Subgroups — C₂₃×#61706 #19209332

Order 5888.

2022 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3345	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3343	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3114	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3092	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂₃×#553	—	2	2	no	—
18	C₂₃×#553	C₂²	1	2	yes	complemented
19	C₂₃×#552	C₂²	1	2	yes	complemented
20	C₂₃×#551	—	2	2	no	—
21	C₂₃×#548	C₂²	1	2	yes	complemented
22	C₂₃×#547	—	2	2	no	—
23	C₂₃×#547	—	2	2	no	—
24	C₂₃×#547	C₂²	1	4	yes	—
25	C₂₃×#547	C₂²	1	4	yes	complemented
26	C₂₃×#546	C₂²	1	2	yes	complemented
27	C₂₃×#539	—	2	1	no	—
28	C₂₃×#538	—	2	1	no	—
29	C₂₃×#534	—	2	1	no	—
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₂₃×#525	C₂²	1	2	yes	—
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×#123	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#518	—	2	1	no	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#501	C₂²	1	4	yes	complemented
46	C₂₃×#489	C₂²	1	4	yes	complemented
47	C₂₃×#484	C₂²	1	4	yes	complemented
48	C₂₃×#483	C₂²	1	2	yes	complemented
49	C₂₃×#483	C₂²	1	2	yes	complemented
50	C₂₃×#483	C₂²	1	4	yes	complemented
51	C₂₃×#483	C₂²	1	2	yes	complemented
52	C₂₃×#482	C₂²	1	4	yes	complemented
53	C₂₃×#481	C₂²	1	2	yes	complemented
54	C₂₃×#481	C₂²	1	4	yes	complemented
55	C₂₃×#480	C₂²	1	2	yes	—
56	C₂₃×#480	C₂²	1	2	yes	—
57	C₂₃×#480	C₂²	1	2	yes	—
58	C₂₃×#480	C₂²	1	2	yes	complemented
59	C₂₃×#480	C₂²	1	4	yes	complemented
60	C₂₃×#478	C₂²	1	4	yes	complemented
61	C₂₃×#477	C₂²	1	4	yes	complemented
62	C₂₃×#476	C₂²	1	4	yes	complemented
63	C₂₃×#469	C₂²	1	4	yes	complemented
64	C₂₃×#468	C₂²	1	4	yes	complemented
65	C₂₃×#466	C₂²	1	4	yes	complemented
66	C₂₃×#465	C₂²	1	4	yes	complemented
67	C₂₃×#463	C₂²	1	4	yes	complemented
68	C₂₃×#450	C₂²	1	2	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#448	C₂²	1	2	yes	complemented
71	C₂₃×#447	C₂²	1	2	yes	—
72	C₂₃×#447	C₂²	1	2	yes	complemented
73	C₂₃×#442	C₂²	1	4	yes	complemented
74	C₂₃×#440	C₂²	1	4	yes	complemented
75	C₂₃×#435	C₂²	1	4	yes	complemented
76	C₂₃×#435	C₂²	1	4	yes	complemented
77	C₂₃×#432	C₂²	1	2	yes	complemented
78	C₂₃×#428	C₂²	1	4	yes	complemented
79	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
80	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
81	C₂₃×#417	C₂²	1	4	yes	complemented
82	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
84	C₂₃×#407	C₂²	1	2	yes	complemented
85	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×#41×C₂₃	—	2	4	no	—
88	C₂×#41×C₂₃	—	2	4	no	—
89	C₂×#41×C₂₃	—	4	8	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂²×Q₈×C₂₃	—	2	1	no	—
92	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₂₃	—	2	1	no	—
94	C₂²×D₄×C₂₃	—	2	1	no	—
95	C₂²×D₄×C₂₃	—	2	1	no	—
96	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
97	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	—	2	1	no	—
100	C₂³×C₄×C₂₃	—	2	1	no	—
101	C₂³×C₄×C₂₃	—	2	1	no	—
102	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×D₈×C₂₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₂₃×#126	—	2	2	no	—
112	C₂₃×#126	—	2	2	no	—
113	C₂₃×#126	—	2	2	no	—
114	C₂₃×#125	—	2	2	no	—
115	C₂₃×#125	C₂³	1	2	yes	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#124	C₂³	1	2	yes	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×#123	—	2	2	no	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×#123	—	2	4	no	—
