Subgroups — C₂₃×#60757 #19208383

Order 5888.

2310 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3200	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3010	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
23	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₂₃	—	2	1	no	—
25	C₂₃×#548	—	2	1	no	—
26	C₂₃×#547	—	2	2	no	—
27	C₂₃×#547	—	2	1	no	—
28	C₂₃×#546	—	2	2	no	—
29	C₂₃×#546	—	2	1	no	—
30	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#537	C₂²	1	2	yes	complemented
32	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#536	C₂²	1	2	yes	complemented
34	C₂₃×#535	—	2	2	no	—
35	C₂₃×#535	—	2	1	no	—
36	C₂₃×#535	—	2	1	no	—
37	C₂₃×#535	C₂²	1	4	yes	—
38	C₂₃×#535	C₂²	1	2	yes	—
39	C₂₃×#535	C₂²	1	2	yes	—
40	C₂×C₂₃×#127	—	2	1	no	—
41	C₂×C₂₃×#124	—	2	1	no	—
42	C₂₃×#525	C₂²	1	1	yes	characteristic
43	C₂₃×#525	C₂²	1	2	yes	complemented
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₂×C₂₃×#121	C₂²	1	2	yes	—
47	C₂×C₂₃×#121	C₂²	1	2	yes	—
48	C₂×C₂₃×#120	—	2	2	no	—
49	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
51	C₂₃×#485	C₂²	1	4	yes	complemented
52	C₂₃×#485	C₂²	1	2	yes	complemented
53	C₂₃×#484	C₂²	1	2	yes	complemented
54	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#483	C₂²	1	2	yes	complemented
57	C₂₃×#482	C₂²	1	4	yes	complemented
58	C₂₃×#482	C₂²	1	4	yes	complemented
59	C₂₃×#482	C₂²	1	2	yes	complemented
60	C₂₃×#481	C₂²	1	4	yes	complemented
61	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#480	C₂²	1	4	yes	complemented
63	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#469	C₂²	1	4	yes	complemented
65	C₂₃×#468	C₂²	1	4	yes	complemented
66	C₂₃×#468	C₂²	1	4	yes	complemented
67	C₂₃×#468	C₂²	1	4	yes	complemented
68	C₂₃×#466	C₂²	1	4	yes	complemented
69	C₂₃×#465	C₂²	1	4	yes	complemented
70	C₂₃×#465	C₂²	1	4	yes	complemented
71	C₂₃×#465	C₂²	1	4	yes	complemented
72	C₂₃×#450	C₂²	1	2	yes	—
73	C₂₃×#450	C₂²	1	2	yes	—
74	C₂₃×#450	C₂²	1	2	yes	—
75	C₂₃×#450	C₂²	1	4	yes	complemented
76	C₂₃×#450	C₂²	1	2	yes	complemented
77	C₂₃×#449	C₂²	1	4	yes	complemented
78	C₂₃×#449	C₂²	1	4	yes	complemented
79	C₂₃×#448	C₂²	1	4	yes	complemented
80	C₂₃×#448	C₂²	1	4	yes	complemented
81	C₂₃×#447	C₂²	1	2	yes	—
82	C₂₃×#447	C₂²	1	2	yes	complemented
83	C₂₃×#428	C₂²	1	2	yes	complemented
84	C₂₃×#427	C₂²	1	2	yes	complemented
85	C₂₃×#419	C₂²	1	2	yes	complemented
86	C₂₃×#418	C₂²	1	2	yes	complemented
87	C₂₃×#416	C₂²	1	2	yes	complemented
88	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
89	C₂₃×#408	C₂²	1	2	yes	complemented
90	C₂₃×#408	C₂²	1	4	yes	complemented
91	C₂₃×#407	C₂²	1	1	yes	characteristic
92	C₂₃×#407	C₂²	1	2	yes	complemented
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂⁵×C₂₃	—	2	1	no	—
96	C₂₃×2₋¹⁺⁴	—	4	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	1	no	—
99	C₂×#41×C₂₃	—	4	4	no	—
100	C₂×#41×C₂₃	D₄	1	2	yes	—
101	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
102	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
