Subgroups — C₂₃×#60727 #19208353

Order 5888.

1902 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3181	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3180	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3175	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3173	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3063	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2947	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₃×#131	C₂²	1	2	yes	—
21	C₂₃×#559	—	2	1	no	—
22	C₂₃×#559	—	2	1	no	—
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#556	—	2	1	no	—
26	C₂₃×#555	—	2	1	no	—
27	C₂₃×#554	—	2	1	no	—
28	C₂₃×#553	—	2	2	no	—
29	C₂₃×#551	—	2	2	no	—
30	C₂₃×#551	—	2	2	no	—
31	C₂₃×#548	—	2	2	no	—
32	C₂₃×#547	—	2	1	no	—
33	C₂₃×#542	C₂²	1	2	yes	—
34	C₂₃×#542	C₂²	1	2	yes	—
35	C₂₃×#542	C₂²	1	4	yes	complemented
36	C₂₃×#537	C₂²	1	2	yes	—
37	C₂₃×#536	C₂²	1	1	yes	characteristic
38	C₂₃×#535	C₂²	1	1	yes	characteristic
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂₃×#533	C₂²	1	2	yes	complemented
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂₃×#532	C₂²	1	2	yes	complemented
43	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂₃×#529	C₂²	1	2	yes	—
45	C₂₃×#529	C₂²	1	2	yes	—
46	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
47	C₂₃×#520	C₂²	1	2	yes	—
48	C₂₃×#519	C₂²	1	1	yes	characteristic
49	C₂₃×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#501	C₂²	1	2	yes	complemented
53	C₂₃×#500	C₂²	1	2	yes	complemented
54	C₂₃×#498	C₂²	1	2	yes	complemented
55	C₂₃×#497	C₂²	1	2	yes	—
56	C₂₃×#496	C₂²	1	2	yes	—
57	C₂₃×#495	C₂²	1	4	yes	—
58	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#489	C₂²	1	2	yes	—
63	C₂₃×#489	C₂²	1	4	yes	—
64	C₂₃×#489	C₂²	1	2	yes	—
65	C₂₃×#489	C₂²	1	2	yes	complemented
66	C₂₃×#489	C₂²	1	2	yes	complemented
67	C₂₃×#470	C₂²	1	4	yes	complemented
68	C₂₃×#469	C₂²	1	4	yes	—
69	C₂₃×#468	C₂²	1	4	yes	—
70	C₂₃×#468	C₂²	1	4	yes	complemented
71	C₂₃×#467	C₂²	1	4	yes	complemented
72	C₂₃×#466	C₂²	1	4	yes	—
73	C₂₃×#465	C₂²	1	4	yes	—
74	C₂₃×#465	C₂²	1	4	yes	complemented
75	C₂₃×#442	C₂²	1	4	yes	—
76	C₂₃×#441	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	—
78	C₂₃×#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
82	C₄×D₈×C₂₃	C₂²	1	4	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	2	yes	—
85	C₂₃×#416	C₂²	1	2	yes	—
86	C₂₃×#416	C₂²	1	2	yes	—
87	C₂×C₂₃×#103	C₂²	1	2	yes	—
88	C₂×C₂₃×#102	C₂²	1	2	yes	—
89	C₂₃×#405	C₂²	1	2	yes	—
90	C₂₃×#405	C₂²	1	4	yes	complemented
91	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
92	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
93	C₂×C₂₃×#97	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	C₂³	1	2	yes	—
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂₃×#137	—	2	8	no	—
102	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
103	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×D₈×C₂₃	C₂³	1	4	yes	—
107	C₂₃×#131	—	2	8	no	—
108	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×#127	—	2	1	no	—
121	C₂₃×#127	C₂³	1	1	yes	characteristic
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#126	—	2	4	no	—
