Subgroups — C₂₃×#60885 #19208511

Order 5888.

1682 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3243	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3240	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3240	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3239	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3097	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3096	C₂	1	2	yes	maximal
15	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3081	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#559	—	2	1	no	—
19	C₂₃×#559	—	2	1	no	—
20	Q₈²×C₂₃	—	2	1	no	—
21	C₂₃×#557	—	2	1	no	—
22	C₂₃×#556	—	2	1	no	—
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#554	—	2	2	no	—
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#551	—	2	2	no	—
27	C₂₃×#551	—	2	2	no	—
28	D₄×Q₈×C₂₃	—	2	2	no	—
29	D₄×Q₈×C₂₃	—	2	1	no	—
30	C₂₃×#544	C₂²	1	2	yes	—
31	C₂₃×#544	C₂²	1	4	yes	complemented
32	C₂₃×#542	C₂²	1	2	yes	—
33	C₂₃×#542	C₂²	1	2	yes	—
34	C₂₃×#536	C₂²	1	1	yes	characteristic
35	C₂₃×#535	C₂²	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#533	C₂²	1	2	yes	complemented
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂₃×#529	C₂²	1	2	yes	—
42	C₂₃×#529	C₂²	1	2	yes	—
43	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
44	C₂₃×#520	C₂²	1	2	yes	—
45	C₂₃×#519	C₂²	1	1	yes	characteristic
46	C₂₃×#518	C₂²	1	1	yes	characteristic
47	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#501	C₂²	1	2	yes	complemented
50	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#501	C₂²	1	2	yes	complemented
55	C₂₃×#501	C₂²	1	2	yes	complemented
56	C₂₃×#500	C₂²	1	2	yes	complemented
57	C₂₃×#498	C₂²	1	2	yes	complemented
58	C₂₃×#489	C₂²	1	2	yes	—
59	C₂₃×#489	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	2	yes	—
61	C₂₃×#489	C₂²	1	2	yes	—
62	C₂₃×#489	C₂²	1	4	yes	—
63	C₂₃×#488	C₂²	1	4	yes	—
64	C₂₃×#485	C₂²	1	4	yes	complemented
65	C₂₃×#485	C₂²	1	4	yes	complemented
66	C₂₃×#484	C₂²	1	4	yes	complemented
67	C₂₃×#483	C₂²	1	4	yes	complemented
68	C₂₃×#482	C₂²	1	4	yes	—
69	C₂₃×#482	C₂²	1	4	yes	—
70	C₂₃×#481	C₂²	1	4	yes	—
71	C₂₃×#480	C₂²	1	4	yes	—
72	C₂₃×#479	C₂²	1	4	yes	complemented
73	C₂₃×#479	C₂²	1	4	yes	complemented
74	C₂₃×#478	C₂²	1	4	yes	—
75	C₂₃×#478	C₂²	1	4	yes	—
76	C₂₃×#477	C₂²	1	4	yes	complemented
77	C₂₃×#476	C₂²	1	4	yes	—
78	C₂₃×#475	C₂²	1	4	yes	complemented
79	C₂₃×#474	C₂²	1	4	yes	—
80	C₂₃×#433	C₂²	1	4	yes	complemented
81	C₂₃×#432	C₂²	1	2	yes	complemented
82	C₂₃×#432	C₂²	1	2	yes	complemented
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	2	yes	—
85	C₂₃×#427	C₂²	1	2	yes	—
86	C₂₃×#427	C₂²	1	2	yes	—
87	C₂₃×#424	C₂²	1	2	yes	—
88	C₂₃×#419	C₂²	1	2	yes	—
89	C₂₃×#418	C₂²	1	2	yes	—
90	C₂×C₂₃×#103	C₂²	1	2	yes	—
91	C₂×C₂₃×#102	C₂²	1	2	yes	—
92	C₂₃×#408	C₂²	1	2	yes	—
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	1	no	—
97	C₂²×Q₈×C₂₃	—	2	2	no	—
98	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×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	1	no	—
106	C₂₃×C₄⋊Q₈	—	2	2	no	—
107	C₂₃×C₄⋊Q₈	—	2	1	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	1	no	—
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	4	no	—
123	C₂₃×#125	C₂³	1	4	yes	—
124	C₂₃×#125	C₂³	1	2	yes	—
125	C₂₃×#125	C₂³	1	1	yes	characteristic
126	C₂₃×#125	C₂³	1	1	yes	characteristic
127	C₂₃×#124	—	2	1	no	—
128	C₂₃×#124	—	2	1	no	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	—	2	2	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×#123	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	1	no	—
144	C₂₃×C₂²⋊Q₈	—	2	1	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	4	no	—