103	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×#41×C₂₃	C₂³	1	2	yes	—
107	C₂×#41×C₂₃	C₂³	1	2	yes	complemented
108	C₂²×Q₈×C₂₃	—	2	1	no	—
109	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
110	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₂₃	C₂³	1	2	yes	complemented
112	C₂²×D₄×C₂₃	—	2	2	no	—
113	C₂²×D₄×C₂₃	—	2	2	no	—
114	C₂²×D₄×C₂₃	—	2	1	no	—
115	C₂²×D₄×C₂₃	—	2	1	no	—
116	C₂²×D₄×C₂₃	—	2	1	no	—
117	C₂²×D₄×C₂₃	—	4	4	no	—
118	C₂²×D₄×C₂₃	D₄	1	2	yes	—
119	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
125	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
126	C₂×SD₁₆×C₂₃	—	4	4	no	—
127	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
130	C₂×D₈×C₂₃	C₂³	1	4	yes	—
131	C₂₃×#131	—	4	4	no	—
132	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
136	C₂₃×C₄⋊Q₈	—	2	1	no	—
137	C₂₃×C₄⋊Q₈	—	2	2	no	—
138	C₂₃×#127	—	2	2	no	—
139	C₂₃×#127	—	2	2	no	—
140	C₂₃×#127	—	2	4	no	—
141	C₂₃×#124	—	2	2	no	—
142	C₂₃×#124	—	2	2	no	—
143	C₂₃×#124	—	2	4	no	—
144	C₂₃×#124	—	2	1	no	—
145	C₂₃×#124	—	2	2	no	—
146	C₂₃×#123	—	2	2	no	—
147	C₂₃×#123	—	2	2	no	—
148	C₂₃×#123	—	2	2	no	—
149	C₂₃×#123	—	2	1	no	—
150	C₂₃×#123	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	—	2	1	no	—
153	C₂₃×C₂²⋊Q₈	—	2	1	no	—
154	C₂₃×C₂²⋊Q₈	—	2	2	no	—
155	C₂₃×C₂²⋊Q₈	—	2	1	no	—
156	C₂₃×C₂²⋊Q₈	—	2	2	no	—
157	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
162	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
163	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
164	C₂₃×#121	—	2	2	no	—
165	C₂₃×#121	—	2	2	no	—
166	C₂₃×#121	—	2	2	no	—
167	C₂₃×#121	—	2	2	no	—
168	C₂₃×#121	—	2	1	no	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	C₂³	1	1	yes	characteristic
174	C₂₃×#121	C₂³	1	1	yes	characteristic
175	C₂₃×#121	C₂³	1	4	yes	—
176	C₂₃×#121	C₂³	1	4	yes	—
177	C₂₃×#121	C₂³	1	4	yes	—
178	C₂₃×#121	C₂³	1	4	yes	—
179	C₂₃×#121	C₂³	1	2	yes	complemented
180	C₂₃×#120	—	2	1	no	—
181	C₂₃×#120	—	2	2	no	—
182	C₂₃×#120	—	2	4	no	—
183	C₂₃×#120	—	2	4	no	—
184	C₂₃×#120	—	2	4	no	—
185	C₂₃×#120	—	2	4	no	—
186	C₄×Q₈×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	2	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	—	2	1	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	C₂³	1	2	yes	—
196	C₂₃×#117	C₂³	1	1	yes	characteristic
197	C₂₃×#117	C₂³	1	2	yes	—
198	C₂₃×#117	C₂³	1	2	yes	complemented
199	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
205	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
209	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
210	C₂×C₄²×C₂₃	—	2	1	no	—
211	C₂₃×#107	C₂³	1	2	yes	complemented
212	C₂₃×#107	C₂³	1	2	yes	complemented
213	C₂₃×#107	C₂³	1	4	yes	complemented
214	C₂₃×#106	C₂³	1	2	yes	complemented
215	C₂₃×#106	C₂³	1	2	yes	complemented
216	C₂₃×#106	C₂³	1	4	yes	complemented
217	C₂₃×#103	C₂³	1	2	yes	complemented
218	C₂₃×#103	C₂³	1	2	yes	complemented
219	C₂₃×#103	C₂³	1	4	yes	complemented
220	C₂₃×#103	C₂³	1	4	yes	complemented
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	4	yes	—