125	C₂₃×#126	—	2	2	no	—
126	C₂₃×#126	—	2	2	no	—
127	C₂₃×#125	—	2	2	no	—
128	C₂₃×#125	C₂³	1	1	yes	characteristic
129	C₂₃×#125	C₂³	1	1	yes	characteristic
130	C₂₃×#124	—	2	1	no	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	4	no	—
133	C₂₃×#124	—	2	2	no	—
134	C₂₃×#124	—	2	2	no	—
135	C₂₃×#124	—	2	2	no	—
136	C₂₃×#124	—	2	1	no	—
137	C₂₃×#124	—	2	1	no	—
138	C₂₃×#124	C₂³	1	2	yes	—
139	C₂₃×#124	C₂³	1	2	yes	—
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	2	no	—
144	C₂₃×#123	—	2	4	no	—
145	C₂₃×#123	—	2	2	no	—
146	C₂₃×#123	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	1	no	—
150	C₂₃×C₂²⋊Q₈	—	2	1	no	—
151	C₂₃×C₂²⋊Q₈	—	2	4	no	—
152	C₂₃×C₂²⋊Q₈	—	2	2	no	—
153	C₂₃×C₂²⋊Q₈	—	2	2	no	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	1	no	—
160	C₂₃×#121	—	2	1	no	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	C₂³	1	2	yes	—
163	C₂₃×#121	C₂³	1	4	yes	—
164	C₂₃×#121	C₂³	1	2	yes	—
165	C₂₃×#120	—	2	2	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	1	no	—
171	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	—	2	4	no	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	1	no	—
184	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₂₃	D₄	1	2	yes	—
186	C₄×D₄×C₂₃	D₄	1	2	yes	—
187	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₂₃	C₂³	1	2	yes	—
189	C₄×D₄×C₂₃	C₂³	1	4	yes	—
190	C₄×D₄×C₂₃	C₂³	1	2	yes	—
191	C₂₃×#117	—	2	2	no	—
192	C₂₃×#117	—	2	2	no	—
193	C₂₃×#117	—	2	2	no	—
194	C₂₃×#117	—	2	2	no	—
195	C₂₃×#117	—	2	2	no	—
196	C₂₃×#117	C₂³	1	1	yes	characteristic
197	C₂₃×#117	C₂³	1	1	yes	characteristic
198	C₂₃×#117	C₂³	1	1	yes	characteristic
199	C₂₃×#117	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
208	C₂₃×#107	C₂³	1	4	yes	—
209	C₂₃×#107	C₂³	1	4	yes	—
210	C₂₃×#106	C₂³	1	4	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	2	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	2	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×#97	C₂³	1	1	yes	characteristic
225	C₂₃×#97	C₂³	1	1	yes	characteristic
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₂₃×#97	C₂³	1	2	yes	—
228	C₂₃×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₂₃	C₂³	1	2	yes	—
230	C₄×C₈×C₂₃	C₂³	1	4	yes	—
231	C₂⁴×C₂₃	—	2	1	no	—
232	#41×C₂₃	—	2	4	no	—
233	#41×C₂₃	—	2	4	no	—
234	#41×C₂₃	—	2	4	no	—
235	#41×C₂₃	—	8	4	no	—
236	C₂×Q₈×C₂₃	—	2	1	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	1	no	—
239	C₂×Q₈×C₂₃	—	2	1	no	—
240	C₂×Q₈×C₂₃	—	2	2	no	—
241	C₂×Q₈×C₂₃	—	2	4	no	—
242	C₂×Q₈×C₂₃	—	8	2	no	—
243	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
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	4	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	—	2	1	no	—
253	C₂×D₄×C₂₃	—	2	4	no	—
254	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₂₃	—	2	8	no	—
271	SD₁₆×C₂₃	—	2	8	no	—
272	SD₁₆×C₂₃	—	2	8	no	—
273	D₈×C₂₃	—	2	8	no	—
274	M₁₆×C₂₃	—	2	8	no	—
275	M₁₆×C₂₃	#41	1	8	yes	complemented
276	C₂×C₈×C₂₃	—	2	4	no	—
277	C₂×C₈×C₂₃	—	2	8	no	—
278	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	4	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	2	no	—
