Subgroups — C₂₃×#62580 #19210206

Order 5888.

1790 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3319	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3311	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3235	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3219	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3135	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#559	—	2	1	no	—
19	C₂₃×#559	C₂²	1	2	yes	—
20	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#556	—	2	2	no	—
22	C₂₃×#556	—	2	1	no	—
23	C₂₃×#556	C₂²	1	2	yes	—
24	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#555	C₂²	1	2	yes	—
26	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#550	—	2	1	no	—
28	C₂₃×#550	C₂²	1	2	yes	—
29	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#548	—	2	1	no	—
31	C₂₃×#546	—	2	2	no	—
32	C₂₃×#546	C₂²	1	4	yes	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#542	—	2	2	no	—
35	C₂₃×#540	—	2	2	no	—
36	C₂₃×#535	—	2	1	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂₃×#533	C₂²	1	2	yes	complemented
40	C₂₃×#532	C₂²	1	2	yes	—
41	C₂₃×#532	C₂²	1	2	yes	—
42	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
43	C₂₃×#529	C₂²	1	1	yes	characteristic
44	C₂₃×#529	C₂²	1	2	yes	complemented
45	C₂₃×#519	—	2	1	no	—
46	C₂₃×#518	—	2	1	no	—
47	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#501	C₂²	1	2	yes	complemented
50	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#496	C₂²	1	2	yes	—
52	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#491	C₂²	1	2	yes	complemented
54	C₂₃×#490	C₂²	1	2	yes	—
55	C₂₃×#490	C₂²	1	2	yes	—
56	C₂₃×#490	C₂²	1	2	yes	—
57	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#489	C₂²	1	4	yes	complemented
59	C₂₃×#489	C₂²	1	4	yes	complemented
60	C₂₃×#486	C₂²	1	2	yes	—
61	C₂₃×#486	C₂²	1	2	yes	—
62	C₂₃×#485	C₂²	1	4	yes	—
63	C₂₃×#482	C₂²	1	4	yes	complemented
64	C₂₃×#482	C₂²	1	4	yes	complemented
65	C₂₃×#477	C₂²	1	2	yes	complemented
66	C₂₃×#476	C₂²	1	4	yes	complemented
67	C₂₃×#475	C₂²	1	2	yes	complemented
68	C₂₃×#474	C₂²	1	4	yes	complemented
69	C₂₃×#470	C₂²	1	2	yes	—
70	C₂₃×#468	C₂²	1	2	yes	—
71	C₂₃×#466	C₂²	1	4	yes	complemented
72	C₂₃×#465	C₂²	1	4	yes	complemented
73	C₂₃×#464	C₂²	1	4	yes	complemented
74	C₂₃×#463	C₂²	1	4	yes	complemented
75	C₂₃×#460	C₂²	1	2	yes	—
76	C₂₃×#459	C₂²	1	2	yes	—
77	C₂₃×#452	C₂²	1	4	yes	complemented
78	C₂₃×#450	C₂²	1	2	yes	—
79	C₂₃×#449	C₂²	1	4	yes	complemented
80	C₂₃×#447	C₂²	1	2	yes	—
81	C₂₃×#446	C₂²	1	2	yes	complemented
82	C₂₃×#442	C₂²	1	4	yes	complemented
83	C₂₃×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#435	C₂²	1	4	yes	—
87	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
88	C₂₃×#432	C₂²	1	1	yes	characteristic
89	C₂₃×#432	C₂²	1	2	yes	complemented
90	C₂₃×#418	C₂²	1	4	yes	—
91	C₂₃×#416	C₂²	1	4	yes	complemented
92	C₂₃×#416	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
97	C₂×#41×C₂₃	C₂³	1	4	yes	—
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×D₈×C₂₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	—	2	1	no	—
118	C₂₃×#127	—	2	1	no	—
