Subgroups — C₂₃×#61578 #19209204

Order 5888.

2114 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3321	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3313	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3271	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3269	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3004	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
19	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#556	C₂²	1	2	yes	complemented
22	C₂₃×#555	C₂²	1	2	yes	complemented
23	C₂₃×#553	—	2	2	no	—
24	C₂₃×#550	C₂²	1	2	yes	complemented
25	C₂₃×#548	—	2	2	no	—
26	C₂₃×#548	—	2	2	no	—
27	C₂₃×#548	C₂²	1	4	yes	—
28	C₂₃×#548	C₂²	1	4	yes	—
29	C₂₃×#547	C₂²	1	2	yes	complemented
30	C₂₃×#538	—	2	1	no	—
31	C₂₃×#538	—	2	1	no	—
32	C₂₃×#535	—	2	1	no	—
33	C₂₃×#533	C₂²	1	1	yes	characteristic
34	C₂₃×#532	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#124	—	2	1	no	—
36	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
37	C₂₃×#525	C₂²	1	2	yes	—
38	C₂₃×#525	C₂²	1	2	yes	—
39	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	—	2	1	no	—
42	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	—	2	1	no	—
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#497	C₂²	1	2	yes	complemented
48	C₂₃×#496	C₂²	1	2	yes	complemented
49	C₂₃×#489	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#485	C₂²	1	4	yes	complemented
52	C₂₃×#483	C₂²	1	2	yes	—
53	C₂₃×#482	C₂²	1	4	yes	complemented
54	C₂₃×#480	C₂²	1	2	yes	—
55	C₂₃×#477	C₂²	1	2	yes	complemented
56	C₂₃×#475	C₂²	1	2	yes	complemented
57	C₂₃×#469	C₂²	1	4	yes	complemented
58	C₂₃×#468	C₂²	1	4	yes	complemented
59	C₂₃×#467	C₂²	1	4	yes	complemented
60	C₂₃×#465	C₂²	1	4	yes	complemented
61	C₂₃×#464	C₂²	1	4	yes	complemented
62	C₂₃×#463	C₂²	1	4	yes	complemented
63	C₂₃×#462	C₂²	1	2	yes	complemented
64	C₂₃×#460	C₂²	1	2	yes	complemented
65	C₂₃×#452	C₂²	1	4	yes	complemented
66	C₂₃×#452	C₂²	1	4	yes	complemented
67	C₂₃×#451	C₂²	1	2	yes	—
68	C₂₃×#451	C₂²	1	2	yes	—
69	C₂₃×#451	C₂²	1	4	yes	complemented
70	C₂₃×#450	C₂²	1	2	yes	—
71	C₂₃×#449	C₂²	1	4	yes	complemented
72	C₂₃×#449	C₂²	1	4	yes	complemented
73	C₂₃×#448	C₂²	1	2	yes	—
74	C₂₃×#448	C₂²	1	2	yes	—
75	C₂₃×#448	C₂²	1	4	yes	complemented
76	C₂₃×#447	C₂²	1	2	yes	—
77	C₂₃×#441	C₂²	1	4	yes	complemented
78	C₂₃×#440	C₂²	1	4	yes	complemented
79	C₂₃×#435	C₂²	1	4	yes	complemented
80	C₂₃×#435	C₂²	1	4	yes	complemented
81	C₂₃×#432	C₂²	1	1	yes	characteristic
82	C₂₃×#432	C₂²	1	1	yes	characteristic
83	C₂₃×#419	C₂²	1	4	yes	complemented
84	C₂₃×#416	C₂²	1	4	yes	complemented
85	C₂₃×#407	C₂²	1	2	yes	—
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
87	C₂×#41×C₂₃	—	2	2	no	—
88	C₂×#41×C₂₃	—	2	1	no	—
89	C₂×#41×C₂₃	—	4	4	no	—
90	C₂×#41×C₂₃	C₂³	1	4	yes	—
91	C₂×#41×C₂₃	C₂³	1	2	yes	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂²×Q₈×C₂₃	—	2	2	no	—
94	C₂²×Q₈×C₂₃	—	2	1	no	—
95	C₂²×Q₈×C₂₃	—	4	4	no	—
96	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
98	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₂₃	—	2	1	no	—
104	C₂³×C₄×C₂₃	—	2	1	no	—
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×#137	—	4	8	no	—
108	C₂₃×#135	—	4	8	no	—
109	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×D₈×C₂₃	C₂³	1	4	yes	—
115	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×#127	—	2	2	no	—
121	C₂₃×#127	C₂³	1	1	yes	characteristic
