Subgroups — C₂₃×#60874 #19208500

Order 5888.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3243	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3242	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3239	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3236	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3230	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3164	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3083	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#556	—	2	1	no	—
19	C₂₃×#554	—	2	1	no	—
20	C₂₃×#552	—	2	2	no	—
21	C₂₃×#552	—	2	1	no	—
22	C₂₃×#552	—	2	1	no	—
23	C₂₃×#551	—	2	2	no	—
24	C₂₃×#544	—	2	2	no	—
25	C₂₃×#544	—	2	1	no	—
26	C₂₃×#544	—	2	1	no	—
27	C₂₃×#544	C₂²	1	4	yes	—
28	C₂₃×#544	C₂²	1	2	yes	—
29	C₂₃×#544	C₂²	1	2	yes	—
30	C₂₃×#544	C₂²	1	1	yes	characteristic
31	C₂₃×#542	C₂²	1	2	yes	—
32	C₂₃×#541	C₂²	1	2	yes	—
33	C₂₃×#536	C₂²	1	1	yes	characteristic
34	C₂₃×#533	C₂²	1	2	yes	—
35	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂×C₂₃×#125	—	2	1	no	—
39	C₂×C₂₃×#125	C₂²	1	2	yes	—
40	C₂₃×#525	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂₃×#520	C₂²	1	1	yes	characteristic
44	C₂₃×#519	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	4	yes	complemented
49	C₂₃×#501	C₂²	1	4	yes	complemented
50	C₂₃×#500	C₂²	1	4	yes	complemented
51	C₂₃×#499	C₂²	1	4	yes	complemented
52	C₂₃×#491	C₂²	1	4	yes	complemented
53	C₂₃×#489	C₂²	1	4	yes	complemented
54	C₂₃×#488	C₂²	1	4	yes	complemented
55	C₂₃×#487	C₂²	1	4	yes	complemented
56	C₂₃×#485	C₂²	1	2	yes	—
57	C₂₃×#485	C₂²	1	4	yes	—
58	C₂₃×#484	C₂²	1	1	yes	characteristic
59	C₂₃×#484	C₂²	1	2	yes	—
60	C₂₃×#484	C₂²	1	2	yes	—
61	C₂₃×#484	C₂²	1	2	yes	—
62	C₂₃×#484	C₂²	1	2	yes	—
63	C₂₃×#484	C₂²	1	4	yes	—
64	C₂₃×#483	C₂²	1	2	yes	—
65	C₂₃×#483	C₂²	1	1	yes	characteristic
66	C₂₃×#483	C₂²	1	2	yes	—
67	C₂₃×#482	C₂²	1	2	yes	—
68	C₂₃×#481	C₂²	1	2	yes	—
69	C₂₃×#481	C₂²	1	1	yes	characteristic
70	C₂₃×#480	C₂²	1	1	yes	characteristic
71	C₂₃×#480	C₂²	1	2	yes	—
72	C₂₃×#479	C₂²	1	4	yes	complemented
73	C₂₃×#479	C₂²	1	4	yes	complemented
74	C₂₃×#479	C₂²	1	4	yes	complemented
75	C₂₃×#478	C₂²	1	4	yes	complemented
76	C₂₃×#477	C₂²	1	4	yes	complemented
77	C₂₃×#477	C₂²	1	4	yes	complemented
78	C₂₃×#475	C₂²	1	4	yes	complemented
79	C₂₃×#474	C₂²	1	4	yes	complemented
80	C₂₃×#433	C₂²	1	4	yes	—
81	C₂₃×#432	C₂²	1	2	yes	—
82	C₂₃×#431	C₂²	1	2	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	2	yes	—
85	C₂₃×#427	C₂²	1	2	yes	—
86	C₂×C₂₃×#107	C₂²	1	2	yes	—
87	C₂₃×#424	C₂²	1	2	yes	—
88	C₂₃×#419	C₂²	1	2	yes	—
89	C₂₃×#417	C₂²	1	2	yes	—
90	C₂₃×#416	C₂²	1	2	yes	—
91	C₂×C₂₃×#103	C₂²	1	2	yes	—
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	2	no	—
97	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	—	2	1	no	—
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂₃×C₄⋊Q₈	—	2	1	no	—
103	C₂₃×C₄⋊Q₈	—	2	2	no	—
104	C₂₃×C₄⋊Q₈	—	2	4	no	—
105	C₂₃×C₄⋊Q₈	—	2	2	no	—
106	C₂₃×C₄⋊Q₈	—	2	2	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₂₃×#126	—	2	2	no	—
113	C₂₃×#126	—	2	2	no	—
114	C₂₃×#126	—	2	2	no	—
115	C₂₃×#126	—	2	2	no	—
116	C₂₃×#125	—	2	2	no	—
117	C₂₃×#125	—	2	1	no	—
118	C₂₃×#125	—	2	2	no	—
119	C₂₃×#125	—	2	2	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	—	2	4	no	—
122	C₂₃×#125	—	2	2	no	—
123	C₂₃×#125	—	2	2	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	C₂³	1	4	yes	—
126	C₂₃×#125	C₂³	1	4	yes	—
127	C₂₃×#125	C₂³	1	2	yes	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	C₂³	1	2	yes	—
