	1	yes	characteristic
857	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
858	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3503	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3369	C₂	semidirect
5. C₂₃×#3316	C₂	semidirect
6. C₂₃×#3314	C₂	semidirect
7. C₂₃×#3299	C₂	semidirect
8. C₂₃×#3295	C₂	semidirect
9. C₂₃×#3239	C₂	semidirect
10. C₂₃×#3238	C₂	semidirect
11. C₂₃×#3216	C₂	semidirect
12. C₂₃×#3215	C₂	semidirect
13. C₂₃×#3181	C₂	semidirect
14. C₂₃×#3172	C₂	semidirect
15. C₂₃×#3141	C₂	semidirect
16. C₂×C₂₃×#489	C₂	semidirect
17. C₂₃×#2970	C₂	semidirect
19. Q₈²×C₂₃	C₂²	semidirect
24. C₂₃×#554	C₂²	semidirect
37. C₂₃×#533	C₂²	semidirect
38. C₂₃×#533	C₂²	semidirect
40. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
51. C₂₃×#497	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
56. C₂₃×#489	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#489	C₂²	semidirect
59. C₂₃×#489	C₂²	semidirect
60. C₂₃×#487	C₂²	semidirect
62. C₂₃×#484	C₂²	semidirect
63. C₂₃×#483	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#470	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
75. C₂₃×#464	C₂²	semidirect
76. C₂₃×#462	C₂²	semidirect
78. C₂₃×#452	C₂²	semidirect
79. C₂₃×#451	C₂²	semidirect
81. C₂₃×#446	C₂²	semidirect
82. C₂₃×#441	C₂²	semidirect
83. C₂₃×#440	C₂²	semidirect
84. C₄×Q₁₆×C₂₃	C₂²	semidirect
86. C₂₃×#435	C₂²	semidirect
88. C₂₃×#432	C₂²	semidirect
89. C₂₃×#432	C₂²	semidirect
90. C₂₃×#417	C₂²	semidirect
91. C₂×C₂₃×#103	C₂²	semidirect
93. C₄×M₁₆×C₂₃	C₂²	semidirect
94. C₂×C₂₃×#97	C₂²	semidirect
334. #62582	C₂₃	direct (N × H)
394. #3503	C₂×C₂₃	semidirect
395. #3375	C₂×C₂₃	semidirect
396. #3369	C₂×C₂₃	semidirect
397. #3316	C₂×C₂₃	semidirect
398. #3314	C₂×C₂₃	semidirect
399. #3299	C₂×C₂₃	semidirect
400. #3295	C₂×C₂₃	semidirect
401. #3239	C₂×C₂₃	semidirect
402. #3238	C₂×C₂₃	semidirect
403. #3216	C₂×C₂₃	semidirect
404. #3215	C₂×C₂₃	semidirect
405. #3181	C₂×C₂₃	semidirect
406. #3172	C₂×C₂₃	semidirect
407. #3141	C₂×C₂₃	semidirect
408. C₂×#489	C₂×C₂₃	semidirect
409. #2970	C₂×C₂₃	semidirect
441. Q₈²	C₂²×C₂₃	semidirect
446. #554	C₂²×C₂₃	semidirect
459. #533	C₂²×C₂₃	semidirect
460. #533	C₂²×C₂₃	semidirect
462. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
463. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
470. #501	C₂²×C₂₃	semidirect
471. #501	C₂²×C₂₃	semidirect
473. #497	C₂²×C₂₃	semidirect
474. #491	C₂²×C₂₃	semidirect
478. #489	C₂²×C₂₃	semidirect
479. #489	C₂²×C₂₃	semidirect
480. #489	C₂²×C₂₃	semidirect
481. #489	C₂²×C₂₃	semidirect
482. #487	C₂²×C₂₃	semidirect
484. #484	C₂²×C₂₃	semidirect
485. #483	C₂²×C₂₃	semidirect
488. #477	C₂²×C₂₃	semidirect
490. #475	C₂²×C₂₃	semidirect
491. #474	C₂²×C₂₃	semidirect
492. #470	C₂²×C₂₃	semidirect
494. #467	C₂²×C₂₃	semidirect
497. #464	C₂²×C₂₃	semidirect
498. #462	C₂²×C₂₃	semidirect
500. #452	C₂²×C₂₃	semidirect
501. #451	C₂²×C₂₃	semidirect
503. #446	C₂²×C₂₃	semidirect
504. #441	C₂²×C₂₃	semidirect
505. #440	C₂²×C₂₃	semidirect
506. C₄×Q₁₆	C₂²×C₂₃	semidirect
508. #435	C₂²×C₂₃	semidirect
510. #432	C₂²×C₂₃	semidirect
511. #432	C₂²×C₂₃	semidirect
512. #417	C₂²×C₂₃	semidirect
513. C₂×#103	C₂²×C₂₃	semidirect
515. C₄×M₁₆	C₂²×C₂₃	semidirect
516. C₂×#97	C₂²×C₂₃	semidirect
657. C₂₃	#62582	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×#3514	2
C₂₃×#3503	2
C₂₃×#3375	2
C₂₃×#3369	2
C₂₃×#3316	2
C₂₃×#3314	2
C₂₃×#3299	2
C₂₃×#3295	2
C₂₃×#3239	2
C₂₃×#3238	2
C₂₃×#3216	2
C₂₃×#3215	2
C₂₃×#3181	2
C₂₃×#3172	2
C₂₃×#3141	2
C₂×C₂₃×#489	2
C₂₃×#2970	2
#62582	23

Subgroups — C23×#62582 #19210208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62582 #19210208