Subgroups — C₂₃×#60695 #19208321

Order 5888.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3179	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3176	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3171	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3169	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#544	C₂²	1	2	yes	—
24	C₂₃×#542	—	2	2	no	—
25	C₂₃×#542	C₂²	1	4	yes	complemented
26	C₂₃×#540	—	2	2	no	—
27	C₂₃×#540	C₂²	1	4	yes	complemented
28	C₂₃×#538	—	2	4	no	—
29	C₂₃×#537	C₂²	1	2	yes	—
30	C₂₃×#535	C₂²	1	2	yes	—
31	C₂₃×#535	C₂²	1	2	yes	—
32	C₂₃×#532	—	2	2	no	—
33	C₂₃×#532	C₂²	1	4	yes	complemented
34	C₂₃×#529	—	2	2	no	—
35	C₂₃×#529	C₂²	1	4	yes	complemented
36	C₂₃×#525	—	2	4	no	—
37	C₄×#41×C₂₃	C₂²	1	2	yes	—
38	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
40	C₂₃×#501	C₂²	1	4	yes	complemented
41	C₂₃×#500	C₂²	1	2	yes	complemented
42	C₂₃×#499	C₂²	1	2	yes	complemented
43	C₂₃×#496	C₂²	1	4	yes	—
44	C₂₃×#495	C₂²	1	2	yes	—
45	C₂₃×#493	C₂²	1	2	yes	—
46	C₂₃×#490	C₂²	1	4	yes	complemented
47	C₂₃×#489	C₂²	1	4	yes	complemented
48	C₂₃×#488	C₂²	1	4	yes	complemented
49	C₂₃×#486	C₂²	1	4	yes	complemented
50	C₂₃×#469	C₂²	1	4	yes	—
51	C₂₃×#469	C₂²	1	4	yes	complemented
52	C₂₃×#468	C₂²	1	4	yes	complemented
53	C₂₃×#468	C₂²	1	4	yes	complemented
54	C₂₃×#467	C₂²	1	2	yes	complemented
55	C₂₃×#466	C₂²	1	2	yes	—
56	C₂₃×#466	C₂²	1	2	yes	—
57	C₂₃×#466	C₂²	1	2	yes	complemented
58	C₂₃×#466	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#442	C₂²	1	4	yes	complemented
61	C₂₃×#440	C₂²	1	4	yes	complemented
62	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
65	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
66	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
67	C₄×D₈×C₂₃	C₂²	1	2	yes	—
68	C₄×D₈×C₂₃	C₂²	1	2	yes	—
69	C₄×D₈×C₂₃	C₂²	1	2	yes	—
70	C₄×D₈×C₂₃	C₂²	1	2	yes	—
71	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
73	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#428	C₂²	1	2	yes	—
75	C₂₃×#427	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
77	C₂₃×#418	C₂²	1	2	yes	—
78	C₂₃×#417	C₂²	1	2	yes	—
79	C₂₃×#416	C₂²	1	2	yes	—
80	C₂×C₂₃×#102	C₂²	1	2	yes	—
81	C₂₃×#405	C₂²	1	1	yes	characteristic
82	C₂₃×#405	C₂²	1	1	yes	characteristic
83	C₂₃×#405	C₂²	1	2	yes	complemented
84	C₂₃×#405	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
89	C₂×#41×C₂₃	—	2	4	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	—	2	2	no	—
94	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
95	C₂₃×#135	—	2	4	no	—
96	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	—	2	4	no	—
100	C₂×D₈×C₂₃	C₂³	1	2	yes	—
101	C₂×D₈×C₂₃	C₂³	1	2	yes	—
102	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×D₈×C₂₃	C₂³	1	4	yes	—
104	C₂₃×#131	—	2	4	no	—
105	C₂₃×#131	—	2	4	no	—
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	—	2	2	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	C₂³	1	4	yes	—
118	C₂₃×#126	—	2	4	no	—