225	C₂₃×#102	C₂³	1	2	yes	complemented
226	C₂₃×#102	C₂³	1	2	yes	complemented
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
233	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
234	C₂⁴×C₂₃	—	2	2	no	—
235	C₂⁴×C₂₃	—	2	2	no	—
236	C₂⁴×C₂₃	—	2	2	no	—
237	C₂⁴×C₂₃	—	4	4	no	—
238	C₂⁴×C₂₃	—	8	2	no	—
239	C₂⁴×C₂₃	—	8	2	no	—
240	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
242	#41×C₂₃	—	2	4	no	—
243	#41×C₂₃	—	2	4	no	—
244	#41×C₂₃	—	2	4	no	—
245	#41×C₂₃	—	4	4	no	—
246	#41×C₂₃	—	4	4	no	—
247	#41×C₂₃	—	4	2	no	—
248	#41×C₂₃	—	4	2	no	—
249	#41×C₂₃	—	4	4	no	—
250	#41×C₂₃	—	4	8	no	—
251	#41×C₂₃	—	4	4	no	—
252	C₂×Q₈×C₂₃	—	2	1	no	—
253	C₂×Q₈×C₂₃	—	2	2	no	—
254	C₂×Q₈×C₂₃	—	2	4	no	—
255	C₂×Q₈×C₂₃	—	4	2	no	—
256	C₂×Q₈×C₂₃	—	4	4	no	—
257	C₂×Q₈×C₂₃	—	4	4	no	—
258	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₂₃	—	2	1	no	—
264	C₂×D₄×C₂₃	—	2	1	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	1	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	4	no	—
269	C₂×D₄×C₂₃	—	2	4	no	—
270	C₂×D₄×C₂₃	—	2	4	no	—
271	C₂×D₄×C₂₃	—	2	4	no	—
272	C₂×D₄×C₂₃	—	2	2	no	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	2	2	no	—
275	C₂×D₄×C₂₃	—	2	4	no	—
276	C₂×D₄×C₂₃	—	2	4	no	—
277	C₂×D₄×C₂₃	—	4	4	no	—
278	C₂×D₄×C₂₃	—	4	4	no	—
279	C₂×D₄×C₂₃	—	4	2	no	—
280	C₂×D₄×C₂₃	—	4	4	no	—
281	C₂×D₄×C₂₃	—	4	4	no	—
282	C₂×D₄×C₂₃	—	4	4	no	—
283	C₂×D₄×C₂₃	—	4	4	no	—
284	C₂×D₄×C₂₃	—	8	4	no	—
285	C₂×D₄×C₂₃	—	8	4	no	—
286	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
294	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	—	2	4	no	—
296	C₂²×C₄×C₂₃	—	2	1	no	—
297	C₂²×C₄×C₂₃	—	2	1	no	—
298	C₂²×C₄×C₂₃	—	2	1	no	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	—	2	1	no	—
301	C₂²×C₄×C₂₃	—	2	2	no	—
302	C₂²×C₄×C₂₃	—	2	1	no	—
303	C₂²×C₄×C₂₃	—	2	2	no	—
304	C₂²×C₄×C₂₃	—	4	4	no	—
305	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	SD₁₆×C₂₃	—	4	4	no	—
317	SD₁₆×C₂₃	—	4	4	no	—
318	SD₁₆×C₂₃	—	4	4	no	—
319	D₈×C₂₃	—	4	4	no	—
320	M₁₆×C₂₃	—	2	4	no	—
321	M₁₆×C₂₃	—	4	4	no	—
322	C₂×C₈×C₂₃	—	2	4	no	—
323	C₂×C₈×C₂₃	—	4	4	no	—
324	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	1	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	1	no	—
333	C₄⋊C₄×C₂₃	—	2	1	no	—
334	C₄⋊C₄×C₂₃	—	2	1	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	1	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	1	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	1	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	1	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	4	no	—
355	C₂²⋊C₄×C₂₃	—	2	4	no	—
356	C₂²⋊C₄×C₂₃	—	2	4	no	—
357	C₂²⋊C₄×C₂₃	—	2	4	no	—
358	C₂²⋊C₄×C₂₃	—	2	1	no	—
359	C₂²⋊C₄×C₂₃	—	2	1	no	—
360	C₂²⋊C₄×C₂₃	—	2	2	no	—
361	C₄²×C₂₃	—	2	2	no	—
362	C₄²×C₂₃	—	2	2	no	—
363	C₄²×C₂₃	—	2	1	no	—
364	C₄²×C₂₃	—	2	2	no	—
365	#60757	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂³×C₂₃	—	2	2	no	—
367	C₂³×C₂₃	—	2	2	no	—
368	C₂³×C₂₃	—	2	4	no	—
369	C₂³×C₂₃	—	2	1	no	—
370	C₂³×C₂₃	—	2	4	no	—