329	C₄²×C₂₃	—	2	4	no	—
330	C₄²×C₂₃	—	2	1	no	—
331	C₄²×C₂₃	—	2	1	no	—
332	C₄²×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	C₂×D₄	1	2	yes	—
334	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
337	C₄²×C₂₃	C₂⁴	1	2	yes	—
338	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
339	#60727	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	8	1	no	—
344	C₂³×C₂₃	—	8	1	no	—
345	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	4	no	—
350	Q₈×C₂₃	—	2	2	no	—
351	Q₈×C₂₃	—	4	4	no	—
352	Q₈×C₂₃	—	4	2	no	—
353	Q₈×C₂₃	—	8	1	no	—
354	Q₈×C₂₃	—	8	1	no	—
355	Q₈×C₂₃	—	8	2	no	—
356	D₄×C₂₃	—	2	4	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	2	no	—
359	D₄×C₂₃	—	2	4	no	—
360	D₄×C₂₃	—	2	2	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	—	4	4	no	—
364	D₄×C₂₃	—	4	2	no	—
365	D₄×C₂₃	—	8	2	no	—
366	D₄×C₂₃	—	8	2	no	—
367	D₄×C₂₃	—	8	4	no	—
368	C₂×C₄×C₂₃	—	2	4	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	1	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	1	no	—
378	C₂×C₄×C₂₃	—	4	1	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	2	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	—	8	2	no	—
384	C₂×C₄×C₂₃	—	8	4	no	—
385	C₂×C₄×C₂₃	—	8	2	no	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
395	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	2	no	—
398	C₈×C₂₃	C₂×#41	1	8	yes	—
399	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3510	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3181	C₂×C₂₃	1	2	yes	complemented
402	#3180	C₂×C₂₃	1	2	yes	complemented
403	#3175	C₂×C₂₃	1	4	yes	complemented
404	#3173	C₂×C₂₃	1	4	yes	complemented
405	#3172	C₂×C₂₃	1	2	yes	complemented
406	#3171	C₂×C₂₃	1	2	yes	complemented
407	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3135	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3063	C₂×C₂₃	1	2	yes	complemented
412	#3062	C₂×C₂₃	1	2	yes	complemented
413	#2947	C₂×C₂₃	1	2	yes	complemented
414	#2946	C₂×C₂₃	1	2	yes	complemented
415	#2875	C₂×C₂₃	1	1	yes	characteristic, complemented
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	2	2	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	4	2	no	—
425	C₂²×C₂₃	—	4	2	no	—
426	C₂²×C₂₃	—	4	2	no	—
427	C₂²×C₂₃	—	16	2	no	—
428	C₂²×C₂₃	#532	1	2	yes	—
429	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	2	1	no	—
436	C₄×C₂₃	—	2	2	no	—
437	C₄×C₂₃	—	4	4	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	1	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	—	4	1	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	#532	1	2	yes	—
445	C₄×C₂₃	C₂²×#41	1	2	yes	—
446	C₂×#137	C₂²×C₂₃	1	2	yes	—
447	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
448	C₂×#131	C₂²×C₂₃	1	2	yes	—
449	#559	—	2	1	no	—
450	#559	—	2	1	no	—
451	#556	—	2	1	no	—
452	#556	—	2	1	no	—
453	#556	—	2	1	no	—
454	#555	—	2	1	no	—
455	#554	—	2	1	no	—
456	#553	—	2	2	no	—
457	#551	—	2	2	no	—
458	#551	—	2	2	no	—
459	#548	—	2	2	no	—
460	#547	—	2	1	no	—
461	#542	C₂²×C₂₃	1	2	yes	—
462	#542	C₂²×C₂₃	1	2	yes	—
463	#542	C₂²×C₂₃	1	4	yes	complemented
464	#537	C₂²×C₂₃	1	2	yes	—