124	C₂₃×#123	—	2	4	no	—
125	C₂₃×#123	—	2	4	no	—
126	C₂₃×#123	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	1	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	—	2	2	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	1	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	C₂³	1	2	yes	—
144	C₂₃×#121	C₂³	1	4	yes	—
145	C₂₃×#121	C₂³	1	2	yes	—
146	C₂₃×#121	C₂³	1	2	yes	—
147	C₂₃×#121	C₂³	1	2	yes	—
148	C₂₃×#121	C₂³	1	2	yes	—
149	C₂₃×#120	—	2	2	no	—
150	C₂₃×#120	—	2	2	no	—
151	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
152	C₄×D₄×C₂₃	—	2	2	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	—	2	2	no	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	D₄	1	2	yes	—
159	C₄×D₄×C₂₃	D₄	1	2	yes	—
160	C₄×D₄×C₂₃	C₂³	1	4	yes	—
161	C₄×D₄×C₂₃	C₂³	1	2	yes	—
162	C₄×D₄×C₂₃	C₂³	1	2	yes	—
163	C₄×D₄×C₂₃	C₂³	1	2	yes	—
164	C₂₃×#117	—	2	2	no	—
165	C₂₃×#117	—	2	2	no	—
166	C₂₃×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
173	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂₃×#107	C₂³	1	4	yes	—
193	C₂₃×#107	C₂³	1	4	yes	—
194	C₂₃×#107	C₂³	1	4	yes	—
195	C₂₃×#106	C₂³	1	4	yes	—
196	C₂₃×#106	C₂³	1	4	yes	—
197	C₂₃×#106	C₂³	1	4	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	4	yes	—
200	C₂₃×#103	C₂³	1	4	yes	—
201	C₂₃×#103	C₂³	1	4	yes	—
202	C₂₃×#102	C₂³	1	4	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₂₃×#97	C₂³	1	4	yes	—
213	C₂⁴×C₂₃	—	2	1	no	—
214	C₂⁴×C₂₃	—	2	1	no	—
215	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
217	#41×C₂₃	—	4	4	no	—
218	#41×C₂₃	—	4	16	no	—
219	#41×C₂₃	—	4	16	no	—
220	C₂×Q₈×C₂₃	—	2	4	no	—
221	C₂×Q₈×C₂₃	—	2	1	no	—
222	C₂×Q₈×C₂₃	—	4	4	no	—
223	C₂×Q₈×C₂₃	—	4	2	no	—
224	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₂₃	—	2	4	no	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	2	no	—
228	C₂×D₄×C₂₃	—	2	4	no	—
229	C₂×D₄×C₂₃	—	2	2	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	2	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	1	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	2	no	—
237	C₂×D₄×C₂₃	—	4	4	no	—
238	C₂×D₄×C₂₃	—	4	4	no	—
239	C₂×D₄×C₂₃	—	4	4	no	—
240	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	1	no	—
246	C₂²×C₄×C₂₃	—	2	1	no	—
247	C₂²×C₄×C₂₃	—	2	1	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	1	no	—
253	C₂²×C₄×C₂₃	—	2	4	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	4	2	no	—
257	C₂²×C₄×C₂₃	—	4	2	no	—
258	C₂²×C₄×C₂₃	—	4	4	no	—
259	C₂²×C₄×C₂₃	—	4	4	no	—
260	C₂²×C₄×C₂₃	—	4	4	no	—
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	SD₁₆×C₂₃	—	4	4	no	—
273	D₈×C₂₃	—	4	4	no	—
274	M₁₆×C₂₃	—	4	4	no	—
275	C₂×C₈×C₂₃	—	4	2	no	—
276	C₂×C₈×C₂₃	—	4	2	no	—
277	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
278	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	4	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	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	2	no	—
306	C₂²⋊C₄×C₂₃	—	2	2	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	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	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	C₂×D₄	1	2	yes	—
322	C₄²×C₂₃	C₂⁴	1	2	yes	—
323	#61706	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂³×C₂₃	—	2	2	no	—
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	4	1	no	—