371	C₂³×C₂₃	—	4	1	no	—
372	C₂³×C₂₃	—	4	2	no	—
373	C₂³×C₂₃	—	4	2	no	—
374	C₂³×C₂₃	—	4	4	no	—
375	C₂³×C₂₃	—	4	4	no	—
376	C₂³×C₂₃	—	4	4	no	—
377	C₂³×C₂₃	—	4	4	no	—
378	C₂³×C₂₃	—	4	4	no	—
379	C₂³×C₂₃	—	8	2	no	—
380	C₂³×C₂₃	—	8	2	no	—
381	C₂³×C₂₃	—	8	2	no	—
382	C₂³×C₂₃	—	8	2	no	—
383	C₂³×C₂₃	—	8	16	no	—
384	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
387	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	Q₈×C₂₃	—	2	2	no	—
390	Q₈×C₂₃	—	2	2	no	—
391	Q₈×C₂₃	—	2	4	no	—
392	Q₈×C₂₃	—	2	2	no	—
393	Q₈×C₂₃	—	4	2	no	—
394	Q₈×C₂₃	—	4	4	no	—
395	Q₈×C₂₃	—	4	2	no	—
396	D₄×C₂₃	—	2	4	no	—
397	D₄×C₂₃	—	2	4	no	—
398	D₄×C₂₃	—	2	2	no	—
399	D₄×C₂₃	—	2	2	no	—
400	D₄×C₂₃	—	2	2	no	—
401	D₄×C₂₃	—	2	4	no	—
402	D₄×C₂₃	—	2	4	no	—
403	D₄×C₂₃	—	4	2	no	—
404	D₄×C₂₃	—	4	2	no	—
405	D₄×C₂₃	—	4	2	no	—
406	D₄×C₂₃	—	4	4	no	—
407	D₄×C₂₃	—	4	4	no	—
408	D₄×C₂₃	—	4	4	no	—
409	D₄×C₂₃	—	4	2	no	—
410	D₄×C₂₃	—	4	2	no	—
411	D₄×C₂₃	—	4	4	no	—
412	D₄×C₂₃	—	8	2	no	—
413	D₄×C₂₃	—	8	1	no	—
414	D₄×C₂₃	—	8	4	no	—
415	D₄×C₂₃	—	8	4	no	—
416	D₄×C₂₃	—	8	4	no	—
417	D₄×C₂₃	—	8	4	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	4	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	4	no	—
425	C₂×C₄×C₂₃	—	2	1	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	4	2	no	—
433	C₂×C₄×C₂₃	—	4	2	no	—
434	C₂×C₄×C₂₃	—	4	2	no	—
435	C₂×C₄×C₂₃	—	4	4	no	—
436	C₂×C₄×C₂₃	—	4	2	no	—
437	C₂×C₄×C₂₃	—	4	4	no	—
438	C₂×C₄×C₂₃	—	4	2	no	—
439	C₂×C₄×C₂₃	—	4	2	no	—
440	C₂×C₄×C₂₃	—	4	2	no	—
441	C₂×C₄×C₂₃	—	8	1	no	—
442	C₂×C₄×C₂₃	—	8	2	no	—
443	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
449	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
450	C₈×C₂₃	—	2	2	no	—
451	C₈×C₂₃	—	2	2	no	—
452	C₈×C₂₃	—	2	4	no	—
453	#3489	C₂×C₂₃	1	1	yes	characteristic, complemented
454	C₂×#535	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#3200	C₂×C₂₃	1	4	yes	complemented
456	#3198	C₂×C₂₃	1	4	yes	complemented
457	#3194	C₂×C₂₃	1	2	yes	complemented
458	#3193	C₂×C₂₃	1	2	yes	complemented
459	#3188	C₂×C₂₃	1	2	yes	complemented
460	#3187	C₂×C₂₃	1	2	yes	complemented
461	#3096	C₂×C₂₃	1	2	yes	complemented
462	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#3062	C₂×C₂₃	1	2	yes	complemented
465	#3057	C₂×C₂₃	1	2	yes	complemented
466	#3010	C₂×C₂₃	1	2	yes	complemented
467	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
468	C₂×#450	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
470	C₂²×C₂₃	—	2	1	no	—
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	1	no	—
474	C₂²×C₂₃	—	2	2	no	—
475	C₂²×C₂₃	—	2	2	no	—
476	C₂²×C₂₃	—	2	1	no	—
477	C₂²×C₂₃	—	2	1	no	—
478	C₂²×C₂₃	—	2	2	no	—
479	C₂²×C₂₃	—	2	2	no	—
480	C₂²×C₂₃	—	2	2	no	—
481	C₂²×C₂₃	—	2	2	no	—
482	C₂²×C₂₃	—	2	1	no	—
483	C₂²×C₂₃	—	4	4	no	—
484	C₂²×C₂₃	—	4	1	no	—
485	C₂²×C₂₃	—	4	4	no	—
486	C₂²×C₂₃	—	4	1	no	—
487	C₂²×C₂₃	—	4	4	no	—
488	C₂²×C₂₃	—	4	1	no	—
489	C₂²×C₂₃	—	4	4	no	—
490	C₂²×C₂₃	—	8	4	no	—
491	C₂²×C₂₃	—	8	8	no	—
492	C₂²×C₂₃	—	8	8	no	—
493	C₂²×C₂₃	—	8	8	no	—