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	C₂³	1	4	yes	—
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	—	2	4	no	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	C₂³	1	4	yes	—
126	C₂₃×#123	—	2	4	no	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×#121	—	2	4	no	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	4	no	—
141	C₂₃×#121	C₂³	1	4	yes	—
142	C₂₃×#121	C₂³	1	4	yes	—
143	C₂₃×#121	C₂³	1	4	yes	—
144	C₂₃×#120	—	2	4	no	—
145	C₂₃×#120	—	2	4	no	—
146	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	2	no	—
152	C₄×D₄×C₂₃	—	2	4	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	—	2	4	no	—
156	C₄×D₄×C₂₃	D₄	1	2	yes	—
157	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
158	C₄×D₄×C₂₃	D₄	1	2	yes	—
159	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₂₃	C₂³	1	4	yes	—
161	C₄×D₄×C₂₃	C₂³	1	4	yes	—
162	C₄×D₄×C₂₃	C₂³	1	2	yes	—
163	C₄×D₄×C₂₃	C₂³	1	2	yes	—
164	C₂₃×#117	—	2	2	no	—
165	C₂₃×#117	—	2	4	no	—
166	C₂₃×#117	C₂³	1	2	yes	—
167	C₂₃×#117	C₂³	1	1	yes	characteristic
168	C₂₃×#117	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
171	C₂×C₄²×C₂₃	—	2	2	no	—
172	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
174	C₂₃×#107	C₂³	1	2	yes	—
175	C₂₃×#107	C₂³	1	2	yes	—
176	C₂₃×#107	C₂³	1	1	yes	characteristic
177	C₂₃×#107	C₂³	1	1	yes	characteristic
178	C₂₃×#107	C₂³	1	4	yes	—
179	C₂₃×#106	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	4	yes	—
181	C₂₃×#103	C₂³	1	2	yes	—
182	C₂₃×#103	C₂³	1	2	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#102	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	4	yes	—
186	C₂₃×#102	C₂³	1	2	yes	—
187	C₂₃×#102	C₂³	1	2	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×#102	C₂³	1	4	yes	—
191	C₂₃×#97	C₂³	1	2	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₂₃×#97	C₂³	1	2	yes	—
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₂₃	C₂³	1	2	yes	—
199	C₄×C₈×C₂₃	C₂³	1	2	yes	—
200	C₄×C₈×C₂₃	C₂³	1	2	yes	—
201	C₂⁴×C₂₃	—	2	2	no	—
202	#41×C₂₃	—	2	2	no	—
203	#41×C₂₃	—	2	2	no	—
204	#41×C₂₃	—	2	4	no	—
205	#41×C₂₃	—	2	4	no	—
206	#41×C₂₃	—	8	8	no	—
207	C₂×Q₈×C₂₃	—	2	4	no	—
208	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₃	—	2	2	no	—
211	C₂×D₄×C₂₃	—	2	4	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	2	no	—
215	C₂×D₄×C₂₃	—	2	4	no	—
216	C₂×D₄×C₂₃	—	2	4	no	—
217	C₂×D₄×C₂₃	—	2	4	no	—
218	C₂×D₄×C₂₃	—	2	4	no	—
219	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
222	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	—	2	2	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	2	no	—
226	C₂²×C₄×C₂₃	—	2	4	no	—
227	C₂²×C₄×C₂₃	—	2	2	no	—
228	C₂²×C₄×C₂₃	—	2	4	no	—
229	C₂²×C₄×C₂₃	—	8	4	no	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₂₃	—	2	2	no	—
237	SD₁₆×C₂₃	—	2	4	no	—
238	SD₁₆×C₂₃	—	2	8	no	—
239	D₈×C₂₃	—	2	4	no	—
240	D₈×C₂₃	—	2	4	no	—
241	D₈×C₂₃	—	2	2	no	—
242	D₈×C₂₃	—	2	8	no	—
243	M₁₆×C₂₃	—	2	2	no	—
244	M₁₆×C₂₃	—	2	4	no	—
245	M₁₆×C₂₃	—	2	4	no	—
246	M₁₆×C₂₃	#41	1	4	yes	complemented