328	C₂³×C₂₃	—	4	1	no	—
329	C₂³×C₂₃	—	4	1	no	—
330	C₂³×C₂₃	—	4	1	no	—
331	C₂³×C₂₃	—	4	2	no	—
332	C₂³×C₂₃	—	4	2	no	—
333	C₂³×C₂₃	—	4	2	no	—
334	C₂³×C₂₃	—	4	2	no	—
335	C₂³×C₂₃	—	8	1	no	—
336	C₂³×C₂₃	—	8	1	no	—
337	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
338	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₂₃	—	2	4	no	—
343	Q₈×C₂₃	—	4	8	no	—
344	Q₈×C₂₃	—	8	1	no	—
345	D₄×C₂₃	—	2	4	no	—
346	D₄×C₂₃	—	2	4	no	—
347	D₄×C₂₃	—	2	4	no	—
348	D₄×C₂₃	—	2	4	no	—
349	D₄×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	4	8	no	—
351	D₄×C₂₃	—	4	4	no	—
352	D₄×C₂₃	—	4	4	no	—
353	D₄×C₂₃	—	4	4	no	—
354	D₄×C₂₃	—	4	4	no	—
355	D₄×C₂₃	—	8	1	no	—
356	D₄×C₂₃	—	8	2	no	—
357	D₄×C₂₃	—	8	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	1	no	—
371	C₂×C₄×C₂₃	—	4	1	no	—
372	C₂×C₄×C₂₃	—	4	1	no	—
373	C₂×C₄×C₂₃	—	4	1	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	8	no	—
376	C₂×C₄×C₂₃	—	4	8	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	4	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	8	2	no	—
384	C₂×C₄×C₂₃	—	8	2	no	—
385	C₂×C₄×C₂₃	—	8	1	no	—
386	C₂×C₄×C₂₃	—	8	1	no	—
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
394	C₈×C₂₃	—	2	4	no	—
395	C₈×C₂₃	—	2	4	no	—
396	#3505	C₂×C₂₃	1	1	yes	characteristic, complemented
397	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#3345	C₂×C₂₃	1	4	yes	complemented
399	#3343	C₂×C₂₃	1	4	yes	complemented
400	#3308	C₂×C₂₃	1	4	yes	complemented
401	#3306	C₂×C₂₃	1	4	yes	complemented
402	#3238	C₂×C₂₃	1	2	yes	complemented
403	#3194	C₂×C₂₃	1	2	yes	complemented
404	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3114	C₂×C₂₃	1	2	yes	complemented
407	#3092	C₂×C₂₃	1	2	yes	complemented
408	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
409	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
411	C₂²×C₂₃	—	2	1	no	—
412	C₂²×C₂₃	—	2	1	no	—
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	4	4	no	—
421	C₂²×C₂₃	—	4	4	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	4	2	no	—
425	C₂²×C₂₃	—	4	2	no	—
426	C₂²×C₂₃	—	4	2	no	—
427	C₂²×C₂₃	—	4	2	no	—
428	C₂²×C₂₃	—	8	4	no	—
429	C₂²×C₂₃	—	16	2	no	—
430	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
431	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
432	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
433	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	2	1	no	—
436	C₄×C₂₃	—	2	2	no	—
437	C₄×C₂₃	—	2	1	no	—
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	2	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	—	4	2	no	—
445	C₄×C₂₃	—	4	2	no	—
446	C₄×C₂₃	#585	1	2	yes	—
447	C₂²×#41	—	2	1	no	—
448	#553	—	2	2	no	—
449	#553	C₂²×C₂₃	1	2	yes	complemented
450	#552	C₂²×C₂₃	1	2	yes	complemented
451	#551	—	2	2	no	—
452	#548	C₂²×C₂₃	1	2	yes	complemented
453	#547	—	2	2	no	—
454	#547	—	2	2	no	—
455	#547	C₂²×C₂₃	1	4	yes	—
456	#547	C₂²×C₂₃	1	4	yes	complemented
457	#546	C₂²×C₂₃	1	2	yes	complemented
458	#539	—	2	1	no	—
459	#538	—	2	1	no	—
460	#534	—	2	1	no	—
461	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#529	C₂²×C₂₃	1	2	yes	—
463	#525	C₂²×C₂₃	1	2	yes	—
464	C₂×#123	—	2	1	no	—
465	C₂×#123	—	2	1	no	—
466	C₂×C₂²⋊Q₈	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#518	—	2	1	no	—
472	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