494	C₂²×C₂₃	#534	1	2	yes	—
495	C₂²×C₂₃	#577	1	2	yes	—
496	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₂₃	—	2	1	no	—
498	C₄×C₂₃	—	2	1	no	—
499	C₄×C₂₃	—	2	2	no	—
500	C₄×C₂₃	—	2	2	no	—
501	C₄×C₂₃	—	4	2	no	—
502	C₄×C₂₃	—	4	1	no	—
503	C₄×C₂₃	—	4	2	no	—
504	C₄×C₂₃	—	4	2	no	—
505	C₄×C₂₃	—	4	1	no	—
506	C₄×C₂₃	—	4	2	no	—
507	C₄×C₂₃	—	4	1	no	—
508	C₄×C₂₃	#534	1	2	yes	—
509	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
510	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
512	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
513	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
514	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
515	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
516	D₄×Q₈	—	2	1	no	—
517	#548	—	2	1	no	—
518	#547	—	2	2	no	—
519	#547	—	2	1	no	—
520	#546	—	2	2	no	—
521	#546	—	2	1	no	—
522	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
523	#537	C₂²×C₂₃	1	2	yes	complemented
524	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#536	C₂²×C₂₃	1	2	yes	complemented
526	#535	—	2	2	no	—
527	#535	—	2	1	no	—
528	#535	—	2	1	no	—
529	#535	C₂²×C₂₃	1	2	yes	—
530	#535	C₂²×C₂₃	1	4	yes	—
531	#535	C₂²×C₂₃	1	2	yes	—
532	C₂×#127	—	2	1	no	—
533	C₂×#124	—	2	1	no	—
534	#525	C₂²×C₂₃	1	1	yes	characteristic
535	#525	C₂²×C₂₃	1	2	yes	complemented
536	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
537	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
538	C₂×#121	C₂²×C₂₃	1	2	yes	—
539	C₂×#121	C₂²×C₂₃	1	2	yes	—
540	C₂×#120	—	2	2	no	—
541	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
542	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
543	#485	C₂²×C₂₃	1	2	yes	complemented
544	#485	C₂²×C₂₃	1	4	yes	complemented
545	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
546	#484	C₂²×C₂₃	1	2	yes	complemented
547	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
548	#483	C₂²×C₂₃	1	2	yes	complemented
549	#482	C₂²×C₂₃	1	2	yes	complemented
550	#482	C₂²×C₂₃	1	4	yes	complemented
551	#482	C₂²×C₂₃	1	4	yes	complemented
552	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
553	#481	C₂²×C₂₃	1	4	yes	complemented
554	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	#480	C₂²×C₂₃	1	4	yes	complemented
556	#469	C₂²×C₂₃	1	4	yes	complemented
557	#468	C₂²×C₂₃	1	4	yes	complemented
558	#468	C₂²×C₂₃	1	4	yes	complemented
559	#468	C₂²×C₂₃	1	4	yes	complemented
560	#466	C₂²×C₂₃	1	4	yes	complemented
561	#465	C₂²×C₂₃	1	4	yes	complemented
562	#465	C₂²×C₂₃	1	4	yes	complemented
563	#465	C₂²×C₂₃	1	4	yes	complemented
564	#450	C₂²×C₂₃	1	2	yes	—
565	#450	C₂²×C₂₃	1	2	yes	—
566	#450	C₂²×C₂₃	1	2	yes	—
567	#450	C₂²×C₂₃	1	4	yes	complemented
568	#450	C₂²×C₂₃	1	2	yes	complemented
569	#449	C₂²×C₂₃	1	4	yes	complemented
570	#449	C₂²×C₂₃	1	4	yes	complemented
571	#448	C₂²×C₂₃	1	4	yes	complemented
572	#448	C₂²×C₂₃	1	4	yes	complemented
573	#447	C₂²×C₂₃	1	2	yes	—
574	#447	C₂²×C₂₃	1	2	yes	complemented
575	#428	C₂²×C₂₃	1	2	yes	complemented
576	#427	C₂²×C₂₃	1	2	yes	complemented