247	C₂×C₈×C₂₃	—	2	2	no	—
248	C₂×C₈×C₂₃	—	2	4	no	—
249	C₂×C₈×C₂₃	—	2	4	no	—
250	C₂×C₈×C₂₃	#41	1	4	yes	complemented
251	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
254	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₂₃	—	2	2	no	—
258	C₄⋊C₄×C₂₃	—	2	2	no	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	4	no	—
261	C₄⋊C₄×C₂₃	—	2	4	no	—
262	C₄⋊C₄×C₂₃	—	2	4	no	—
263	C₄⋊C₄×C₂₃	—	2	4	no	—
264	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
270	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₂₃	—	2	2	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	—	2	2	no	—
276	C₂²⋊C₄×C₂₃	—	2	2	no	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₄²×C₂₃	—	2	2	no	—
286	C₄²×C₂₃	—	2	2	no	—
287	C₄²×C₂₃	—	2	2	no	—
288	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₂₃	C₂×D₄	1	2	yes	—
290	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₂₃	C₂×D₄	1	2	yes	—
292	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₄²×C₂₃	C₂⁴	1	2	yes	—
294	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
295	#60695	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₂₃	—	2	4	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	4	4	no	—
299	C₂³×C₂₃	—	8	2	no	—
300	C₂³×C₂₃	—	8	2	no	—
301	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
302	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₂₃	—	2	2	no	—
304	Q₈×C₂₃	—	2	2	no	—
305	Q₈×C₂₃	—	2	2	no	—
306	Q₈×C₂₃	—	8	4	no	—
307	D₄×C₂₃	—	2	4	no	—
308	D₄×C₂₃	—	2	2	no	—
309	D₄×C₂₃	—	2	4	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	4	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	4	4	no	—
314	D₄×C₂₃	—	4	4	no	—
315	D₄×C₂₃	—	8	4	no	—
316	D₄×C₂₃	—	8	4	no	—
317	D₄×C₂₃	—	8	4	no	—
318	D₄×C₂₃	—	8	4	no	—
319	D₄×C₂₃	—	8	4	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	4	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	4	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	4	no	—
331	C₂×C₄×C₂₃	—	4	8	no	—
332	C₂×C₄×C₂₃	—	4	4	no	—
333	C₂×C₄×C₂₃	—	8	2	no	—
334	C₂×C₄×C₂₃	—	8	4	no	—
335	C₂×C₄×C₂₃	—	8	2	no	—
336	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
346	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
347	C₈×C₂₃	—	2	1	no	—
348	C₈×C₂₃	—	2	1	no	—
349	C₈×C₂₃	—	2	2	no	—
350	C₈×C₂₃	C₂×#41	1	2	yes	—
351	C₈×C₂₃	C₂×#41	1	4	yes	—
352	C₈×C₂₃	C₂×#41	1	2	yes	—
353	#3460	C₂×C₂₃	1	2	yes	complemented
354	#3179	C₂×C₂₃	1	4	yes	complemented
355	#3176	C₂×C₂₃	1	2	yes	complemented
356	#3175	C₂×C₂₃	1	2	yes	complemented
357	#3171	C₂×C₂₃	1	4	yes	complemented
358	#3169	C₂×C₂₃	1	2	yes	complemented
359	#3168	C₂×C₂₃	1	2	yes	complemented
360	#3164	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#3136	C₂×C₂₃	1	2	yes	complemented
363	#3062	C₂×C₂₃	1	2	yes	complemented
364	#3061	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
367	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₄×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂²×C₂₃	—	2	1	no	—
371	C₂²×C₂₃	—	2	1	no	—
372	C₂²×C₂₃	—	2	2	no	—