119	C₂₃×#127	C₂³	1	2	yes	—
120	C₂₃×#127	C₂³	1	2	yes	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#126	—	2	1	no	—
125	C₂₃×#126	—	2	2	no	—
126	C₂₃×#125	—	2	1	no	—
127	C₂₃×#125	C₂³	1	1	yes	characteristic
128	C₂₃×#125	C₂³	1	2	yes	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	2	no	—
134	C₂₃×#124	—	2	2	no	—
135	C₂₃×#124	—	2	2	no	—
136	C₂₃×#124	C₂³	1	4	yes	—
137	C₂₃×#124	C₂³	1	1	yes	characteristic
138	C₂₃×#123	—	2	1	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	4	no	—
141	C₂₃×#123	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	1	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	1	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	4	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	C₂³	1	4	yes	—
160	C₂₃×#121	C₂³	1	1	yes	characteristic
161	C₂₃×#121	C₂³	1	2	yes	—
162	C₂₃×#120	—	2	4	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	—	2	2	no	—
165	C₄×Q₈×C₂₃	—	2	1	no	—
166	C₄×Q₈×C₂₃	—	2	1	no	—
167	C₄×Q₈×C₂₃	—	2	1	no	—
168	C₄×Q₈×C₂₃	—	2	2	no	—
169	C₄×Q₈×C₂₃	—	2	1	no	—
170	C₄×Q₈×C₂₃	—	2	2	no	—
171	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	2	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₂₃	D₄	1	2	yes	—
185	C₄×D₄×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₂₃	C₂³	1	4	yes	—
188	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₂₃	C₂³	1	2	yes	—
190	C₂₃×#117	—	2	1	no	—
191	C₂₃×#117	—	2	2	no	—
192	C₂₃×#117	—	2	1	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	—	2	2	no	—
195	C₂₃×#117	D₄	1	1	yes	characteristic
196	C₂₃×#117	D₄	1	2	yes	—
197	C₂₃×#117	C₂³	1	2	yes	—
198	C₂₃×#117	C₂³	1	2	yes	—
199	C₂₃×#117	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
201	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#107	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₂₃×#103	C₂³	1	2	yes	—
210	C₂₃×#103	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#102	C₂³	1	4	yes	—
215	C₂₃×#102	C₂³	1	4	yes	—
216	C₂₃×#102	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	2	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
222	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₂₃×#97	C₂³	1	1	yes	characteristic
224	C₂₃×#97	C₂³	1	2	yes	—
225	C₂₃×#97	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	2	no	—
229	#41×C₂₃	—	4	2	no	—
230	#41×C₂₃	—	4	4	no	—
231	#41×C₂₃	—	4	4	no	—
232	#41×C₂₃	—	8	4	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	2	no	—
237	C₂×Q₈×C₂₃	—	2	1	no	—
238	C₂×Q₈×C₂₃	—	4	4	no	—
239	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	—	8	2	no	—
254	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	4	no	—
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₂₃	—	4	2	no	—
269	SD₁₆×C₂₃	—	4	4	no	—
270	SD₁₆×C₂₃	—	4	2	no	—
271	D₈×C₂₃	—	4	4	no	—
272	M₁₆×C₂₃	—	4	2	no	—
273	C₂×C₈×C₂₃	—	4	4	no	—
274	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂×D₄	1	2	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	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	1	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	1	no	—