577	#419	C₂²×C₂₃	1	2	yes	complemented
578	#418	C₂²×C₂₃	1	2	yes	complemented
579	#416	C₂²×C₂₃	1	2	yes	complemented
580	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
581	#408	C₂²×C₂₃	1	4	yes	complemented
582	#408	C₂²×C₂₃	1	2	yes	complemented
583	#407	C₂²×C₂₃	1	1	yes	characteristic
584	#407	C₂²×C₂₃	1	2	yes	complemented
585	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
586	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
587	C₂×C₂₃	—	2	2	no	—
588	C₂×C₂₃	—	2	2	no	—
589	C₂×C₂₃	—	4	1	no	—
590	C₂×C₂₃	—	4	2	no	—
591	C₂×C₂₃	—	4	2	no	—
592	C₂×C₂₃	—	8	1	no	—
593	C₂×C₂₃	—	8	4	no	—
594	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
595	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
596	C₂×C₂₃	#3585	1	1	yes	characteristic
597	C₂⁵	—	2	1	no	—
598	2₋¹⁺⁴	—	4	4	no	—
599	C₂×#41	—	2	2	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	4	4	no	—
602	C₂×#41	D₄×C₂₃	1	2	yes	—
603	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
604	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
605	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
608	C₂×#41	C₂³×C₂₃	1	2	yes	—
609	C₂×#41	C₂³×C₂₃	1	2	yes	complemented
610	C₂²×Q₈	—	2	1	no	—
611	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
612	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
613	C₂²×Q₈	C₂³×C₂₃	1	2	yes	complemented
614	C₂²×D₄	—	2	2	no	—
615	C₂²×D₄	—	2	2	no	—
616	C₂²×D₄	—	2	1	no	—
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	—	4	4	no	—
620	C₂²×D₄	D₄×C₂₃	1	2	yes	—
621	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
622	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
623	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
624	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
625	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
627	AGL(1,ℤ/8)	—	4	4	no	—
628	C₂×SD₁₆	—	4	4	no	—
629	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
630	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
631	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
632	C₂×D₈	C₂³×C₂₃	1	4	yes	—
633	#131	—	4	4	no	—
634	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
635	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
636	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
637	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
638	C₄⋊Q₈	—	2	1	no	—
639	C₄⋊Q₈	—	2	2	no	—
640	#127	—	2	2	no	—
641	#127	—	2	2	no	—
642	#127	—	2	4	no	—
643	#124	—	2	2	no	—
644	#124	—	2	2	no	—
645	#124	—	2	4	no	—
646	#124	—	2	1	no	—
647	#124	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	1	no	—
652	#123	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
660	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
662	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
664	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
665	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	1	no	—
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	—	2	2	no	—