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	4	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	4	no	—
379	C₂²×C₂₃	—	4	4	no	—
380	C₂²×C₂₃	—	4	2	no	—
381	C₂²×C₂₃	—	8	8	no	—
382	C₂²×C₂₃	#532	1	2	yes	—
383	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₂₃	—	2	1	no	—
385	C₄×C₂₃	—	2	1	no	—
386	C₄×C₂₃	—	2	2	no	—
387	C₄×C₂₃	—	2	2	no	—
388	C₄×C₂₃	—	2	1	no	—
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	4	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	#532	1	2	yes	—
395	C₄×C₂₃	#576	1	2	yes	—
396	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
397	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
398	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
399	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
403	#544	C₂²×C₂₃	1	2	yes	—
404	#542	—	2	2	no	—
405	#542	C₂²×C₂₃	1	4	yes	complemented
406	#540	—	2	2	no	—
407	#540	C₂²×C₂₃	1	4	yes	complemented
408	#538	—	2	4	no	—
409	#537	C₂²×C₂₃	1	2	yes	—
410	#535	C₂²×C₂₃	1	2	yes	—
411	#535	C₂²×C₂₃	1	2	yes	—
412	#532	—	2	2	no	—
413	#532	C₂²×C₂₃	1	4	yes	complemented
414	#529	—	2	2	no	—
415	#529	C₂²×C₂₃	1	4	yes	complemented
416	#525	—	2	4	no	—
417	C₄×#41	C₂²×C₂₃	1	2	yes	—
418	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
420	#501	C₂²×C₂₃	1	4	yes	complemented
421	#500	C₂²×C₂₃	1	2	yes	complemented
422	#499	C₂²×C₂₃	1	2	yes	complemented
423	#496	C₂²×C₂₃	1	4	yes	—
424	#495	C₂²×C₂₃	1	2	yes	—
425	#493	C₂²×C₂₃	1	2	yes	—
426	#490	C₂²×C₂₃	1	4	yes	complemented
427	#489	C₂²×C₂₃	1	4	yes	complemented
428	#488	C₂²×C₂₃	1	4	yes	complemented
429	#486	C₂²×C₂₃	1	4	yes	complemented
430	#469	C₂²×C₂₃	1	4	yes	—
431	#469	C₂²×C₂₃	1	4	yes	complemented
432	#468	C₂²×C₂₃	1	4	yes	complemented
433	#468	C₂²×C₂₃	1	4	yes	complemented
434	#467	C₂²×C₂₃	1	2	yes	complemented
435	#466	C₂²×C₂₃	1	2	yes	—
436	#466	C₂²×C₂₃	1	2	yes	—
437	#466	C₂²×C₂₃	1	2	yes	complemented
438	#466	C₂²×C₂₃	1	4	yes	complemented
439	#465	C₂²×C₂₃	1	4	yes	complemented
440	#442	C₂²×C₂₃	1	4	yes	complemented
441	#440	C₂²×C₂₃	1	4	yes	complemented
442	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
445	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
446	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
447	C₄×D₈	C₂²×C₂₃	1	2	yes	—
448	C₄×D₈	C₂²×C₂₃	1	2	yes	—
449	C₄×D₈	C₂²×C₂₃	1	2	yes	—
450	C₄×D₈	C₂²×C₂₃	1	2	yes	—
451	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
453	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#428	C₂²×C₂₃	1	2	yes	—
455	#427	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
457	#418	C₂²×C₂₃	1	2	yes	—
458	#417	C₂²×C₂₃	1	2	yes	—
459	#416	C₂²×C₂₃	1	2	yes	—
460	C₂×#102	C₂²×C₂₃	1	2	yes	—
461	#405	C₂²×C₂₃	1	1	yes	characteristic
462	#405	C₂²×C₂₃	1	1	yes	characteristic
463	#405	C₂²×C₂₃	1	2	yes	complemented
464	#405	C₂²×C₂₃	1	2	yes	complemented
465	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
466	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
