Subgroups — C₂₃×#60854 #19208480

Order 5888.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3240	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3239	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3237	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3236	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3235	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3234	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3162	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3135	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3091	C₂	1	4	yes	maximal, complemented
13	C₂₃×#3076	C₂	1	4	yes	maximal, complemented
14	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#533	—	2	1	no	—
16	C₂₃×#533	—	2	1	no	—
17	C₂₃×#533	—	2	1	no	—
18	C₂₃×#533	—	2	1	no	—
19	C₂₃×#533	C₂²	1	1	yes	characteristic
20	C₂₃×#533	C₂²	1	1	yes	characteristic
21	C₂₃×#533	C₂²	1	2	yes	—
22	C₂₃×#533	C₂²	1	2	yes	—
23	C₂₃×#533	C₂²	1	2	yes	—
24	C₂₃×#533	C₂²	1	2	yes	—
25	C₂₃×#533	C₂²	1	1	yes	characteristic
26	C₂₃×#532	C₂²	1	1	yes	characteristic
27	C₂₃×#532	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	—	2	1	no	—
33	C₂₃×#529	—	2	1	no	—
34	C₂₃×#529	—	2	1	no	—
35	C₂₃×#529	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂×C₂₃×#125	C₂²	1	2	yes	—
38	C₂₃×#525	—	2	1	no	—
39	C₂₃×#525	—	2	1	no	—
40	C₂₃×#525	C₂²	1	2	yes	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
43	C₄×#41×C₂₃	—	2	1	no	—
44	C₄×#41×C₂₃	—	2	1	no	—
45	C₄×#41×C₂₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
47	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
48	C₂×C₂₃×#117	C₂²	1	2	yes	—
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#501	C₂²	1	4	yes	complemented
51	C₂₃×#501	C₂²	1	4	yes	complemented
52	C₂₃×#501	C₂²	1	4	yes	complemented
53	C₂₃×#501	C₂²	1	4	yes	complemented
54	C₂₃×#491	C₂²	1	4	yes	complemented
55	C₂₃×#490	C₂²	1	4	yes	complemented
56	C₂₃×#489	C₂²	1	4	yes	complemented
57	C₂₃×#489	C₂²	1	4	yes	complemented
58	C₂₃×#485	C₂²	1	8	yes	—
59	C₂₃×#484	C₂²	1	4	yes	—
60	C₂₃×#483	C₂²	1	4	yes	—
61	C₂₃×#482	C₂²	1	8	yes	—
62	C₂₃×#481	C₂²	1	4	yes	—
63	C₂₃×#480	C₂²	1	4	yes	—
64	C₂₃×#479	C₂²	1	8	yes	complemented
65	C₂₃×#478	C₂²	1	8	yes	complemented
66	C₂₃×#477	C₂²	1	4	yes	complemented
67	C₂₃×#476	C₂²	1	4	yes	complemented
68	C₂₃×#475	C₂²	1	4	yes	complemented
69	C₂₃×#474	C₂²	1	4	yes	complemented
70	C₂₃×#432	C₂²	1	2	yes	—
71	C₂₃×#432	C₂²	1	2	yes	—
72	C₂₃×#432	C₂²	1	2	yes	—
73	C₂₃×#432	C₂²	1	2	yes	—
74	C₂₃×#427	C₂²	1	8	yes	—
75	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
76	C₂₃×#416	C₂²	1	8	yes	—
77	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
78	C₂×C₂₃×#97	C₂²	1	2	yes	—
79	C₂×#41×C₂₃	—	2	1	no	—
80	C₂×#41×C₂₃	—	2	1	no	—
81	C₂×#41×C₂₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₂₃	—	2	1	no	—
83	C₂²×Q₈×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
88	C₂₃×C₄⋊Q₈	—	2	1	no	—
89	C₂₃×C₄⋊Q₈	—	2	1	no	—
90	C₂₃×C₄⋊Q₈	—	2	1	no	—
91	C₂₃×C₄⋊Q₈	—	2	1	no	—
92	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₂₃×#127	C₂³	1	1	yes	characteristic
100	C₂₃×#126	—	2	2	no	—
101	C₂₃×#126	—	2	2	no	—
102	C₂₃×#125	—	2	2	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	—	2	1	no	—
105	C₂₃×#125	—	2	1	no	—
106	C₂₃×#125	C₂³	1	4	yes	—
107	C₂₃×#125	C₂³	1	4	yes	—
108	C₂₃×#125	C₂³	1	2	yes	—
109	C₂₃×#124	—	2	1	no	—
110	C₂₃×#124	—	2	1	no	—
111	C₂₃×#124	C₂³	1	2	yes	—
112	C₂₃×#123	—	2	2	no	—