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	1	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	1	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	4	no	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
146	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₂₃×#121	C₂³	1	1	yes	characteristic
150	C₂₃×#121	C₂³	1	1	yes	characteristic
151	C₂₃×#120	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	—	2	1	no	—
154	C₄×Q₈×C₂₃	—	2	2	no	—
155	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	1	no	—
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	C₂³	1	2	yes	—
163	C₂₃×#117	—	2	2	no	—
164	C₂₃×#117	—	2	1	no	—
165	C₂₃×#117	—	2	1	no	—
166	C₂₃×#117	—	2	1	no	—
167	C₂₃×#117	—	2	2	no	—
168	C₂₃×#117	—	2	2	no	—
169	C₂₃×#117	D₄	1	1	yes	characteristic
170	C₂₃×#117	D₄	1	2	yes	—
171	C₂₃×#117	D₄	1	1	yes	characteristic
172	C₂₃×#117	C₂³	1	2	yes	—
173	C₂₃×#117	C₂³	1	1	yes	characteristic
174	C₂₃×#117	C₂³	1	2	yes	—
175	C₂₃×#117	C₂³	1	1	yes	characteristic
176	C₂₃×#117	C₂³	1	1	yes	characteristic
177	C₂₃×#117	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
183	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
184	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
197	C₂×C₄²×C₂₃	—	2	1	no	—
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂₃×#107	C₂³	1	4	yes	—
200	C₂₃×#107	C₂³	1	4	yes	—
201	C₂₃×#107	C₂³	1	2	yes	—
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	2	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₂₃×#103	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₂₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₂₃	C₂³	1	4	yes	—
228	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
229	#41×C₂₃	—	2	4	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	—	2	2	no	—
232	C₂×Q₈×C₂₃	—	2	4	no	—
233	C₂×Q₈×C₂₃	—	2	4	no	—
234	C₂×Q₈×C₂₃	—	2	4	no	—
235	C₂×Q₈×C₂₃	—	8	4	no	—
236	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₂₃	—	2	1	no	—
239	C₂×D₄×C₂₃	—	2	1	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	—	2	4	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	1	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	1	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	1	no	—
251	C₂²×C₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	8	2	no	—
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	M₁₆×C₂₃	—	2	4	no	—
262	C₂×C₈×C₂₃	—	2	4	no	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	1	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	4	no	—
274	C₄⋊C₄×C₂₃	—	2	4	no	—
275	C₄⋊C₄×C₂₃	—	2	4	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	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	2	no	—
290	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂²⋊C₄×C₂₃	—	2	1	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	2	no	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	1	no	—
324	C₄²×C₂₃	C₂×D₄	1	2	yes	—
325	C₄²×C₂₃	C₂×D₄	1	2	yes	—
326	C₄²×C₂₃	C₂⁴	1	2	yes	—
327	C₄²×C₂₃	C₂⁴	1	2	yes	—
328	#60874	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	1	no	—
332	C₂³×C₂₃	—	4	1	no	—
333	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₂₃	—	2	4	no	—
337	Q₈×C₂₃	—	2	2	no	—
338	Q₈×C₂₃	—	4	2	no	—
339	Q₈×C₂₃	—	8	2	no	—
340	Q₈×C₂₃	—	8	4	no	—
341	Q₈×C₂₃	—	8	4	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	4	2	no	—
344	D₄×C₂₃	—	4	2	no	—
345	D₄×C₂₃	—	8	1	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	4	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	4	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	4	no	—
362	C₂×C₄×C₂₃	—	4	2	no	—
363	C₂×C₄×C₂₃	—	4	2	no	—