467	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
469	C₂×C₂₃	—	2	2	no	—
470	C₂×C₂₃	—	4	2	no	—
471	C₂×C₂₃	—	8	2	no	—
472	C₂×C₂₃	—	8	4	no	—
473	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
474	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
475	C₂×C₂₃	#3584	1	1	yes	characteristic
476	C₂×#41	—	2	4	no	—
477	C₂×#41	C₂³×C₂₃	1	2	yes	—
478	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
480	C₂³×C₄	—	2	2	no	—
481	AGL(1,ℤ/8)	—	2	8	no	—
482	#135	—	2	4	no	—
483	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
484	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
485	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
486	C₂×D₈	—	2	4	no	—
487	C₂×D₈	C₂³×C₂₃	1	2	yes	—
488	C₂×D₈	C₂³×C₂₃	1	2	yes	—
489	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×D₈	C₂³×C₂₃	1	4	yes	—
491	#131	—	2	4	no	—
492	#131	—	2	4	no	—
493	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
495	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
496	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
499	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
500	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
503	#127	—	2	2	no	—
504	#127	C₂³×C₂₃	1	4	yes	—
505	#126	—	2	4	no	—
506	#126	—	2	4	no	—
507	#125	—	2	2	no	—
508	#125	C₂³×C₂₃	1	4	yes	—
509	#124	—	2	2	no	—
510	#124	—	2	4	no	—
511	#124	—	2	4	no	—
512	#124	C₂³×C₂₃	1	4	yes	—
513	#123	—	2	4	no	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
521	#121	—	2	4	no	—
522	#121	—	2	2	no	—
523	#121	—	2	4	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	C₂³×C₂₃	1	4	yes	—
529	#121	C₂³×C₂₃	1	4	yes	—
530	#121	C₂³×C₂₃	1	4	yes	—
531	#120	—	2	4	no	—
532	#120	—	2	4	no	—
533	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
534	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
535	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
536	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	D₄×C₂₃	1	2	yes	—
544	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
545	C₄×D₄	D₄×C₂₃	1	2	yes	—
546	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
547	C₄×D₄	C₂³×C₂₃	1	4	yes	—
548	C₄×D₄	C₂³×C₂₃	1	4	yes	—
549	C₄×D₄	C₂³×C₂₃	1	2	yes	—
550	C₄×D₄	C₂³×C₂₃	1	2	yes	—
551	#117	—	2	2	no	—
552	#117	—	2	4	no	—
553	#117	C₂³×C₂₃	1	2	yes	—
554	#117	C₂³×C₂₃	1	1	yes	characteristic
555	#117	C₂³×C₂₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₄²	—	2	2	no	—
559	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
561	#107	C₂³×C₂₃	1	2	yes	—
562	#107	C₂³×C₂₃	1	2	yes	—
563	#107	C₂³×C₂₃	1	1	yes	characteristic
564	#107	C₂³×C₂₃	1	1	yes	characteristic
565	#107	C₂³×C₂₃	1	4	yes	—
566	#106	C₂³×C₂₃	1	2	yes	—
567	#106	C₂³×C₂₃	1	4	yes	—
568	#103	C₂³×C₂₃	1	2	yes	—
569	#103	C₂³×C₂₃	1	2	yes	—
570	#103	C₂³×C₂₃	1	4	yes	—
571	#102	C₂³×C₂₃	1	4	yes	—
572	#102	C₂³×C₂₃	1	4	yes	—
573	#102	C₂³×C₂₃	1	2	yes	—
574	#102	C₂³×C₂₃	1	2	yes	—
575	#102	C₂³×C₂₃	1	4	yes	—
576	#102	C₂³×C₂₃	1	4	yes	—
577	#102	C₂³×C₂₃	1	4	yes	—
578	#97	C₂³×C₂₃	1	2	yes	—