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#125	—	2	1	no	—
125	C₂₃×#124	—	2	2	no	—
126	C₂₃×#124	—	2	4	no	—
127	C₂₃×#124	—	2	4	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	—	2	1	no	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	1	no	—
133	C₂₃×#124	C₂³	1	2	yes	—
134	C₂₃×#124	C₂³	1	2	yes	—
135	C₂₃×#123	—	2	2	no	—
136	C₂₃×#123	—	2	2	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	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	—	2	4	no	—
150	C₂₃×#121	—	2	2	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	C₂³	1	4	yes	—
156	C₂₃×#121	C₂³	1	2	yes	—
157	C₂₃×#121	C₂³	1	2	yes	—
158	C₂₃×#121	C₂³	1	2	yes	—
159	C₂₃×#120	—	2	2	no	—
160	C₂₃×#120	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	2	no	—
162	C₄×Q₈×C₂₃	—	2	1	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	—	2	1	no	—
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	4	no	—
174	C₄×D₄×C₂₃	—	2	4	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	D₄	1	2	yes	—
177	C₄×D₄×C₂₃	D₄	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₂₃×#117	—	2	1	no	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	C₂³	1	2	yes	—
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	—	2	1	no	—
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂₃×#107	C₂³	1	4	yes	—
199	C₂₃×#106	C₂³	1	4	yes	—
200	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#103	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	4	yes	—
208	C₂₃×#102	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₂₃×#97	C₂³	1	2	yes	—
215	C₂₃×#97	C₂³	1	2	yes	—
216	C₂⁴×C₂₃	—	2	1	no	—
217	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
219	#41×C₂₃	—	2	8	no	—
220	#41×C₂₃	—	4	4	no	—
221	#41×C₂₃	—	4	4	no	—
222	#41×C₂₃	—	4	4	no	—
223	#41×C₂₃	—	4	4	no	—
224	#41×C₂₃	—	4	8	no	—
225	C₂×Q₈×C₂₃	—	2	4	no	—
226	C₂×Q₈×C₂₃	—	2	1	no	—
227	C₂×Q₈×C₂₃	—	2	1	no	—
228	C₂×Q₈×C₂₃	—	2	4	no	—
229	C₂×Q₈×C₂₃	—	2	1	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	—	2	8	no	—
232	C₂×Q₈×C₂₃	—	4	4	no	—
233	C₂×Q₈×C₂₃	—	4	2	no	—
234	C₂×Q₈×C₂₃	—	4	4	no	—
235	C₂×Q₈×C₂₃	—	4	8	no	—
236	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	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	1	no	—
249	C₂×D₄×C₂₃	—	4	2	no	—
250	C₂×D₄×C₂₃	—	4	2	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	4	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	4	2	no	—
266	C₂²×C₄×C₂₃	—	4	2	no	—
267	C₂²×C₄×C₂₃	—	4	4	no	—
268	C₂²×C₄×C₂₃	—	4	4	no	—
269	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	Q₁₆×C₂₃	—	2	8	no	—
279	Q₁₆×C₂₃	—	4	4	no	—
280	SD₁₆×C₂₃	—	2	8	no	—
281	SD₁₆×C₂₃	—	4	4	no	—
282	SD₁₆×C₂₃	—	4	4	no	—
283	D₈×C₂₃	—	4	4	no	—
284	M₁₆×C₂₃	—	4	4	no	—
285	C₂×C₈×C₂₃	—	4	4	no	—
286	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
287	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₄⋊C₄×C₂₃	—	2	4	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	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	4	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	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	2	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	#61578	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	4	1	no	—
339	C₂³×C₂₃	—	4	1	no	—
340	C₂³×C₂₃	—	4	1	no	—
341	C₂³×C₂₃	—	4	1	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	—	4	2	no	—
345	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