364	C₂×C₄×C₂₃	—	4	2	no	—
365	C₂×C₄×C₂₃	—	4	2	no	—
366	C₂×C₄×C₂₃	—	8	2	no	—
367	C₂×C₄×C₂₃	—	8	1	no	—
368	C₂×C₄×C₂₃	—	8	2	no	—
369	C₂×C₄×C₂₃	—	8	2	no	—
370	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
378	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
379	C₈×C₂₃	—	2	2	no	—
380	C₈×C₂₃	—	2	2	no	—
381	C₈×C₂₃	—	2	4	no	—
382	#3495	C₂×C₂₃	1	1	yes	characteristic
383	C₂×#544	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#3243	C₂×C₂₃	1	4	yes	complemented
385	#3242	C₂×C₂₃	1	4	yes	complemented
386	#3239	C₂×C₂₃	1	2	yes	complemented
387	#3236	C₂×C₂₃	1	2	yes	complemented
388	#3232	C₂×C₂₃	1	2	yes	complemented
389	#3230	C₂×C₂₃	1	2	yes	complemented
390	#3164	C₂×C₂₃	1	2	yes	complemented
391	#3137	C₂×C₂₃	1	2	yes	complemented
392	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#3092	C₂×C₂₃	1	1	yes	characteristic
394	#3091	C₂×C₂₃	1	1	yes	characteristic
395	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3083	C₂×C₂₃	1	2	yes	complemented
397	#3082	C₂×C₂₃	1	2	yes	complemented
398	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
399	C₂²×C₂₃	—	2	1	no	—
400	C₂²×C₂₃	—	2	1	no	—
401	C₂²×C₂₃	—	2	1	no	—
402	C₂²×C₂₃	—	2	1	no	—
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	1	no	—
406	C₂²×C₂₃	—	4	4	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	1	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	#536	1	2	yes	—
411	C₂²×C₂₃	#578	1	2	yes	—
412	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₂₃	—	2	2	no	—
414	C₄×C₂₃	—	2	2	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	2	no	—
418	C₄×C₂₃	—	2	2	no	—
419	C₄×C₂₃	—	4	4	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	1	no	—
423	C₄×C₂₃	—	4	1	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	1	no	—
427	C₄×C₂₃	#536	1	2	yes	—
428	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
429	#556	—	2	1	no	—
430	#554	—	2	1	no	—
431	#552	—	2	2	no	—
432	#552	—	2	1	no	—
433	#552	—	2	1	no	—
434	#551	—	2	2	no	—
435	#544	—	2	2	no	—
436	#544	—	2	1	no	—
437	#544	—	2	1	no	—
438	#544	C₂²×C₂₃	1	2	yes	—
439	#544	C₂²×C₂₃	1	2	yes	—
440	#544	C₂²×C₂₃	1	1	yes	characteristic
441	#544	C₂²×C₂₃	1	4	yes	—
442	#542	C₂²×C₂₃	1	2	yes	—
443	#541	C₂²×C₂₃	1	2	yes	—
444	#536	C₂²×C₂₃	1	1	yes	characteristic
445	#533	C₂²×C₂₃	1	2	yes	—
446	C₂×C₄⋊Q₈	—	2	1	no	—
447	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
448	#529	C₂²×C₂₃	1	2	yes	—
449	C₂×#125	—	2	1	no	—
450	C₂×#125	C₂²×C₂₃	1	2	yes	—
451	#525	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₂²⋊Q₈	—	2	2	no	—
453	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
454	#520	C₂²×C₂₃	1	1	yes	characteristic
455	#519	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
459	#501	C₂²×C₂₃	1	4	yes	complemented
460	#501	C₂²×C₂₃	1	4	yes	complemented
461	#500	C₂²×C₂₃	1	4	yes	complemented
462	#499	C₂²×C₂₃	1	4	yes	complemented
463	#491	C₂²×C₂₃	1	4	yes	complemented
464	#489	C₂²×C₂₃	1	4	yes	complemented
465	#488	C₂²×C₂₃	1	4	yes	complemented
466	#487	C₂²×C₂₃	1	4	yes	complemented
467	#485	C₂²×C₂₃	1	2	yes	—
468	#485	C₂²×C₂₃	1	4	yes	—
469	#484	C₂²×C₂₃	1	2	yes	—
470	#484	C₂²×C₂₃	1	2	yes	—
471	#484	C₂²×C₂₃	1	4	yes	—
472	#484	C₂²×C₂₃	1	1	yes	characteristic
473	#484	C₂²×C₂₃	1	2	yes	—
474	#484	C₂²×C₂₃	1	2	yes	—
475	#483	C₂²×C₂₃	1	1	yes	characteristic
476	#483	C₂²×C₂₃	1	2	yes	—
477	#483	C₂²×C₂₃	1	2	yes	—
478	#482	C₂²×C₂₃	1	2	yes	—
479	#481	C₂²×C₂₃	1	1	yes	characteristic
480	#481	C₂²×C₂₃	1	2	yes	—
481	#480	C₂²×C₂₃	1	1	yes	characteristic
482	#480	C₂²×C₂₃	1	2	yes	—
483	#479	C₂²×C₂₃	1	4	yes	complemented