475	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	#501	C₂²×C₂₃	1	4	yes	complemented
477	#489	C₂²×C₂₃	1	4	yes	complemented
478	#484	C₂²×C₂₃	1	4	yes	complemented
479	#483	C₂²×C₂₃	1	4	yes	complemented
480	#483	C₂²×C₂₃	1	2	yes	complemented
481	#483	C₂²×C₂₃	1	2	yes	complemented
482	#483	C₂²×C₂₃	1	2	yes	complemented
483	#482	C₂²×C₂₃	1	4	yes	complemented
484	#481	C₂²×C₂₃	1	2	yes	complemented
485	#481	C₂²×C₂₃	1	4	yes	complemented
486	#480	C₂²×C₂₃	1	2	yes	—
487	#480	C₂²×C₂₃	1	2	yes	—
488	#480	C₂²×C₂₃	1	2	yes	—
489	#480	C₂²×C₂₃	1	4	yes	complemented
490	#480	C₂²×C₂₃	1	2	yes	complemented
491	#478	C₂²×C₂₃	1	4	yes	complemented
492	#477	C₂²×C₂₃	1	4	yes	complemented
493	#476	C₂²×C₂₃	1	4	yes	complemented
494	#469	C₂²×C₂₃	1	4	yes	complemented
495	#468	C₂²×C₂₃	1	4	yes	complemented
496	#466	C₂²×C₂₃	1	4	yes	complemented
497	#465	C₂²×C₂₃	1	4	yes	complemented
498	#463	C₂²×C₂₃	1	4	yes	complemented
499	#450	C₂²×C₂₃	1	2	yes	complemented
500	#449	C₂²×C₂₃	1	4	yes	complemented
501	#448	C₂²×C₂₃	1	2	yes	complemented
502	#447	C₂²×C₂₃	1	2	yes	—
503	#447	C₂²×C₂₃	1	2	yes	complemented
504	#442	C₂²×C₂₃	1	4	yes	complemented
505	#440	C₂²×C₂₃	1	4	yes	complemented
506	#435	C₂²×C₂₃	1	4	yes	complemented
507	#435	C₂²×C₂₃	1	4	yes	complemented
508	#432	C₂²×C₂₃	1	2	yes	complemented
509	#428	C₂²×C₂₃	1	4	yes	complemented
510	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
511	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
512	#417	C₂²×C₂₃	1	4	yes	complemented
513	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
514	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
515	#407	C₂²×C₂₃	1	2	yes	complemented
516	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
518	C₂×C₂₃	—	2	2	no	—
519	C₂×C₂₃	—	2	2	no	—
520	C₂×C₂₃	—	2	2	no	—
521	C₂×C₂₃	—	4	2	no	—
522	C₂×C₂₃	—	8	2	no	—
523	C₂×C₂₃	—	8	2	no	—
524	C₂×C₂₃	#3485	1	1	yes	characteristic
525	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
526	C₂×C₂₃	#3586	1	1	yes	characteristic
527	C₂×#41	—	2	4	no	—
528	C₂×#41	—	2	4	no	—
529	C₂×#41	—	4	8	no	—
530	C₂×#41	C₂³×C₂₃	1	2	yes	—
531	C₂²×Q₈	—	2	1	no	—
532	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
545	C₂×D₈	C₂³×C₂₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
547	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
548	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	C₂³×C₂₃	1	2	yes	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₂₃	1	2	yes	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	#123	—	2	4	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	C₂³×C₂₃	1	2	yes	—
584	#121	C₂³×C₂₃	1	2	yes	—
585	#121	C₂³×C₂₃	1	2	yes	—
586	#121	C₂³×C₂₃	1	2	yes	—
587	#121	C₂³×C₂₃	1	4	yes	—
588	#121	C₂³×C₂₃	1	2	yes	—
589	#120	—	2	2	no	—
590	#120	—	2	2	no	—
591	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	D₄×C₂₃	1	2	yes	—
599	C₄×D₄	D₄×C₂₃	1	2	yes	—
600	C₄×D₄	C₂³×C₂₃	1	4	yes	—
601	C₄×D₄	C₂³×C₂₃	1	2	yes	—
602	C₄×D₄	C₂³×C₂₃	1	2	yes	—
603	C₄×D₄	C₂³×C₂₃	1	2	yes	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
632	#107	C₂³×C₂₃	1	4	yes	—
633	#107	C₂³×C₂₃	1	4	yes	—
634	#107	C₂³×C₂₃	1	4	yes	—
635	#106	C₂³×C₂₃	1	4	yes	—
636	#106	C₂³×C₂₃	1	4	yes	—
637	#106	C₂³×C₂₃	1	4	yes	—
638	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
639	#103	C₂³×C₂₃	1	4	yes	—
640	#103	C₂³×C₂₃	1	4	yes	—
641	#103	C₂³×C₂₃	1	4	yes	—
642	#102	C₂³×C₂₃	1	4	yes	—