347	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₂₃	—	2	4	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	2	4	no	—
351	Q₈×C₂₃	—	2	4	no	—
352	Q₈×C₂₃	—	4	8	no	—
353	Q₈×C₂₃	—	4	2	no	—
354	Q₈×C₂₃	—	4	2	no	—
355	Q₈×C₂₃	—	8	1	no	—
356	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
357	D₄×C₂₃	—	2	4	no	—
358	D₄×C₂₃	—	2	4	no	—
359	D₄×C₂₃	—	4	2	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	4	8	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	—	4	2	no	—
364	D₄×C₂₃	—	4	8	no	—
365	D₄×C₂₃	—	4	4	no	—
366	D₄×C₂₃	—	8	1	no	—
367	D₄×C₂₃	—	8	2	no	—
368	D₄×C₂₃	—	8	2	no	—
369	D₄×C₂₃	—	8	2	no	—
370	D₄×C₂₃	—	8	2	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	4	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	4	1	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	1	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	4	1	no	—
387	C₂×C₄×C₂₃	—	4	8	no	—
388	C₂×C₄×C₂₃	—	4	8	no	—
389	C₂×C₄×C₂₃	—	4	4	no	—
390	C₂×C₄×C₂₃	—	4	2	no	—
391	C₂×C₄×C₂₃	—	4	2	no	—
392	C₂×C₄×C₂₃	—	8	2	no	—
393	C₂×C₄×C₂₃	—	8	2	no	—
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
402	C₈×C₂₃	—	2	4	no	—
403	C₈×C₂₃	—	2	4	no	—
404	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
405	C₂×#548	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3321	C₂×C₂₃	1	4	yes	complemented
407	#3313	C₂×C₂₃	1	4	yes	complemented
408	#3271	C₂×C₂₃	1	4	yes	complemented
409	#3269	C₂×C₂₃	1	4	yes	complemented
410	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3213	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#3194	C₂×C₂₃	1	2	yes	complemented
413	#3190	C₂×C₂₃	1	2	yes	complemented
414	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#3112	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3004	C₂×C₂₃	1	2	yes	complemented
417	#3002	C₂×C₂₃	1	2	yes	complemented
418	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	2	no	—
422	C₂²×C₂₃	—	2	2	no	—
423	C₂²×C₂₃	—	2	2	no	—
424	C₂²×C₂₃	—	2	2	no	—
425	C₂²×C₂₃	—	2	2	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	4	4	no	—
428	C₂²×C₂₃	—	4	2	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	4	2	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	8	2	no	—
435	C₂²×C₂₃	—	8	4	no	—
436	C₂²×C₂₃	#575	1	2	yes	—
437	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	4	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	2	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	2	1	no	—
446	C₄×C₂₃	—	4	2	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	4	2	no	—
449	C₄×C₂₃	—	4	2	no	—
450	C₄×C₂₃	—	4	2	no	—
451	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
452	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
453	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
455	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
456	#559	—	2	2	no	—
457	#556	C₂²×C₂₃	1	2	yes	complemented
458	#555	C₂²×C₂₃	1	2	yes	complemented
459	#553	—	2	2	no	—
460	#550	C₂²×C₂₃	1	2	yes	complemented
461	#548	—	2	2	no	—
462	#548	—	2	2	no	—
463	#548	C₂²×C₂₃	1	4	yes	—
464	#548	C₂²×C₂₃	1	4	yes	—
465	#547	C₂²×C₂₃	1	2	yes	complemented
466	#538	—	2	1	no	—
467	#538	—	2	1	no	—
468	#535	—	2	1	no	—
469	#533	C₂²×C₂₃	1	1	yes	characteristic
470	#532	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×#124	—	2	1	no	—
472	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
473	#525	C₂²×C₂₃	1	2	yes	—