484	#479	C₂²×C₂₃	1	4	yes	complemented
485	#479	C₂²×C₂₃	1	4	yes	complemented
486	#478	C₂²×C₂₃	1	4	yes	complemented
487	#477	C₂²×C₂₃	1	4	yes	complemented
488	#477	C₂²×C₂₃	1	4	yes	complemented
489	#475	C₂²×C₂₃	1	4	yes	complemented
490	#474	C₂²×C₂₃	1	4	yes	complemented
491	#433	C₂²×C₂₃	1	4	yes	—
492	#432	C₂²×C₂₃	1	2	yes	—
493	#431	C₂²×C₂₃	1	2	yes	—
494	#428	C₂²×C₂₃	1	2	yes	—
495	#428	C₂²×C₂₃	1	2	yes	—
496	#427	C₂²×C₂₃	1	2	yes	—
497	C₂×#107	C₂²×C₂₃	1	2	yes	—
498	#424	C₂²×C₂₃	1	2	yes	—
499	#419	C₂²×C₂₃	1	2	yes	—
500	#417	C₂²×C₂₃	1	2	yes	—
501	#416	C₂²×C₂₃	1	2	yes	—
502	C₂×#103	C₂²×C₂₃	1	2	yes	—
503	#407	C₂²×C₂₃	1	1	yes	characteristic
504	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
505	#405	C₂²×C₂₃	1	2	yes	—
506	C₂×C₂₃	—	2	2	no	—
507	C₂×C₂₃	—	2	2	no	—
508	C₂×C₂₃	—	4	1	no	—
509	C₂×C₂₃	—	8	1	no	—
510	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
511	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
512	C₂×C₂₃	#3585	1	1	yes	characteristic
513	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
514	C₂²×Q₈	—	2	2	no	—
515	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
519	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
520	C₄⋊Q₈	—	2	2	no	—
521	C₄⋊Q₈	—	2	4	no	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
528	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
529	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
530	#126	—	2	2	no	—
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	4	no	—
537	#125	—	2	2	no	—
538	#125	—	2	2	no	—
539	#125	—	2	1	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	C₂³×C₂₃	1	4	yes	—
544	#125	C₂³×C₂₃	1	4	yes	—
545	#125	C₂³×C₂₃	1	2	yes	—
546	#124	—	2	2	no	—
547	#124	C₂³×C₂₃	1	2	yes	—
548	#123	—	2	1	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
566	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
567	#121	C₂³×C₂₃	1	1	yes	characteristic
568	#121	C₂³×C₂₃	1	1	yes	characteristic
569	#120	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
574	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
575	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	C₂³×C₂₃	1	2	yes	—
581	#117	—	2	1	no	—
582	#117	—	2	1	no	—
583	#117	—	2	2	no	—
584	#117	—	2	1	no	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	D₄×C₂₃	1	1	yes	characteristic
588	#117	D₄×C₂₃	1	2	yes	—
589	#117	D₄×C₂₃	1	1	yes	characteristic
590	#117	C₂³×C₂₃	1	2	yes	—
591	#117	C₂³×C₂₃	1	2	yes	—
592	#117	C₂³×C₂₃	1	1	yes	characteristic
593	#117	C₂³×C₂₃	1	1	yes	characteristic
594	#117	C₂³×C₂₃	1	1	yes	characteristic
595	#117	C₂³×C₂₃	1	2	yes	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
615	C₂×C₄²	—	2	1	no	—
616	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
617	#107	C₂³×C₂₃	1	4	yes	—
618	#107	C₂³×C₂₃	1	4	yes	—
619	#107	C₂³×C₂₃	1	2	yes	—
620	#107	C₂³×C₂₃	1	2	yes	—
621	#107	C₂³×C₂₃	1	4	yes	—
622	#107	C₂³×C₂₃	1	4	yes	—
623	#106	C₂³×C₂₃	1	2	yes	—
624	#106	C₂³×C₂₃	1	2	yes	—
625	#106	C₂³×C₂₃	1	4	yes	—
626	#106	C₂³×C₂₃	1	4	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
629	#103	C₂³×C₂₃	1	4	yes	—
630	#103	C₂³×C₂₃	1	4	yes	—
631	#103	C₂³×C₂₃	1	2	yes	—
632	#103	C₂³×C₂₃	1	2	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#103	C₂³×C₂₃	1	4	yes	—
635	#103	C₂³×C₂₃	1	4	yes	—
636	#102	C₂³×C₂₃	1	2	yes	—
637	#102	C₂³×C₂₃	1	2	yes	—
638	#102	C₂³×C₂₃	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
640	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
644	#97	C₂³×C₂₃	1	4	yes	—
645	C₄×C₈	C₂³×C₂₃	1	4	yes	—
646	C₂₃	#60874	1	1	yes	characteristic, direct product factor, Sylow