113	C₂₃×#123	—	2	2	no	—
114	C₂₃×#123	—	2	2	no	—
115	C₂₃×C₂²⋊Q₈	—	2	2	no	—
116	C₂₃×C₂²⋊Q₈	—	2	2	no	—
117	C₂₃×C₂²⋊Q₈	—	2	2	no	—
118	C₂₃×C₂²⋊Q₈	—	2	2	no	—
119	C₂₃×C₂²⋊Q₈	—	2	2	no	—
120	C₂₃×C₂²⋊Q₈	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	1	no	—
124	C₂₃×C₂²⋊Q₈	—	2	1	no	—
125	C₂₃×C₂²⋊Q₈	—	2	1	no	—
126	C₂₃×C₂²⋊Q₈	—	2	1	no	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×#121	—	2	1	no	—
130	C₂₃×#121	—	2	1	no	—
131	C₂₃×#121	—	2	1	no	—
132	C₂₃×#121	—	2	1	no	—
133	C₂₃×#121	C₂³	1	2	yes	—
134	C₂₃×#121	C₂³	1	2	yes	—
135	C₂₃×#120	—	2	2	no	—
136	C₄×Q₈×C₂₃	—	2	2	no	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	2	no	—
139	C₄×Q₈×C₂₃	—	2	2	no	—
140	C₄×Q₈×C₂₃	—	2	2	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	—	2	1	no	—
145	C₄×Q₈×C₂₃	—	2	1	no	—
146	C₄×Q₈×C₂₃	—	2	1	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	2	no	—
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	1	no	—
157	C₄×D₄×C₂₃	—	2	1	no	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	—	2	1	no	—
160	C₄×D₄×C₂₃	C₂³	1	2	yes	—
161	C₄×D₄×C₂₃	C₂³	1	2	yes	—
162	C₂₃×#117	—	2	2	no	—
163	C₂₃×#117	—	2	2	no	—
164	C₂₃×#117	—	2	1	no	—
165	C₂₃×#117	—	2	1	no	—
166	C₂₃×#117	—	2	2	no	—
167	C₂₃×#117	—	2	2	no	—
168	C₂₃×#117	—	2	2	no	—
169	C₂₃×#117	C₂³	1	4	yes	—
170	C₂₃×#117	C₂³	1	2	yes	—
171	C₂₃×#117	C₂³	1	4	yes	—
172	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
173	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
174	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
175	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
179	C₂×C₄²×C₂₃	—	2	2	no	—
180	C₂×C₄²×C₂₃	—	2	2	no	—
181	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
182	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂₃×#107	C₂³	1	8	yes	—
194	C₂₃×#107	C₂³	1	8	yes	—
195	C₂₃×#106	C₂³	1	8	yes	—
196	C₂₃×#106	C₂³	1	8	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	8	yes	—
200	C₂₃×#103	C₂³	1	8	yes	—
201	C₂₃×#102	C₂³	1	8	yes	—
202	C₂₃×#102	C₂³	1	8	yes	—
203	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₂₃×#97	C₂³	1	4	yes	—
206	C₂₃×#97	C₂³	1	4	yes	—
207	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
208	#41×C₂₃	—	2	8	no	—
209	#41×C₂₃	—	4	4	no	—
210	#41×C₂₃	—	4	4	no	—
211	C₂×Q₈×C₂₃	—	2	1	no	—
212	C₂×Q₈×C₂₃	—	2	1	no	—
213	C₂×Q₈×C₂₃	—	2	2	no	—
214	C₂×Q₈×C₂₃	—	2	2	no	—
215	C₂×Q₈×C₂₃	—	2	2	no	—
216	C₂×Q₈×C₂₃	—	2	2	no	—
217	C₂×Q₈×C₂₃	—	4	4	no	—
218	C₂×Q₈×C₂₃	—	4	4	no	—
219	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
220	C₂×D₄×C₂₃	—	2	2	no	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	2	2	no	—
223	C₂×D₄×C₂₃	—	2	1	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	—	2	4	no	—
227	C₂²×C₄×C₂₃	—	2	2	no	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	2	2	no	—
230	C₂²×C₄×C₂₃	—	2	2	no	—
231	C₂²×C₄×C₂₃	—	2	2	no	—
232	C₂²×C₄×C₂₃	—	4	2	no	—
233	C₂²×C₄×C₂₃	—	4	2	no	—
234	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₂₃	—	2	8	no	—
253	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	4	no	—
258	C₄⋊C₄×C₂₃	—	2	2	no	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	2	no	—
261	C₄⋊C₄×C₂₃	—	2	2	no	—
262	C₄⋊C₄×C₂₃	—	2	2	no	—
263	C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
275	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	2	no	—
281	C₂²⋊C₄×C₂₃	—	2	2	no	—
282	C₂²⋊C₄×C₂₃	—	2	2	no	—
283	C₂²⋊C₄×C₂₃	—	2	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	2	no	—