474	#525	C₂²×C₂₃	1	2	yes	—
475	C₂×C₂²⋊Q₈	—	2	1	no	—
476	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#121	—	2	1	no	—
478	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
479	#520	—	2	1	no	—
480	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×C₄×D₄	—	2	1	no	—
482	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
483	#497	C₂²×C₂₃	1	2	yes	complemented
484	#496	C₂²×C₂₃	1	2	yes	complemented
485	#489	C₂²×C₂₃	1	2	yes	complemented
486	#489	C₂²×C₂₃	1	2	yes	complemented
487	#485	C₂²×C₂₃	1	4	yes	complemented
488	#483	C₂²×C₂₃	1	2	yes	—
489	#482	C₂²×C₂₃	1	4	yes	complemented
490	#480	C₂²×C₂₃	1	2	yes	—
491	#477	C₂²×C₂₃	1	2	yes	complemented
492	#475	C₂²×C₂₃	1	2	yes	complemented
493	#469	C₂²×C₂₃	1	4	yes	complemented
494	#468	C₂²×C₂₃	1	4	yes	complemented
495	#467	C₂²×C₂₃	1	4	yes	complemented
496	#465	C₂²×C₂₃	1	4	yes	complemented
497	#464	C₂²×C₂₃	1	4	yes	complemented
498	#463	C₂²×C₂₃	1	4	yes	complemented
499	#462	C₂²×C₂₃	1	2	yes	complemented
500	#460	C₂²×C₂₃	1	2	yes	complemented
501	#452	C₂²×C₂₃	1	4	yes	complemented
502	#452	C₂²×C₂₃	1	4	yes	complemented
503	#451	C₂²×C₂₃	1	2	yes	—
504	#451	C₂²×C₂₃	1	2	yes	—
505	#451	C₂²×C₂₃	1	4	yes	complemented
506	#450	C₂²×C₂₃	1	2	yes	—
507	#449	C₂²×C₂₃	1	4	yes	complemented
508	#449	C₂²×C₂₃	1	4	yes	complemented
509	#448	C₂²×C₂₃	1	2	yes	—
510	#448	C₂²×C₂₃	1	2	yes	—
511	#448	C₂²×C₂₃	1	4	yes	complemented
512	#447	C₂²×C₂₃	1	2	yes	—
513	#441	C₂²×C₂₃	1	4	yes	complemented
514	#440	C₂²×C₂₃	1	4	yes	complemented
515	#435	C₂²×C₂₃	1	4	yes	complemented
516	#435	C₂²×C₂₃	1	4	yes	complemented
517	#432	C₂²×C₂₃	1	1	yes	characteristic
518	#432	C₂²×C₂₃	1	1	yes	characteristic
519	#419	C₂²×C₂₃	1	4	yes	complemented
520	#416	C₂²×C₂₃	1	4	yes	complemented
521	#407	C₂²×C₂₃	1	2	yes	—
522	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	4	2	no	—
525	C₂×C₂₃	—	4	2	no	—
526	C₂×C₂₃	—	8	2	no	—
527	C₂×C₂₃	—	8	2	no	—
528	C₂×C₂₃	#3484	1	1	yes	characteristic
529	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
530	C₂×C₂₃	#3586	1	1	yes	characteristic
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	4	4	no	—
534	C₂×#41	C₂³×C₂₃	1	4	yes	—
535	C₂×#41	C₂³×C₂₃	1	2	yes	—
536	C₂×#41	C₂³×C₂₃	1	2	yes	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	4	4	no	—
540	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
542	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₂²×D₄	—	2	1	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
547	C₂³×C₄	—	2	1	no	—
548	C₂³×C₄	—	2	1	no	—
549	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
551	#137	—	4	8	no	—
552	#135	—	4	8	no	—
553	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
554	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
558	C₂×D₈	C₂³×C₂₃	1	4	yes	—
559	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
560	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
561	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	#127	—	2	2	no	—
565	#127	C₂³×C₂₃	1	1	yes	characteristic
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#125	—	2	1	no	—
569	#124	—	2	2	no	—
570	#124	—	2	4	no	—
571	#124	—	2	4	no	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	—	2	1	no	—
575	#124	—	2	1	no	—
576	#124	—	2	1	no	—
577	#124	C₂³×C₂₃	1	2	yes	—
578	#124	C₂³×C₂₃	1	2	yes	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
591	#121	—	2	4	no	—