643	#102	C₂³×C₂₃	1	4	yes	—
644	#102	C₂³×C₂₃	1	4	yes	—
645	#102	C₂³×C₂₃	1	4	yes	—
646	#102	C₂³×C₂₃	1	4	yes	—
647	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
648	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
651	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
652	#97	C₂³×C₂₃	1	4	yes	—
653	C₂₃	#61706	1	1	yes	characteristic, direct product factor, Sylow
654	C₂⁴	—	2	1	no	—
655	C₂⁴	—	2	1	no	—
656	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
658	#41	—	4	4	no	—
659	#41	—	4	16	no	—
660	#41	—	4	16	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	4	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	2	yes	—
683	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	4	no	—
700	C₂²×C₄	—	4	4	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
713	SD₁₆	—	4	4	no	—
714	D₈	—	4	4	no	—
715	M₁₆	—	4	4	no	—
716	C₂×C₈	—	4	2	no	—
717	C₂×C₈	—	4	2	no	—
718	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
719	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
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	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄×C₂₃	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
758	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
759	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×D₄×C₂₃	1	2	yes	—
763	C₄²	C₂⁴×C₂₃	1	2	yes	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	8	1	no	—
776	C₂³	—	8	1	no	—
777	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
778	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
779	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
780	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	4	8	no	—
784	Q₈	—	8	1	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	4	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	8	2	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
833	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
834	C₈	—	2	4	no	—
835	C₈	—	2	4	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	8	4	no	—
854	C₂²	—	16	2	no	—
855	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
856	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
857	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
858	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
859	C₄	—	2	1	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	C₂₃×#585	1	2	yes	—
872	C₂	—	2	2	no	—
873	C₂	—	2	2	no	—
874	C₂	—	2	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	8	2	no	—
877	C₂	—	8	2	no	—
878	C₂	C₂₃×#3485	1	1	yes	characteristic
879	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
880	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×#3505	C₂	semidirect
2. C₂×C₂₃×#547	C₂	semidirect
3. C₂₃×#3345	C₂	semidirect
4. C₂₃×#3343	C₂	semidirect
5. C₂₃×#3308	C₂	semidirect
6. C₂₃×#3306	C₂	semidirect
7. C₂₃×#3238	C₂	semidirect
8. C₂₃×#3194	C₂	semidirect
9. C₂₃×#3187	C₂	semidirect
10. C₂₃×#3186	C₂	semidirect
11. C₂₃×#3114	C₂	semidirect
12. C₂₃×#3092	C₂	semidirect
13. C₂×C₂₃×#483	C₂	semidirect
14. C₂×C₂₃×#480	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
18. C₂₃×#553	C₂²	semidirect
19. C₂₃×#552	C₂²	semidirect
21. C₂₃×#548	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
26. C₂₃×#546	C₂²	semidirect
30. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₂₃×#121	C₂²	semidirect