579	#97	C₂³×C₂₃	1	2	yes	—
580	#97	C₂³×C₂₃	1	2	yes	—
581	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
582	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
584	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₂₃	1	2	yes	—
586	C₄×C₈	C₂³×C₂₃	1	2	yes	—
587	C₄×C₈	C₂³×C₂₃	1	2	yes	—
588	C₂₃	#60695	1	1	yes	characteristic, direct product factor, Sylow
589	C₂⁴	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	8	8	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
608	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
609	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
610	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	8	4	no	—
618	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
620	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
624	Q₁₆	—	2	2	no	—
625	SD₁₆	—	2	4	no	—
626	SD₁₆	—	2	8	no	—
627	D₈	—	2	4	no	—
628	D₈	—	2	4	no	—
629	D₈	—	2	2	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	4	no	—
634	M₁₆	#41×C₂₃	1	4	yes	complemented
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	#41×C₂₃	1	4	yes	complemented
639	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
642	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
643	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
644	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₂₃	1	2	yes	—
679	C₄²	C₂×D₄×C₂₃	1	2	yes	—
680	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₄²	C₂⁴×C₂₃	1	2	yes	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	2	no	—
688	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
689	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	8	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
732	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
733	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×#41×C₂₃	1	2	yes	—
738	C₈	C₂×#41×C₂₃	1	4	yes	—
739	C₈	C₂×#41×C₂₃	1	2	yes	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	8	8	no	—
752	C₂²	C₂₃×#532	1	2	yes	—
753	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₂₃×#532	1	2	yes	—
765	C₄	C₂₃×#576	1	2	yes	—
766	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
767	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	8	4	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
773	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
774	C₂	C₂₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3460	C₂	semidirect
2. C₂₃×#3179	C₂	semidirect
3. C₂₃×#3176	C₂	semidirect
4. C₂₃×#3175	C₂	semidirect
5. C₂₃×#3171	C₂	semidirect
6. C₂₃×#3169	C₂	semidirect
7. C₂₃×#3168	C₂	semidirect
8. C₂₃×#3164	C₂	semidirect
9. C₂₃×#3155	C₂	semidirect
10. C₂₃×#3136	C₂	semidirect
11. C₂₃×#3062	C₂	semidirect
12. C₂₃×#3061	C₂	semidirect
13. C₂₃×#3058	C₂	semidirect
14. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₄×C₂₃×#135	C₂	semidirect
16. C₂×C₄×D₈×C₂₃	C₂	semidirect
17. C₄×C₂₃×#131	C₂	semidirect
25. C₂₃×#542	C₂²	semidirect
27. C₂₃×#540	C₂²	semidirect
33. C₂₃×#532	C₂²	semidirect