674	#121	—	2	2	no	—
675	#121	C₂³×C₂₃	1	4	yes	—
676	#121	C₂³×C₂₃	1	4	yes	—
677	#121	C₂³×C₂₃	1	4	yes	—
678	#121	C₂³×C₂₃	1	4	yes	—
679	#121	C₂³×C₂₃	1	1	yes	characteristic
680	#121	C₂³×C₂₃	1	1	yes	characteristic
681	#121	C₂³×C₂₃	1	2	yes	complemented
682	#120	—	2	1	no	—
683	#120	—	2	2	no	—
684	#120	—	2	4	no	—
685	#120	—	2	4	no	—
686	#120	—	2	4	no	—
687	#120	—	2	4	no	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×D₄	—	2	1	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	#117	—	2	1	no	—
696	#117	—	2	1	no	—
697	#117	C₂³×C₂₃	1	2	yes	—
698	#117	C₂³×C₂₃	1	2	yes	—
699	#117	C₂³×C₂₃	1	1	yes	characteristic
700	#117	C₂³×C₂₃	1	2	yes	complemented
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	2	no	—
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	2	no	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	—	2	2	no	—
712	C₂×C₄²	—	2	1	no	—
713	#107	C₂³×C₂₃	1	2	yes	complemented
714	#107	C₂³×C₂₃	1	2	yes	complemented
715	#107	C₂³×C₂₃	1	4	yes	complemented
716	#106	C₂³×C₂₃	1	2	yes	complemented
717	#106	C₂³×C₂₃	1	2	yes	complemented
718	#106	C₂³×C₂₃	1	4	yes	complemented
719	#103	C₂³×C₂₃	1	2	yes	complemented
720	#103	C₂³×C₂₃	1	2	yes	complemented
721	#103	C₂³×C₂₃	1	4	yes	complemented
722	#103	C₂³×C₂₃	1	4	yes	complemented
723	#102	C₂³×C₂₃	1	4	yes	—
724	#102	C₂³×C₂₃	1	4	yes	—
725	#102	C₂³×C₂₃	1	4	yes	—
726	#102	C₂³×C₂₃	1	4	yes	—
727	#102	C₂³×C₂₃	1	2	yes	complemented
728	#102	C₂³×C₂₃	1	2	yes	complemented
729	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
730	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
731	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
735	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
736	C₂₃	#60757	1	1	yes	characteristic, direct product factor, Sylow
737	C₂⁴	—	2	2	no	—
738	C₂⁴	—	2	2	no	—
739	C₂⁴	—	2	2	no	—
740	C₂⁴	—	4	4	no	—
741	C₂⁴	—	8	2	no	—
742	C₂⁴	—	8	2	no	—
743	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
744	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
745	#41	—	2	4	no	—
746	#41	—	2	4	no	—
747	#41	—	2	4	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	4	no	—
753	#41	—	4	8	no	—
754	#41	—	4	4	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	—	4	4	no	—
760	C₂×Q₈	—	4	4	no	—
761	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
764	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
765	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	4	4	no	—
781	C₂×D₄	—	4	4	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	4	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	8	4	no	—
788	C₂×D₄	—	8	4	no	—
789	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
790	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
791	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
792	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
793	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
794	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
795	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