149	C₂₃×C₂²⋊Q₈	—	2	4	no	—
150	C₂₃×C₂²⋊Q₈	—	2	4	no	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	2	yes	—
154	C₂₃×#121	C₂³	1	2	yes	—
155	C₂₃×#120	—	2	2	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	—	2	2	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	—	2	1	no	—
165	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	—	2	4	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	1	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	D₄	1	2	yes	—
176	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₂₃	D₄	1	2	yes	—
178	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂₃×#117	C₂³	1	1	yes	characteristic
186	C₂₃×#117	C₂³	1	1	yes	characteristic
187	C₂₃×#117	C₂³	1	4	yes	—
188	C₂₃×#117	C₂³	1	1	yes	characteristic
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂₃×#107	C₂³	1	2	yes	—
200	C₂₃×#107	C₂³	1	2	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	2	yes	—
208	C₂₃×#106	C₂³	1	2	yes	—
209	C₂₃×#106	C₂³	1	4	yes	—
210	C₂₃×#106	C₂³	1	4	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₂₃×#97	C₂³	1	1	yes	characteristic
224	C₂₃×#97	C₂³	1	1	yes	characteristic
225	C₂₃×#97	C₂³	1	2	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	1	no	—
229	#41×C₂₃	—	2	4	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	2	1	no	—
236	C₂×Q₈×C₂₃	—	2	4	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	4	no	—
239	C₂×Q₈×C₂₃	—	8	2	no	—
240	C₂×Q₈×C₂₃	—	8	4	no	—
241	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	—	2	1	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	2	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
292	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
298	C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
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	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	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	4	no	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	2	1	no	—
321	C₄²×C₂₃	C₂×D₄	1	2	yes	—
322	C₄²×C₂₃	C₂×D₄	1	2	yes	—
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂⁴	1	2	yes	—
326	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#60885	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	4	2	no	—
331	C₂³×C₂₃	—	8	1	no	—
332	C₂³×C₂₃	—	8	1	no	—
333	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	2	4	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	Q₈×C₂₃	—	4	2	no	—
339	Q₈×C₂₃	—	4	4	no	—
340	Q₈×C₂₃	—	4	2	no	—
341	Q₈×C₂₃	—	8	1	no	—
342	Q₈×C₂₃	—	8	1	no	—
343	Q₈×C₂₃	—	8	4	no	—
344	Q₈×C₂₃	—	8	2	no	—
345	D₄×C₂₃	—	2	4	no	—
346	D₄×C₂₃	—	2	2	no	—
347	D₄×C₂₃	—	2	4	no	—
348	D₄×C₂₃	—	4	2	no	—
349	D₄×C₂₃	—	8	2	no	—
350	D₄×C₂₃	—	8	2	no	—
351	C₂×C₄×C₂₃	—	2	4	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	4	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	2	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	2	no	—
365	C₂×C₄×C₂₃	—	8	2	no	—
366	C₂×C₄×C₂₃	—	8	2	no	—
367	C₂×C₄×C₂₃	—	8	2	no	—
368	C₂×C₄×C₂₃	—	8	4	no	—
369	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	#3510	C₂×C₂₃	1	1	yes	characteristic
383	#3503	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#3244	C₂×C₂₃	1	4	yes	complemented
385	#3243	C₂×C₂₃	1	4	yes	complemented
386	#3240	C₂×C₂₃	1	2	yes	complemented
387	#3240	C₂×C₂₃	1	2	yes	complemented
388	#3239	C₂×C₂₃	1	2	yes	complemented
389	#3238	C₂×C₂₃	1	2	yes	complemented
390	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3162	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#3140	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#3097	C₂×C₂₃	1	2	yes	complemented
395	#3096	C₂×C₂₃	1	2	yes	—