328	C₄²×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	2	yes	—
331	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	2	yes	—
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
335	#62580	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₂₃	—	2	1	no	—
337	C₂³×C₂₃	—	2	4	no	—
338	C₂³×C₂₃	—	4	4	no	—
339	C₂³×C₂₃	—	8	2	no	—
340	C₂³×C₂₃	—	8	2	no	—
341	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	2	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	2	no	—
349	Q₈×C₂₃	—	4	2	no	—
350	Q₈×C₂₃	—	8	2	no	—
351	Q₈×C₂₃	—	8	1	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	2	4	no	—
356	D₄×C₂₃	—	4	2	no	—
357	D₄×C₂₃	—	4	4	no	—
358	D₄×C₂₃	—	4	4	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	8	2	no	—
361	D₄×C₂₃	—	8	2	no	—
362	D₄×C₂₃	—	8	2	no	—
363	D₄×C₂₃	—	8	1	no	—
364	D₄×C₂₃	—	8	4	no	—
365	D₄×C₂₃	—	8	4	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	4	no	—
380	C₂×C₄×C₂₃	—	4	2	no	—
381	C₂×C₄×C₂₃	—	8	4	no	—
382	C₂×C₄×C₂₃	—	8	4	no	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
392	C₈×C₂₃	—	2	2	no	—
393	C₈×C₂₃	—	2	4	no	—
394	C₈×C₂₃	—	2	2	no	—
395	#3518	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#3375	C₂×C₂₃	1	2	yes	complemented
398	#3373	C₂×C₂₃	1	2	yes	complemented
399	#3319	C₂×C₂₃	1	4	yes	complemented
400	#3311	C₂×C₂₃	1	4	yes	complemented
401	#3305	C₂×C₂₃	1	2	yes	complemented
402	#3304	C₂×C₂₃	1	2	yes	complemented
403	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3235	C₂×C₂₃	1	2	yes	complemented
405	#3219	C₂×C₂₃	1	2	yes	complemented
406	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3180	C₂×C₂₃	1	2	yes	complemented
408	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#3135	C₂×C₂₃	1	2	yes	complemented
411	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	4	4	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	4	4	no	—
421	C₂²×C₂₃	—	4	1	no	—
422	C₂²×C₂₃	—	4	1	no	—
423	C₂²×C₂₃	—	4	4	no	—
424	C₂²×C₂₃	—	16	4	no	—
425	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₂₃	—	2	1	no	—
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	1	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	4	2	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	1	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	1	no	—
438	C₄×C₂₃	—	4	2	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₄×C₂₃	#575	1	2	yes	—
441	C₄×C₂₃	#585	1	2	yes	—
442	#559	—	2	1	no	—
443	#559	C₂²×C₂₃	1	2	yes	—
444	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#556	—	2	2	no	—
446	#556	—	2	1	no	—
447	#556	C₂²×C₂₃	1	2	yes	—
448	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#555	C₂²×C₂₃	1	2	yes	—
450	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#550	—	2	1	no	—
452	#550	C₂²×C₂₃	1	2	yes	—
453	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#548	—	2	1	no	—
455	#546	—	2	2	no	—
456	#546	C₂²×C₂₃	1	4	yes	—
457	#542	—	2	1	no	—
458	#542	—	2	2	no	—
459	#540	—	2	2	no	—
460	#535	—	2	1	no	—
461	#533	C₂²×C₂₃	1	1	yes	characteristic
462	#533	C₂²×C₂₃	1	1	yes	characteristic
463	#533	C₂²×C₂₃	1	2	yes	complemented
464	#532	C₂²×C₂₃	1	2	yes	—