42. C₂×C₄×D₄×C₂₃	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#484	C₂²	semidirect
48. C₂₃×#483	C₂²	semidirect
49. C₂₃×#483	C₂²	semidirect
50. C₂₃×#483	C₂²	semidirect
51. C₂₃×#483	C₂²	semidirect
52. C₂₃×#482	C₂²	semidirect
53. C₂₃×#481	C₂²	semidirect
54. C₂₃×#481	C₂²	semidirect
58. C₂₃×#480	C₂²	semidirect
59. C₂₃×#480	C₂²	semidirect
60. C₂₃×#478	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
62. C₂₃×#476	C₂²	semidirect
63. C₂₃×#469	C₂²	semidirect
64. C₂₃×#468	C₂²	semidirect
65. C₂₃×#466	C₂²	semidirect
66. C₂₃×#465	C₂²	semidirect
67. C₂₃×#463	C₂²	semidirect
68. C₂₃×#450	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#448	C₂²	semidirect
72. C₂₃×#447	C₂²	semidirect
73. C₂₃×#442	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₂₃×#435	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₂₃×#432	C₂²	semidirect
78. C₂₃×#428	C₂²	semidirect
79. C₂×C₂₃×#107	C₂²	semidirect
80. C₂×C₂₃×#106	C₂²	semidirect
81. C₂₃×#417	C₂²	semidirect
82. C₂×C₂₃×#103	C₂²	semidirect
83. C₂×C₂₃×#102	C₂²	semidirect
84. C₂₃×#407	C₂²	semidirect
323. #61706	C₂₃	direct (N × H)
396. #3505	C₂×C₂₃	semidirect
397. C₂×#547	C₂×C₂₃	semidirect
398. #3345	C₂×C₂₃	semidirect
399. #3343	C₂×C₂₃	semidirect
400. #3308	C₂×C₂₃	semidirect
401. #3306	C₂×C₂₃	semidirect
402. #3238	C₂×C₂₃	semidirect
403. #3194	C₂×C₂₃	semidirect
404. #3187	C₂×C₂₃	semidirect
405. #3186	C₂×C₂₃	semidirect
406. #3114	C₂×C₂₃	semidirect
407. #3092	C₂×C₂₃	semidirect
408. C₂×#483	C₂×C₂₃	semidirect
409. C₂×#480	C₂×C₂₃	semidirect
410. #2973	C₂×C₂₃	semidirect
449. #553	C₂²×C₂₃	semidirect
450. #552	C₂²×C₂₃	semidirect
452. #548	C₂²×C₂₃	semidirect
456. #547	C₂²×C₂₃	semidirect
457. #546	C₂²×C₂₃	semidirect
461. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
470. C₂×#121	C₂²×C₂₃	semidirect
473. C₂×C₄×D₄	C₂²×C₂₃	semidirect
475. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
476. #501	C₂²×C₂₃	semidirect
477. #489	C₂²×C₂₃	semidirect
478. #484	C₂²×C₂₃	semidirect
479. #483	C₂²×C₂₃	semidirect
480. #483	C₂²×C₂₃	semidirect
481. #483	C₂²×C₂₃	semidirect
482. #483	C₂²×C₂₃	semidirect
483. #482	C₂²×C₂₃	semidirect
484. #481	C₂²×C₂₃	semidirect
485. #481	C₂²×C₂₃	semidirect
489. #480	C₂²×C₂₃	semidirect
490. #480	C₂²×C₂₃	semidirect
491. #478	C₂²×C₂₃	semidirect
492. #477	C₂²×C₂₃	semidirect
493. #476	C₂²×C₂₃	semidirect
494. #469	C₂²×C₂₃	semidirect
495. #468	C₂²×C₂₃	semidirect
496. #466	C₂²×C₂₃	semidirect
497. #465	C₂²×C₂₃	semidirect
498. #463	C₂²×C₂₃	semidirect
499. #450	C₂²×C₂₃	semidirect
500. #449	C₂²×C₂₃	semidirect
501. #448	C₂²×C₂₃	semidirect
503. #447	C₂²×C₂₃	semidirect
504. #442	C₂²×C₂₃	semidirect
505. #440	C₂²×C₂₃	semidirect
506. #435	C₂²×C₂₃	semidirect
507. #435	C₂²×C₂₃	semidirect
508. #432	C₂²×C₂₃	semidirect
509. #428	C₂²×C₂₃	semidirect
510. C₂×#107	C₂²×C₂₃	semidirect
511. C₂×#106	C₂²×C₂₃	semidirect
512. #417	C₂²×C₂₃	semidirect
513. C₂×#103	C₂²×C₂₃	semidirect
514. C₂×#102	C₂²×C₂₃	semidirect
515. #407	C₂²×C₂₃	semidirect
653. C₂₃	#61706	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×#3505	2
C₂×C₂₃×#547	2
C₂₃×#3345	2
C₂₃×#3343	2
C₂₃×#3308	2
C₂₃×#3306	2
C₂₃×#3238	2
C₂₃×#3194	2
C₂₃×#3187	2
C₂₃×#3186	2
C₂₃×#3114	2
C₂₃×#3092	2
C₂×C₂₃×#483	2
C₂×C₂₃×#480	2
C₂₃×#2973	2
#61706	23

Subgroups — C23×#61706 #19209332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61706 #19209332