396	#3082	C₂×C₂₃	1	2	yes	complemented
397	#3081	C₂×C₂₃	1	2	yes	complemented
398	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
399	C₂²×C₂₃	—	2	1	no	—
400	C₂²×C₂₃	—	2	1	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	2	2	no	—
403	C₂²×C₂₃	—	2	2	no	—
404	C₂²×C₂₃	—	4	2	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	16	2	no	—
408	C₂²×C₂₃	#536	1	2	yes	—
409	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₂₃	—	2	1	no	—
411	C₄×C₂₃	—	2	2	no	—
412	C₄×C₂₃	—	2	1	no	—
413	C₄×C₂₃	—	2	1	no	—
414	C₄×C₂₃	—	2	2	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	2	no	—
417	C₄×C₂₃	—	4	4	no	—
418	C₄×C₂₃	—	4	2	no	—
419	C₄×C₂₃	—	4	1	no	—
420	C₄×C₂₃	—	4	1	no	—
421	C₄×C₂₃	—	4	1	no	—
422	C₄×C₂₃	—	4	1	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	#536	1	2	yes	—
426	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
427	#559	—	2	1	no	—
428	#559	—	2	1	no	—
429	Q₈²	—	2	1	no	—
430	#557	—	2	1	no	—
431	#556	—	2	1	no	—
432	#556	—	2	1	no	—
433	#554	—	2	2	no	—
434	#554	—	2	1	no	—
435	#551	—	2	2	no	—
436	#551	—	2	2	no	—
437	D₄×Q₈	—	2	2	no	—
438	D₄×Q₈	—	2	1	no	—
439	#544	C₂²×C₂₃	1	2	yes	—
440	#544	C₂²×C₂₃	1	4	yes	complemented
441	#542	C₂²×C₂₃	1	2	yes	—
442	#542	C₂²×C₂₃	1	2	yes	—
443	#536	C₂²×C₂₃	1	1	yes	characteristic
444	#535	C₂²×C₂₃	1	1	yes	characteristic
445	#533	C₂²×C₂₃	1	1	yes	characteristic
446	#533	C₂²×C₂₃	1	1	yes	characteristic
447	#533	C₂²×C₂₃	1	2	yes	complemented
448	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
450	#529	C₂²×C₂₃	1	2	yes	—
451	#529	C₂²×C₂₃	1	2	yes	—
452	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
453	#520	C₂²×C₂₃	1	2	yes	—
454	#519	C₂²×C₂₃	1	1	yes	characteristic
455	#518	C₂²×C₂₃	1	1	yes	characteristic
456	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
457	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#501	C₂²×C₂₃	1	2	yes	complemented
462	#501	C₂²×C₂₃	1	2	yes	complemented
463	#501	C₂²×C₂₃	1	2	yes	complemented
464	#501	C₂²×C₂₃	1	2	yes	complemented
465	#500	C₂²×C₂₃	1	2	yes	complemented
466	#498	C₂²×C₂₃	1	2	yes	complemented
467	#489	C₂²×C₂₃	1	2	yes	—
468	#489	C₂²×C₂₃	1	2	yes	—
469	#489	C₂²×C₂₃	1	4	yes	—
470	#489	C₂²×C₂₃	1	2	yes	—
471	#489	C₂²×C₂₃	1	2	yes	—
472	#488	C₂²×C₂₃	1	4	yes	—
473	#485	C₂²×C₂₃	1	4	yes	complemented
474	#485	C₂²×C₂₃	1	4	yes	complemented
475	#484	C₂²×C₂₃	1	4	yes	complemented
476	#483	C₂²×C₂₃	1	4	yes	complemented
477	#482	C₂²×C₂₃	1	4	yes	—
478	#482	C₂²×C₂₃	1	4	yes	—
479	#481	C₂²×C₂₃	1	4	yes	—
480	#480	C₂²×C₂₃	1	4	yes	—
481	#479	C₂²×C₂₃	1	4	yes	complemented
482	#479	C₂²×C₂₃	1	4	yes	complemented
483	#478	C₂²×C₂₃	1	4	yes	—
484	#478	C₂²×C₂₃	1	4	yes	—
485	#477	C₂²×C₂₃	1	4	yes	complemented
486	#476	C₂²×C₂₃	1	4	yes	—
487	#475	C₂²×C₂₃	1	4	yes	complemented
488	#474	C₂²×C₂₃	1	4	yes	—
489	#433	C₂²×C₂₃	1	4	yes	complemented
490	#432	C₂²×C₂₃	1	2	yes	complemented
491	#432	C₂²×C₂₃	1	2	yes	complemented
492	#428	C₂²×C₂₃	1	2	yes	—
493	#428	C₂²×C₂₃	1	2	yes	—
494	#427	C₂²×C₂₃	1	2	yes	—
495	#427	C₂²×C₂₃	1	2	yes	—
496	#424	C₂²×C₂₃	1	2	yes	—
497	#419	C₂²×C₂₃	1	2	yes	—
498	#418	C₂²×C₂₃	1	2	yes	—
499	C₂×#103	C₂²×C₂₃	1	2	yes	—
500	C₂×#102	C₂²×C₂₃	1	2	yes	—
501	#408	C₂²×C₂₃	1	2	yes	—
502	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
503	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
504	C₂×C₂₃	—	2	2	no	—
505	C₂×C₂₃	—	4	2	no	—
506	C₂×C₂₃	—	8	2	no	—
507	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
508	C₂×C₂₃	#3585	1	1	yes	characteristic
509	C₂×C₂₃	#3586	1	1	yes	characteristic
510	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	—	2	2	no	—
513	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