465	#532	C₂²×C₂₃	1	2	yes	—
466	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
467	#529	C₂²×C₂₃	1	1	yes	characteristic
468	#529	C₂²×C₂₃	1	2	yes	complemented
469	#519	—	2	1	no	—
470	#518	—	2	1	no	—
471	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
472	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#501	C₂²×C₂₃	1	2	yes	complemented
474	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#496	C₂²×C₂₃	1	2	yes	—
476	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#491	C₂²×C₂₃	1	2	yes	complemented
478	#490	C₂²×C₂₃	1	2	yes	—
479	#490	C₂²×C₂₃	1	2	yes	—
480	#490	C₂²×C₂₃	1	2	yes	—
481	#489	C₂²×C₂₃	1	4	yes	complemented
482	#489	C₂²×C₂₃	1	4	yes	complemented
483	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#486	C₂²×C₂₃	1	2	yes	—
485	#486	C₂²×C₂₃	1	2	yes	—
486	#485	C₂²×C₂₃	1	4	yes	—
487	#482	C₂²×C₂₃	1	4	yes	complemented
488	#482	C₂²×C₂₃	1	4	yes	complemented
489	#477	C₂²×C₂₃	1	2	yes	complemented
490	#476	C₂²×C₂₃	1	4	yes	complemented
491	#475	C₂²×C₂₃	1	2	yes	complemented
492	#474	C₂²×C₂₃	1	4	yes	complemented
493	#470	C₂²×C₂₃	1	2	yes	—
494	#468	C₂²×C₂₃	1	2	yes	—
495	#466	C₂²×C₂₃	1	4	yes	complemented
496	#465	C₂²×C₂₃	1	4	yes	complemented
497	#464	C₂²×C₂₃	1	4	yes	complemented
498	#463	C₂²×C₂₃	1	4	yes	complemented
499	#460	C₂²×C₂₃	1	2	yes	—
500	#459	C₂²×C₂₃	1	2	yes	—
501	#452	C₂²×C₂₃	1	4	yes	complemented
502	#450	C₂²×C₂₃	1	2	yes	—
503	#449	C₂²×C₂₃	1	4	yes	complemented
504	#447	C₂²×C₂₃	1	2	yes	—
505	#446	C₂²×C₂₃	1	2	yes	complemented
506	#442	C₂²×C₂₃	1	4	yes	complemented
507	#440	C₂²×C₂₃	1	4	yes	complemented
508	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
509	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
510	#435	C₂²×C₂₃	1	4	yes	—
511	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
512	#432	C₂²×C₂₃	1	1	yes	characteristic
513	#432	C₂²×C₂₃	1	2	yes	complemented
514	#418	C₂²×C₂₃	1	4	yes	—
515	#416	C₂²×C₂₃	1	4	yes	complemented
516	#416	C₂²×C₂₃	1	4	yes	complemented
517	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
518	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
519	C₂×C₂₃	—	4	2	no	—
520	C₂×C₂₃	—	4	1	no	—
521	C₂×C₂₃	—	8	1	no	—
522	C₂×C₂₃	—	8	4	no	—
523	C₂×C₂₃	#3500	1	1	yes	characteristic
524	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
525	C₂×C₂₃	#3585	1	1	yes	characteristic
526	C₂×#41	—	2	2	no	—
527	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
528	C₂×#41	C₂³×C₂₃	1	4	yes	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
536	C₂×D₈	C₂³×C₂₃	1	4	yes	—
537	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
547	#127	—	2	2	no	—
548	#127	—	2	1	no	—
549	#127	—	2	1	no	—
550	#127	C₂³×C₂₃	1	2	yes	—
551	#127	C₂³×C₂₃	1	2	yes	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#126	—	2	1	no	—
556	#126	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	C₂³×C₂₃	1	1	yes	characteristic
559	#125	C₂³×C₂₃	1	2	yes	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	C₂³×C₂₃	1	1	yes	characteristic
568	#124	C₂³×C₂₃	1	4	yes	—
569	#123	—	2	1	no	—