289	C₄²×C₂₃	—	2	2	no	—
290	C₄²×C₂₃	—	2	2	no	—
291	C₄²×C₂₃	—	2	4	no	—
292	C₄²×C₂₃	—	2	2	no	—
293	C₄²×C₂₃	—	2	4	no	—
294	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
310	#60854	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₂₃	—	2	2	no	—
312	C₂³×C₂₃	—	2	2	no	—
313	C₂³×C₂₃	—	2	2	no	—
314	C₂³×C₂₃	—	4	1	no	—
315	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₂₃	—	2	4	no	—
319	Q₈×C₂₃	—	4	4	no	—
320	Q₈×C₂₃	—	4	4	no	—
321	Q₈×C₂₃	—	4	4	no	—
322	Q₈×C₂₃	—	4	2	no	—
323	Q₈×C₂₃	—	4	2	no	—
324	Q₈×C₂₃	—	4	4	no	—
325	D₄×C₂₃	—	2	4	no	—
326	D₄×C₂₃	—	4	2	no	—
327	D₄×C₂₃	—	4	2	no	—
328	D₄×C₂₃	—	4	4	no	—
329	D₄×C₂₃	—	4	4	no	—
330	D₄×C₂₃	—	4	4	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	4	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	4	no	—
354	C₂×C₄×C₂₃	—	4	4	no	—
355	C₂×C₄×C₂₃	—	4	4	no	—
356	C₂×C₄×C₂₃	—	4	4	no	—
357	C₂×C₄×C₂₃	—	4	4	no	—
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
370	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
371	C₈×C₂₃	—	2	8	no	—
372	#3444	C₂×C₂₃	1	1	yes	characteristic
373	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3240	C₂×C₂₃	1	4	yes	complemented
375	#3239	C₂×C₂₃	1	2	yes	complemented
376	#3238	C₂×C₂₃	1	2	yes	complemented
377	#3237	C₂×C₂₃	1	2	yes	complemented
378	#3236	C₂×C₂₃	1	2	yes	complemented
379	#3235	C₂×C₂₃	1	2	yes	complemented
380	#3234	C₂×C₂₃	1	2	yes	complemented
381	#3162	C₂×C₂₃	1	2	yes	complemented
382	#3135	C₂×C₂₃	1	2	yes	complemented
383	#3091	C₂×C₂₃	1	4	yes	complemented
384	#3076	C₂×C₂₃	1	4	yes	complemented
385	C₂×#432	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₂²×C₂₃	—	2	1	no	—
387	C₂²×C₂₃	—	2	1	no	—
388	C₂²×C₂₃	—	2	1	no	—
389	C₂²×C₂₃	—	2	1	no	—
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	1	no	—
392	C₂²×C₂₃	—	2	1	no	—
393	C₂²×C₂₃	—	4	4	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	#536	1	2	yes	—
398	C₂²×C₂₃	#575	1	2	yes	—
399	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₂₃	—	2	1	no	—
401	C₄×C₂₃	—	2	1	no	—
402	C₄×C₂₃	—	2	1	no	—
403	C₄×C₂₃	—	2	1	no	—
404	C₄×C₂₃	—	2	1	no	—
405	C₄×C₂₃	—	2	1	no	—
406	C₄×C₂₃	—	2	1	no	—
407	C₄×C₂₃	—	2	1	no	—
408	C₄×C₂₃	—	2	1	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	4	no	—
413	C₄×C₂₃	—	4	4	no	—
414	C₄×C₂₃	#536	1	2	yes	—
415	C₄×C₂₃	#575	1	2	yes	—
416	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
417	#533	—	2	1	no	—
418	#533	—	2	1	no	—
419	#533	—	2	1	no	—
420	#533	—	2	1	no	—
421	#533	C₂²×C₂₃	1	1	yes	characteristic
422	#533	C₂²×C₂₃	1	1	yes	characteristic
423	#533	C₂²×C₂₃	1	2	yes	—
424	#533	C₂²×C₂₃	1	2	yes	—
425	#533	C₂²×C₂₃	1	1	yes	characteristic
426	#533	C₂²×C₂₃	1	2	yes	—
427	#533	C₂²×C₂₃	1	2	yes	—
428	#532	C₂²×C₂₃	1	1	yes	characteristic
429	#532	C₂²×C₂₃	1	1	yes	characteristic
430	#532	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
433	#529	—	2	1	no	—
434	#529	—	2	1	no	—
435	#529	—	2	1	no	—
436	#529	—	2	1	no	—
437	#529	C₂²×C₂₃	1	2	yes	—
438	#529	C₂²×C₂₃	1	2	yes	—
439	C₂×#125	C₂²×C₂₃	1	2	yes	—
440	#525	—	2	1	no	—
441	#525	—	2	1	no	—
442	#525	C₂²×C₂₃	1	2	yes	—
443	C₂×C₂²⋊Q₈	—	2	1	no	—
444	C₂×C₂²⋊Q₈	—	2	1	no	—
445	C₄×#41	—	2	1	no	—
446	C₄×#41	—	2	1	no	—
447	C₄×#41	C₂²×C₂₃	1	2	yes	—
448	C₂×C₄×Q₈	—	2	1	no	—
449	C₂×C₄×Q₈	—	2	1	no	—
450	C₂×#117	C₂²×C₂₃	1	2	yes	—
451	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
452	#501	C₂²×C₂₃	1	4	yes	complemented
453	#501	C₂²×C₂₃	1	4	yes	complemented