516	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	—	2	4	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
528	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
531	#127	—	2	1	no	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	4	no	—
538	#125	C₂³×C₂₃	1	1	yes	characteristic
539	#125	C₂³×C₂₃	1	1	yes	characteristic
540	#125	C₂³×C₂₃	1	2	yes	—
541	#125	C₂³×C₂₃	1	4	yes	—
542	#124	—	2	1	no	—
543	#124	—	2	1	no	—
544	#124	—	2	2	no	—
545	#124	—	2	2	no	—
546	#124	—	2	1	no	—
547	#124	—	2	1	no	—
548	#124	C₂³×C₂₃	1	2	yes	—
549	#124	C₂³×C₂₃	1	2	yes	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
567	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
568	#121	C₂³×C₂₃	1	2	yes	—
569	#121	C₂³×C₂₃	1	2	yes	—
570	#120	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
581	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	D₄×C₂₃	1	2	yes	—
591	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
592	C₄×D₄	D₄×C₂₃	1	2	yes	—
593	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
594	C₄×D₄	C₂³×C₂₃	1	2	yes	—
595	C₄×D₄	C₂³×C₂₃	1	2	yes	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	—	2	2	no	—
599	#117	C₂³×C₂₃	1	1	yes	characteristic
600	#117	C₂³×C₂₃	1	1	yes	characteristic
601	#117	C₂³×C₂₃	1	2	yes	—
602	#117	C₂³×C₂₃	1	4	yes	—
603	#117	C₂³×C₂₃	1	1	yes	characteristic
604	#117	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	2	no	—
612	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
614	#107	C₂³×C₂₃	1	2	yes	—
615	#107	C₂³×C₂₃	1	2	yes	—
616	#107	C₂³×C₂₃	1	2	yes	—
617	#107	C₂³×C₂₃	1	2	yes	—
618	#107	C₂³×C₂₃	1	4	yes	—
619	#107	C₂³×C₂₃	1	4	yes	—
620	#106	C₂³×C₂₃	1	2	yes	—
621	#106	C₂³×C₂₃	1	2	yes	—
622	#106	C₂³×C₂₃	1	2	yes	—
623	#106	C₂³×C₂₃	1	2	yes	—
624	#106	C₂³×C₂₃	1	4	yes	—
625	#106	C₂³×C₂₃	1	4	yes	—
626	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
628	#103	C₂³×C₂₃	1	4	yes	—
629	#103	C₂³×C₂₃	1	4	yes	—
630	#103	C₂³×C₂₃	1	4	yes	—
631	#103	C₂³×C₂₃	1	4	yes	—
632	#102	C₂³×C₂₃	1	4	yes	—
633	#102	C₂³×C₂₃	1	4	yes	—
634	#102	C₂³×C₂₃	1	4	yes	—
635	#102	C₂³×C₂₃	1	4	yes	—
636	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
637	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
638	#97	C₂³×C₂₃	1	1	yes	characteristic
639	#97	C₂³×C₂₃	1	1	yes	characteristic
640	#97	C₂³×C₂₃	1	2	yes	—
641	#97	C₂³×C₂₃	1	2	yes	—
642	C₄×C₈	C₂³×C₂₃	1	2	yes	—
643	C₂₃	#60885	1	1	yes	characteristic, direct product factor, Sylow
644	C₂⁴	—	2	1	no	—
645	#41	—	2	4	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	8	2	no	—
656	C₂×Q₈	—	8	4	no	—
657	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
664	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
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	2	yes	—
675	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
677	M₁₆	—	2	4	no	—
678	C₂×C₈	—	2	4	no	—
679	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
680	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
681	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
706	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
708	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	1	no	—
737	C₄²	C₂×D₄×C₂₃	1	2	yes	—
738	C₄²	C₂×D₄×C₂₃	1	2	yes	—
739	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
741	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₄²	C₂⁴×C₂₃	1	2	yes	—
744	C₂³	—	2	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	8	1	no	—
747	C₂³	—	8	1	no	—
748	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
749	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	4	4	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	4	no	—