592	#121	—	2	4	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	#121	—	2	2	no	—
599	#121	C₂³×C₂₃	1	4	yes	—
600	#121	C₂³×C₂₃	1	2	yes	—
601	#121	C₂³×C₂₃	1	2	yes	—
602	#121	C₂³×C₂₃	1	2	yes	—
603	#120	—	2	2	no	—
604	#120	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
611	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	D₄×C₂₃	1	2	yes	—
621	C₄×D₄	D₄×C₂₃	1	2	yes	—
622	C₄×D₄	C₂³×C₂₃	1	2	yes	—
623	C₄×D₄	C₂³×C₂₃	1	2	yes	—
624	C₄×D₄	C₂³×C₂₃	1	2	yes	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	C₂³×C₂₃	1	2	yes	—
628	#117	C₂³×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
642	#107	C₂³×C₂₃	1	4	yes	—
643	#106	C₂³×C₂₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
646	#103	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	4	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	4	yes	—
650	#103	C₂³×C₂₃	1	4	yes	—
651	#102	C₂³×C₂₃	1	4	yes	—
652	#102	C₂³×C₂₃	1	4	yes	—
653	#102	C₂³×C₂₃	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
655	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
656	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
657	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
658	#97	C₂³×C₂₃	1	2	yes	—
659	#97	C₂³×C₂₃	1	2	yes	—
660	C₂₃	#61578	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
664	#41	—	2	8	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	4	8	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	8	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×Q₈	—	4	4	no	—
680	C₂×Q₈	—	4	8	no	—
681	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
701	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
723	Q₁₆	—	2	8	no	—
724	Q₁₆	—	4	4	no	—
725	SD₁₆	—	2	8	no	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	4	no	—
728	D₈	—	4	4	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
732	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
746	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
767	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
768	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
777	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	4	2	no	—
788	C₂³	—	4	2	no	—
789	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
790	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
791	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	Q₈	—	2	4	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	8	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	8	1	no	—
800	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
801	D₄	—	2	4	no	—
802	D₄	—	2	4	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	4	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	C₂×C₄	—	2	4	no	—
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	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
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	C₂⁵×C₂₃	1	1	yes	characteristic
846	C₈	—	2	4	no	—
847	C₈	—	2	4	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	8	2	no	—
864	C₂²	—	8	4	no	—
865	C₂²	C₂₃×#575	1	2	yes	—
866	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
867	C₄	—	2	4	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
881	C₂	—	2	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	4	2	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂₃×#3484	1	1	yes	characteristic
887	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