465	#536	C₂²×C₂₃	1	1	yes	characteristic
466	#535	C₂²×C₂₃	1	1	yes	characteristic
467	#533	C₂²×C₂₃	1	1	yes	characteristic
468	#533	C₂²×C₂₃	1	2	yes	complemented
469	#532	C₂²×C₂₃	1	1	yes	characteristic
470	#532	C₂²×C₂₃	1	2	yes	complemented
471	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
472	#529	C₂²×C₂₃	1	2	yes	—
473	#529	C₂²×C₂₃	1	2	yes	—
474	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
475	#520	C₂²×C₂₃	1	2	yes	—
476	#519	C₂²×C₂₃	1	1	yes	characteristic
477	#518	C₂²×C₂₃	1	1	yes	characteristic
478	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
479	#501	C₂²×C₂₃	1	2	yes	complemented
480	#501	C₂²×C₂₃	1	2	yes	complemented
481	#500	C₂²×C₂₃	1	2	yes	complemented
482	#498	C₂²×C₂₃	1	2	yes	complemented
483	#497	C₂²×C₂₃	1	2	yes	—
484	#496	C₂²×C₂₃	1	2	yes	—
485	#495	C₂²×C₂₃	1	4	yes	—
486	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	#489	C₂²×C₂₃	1	2	yes	—
491	#489	C₂²×C₂₃	1	4	yes	—
492	#489	C₂²×C₂₃	1	2	yes	—
493	#489	C₂²×C₂₃	1	2	yes	complemented
494	#489	C₂²×C₂₃	1	2	yes	complemented
495	#470	C₂²×C₂₃	1	4	yes	complemented
496	#469	C₂²×C₂₃	1	4	yes	—
497	#468	C₂²×C₂₃	1	4	yes	—
498	#468	C₂²×C₂₃	1	4	yes	complemented
499	#467	C₂²×C₂₃	1	4	yes	complemented
500	#466	C₂²×C₂₃	1	4	yes	—
501	#465	C₂²×C₂₃	1	4	yes	—
502	#465	C₂²×C₂₃	1	4	yes	complemented
503	#442	C₂²×C₂₃	1	4	yes	—
504	#441	C₂²×C₂₃	1	4	yes	complemented
505	#440	C₂²×C₂₃	1	4	yes	—
506	#440	C₂²×C₂₃	1	4	yes	complemented
507	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
508	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
509	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
510	C₄×D₈	C₂²×C₂₃	1	4	yes	—
511	#428	C₂²×C₂₃	1	2	yes	—
512	#428	C₂²×C₂₃	1	2	yes	—
513	#416	C₂²×C₂₃	1	2	yes	—
514	#416	C₂²×C₂₃	1	2	yes	—
515	C₂×#103	C₂²×C₂₃	1	2	yes	—
516	C₂×#102	C₂²×C₂₃	1	2	yes	—
517	#405	C₂²×C₂₃	1	2	yes	—
518	#405	C₂²×C₂₃	1	4	yes	complemented
519	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
520	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
521	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
522	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	4	2	no	—
525	C₂×C₂₃	—	8	2	no	—
526	C₂×C₂₃	—	8	2	no	—
527	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
528	C₂×C₂₃	#3585	1	1	yes	characteristic
529	C₂×C₂₃	#3586	1	1	yes	characteristic
530	C₂×#41	—	2	2	no	—
531	C₂×#41	C₂³×C₂₃	1	2	yes	—
532	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
536	#137	—	2	8	no	—
537	AGL(1,ℤ/8)	—	2	8	no	—
538	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
541	C₂×D₈	C₂³×C₂₃	1	4	yes	—
542	#131	—	2	8	no	—
543	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
544	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
545	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
546	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
555	#127	—	2	1	no	—
556	#127	C₂³×C₂₃	1	1	yes	characteristic
557	#126	—	2	2	no	—
558	#126	—	2	2	no	—
559	#126	—	2	4	no	—
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	C₂³×C₂₃	1	1	yes	characteristic
564	#125	C₂³×C₂₃	1	1	yes	characteristic
565	#124	—	2	1	no	—