454	#501	C₂²×C₂₃	1	4	yes	complemented
455	#501	C₂²×C₂₃	1	4	yes	complemented
456	#491	C₂²×C₂₃	1	4	yes	complemented
457	#490	C₂²×C₂₃	1	4	yes	complemented
458	#489	C₂²×C₂₃	1	4	yes	complemented
459	#489	C₂²×C₂₃	1	4	yes	complemented
460	#485	C₂²×C₂₃	1	8	yes	—
461	#484	C₂²×C₂₃	1	4	yes	—
462	#483	C₂²×C₂₃	1	4	yes	—
463	#482	C₂²×C₂₃	1	8	yes	—
464	#481	C₂²×C₂₃	1	4	yes	—
465	#480	C₂²×C₂₃	1	4	yes	—
466	#479	C₂²×C₂₃	1	8	yes	complemented
467	#478	C₂²×C₂₃	1	8	yes	complemented
468	#477	C₂²×C₂₃	1	4	yes	complemented
469	#476	C₂²×C₂₃	1	4	yes	complemented
470	#475	C₂²×C₂₃	1	4	yes	complemented
471	#474	C₂²×C₂₃	1	4	yes	complemented
472	#432	C₂²×C₂₃	1	2	yes	—
473	#432	C₂²×C₂₃	1	2	yes	—
474	#432	C₂²×C₂₃	1	2	yes	—
475	#432	C₂²×C₂₃	1	2	yes	—
476	#427	C₂²×C₂₃	1	8	yes	—
477	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
478	#416	C₂²×C₂₃	1	8	yes	—
479	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
480	C₂×#97	C₂²×C₂₃	1	2	yes	—
481	C₂×C₂₃	—	2	2	no	—
482	C₂×C₂₃	—	2	2	no	—
483	C₂×C₂₃	—	4	1	no	—
484	C₂×C₂₃	—	8	2	no	—
485	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
486	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
487	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
488	C₂×#41	—	2	1	no	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	C₂³×C₂₃	1	2	yes	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
494	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
506	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
508	#127	C₂³×C₂₃	1	1	yes	characteristic
509	#126	—	2	2	no	—
510	#126	—	2	2	no	—
511	#125	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	C₂³×C₂₃	1	4	yes	—
516	#125	C₂³×C₂₃	1	4	yes	—
517	#125	C₂³×C₂₃	1	2	yes	—
518	#124	—	2	1	no	—
519	#124	—	2	1	no	—
520	#124	C₂³×C₂₃	1	2	yes	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	#123	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
537	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
538	#121	—	2	1	no	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	C₂³×C₂₃	1	2	yes	—
543	#121	C₂³×C₂₃	1	2	yes	—
544	#120	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
558	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₂₃	1	2	yes	—
570	C₄×D₄	C₂³×C₂₃	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	1	no	—
574	#117	—	2	1	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	C₂³×C₂₃	1	4	yes	—
579	#117	C₂³×C₂₃	1	4	yes	—
580	#117	C₂³×C₂₃	1	2	yes	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₄²	—	2	2	no	—
589	C₂×C₄²	—	2	2	no	—
590	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
591	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
592	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
593	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
594	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
595	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
602	#107	C₂³×C₂₃	1	8	yes	—
603	#107	C₂³×C₂₃	1	8	yes	—
604	#106	C₂³×C₂₃	1	8	yes	—
605	#106	C₂³×C₂₃	1	8	yes	—
606	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
607	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
608	#103	C₂³×C₂₃	1	8	yes	—
609	#103	C₂³×C₂₃	1	8	yes	—
610	#102	C₂³×C₂₃	1	8	yes	—
611	#102	C₂³×C₂₃	1	8	yes	—
612	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
614	#97	C₂³×C₂₃	1	4	yes	—
615	#97	C₂³×C₂₃	1	4	yes	—
616	C₂₃	#60854	1	1	yes	characteristic, direct product factor, Sylow