757	Q₈	—	8	2	no	—
758	Q₈	—	8	1	no	—
759	Q₈	—	8	1	no	—
760	D₄	—	2	4	no	—
761	D₄	—	2	4	no	—
762	D₄	—	2	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
793	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	2	2	no	—
796	C₈	—	2	4	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	16	2	no	—
806	C₂²	C₂₃×#536	1	2	yes	—
807	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
808	C₄	—	2	2	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	2	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	1	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	4	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	2	no	—
823	C₄	C₂₃×#536	1	2	yes	—
824	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
825	C₂	—	2	2	no	—
826	C₂	—	4	2	no	—
827	C₂	—	8	2	no	—
828	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
829	C₂	C₂₃×#3585	1	1	yes	characteristic
830	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3503	C₂	semidirect
3. C₂₃×#3244	C₂	semidirect
4. C₂₃×#3243	C₂	semidirect
5. C₂₃×#3240	C₂	semidirect
6. C₂₃×#3240	C₂	semidirect
7. C₂₃×#3239	C₂	semidirect
8. C₂₃×#3238	C₂	semidirect
9. C₂₃×#3165	C₂	semidirect
10. C₂₃×#3162	C₂	semidirect
11. C₂₃×#3140	C₂	semidirect
12. C₂×C₂₃×#489	C₂	semidirect
13. C₂₃×#3097	C₂	semidirect
15. C₂₃×#3082	C₂	semidirect
16. C₂₃×#3081	C₂	semidirect
17. C₂₃×#2923	C₂	semidirect
31. C₂₃×#544	C₂²	semidirect
38. C₂₃×#533	C₂²	semidirect
40. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#501	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#501	C₂²	semidirect
53. C₂₃×#501	C₂²	semidirect
54. C₂₃×#501	C₂²	semidirect
55. C₂₃×#501	C₂²	semidirect
56. C₂₃×#500	C₂²	semidirect
57. C₂₃×#498	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#484	C₂²	semidirect
67. C₂₃×#483	C₂²	semidirect
72. C₂₃×#479	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
78. C₂₃×#475	C₂²	semidirect
80. C₂₃×#433	C₂²	semidirect
81. C₂₃×#432	C₂²	semidirect
82. C₂₃×#432	C₂²	semidirect
328. #60885	C₂₃	direct (N × H)
383. #3503	C₂×C₂₃	semidirect
384. #3244	C₂×C₂₃	semidirect
385. #3243	C₂×C₂₃	semidirect
386. #3240	C₂×C₂₃	semidirect
387. #3240	C₂×C₂₃	semidirect
388. #3239	C₂×C₂₃	semidirect
389. #3238	C₂×C₂₃	semidirect
390. #3165	C₂×C₂₃	semidirect
391. #3162	C₂×C₂₃	semidirect
392. #3140	C₂×C₂₃	semidirect
393. C₂×#489	C₂×C₂₃	semidirect
394. #3097	C₂×C₂₃	semidirect
396. #3082	C₂×C₂₃	semidirect
397. #3081	C₂×C₂₃	semidirect
398. #2923	C₂×C₂₃	semidirect
440. #544	C₂²×C₂₃	semidirect
447. #533	C₂²×C₂₃	semidirect
449. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
457. #501	C₂²×C₂₃	semidirect
458. #501	C₂²×C₂₃	semidirect
459. #501	C₂²×C₂₃	semidirect
460. #501	C₂²×C₂₃	semidirect
461. #501	C₂²×C₂₃	semidirect
462. #501	C₂²×C₂₃	semidirect
463. #501	C₂²×C₂₃	semidirect
464. #501	C₂²×C₂₃	semidirect
465. #500	C₂²×C₂₃	semidirect
466. #498	C₂²×C₂₃	semidirect
473. #485	C₂²×C₂₃	semidirect
474. #485	C₂²×C₂₃	semidirect
475. #484	C₂²×C₂₃	semidirect
476. #483	C₂²×C₂₃	semidirect
481. #479	C₂²×C₂₃	semidirect
482. #479	C₂²×C₂₃	semidirect
485. #477	C₂²×C₂₃	semidirect
487. #475	C₂²×C₂₃	semidirect
489. #433	C₂²×C₂₃	semidirect
490. #432	C₂²×C₂₃	semidirect
491. #432	C₂²×C₂₃	semidirect
643. C₂₃	#60885	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×#3510	2
C₂₃×#3503	2
C₂₃×#3244	2
C₂₃×#3243	2
C₂₃×#3240	2
C₂₃×#3239	2
C₂₃×#3238	2
C₂₃×#3165	2
C₂₃×#3162	2
C₂₃×#3140	2
C₂×C₂₃×#489	2
C₂₃×#3097	2
C₂₃×#3096	2
C₂₃×#3082	2
C₂₃×#3081	2
C₂₃×#2923	2
#60885	23

Subgroups — C23×#60885 #19208511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60885 #19208511