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	—	2	4	no	—
570	#124	—	2	1	no	—
571	#124	—	2	1	no	—
572	#124	—	2	2	no	—
573	#124	C₂³×C₂₃	1	2	yes	—
574	#124	C₂³×C₂₃	1	2	yes	—
575	#124	C₂³×C₂₃	1	2	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	4	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
591	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	—	2	1	no	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₂₃	1	2	yes	—
598	#121	C₂³×C₂₃	1	2	yes	—
599	#121	C₂³×C₂₃	1	4	yes	—
600	#120	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
607	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
609	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
620	C₄×D₄	D₄×C₂₃	1	2	yes	—
621	C₄×D₄	D₄×C₂₃	1	2	yes	—
622	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₂₃	1	2	yes	—
624	C₄×D₄	C₂³×C₂₃	1	2	yes	—
625	C₄×D₄	C₂³×C₂₃	1	4	yes	—
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	C₂³×C₂₃	1	1	yes	characteristic
632	#117	C₂³×C₂₃	1	1	yes	characteristic
633	#117	C₂³×C₂₃	1	1	yes	characteristic
634	#117	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
643	#107	C₂³×C₂₃	1	4	yes	—
644	#107	C₂³×C₂₃	1	4	yes	—
645	#106	C₂³×C₂₃	1	4	yes	—
646	#106	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	4	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	2	yes	—
650	#103	C₂³×C₂₃	1	2	yes	—
651	#103	C₂³×C₂₃	1	2	yes	—
652	#103	C₂³×C₂₃	1	2	yes	—
653	#102	C₂³×C₂₃	1	4	yes	—
654	#102	C₂³×C₂₃	1	4	yes	—
655	#102	C₂³×C₂₃	1	2	yes	—
656	#102	C₂³×C₂₃	1	2	yes	—
657	#102	C₂³×C₂₃	1	2	yes	—
658	#102	C₂³×C₂₃	1	2	yes	—
659	#97	C₂³×C₂₃	1	1	yes	characteristic
660	#97	C₂³×C₂₃	1	1	yes	characteristic
661	#97	C₂³×C₂₃	1	2	yes	—
662	#97	C₂³×C₂₃	1	2	yes	—
663	#97	C₂³×C₂₃	1	4	yes	—
664	C₄×C₈	C₂³×C₂₃	1	2	yes	—
665	C₄×C₈	C₂³×C₂₃	1	4	yes	—
666	C₂₃	#60727	1	1	yes	characteristic, direct product factor, Sylow
667	C₂⁴	—	2	1	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	8	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	8	2	no	—
679	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
694	C₂²×C₄	—	2	1	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	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
706	Q₁₆	—	2	8	no	—
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	8	no	—
709	D₈	—	2	8	no	—
710	M₁₆	—	2	8	no	—
711	M₁₆	#41×C₂₃	1	8	yes	complemented
712	C₂×C₈	—	2	4	no	—
713	C₂×C₈	—	2	8	no	—
714	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
716	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₂₃	1	2	yes	—
769	C₄²	C₂×D₄×C₂₃	1	2	yes	—
770	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₂₃	1	2	yes	—
773	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
781	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
782	Q₈	—	2	2	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	4	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	1	no	—
790	Q₈	—	8	1	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
830	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	C₂×#41×C₂₃	1	8	yes	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	16	2	no	—
846	C₂²	C₂₃×#532	1	2	yes	—