617	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
618	#41	—	2	8	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	4	4	no	—
628	C₂×Q₈	—	4	4	no	—
629	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
662	C₂×C₈	—	2	8	no	—
663	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
706	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
708	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
709	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
717	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	1	no	—
724	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
725	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
726	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
727	Q₈	—	2	4	no	—
728	Q₈	—	4	4	no	—
729	Q₈	—	4	4	no	—
730	Q₈	—	4	4	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	4	2	no	—
733	Q₈	—	4	4	no	—
734	D₄	—	2	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
778	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
779	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
780	C₈	—	2	8	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	C₂₃×#536	1	2	yes	—
793	C₂²	C₂₃×#575	1	2	yes	—
794	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	4	no	—
809	C₄	C₂₃×#536	1	2	yes	—
810	C₄	C₂₃×#575	1	2	yes	—
811	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
817	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
818	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3240	C₂	semidirect
4. C₂₃×#3239	C₂	semidirect
5. C₂₃×#3238	C₂	semidirect
6. C₂₃×#3237	C₂	semidirect
7. C₂₃×#3236	C₂	semidirect
8. C₂₃×#3235	C₂	semidirect
9. C₂₃×#3234	C₂	semidirect
10. C₂₃×#3162	C₂	semidirect
11. C₂₃×#3135	C₂	semidirect
12. C₂₃×#3091	C₂	semidirect
13. C₂₃×#3076	C₂	semidirect
14. C₂×C₂₃×#432	C₂	semidirect
50. C₂₃×#501	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#501	C₂²	semidirect
53. C₂₃×#501	C₂²	semidirect
54. C₂₃×#491	C₂²	semidirect
55. C₂₃×#490	C₂²	semidirect
56. C₂₃×#489	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
64. C₂₃×#479	C₂²	semidirect
65. C₂₃×#478	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#476	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
310. #60854	C₂₃	direct (N × H)
373. C₂×#533	C₂×C₂₃	semidirect
374. #3240	C₂×C₂₃	semidirect
375. #3239	C₂×C₂₃	semidirect
376. #3238	C₂×C₂₃	semidirect
377. #3237	C₂×C₂₃	semidirect
378. #3236	C₂×C₂₃	semidirect
379. #3235	C₂×C₂₃	semidirect
380. #3234	C₂×C₂₃	semidirect
381. #3162	C₂×C₂₃	semidirect
382. #3135	C₂×C₂₃	semidirect
383. #3091	C₂×C₂₃	semidirect
384. #3076	C₂×C₂₃	semidirect
385. C₂×#432	C₂×C₂₃	semidirect
452. #501	C₂²×C₂₃	semidirect
453. #501	C₂²×C₂₃	semidirect
454. #501	C₂²×C₂₃	semidirect
455. #501	C₂²×C₂₃	semidirect
456. #491	C₂²×C₂₃	semidirect
457. #490	C₂²×C₂₃	semidirect
458. #489	C₂²×C₂₃	semidirect
459. #489	C₂²×C₂₃	semidirect
466. #479	C₂²×C₂₃	semidirect
467. #478	C₂²×C₂₃	semidirect
468. #477	C₂²×C₂₃	semidirect
469. #476	C₂²×C₂₃	semidirect
470. #475	C₂²×C₂₃	semidirect
471. #474	C₂²×C₂₃	semidirect
616. C₂₃	#60854	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×#3444	2
C₂×C₂₃×#533	2
C₂₃×#3240	2
C₂₃×#3239	2
C₂₃×#3238	2
C₂₃×#3237	2
C₂₃×#3236	2
C₂₃×#3235	2
C₂₃×#3234	2
C₂₃×#3162	2
C₂₃×#3135	2
C₂₃×#3091	2
C₂₃×#3076	2
C₂×C₂₃×#432	2
#60854	23

Subgroups — C23×#60854 #19208480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60854 #19208480