647	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
648	#41	—	2	4	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	8	4	no	—
655	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	8	2	no	—
672	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
680	M₁₆	—	2	4	no	—
681	C₂×C₈	—	2	4	no	—
682	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
683	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
684	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
710	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	1	no	—
743	C₄²	C₂×D₄×C₂₃	1	2	yes	—
744	C₄²	C₂×D₄×C₂₃	1	2	yes	—
745	C₄²	C₂⁴×C₂₃	1	2	yes	—
746	C₄²	C₂⁴×C₂₃	1	2	yes	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
752	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
753	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	8	4	no	—
758	Q₈	—	8	4	no	—
759	Q₈	—	8	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	1	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
795	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
796	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	C₂₃×#536	1	2	yes	—
812	C₂²	C₂₃×#578	1	2	yes	—
813	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	C₂₃×#536	1	2	yes	—
829	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
835	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
836	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×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#544	C₂	semidirect
3. C₂₃×#3243	C₂	semidirect
4. C₂₃×#3242	C₂	semidirect
5. C₂₃×#3239	C₂	semidirect
6. C₂₃×#3236	C₂	semidirect
7. C₂₃×#3232	C₂	semidirect
8. C₂₃×#3230	C₂	semidirect
9. C₂₃×#3164	C₂	semidirect
10. C₂₃×#3137	C₂	semidirect
11. C₂₃×#3095	C₂	semidirect
14. C₂×C₂₃×#484	C₂	semidirect
15. C₂₃×#3083	C₂	semidirect
16. C₂₃×#3082	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#500	C₂²	semidirect
51. C₂₃×#499	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
53. C₂₃×#489	C₂²	semidirect
54. C₂₃×#488	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
72. C₂₃×#479	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#477	C₂²	semidirect
78. C₂₃×#475	C₂²	semidirect
79. C₂₃×#474	C₂²	semidirect
328. #60874	C₂₃	direct (N × H)
383. C₂×#544	C₂×C₂₃	semidirect
384. #3243	C₂×C₂₃	semidirect
385. #3242	C₂×C₂₃	semidirect
386. #3239	C₂×C₂₃	semidirect
387. #3236	C₂×C₂₃	semidirect
388. #3232	C₂×C₂₃	semidirect
389. #3230	C₂×C₂₃	semidirect
390. #3164	C₂×C₂₃	semidirect
391. #3137	C₂×C₂₃	semidirect
392. #3095	C₂×C₂₃	semidirect
395. C₂×#484	C₂×C₂₃	semidirect
396. #3083	C₂×C₂₃	semidirect
397. #3082	C₂×C₂₃	semidirect
398. #2924	C₂×C₂₃	semidirect
459. #501	C₂²×C₂₃	semidirect
460. #501	C₂²×C₂₃	semidirect
461. #500	C₂²×C₂₃	semidirect
462. #499	C₂²×C₂₃	semidirect
463. #491	C₂²×C₂₃	semidirect
464. #489	C₂²×C₂₃	semidirect
465. #488	C₂²×C₂₃	semidirect
466. #487	C₂²×C₂₃	semidirect
483. #479	C₂²×C₂₃	semidirect
484. #479	C₂²×C₂₃	semidirect
485. #479	C₂²×C₂₃	semidirect
486. #478	C₂²×C₂₃	semidirect
487. #477	C₂²×C₂₃	semidirect
488. #477	C₂²×C₂₃	semidirect
489. #475	C₂²×C₂₃	semidirect
490. #474	C₂²×C₂₃	semidirect
646. C₂₃	#60874	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×#3495	2
C₂×C₂₃×#544	2
C₂₃×#3243	2
C₂₃×#3242	2
C₂₃×#3239	2
C₂₃×#3236	2
C₂₃×#3232	2
C₂₃×#3230	2
C₂₃×#3164	2
C₂₃×#3137	2
C₂₃×#3095	2
C₂₃×#3092	2
C₂₃×#3091	2
C₂×C₂₃×#484	2
C₂₃×#3083	2
C₂₃×#3082	2
C₂₃×#2924	2
#60874	23

Subgroups — C23×#60874 #19208500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60874 #19208500