570	#123	—	2	2	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#121	C₂³×C₂₃	1	1	yes	characteristic
591	#121	C₂³×C₂₃	1	2	yes	—
592	#121	C₂³×C₂₃	1	4	yes	—
593	#120	—	2	4	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	D₄×C₂₃	1	2	yes	—
615	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₂₃	1	2	yes	—
618	C₄×D₄	C₂³×C₂₃	1	4	yes	—
619	C₄×D₄	C₂³×C₂₃	1	2	yes	—
620	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	D₄×C₂₃	1	1	yes	characteristic
627	#117	D₄×C₂₃	1	2	yes	—
628	#117	C₂³×C₂₃	1	2	yes	—
629	#117	C₂³×C₂₃	1	2	yes	—
630	#117	C₂³×C₂₃	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
634	#107	C₂³×C₂₃	1	2	yes	—
635	#107	C₂³×C₂₃	1	4	yes	—
636	#106	C₂³×C₂₃	1	2	yes	—
637	#106	C₂³×C₂₃	1	4	yes	—
638	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
640	#103	C₂³×C₂₃	1	2	yes	—
641	#103	C₂³×C₂₃	1	2	yes	—
642	#103	C₂³×C₂₃	1	4	yes	—
643	#103	C₂³×C₂₃	1	4	yes	—
644	#103	C₂³×C₂₃	1	2	yes	—
645	#102	C₂³×C₂₃	1	4	yes	—
646	#102	C₂³×C₂₃	1	4	yes	—
647	#102	C₂³×C₂₃	1	4	yes	—
648	#102	C₂³×C₂₃	1	4	yes	—
649	#102	C₂³×C₂₃	1	4	yes	—
650	#102	C₂³×C₂₃	1	4	yes	—
651	#102	C₂³×C₂₃	1	2	yes	—
652	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
654	#97	C₂³×C₂₃	1	1	yes	characteristic
655	#97	C₂³×C₂₃	1	2	yes	—
656	#97	C₂³×C₂₃	1	4	yes	—
657	#97	C₂³×C₂₃	1	1	yes	characteristic
658	C₄×C₈	C₂³×C₂₃	1	2	yes	—
659	C₂₃	#62580	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁴	—	2	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	8	2	no	—
686	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
688	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
689	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
700	Q₁₆	—	4	2	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	2	no	—
703	D₈	—	4	4	no	—
704	M₁₆	—	4	2	no	—
705	C₂×C₈	—	4	4	no	—
706	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₂₃	1	2	yes	—
761	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₂₃	1	2	yes	—
763	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₂₃	1	2	yes	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	1	no	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	4	2	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	2	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	4	no	—
814	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	C₂₃×#575	1	2	yes	—
855	C₄	C₂₃×#585	1	2	yes	—
856	C₂	—	4	1	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	4	no	—
859	C₂	—	8	1	no	—
860	C₂	C₂₃×#3500	1	1	yes	characteristic
861	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
862	C₂	C₂₃×#3585	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3518	C₂	semidirect
2. C₂₃×#3508	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3373	C₂	semidirect
5. C₂₃×#3319	C₂	semidirect
6. C₂₃×#3311	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3304	C₂	semidirect
9. C₂₃×#3237	C₂	semidirect
10. C₂₃×#3235	C₂	semidirect
11. C₂₃×#3219	C₂	semidirect
12. C₂₃×#3217	C₂	semidirect
13. C₂₃×#3180	C₂	semidirect
14. C₂₃×#3172	C₂	semidirect
15. C₂₃×#3138	C₂	semidirect
16. C₂₃×#3135	C₂	semidirect
17. C₂₃×#2970	C₂	semidirect