35. C₂₃×#529	C₂²	semidirect
40. C₂₃×#501	C₂²	semidirect
41. C₂₃×#500	C₂²	semidirect
42. C₂₃×#499	C₂²	semidirect
46. C₂₃×#490	C₂²	semidirect
47. C₂₃×#489	C₂²	semidirect
48. C₂₃×#488	C₂²	semidirect
49. C₂₃×#486	C₂²	semidirect
51. C₂₃×#469	C₂²	semidirect
52. C₂₃×#468	C₂²	semidirect
53. C₂₃×#468	C₂²	semidirect
54. C₂₃×#467	C₂²	semidirect
57. C₂₃×#466	C₂²	semidirect
58. C₂₃×#466	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
60. C₂₃×#442	C₂²	semidirect
61. C₂₃×#440	C₂²	semidirect
62. C₄×Q₁₆×C₂₃	C₂²	semidirect
63. C₄×Q₁₆×C₂₃	C₂²	semidirect
64. C₄×SD₁₆×C₂₃	C₂²	semidirect
65. C₄×SD₁₆×C₂₃	C₂²	semidirect
66. C₄×SD₁₆×C₂₃	C₂²	semidirect
71. C₄×D₈×C₂₃	C₂²	semidirect
72. C₄×D₈×C₂₃	C₂²	semidirect
73. C₄×D₈×C₂₃	C₂²	semidirect
83. C₂₃×#405	C₂²	semidirect
84. C₂₃×#405	C₂²	semidirect
86. C₄×M₁₆×C₂₃	C₂²	semidirect
88. C₂×C₄×C₈×C₂₃	C₂²	semidirect
246. M₁₆×C₂₃	#41	semidirect
250. C₂×C₈×C₂₃	#41	semidirect
295. #60695	C₂₃	direct (N × H)
353. #3460	C₂×C₂₃	semidirect
354. #3179	C₂×C₂₃	semidirect
355. #3176	C₂×C₂₃	semidirect
356. #3175	C₂×C₂₃	semidirect
357. #3171	C₂×C₂₃	semidirect
358. #3169	C₂×C₂₃	semidirect
359. #3168	C₂×C₂₃	semidirect
360. #3164	C₂×C₂₃	semidirect
361. #3155	C₂×C₂₃	semidirect
362. #3136	C₂×C₂₃	semidirect
363. #3062	C₂×C₂₃	semidirect
364. #3061	C₂×C₂₃	semidirect
365. #3058	C₂×C₂₃	semidirect
366. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
367. C₄×#135	C₂×C₂₃	semidirect
368. C₂×C₄×D₈	C₂×C₂₃	semidirect
369. C₄×#131	C₂×C₂₃	semidirect
405. #542	C₂²×C₂₃	semidirect
407. #540	C₂²×C₂₃	semidirect
413. #532	C₂²×C₂₃	semidirect
415. #529	C₂²×C₂₃	semidirect
420. #501	C₂²×C₂₃	semidirect
421. #500	C₂²×C₂₃	semidirect
422. #499	C₂²×C₂₃	semidirect
426. #490	C₂²×C₂₃	semidirect
427. #489	C₂²×C₂₃	semidirect
428. #488	C₂²×C₂₃	semidirect
429. #486	C₂²×C₂₃	semidirect
431. #469	C₂²×C₂₃	semidirect
432. #468	C₂²×C₂₃	semidirect
433. #468	C₂²×C₂₃	semidirect
434. #467	C₂²×C₂₃	semidirect
437. #466	C₂²×C₂₃	semidirect
438. #466	C₂²×C₂₃	semidirect
439. #465	C₂²×C₂₃	semidirect
440. #442	C₂²×C₂₃	semidirect
441. #440	C₂²×C₂₃	semidirect
442. C₄×Q₁₆	C₂²×C₂₃	semidirect
443. C₄×Q₁₆	C₂²×C₂₃	semidirect
444. C₄×SD₁₆	C₂²×C₂₃	semidirect
445. C₄×SD₁₆	C₂²×C₂₃	semidirect
446. C₄×SD₁₆	C₂²×C₂₃	semidirect
451. C₄×D₈	C₂²×C₂₃	semidirect
452. C₄×D₈	C₂²×C₂₃	semidirect
453. C₄×D₈	C₂²×C₂₃	semidirect
463. #405	C₂²×C₂₃	semidirect
464. #405	C₂²×C₂₃	semidirect
466. C₄×M₁₆	C₂²×C₂₃	semidirect
468. C₂×C₄×C₈	C₂²×C₂₃	semidirect
588. C₂₃	#60695	direct (N × H)
634. M₁₆	#41×C₂₃	semidirect
638. C₂×C₈	#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×#3460	2
C₂₃×#3179	2
C₂₃×#3176	2
C₂₃×#3175	2
C₂₃×#3171	2
C₂₃×#3169	2
C₂₃×#3168	2
C₂₃×#3164	2
C₂₃×#3155	2
C₂₃×#3136	2
C₂₃×#3062	2
C₂₃×#3061	2
C₂₃×#3058	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₄×C₂₃×#135	2
C₂×C₄×D₈×C₂₃	2
C₄×C₂₃×#131	2
#60695	23

Subgroups — C23×#60695 #19208321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60695 #19208321