888	C₂	C₂₃×#3586	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×#3506	C₂	semidirect
2. C₂×C₂₃×#548	C₂	semidirect
3. C₂₃×#3321	C₂	semidirect
4. C₂₃×#3313	C₂	semidirect
5. C₂₃×#3271	C₂	semidirect
6. C₂₃×#3269	C₂	semidirect
7. C₂₃×#3215	C₂	semidirect
8. C₂₃×#3213	C₂	semidirect
9. C₂₃×#3194	C₂	semidirect
10. C₂₃×#3190	C₂	semidirect
11. C₂₃×#3113	C₂	semidirect
12. C₂₃×#3112	C₂	semidirect
13. C₂₃×#3004	C₂	semidirect
14. C₂₃×#3002	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
18. C₂×C₂₃×#137	C₂²	semidirect
19. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#556	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
24. C₂₃×#550	C₂²	semidirect
29. C₂₃×#547	C₂²	semidirect
47. C₂₃×#497	C₂²	semidirect
48. C₂₃×#496	C₂²	semidirect
49. C₂₃×#489	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#485	C₂²	semidirect
53. C₂₃×#482	C₂²	semidirect
55. C₂₃×#477	C₂²	semidirect
56. C₂₃×#475	C₂²	semidirect
57. C₂₃×#469	C₂²	semidirect
58. C₂₃×#468	C₂²	semidirect
59. C₂₃×#467	C₂²	semidirect
60. C₂₃×#465	C₂²	semidirect
61. C₂₃×#464	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#462	C₂²	semidirect
64. C₂₃×#460	C₂²	semidirect
65. C₂₃×#452	C₂²	semidirect
66. C₂₃×#452	C₂²	semidirect
69. C₂₃×#451	C₂²	semidirect
71. C₂₃×#449	C₂²	semidirect
72. C₂₃×#449	C₂²	semidirect
75. C₂₃×#448	C₂²	semidirect
77. C₂₃×#441	C₂²	semidirect
78. C₂₃×#440	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#435	C₂²	semidirect
83. C₂₃×#419	C₂²	semidirect
84. C₂₃×#416	C₂²	semidirect
333. #61578	C₂₃	direct (N × H)
404. #3506	C₂×C₂₃	semidirect
405. C₂×#548	C₂×C₂₃	semidirect
406. #3321	C₂×C₂₃	semidirect
407. #3313	C₂×C₂₃	semidirect
408. #3271	C₂×C₂₃	semidirect
409. #3269	C₂×C₂₃	semidirect
410. #3215	C₂×C₂₃	semidirect
411. #3213	C₂×C₂₃	semidirect
412. #3194	C₂×C₂₃	semidirect
413. #3190	C₂×C₂₃	semidirect
414. #3113	C₂×C₂₃	semidirect
415. #3112	C₂×C₂₃	semidirect
416. #3004	C₂×C₂₃	semidirect
417. #3002	C₂×C₂₃	semidirect
418. #2973	C₂×C₂₃	semidirect
454. C₂×#137	C₂²×C₂₃	semidirect
455. C₂×#135	C₂²×C₂₃	semidirect
457. #556	C₂²×C₂₃	semidirect
458. #555	C₂²×C₂₃	semidirect
460. #550	C₂²×C₂₃	semidirect
465. #547	C₂²×C₂₃	semidirect
483. #497	C₂²×C₂₃	semidirect
484. #496	C₂²×C₂₃	semidirect
485. #489	C₂²×C₂₃	semidirect
486. #489	C₂²×C₂₃	semidirect
487. #485	C₂²×C₂₃	semidirect
489. #482	C₂²×C₂₃	semidirect
491. #477	C₂²×C₂₃	semidirect
492. #475	C₂²×C₂₃	semidirect
493. #469	C₂²×C₂₃	semidirect
494. #468	C₂²×C₂₃	semidirect
495. #467	C₂²×C₂₃	semidirect
496. #465	C₂²×C₂₃	semidirect
497. #464	C₂²×C₂₃	semidirect
498. #463	C₂²×C₂₃	semidirect
499. #462	C₂²×C₂₃	semidirect
500. #460	C₂²×C₂₃	semidirect
501. #452	C₂²×C₂₃	semidirect
502. #452	C₂²×C₂₃	semidirect
505. #451	C₂²×C₂₃	semidirect
507. #449	C₂²×C₂₃	semidirect
508. #449	C₂²×C₂₃	semidirect
511. #448	C₂²×C₂₃	semidirect
513. #441	C₂²×C₂₃	semidirect
514. #440	C₂²×C₂₃	semidirect
515. #435	C₂²×C₂₃	semidirect
516. #435	C₂²×C₂₃	semidirect
519. #419	C₂²×C₂₃	semidirect
520. #416	C₂²×C₂₃	semidirect
660. C₂₃	#61578	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×#3506	2
C₂×C₂₃×#548	2
C₂₃×#3321	2
C₂₃×#3313	2
C₂₃×#3271	2
C₂₃×#3269	2
C₂₃×#3215	2
C₂₃×#3213	2
C₂₃×#3194	2
C₂₃×#3190	2
C₂₃×#3113	2
C₂₃×#3112	2
C₂₃×#3004	2
C₂₃×#3002	2
C₂₃×#2973	2
#61578	23

Subgroups — C23×#61578 #19209204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61578 #19209204