20. Q₈²×C₂₃	C₂²	semidirect
24. C₂₃×#556	C₂²	semidirect
26. C₂₃×#555	C₂²	semidirect
29. D₄×Q₈×C₂₃	C₂²	semidirect
39. C₂₃×#533	C₂²	semidirect
44. C₂₃×#529	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#497	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
53. C₂₃×#491	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#489	C₂²	semidirect
59. C₂₃×#489	C₂²	semidirect
63. C₂₃×#482	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#477	C₂²	semidirect
66. C₂₃×#476	C₂²	semidirect
67. C₂₃×#475	C₂²	semidirect
68. C₂₃×#474	C₂²	semidirect
71. C₂₃×#466	C₂²	semidirect
72. C₂₃×#465	C₂²	semidirect
73. C₂₃×#464	C₂²	semidirect
74. C₂₃×#463	C₂²	semidirect
77. C₂₃×#452	C₂²	semidirect
79. C₂₃×#449	C₂²	semidirect
81. C₂₃×#446	C₂²	semidirect
82. C₂₃×#442	C₂²	semidirect
83. C₂₃×#440	C₂²	semidirect
84. C₄×Q₁₆×C₂₃	C₂²	semidirect
85. C₄×SD₁₆×C₂₃	C₂²	semidirect
87. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#432	C₂²	semidirect
91. C₂₃×#416	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
94. C₂×C₂₃×#97	C₂²	semidirect
335. #62580	C₂₃	direct (N × H)
395. #3518	C₂×C₂₃	semidirect
396. #3508	C₂×C₂₃	semidirect
397. #3375	C₂×C₂₃	semidirect
398. #3373	C₂×C₂₃	semidirect
399. #3319	C₂×C₂₃	semidirect
400. #3311	C₂×C₂₃	semidirect
401. #3305	C₂×C₂₃	semidirect
402. #3304	C₂×C₂₃	semidirect
403. #3237	C₂×C₂₃	semidirect
404. #3235	C₂×C₂₃	semidirect
405. #3219	C₂×C₂₃	semidirect
406. #3217	C₂×C₂₃	semidirect
407. #3180	C₂×C₂₃	semidirect
408. #3172	C₂×C₂₃	semidirect
409. #3138	C₂×C₂₃	semidirect
410. #3135	C₂×C₂₃	semidirect
411. #2970	C₂×C₂₃	semidirect
444. Q₈²	C₂²×C₂₃	semidirect
448. #556	C₂²×C₂₃	semidirect
450. #555	C₂²×C₂₃	semidirect
453. D₄×Q₈	C₂²×C₂₃	semidirect
463. #533	C₂²×C₂₃	semidirect
468. #529	C₂²×C₂₃	semidirect
472. #501	C₂²×C₂₃	semidirect
473. #501	C₂²×C₂₃	semidirect
474. #497	C₂²×C₂₃	semidirect
476. #491	C₂²×C₂₃	semidirect
477. #491	C₂²×C₂₃	semidirect
481. #489	C₂²×C₂₃	semidirect
482. #489	C₂²×C₂₃	semidirect
483. #489	C₂²×C₂₃	semidirect
487. #482	C₂²×C₂₃	semidirect
488. #482	C₂²×C₂₃	semidirect
489. #477	C₂²×C₂₃	semidirect
490. #476	C₂²×C₂₃	semidirect
491. #475	C₂²×C₂₃	semidirect
492. #474	C₂²×C₂₃	semidirect
495. #466	C₂²×C₂₃	semidirect
496. #465	C₂²×C₂₃	semidirect
497. #464	C₂²×C₂₃	semidirect
498. #463	C₂²×C₂₃	semidirect
501. #452	C₂²×C₂₃	semidirect
503. #449	C₂²×C₂₃	semidirect
505. #446	C₂²×C₂₃	semidirect
506. #442	C₂²×C₂₃	semidirect
507. #440	C₂²×C₂₃	semidirect
508. C₄×Q₁₆	C₂²×C₂₃	semidirect
509. C₄×SD₁₆	C₂²×C₂₃	semidirect
511. C₈×D₄	C₂²×C₂₃	semidirect
513. #432	C₂²×C₂₃	semidirect
515. #416	C₂²×C₂₃	semidirect
516. #416	C₂²×C₂₃	semidirect
518. C₂×#97	C₂²×C₂₃	semidirect
659. C₂₃	#62580	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×#3518	2
C₂₃×#3508	2
C₂₃×#3375	2
C₂₃×#3373	2
C₂₃×#3319	2
C₂₃×#3311	2
C₂₃×#3305	2
C₂₃×#3304	2
C₂₃×#3237	2
C₂₃×#3235	2
C₂₃×#3219	2
C₂₃×#3217	2
C₂₃×#3180	2
C₂₃×#3172	2
C₂₃×#3138	2
C₂₃×#3135	2
C₂₃×#2970	2
#62580	23

Subgroups — C23×#62580 #19210206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62580 #19210206