847	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	C₂₃×#532	1	2	yes	—
863	C₄	C₂²×#41×C₂₃	1	2	yes	—
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
869	C₂	C₂₃×#3585	1	1	yes	characteristic
870	C₂	C₂₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3510	C₂	semidirect
3. C₂₃×#3181	C₂	semidirect
4. C₂₃×#3180	C₂	semidirect
5. C₂₃×#3175	C₂	semidirect
6. C₂₃×#3173	C₂	semidirect
7. C₂₃×#3172	C₂	semidirect
8. C₂₃×#3171	C₂	semidirect
9. C₂₃×#3165	C₂	semidirect
10. C₂₃×#3153	C₂	semidirect
11. C₂₃×#3135	C₂	semidirect
12. C₂×C₂₃×#489	C₂	semidirect
13. C₂₃×#3063	C₂	semidirect
14. C₂₃×#3062	C₂	semidirect
15. C₂₃×#2947	C₂	semidirect
16. C₂₃×#2946	C₂	semidirect
17. C₂₃×#2875	C₂	semidirect
35. C₂₃×#542	C₂²	semidirect
40. C₂₃×#533	C₂²	semidirect
42. C₂₃×#532	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#501	C₂²	semidirect
53. C₂₃×#500	C₂²	semidirect
54. C₂₃×#498	C₂²	semidirect
58. C₂₃×#491	C₂²	semidirect
59. C₂₃×#491	C₂²	semidirect
60. C₂₃×#490	C₂²	semidirect
61. C₂₃×#490	C₂²	semidirect
65. C₂₃×#489	C₂²	semidirect
66. C₂₃×#489	C₂²	semidirect
67. C₂₃×#470	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#467	C₂²	semidirect
74. C₂₃×#465	C₂²	semidirect
76. C₂₃×#441	C₂²	semidirect
78. C₂₃×#440	C₂²	semidirect
79. C₄×Q₁₆×C₂₃	C₂²	semidirect
81. C₄×SD₁₆×C₂₃	C₂²	semidirect
90. C₂₃×#405	C₂²	semidirect
92. C₄×M₁₆×C₂₃	C₂²	semidirect
94. C₂×C₂₃×#97	C₂²	semidirect
275. M₁₆×C₂₃	#41	semidirect
339. #60727	C₂₃	direct (N × H)
399. #3511	C₂×C₂₃	semidirect
400. #3510	C₂×C₂₃	semidirect
401. #3181	C₂×C₂₃	semidirect
402. #3180	C₂×C₂₃	semidirect
403. #3175	C₂×C₂₃	semidirect
404. #3173	C₂×C₂₃	semidirect
405. #3172	C₂×C₂₃	semidirect
406. #3171	C₂×C₂₃	semidirect
407. #3165	C₂×C₂₃	semidirect
408. #3153	C₂×C₂₃	semidirect
409. #3135	C₂×C₂₃	semidirect
410. C₂×#489	C₂×C₂₃	semidirect
411. #3063	C₂×C₂₃	semidirect
412. #3062	C₂×C₂₃	semidirect
413. #2947	C₂×C₂₃	semidirect
414. #2946	C₂×C₂₃	semidirect
415. #2875	C₂×C₂₃	semidirect
463. #542	C₂²×C₂₃	semidirect
468. #533	C₂²×C₂₃	semidirect
470. #532	C₂²×C₂₃	semidirect
479. #501	C₂²×C₂₃	semidirect
480. #501	C₂²×C₂₃	semidirect
481. #500	C₂²×C₂₃	semidirect
482. #498	C₂²×C₂₃	semidirect
486. #491	C₂²×C₂₃	semidirect
487. #491	C₂²×C₂₃	semidirect
488. #490	C₂²×C₂₃	semidirect
489. #490	C₂²×C₂₃	semidirect
493. #489	C₂²×C₂₃	semidirect
494. #489	C₂²×C₂₃	semidirect
495. #470	C₂²×C₂₃	semidirect
498. #468	C₂²×C₂₃	semidirect
499. #467	C₂²×C₂₃	semidirect
502. #465	C₂²×C₂₃	semidirect
504. #441	C₂²×C₂₃	semidirect
506. #440	C₂²×C₂₃	semidirect
507. C₄×Q₁₆	C₂²×C₂₃	semidirect
509. C₄×SD₁₆	C₂²×C₂₃	semidirect
518. #405	C₂²×C₂₃	semidirect
520. C₄×M₁₆	C₂²×C₂₃	semidirect
522. C₂×#97	C₂²×C₂₃	semidirect
666. C₂₃	#60727	direct (N × H)
711. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3511	2
C₂₃×#3510	2
C₂₃×#3181	2
C₂₃×#3180	2
C₂₃×#3175	2
C₂₃×#3173	2
C₂₃×#3172	2
C₂₃×#3171	2
C₂₃×#3165	2
C₂₃×#3153	2
C₂₃×#3135	2
C₂×C₂₃×#489	2
C₂₃×#3063	2
C₂₃×#3062	2
C₂₃×#2947	2
C₂₃×#2946	2
C₂₃×#2875	2
#60727	23

Subgroups — C23×#60727 #19208353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60727 #19208353