796	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
797	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	4	4	no	—
808	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
812	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
813	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
819	SD₁₆	—	4	4	no	—
820	SD₁₆	—	4	4	no	—
821	SD₁₆	—	4	4	no	—
822	D₈	—	4	4	no	—
823	M₁₆	—	2	4	no	—
824	M₁₆	—	4	4	no	—
825	C₂×C₈	—	2	4	no	—
826	C₂×C₈	—	4	4	no	—
827	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
829	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
843	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	1	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₄²	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	4	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	4	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	8	2	no	—
882	C₂³	—	8	2	no	—
883	C₂³	—	8	2	no	—
884	C₂³	—	8	2	no	—
885	C₂³	—	8	16	no	—
886	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
887	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
888	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
889	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
890	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	4	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	2	no	—
896	Q₈	—	4	4	no	—
897	Q₈	—	4	2	no	—
898	D₄	—	2	4	no	—
899	D₄	—	2	4	no	—
900	D₄	—	2	2	no	—
901	D₄	—	2	4	no	—
902	D₄	—	2	4	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	2	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	2	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	2	no	—
912	D₄	—	4	2	no	—
913	D₄	—	4	4	no	—
914	D₄	—	8	4	no	—
915	D₄	—	8	4	no	—
916	D₄	—	8	4	no	—
917	D₄	—	8	4	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	4	2	no	—
943	C₂×C₄	—	8	1	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
950	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
951	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	4	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	4	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	8	4	no	—
976	C₂²	—	8	8	no	—
977	C₂²	—	8	8	no	—
978	C₂²	—	8	8	no	—
979	C₂²	C₂₃×#534	1	2	yes	—
980	C₂²	C₂₃×#577	1	2	yes	—
981	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	C₂₃×#534	1	2	yes	—
994	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	2	2	no	—
997	C₂	—	4	1	no	—
998	C₂	—	4	2	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	8	4	no	—
1001	C₂	—	8	1	no	—
1002	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
1003	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1004	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 ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3489	C₂	semidirect
2. C₂×C₂₃×#535	C₂	semidirect
3. C₂₃×#3200	C₂	semidirect
4. C₂₃×#3198	C₂	semidirect
5. C₂₃×#3194	C₂	semidirect
6. C₂₃×#3193	C₂	semidirect
7. C₂₃×#3188	C₂	semidirect
8. C₂₃×#3187	C₂	semidirect
9. C₂₃×#3096	C₂	semidirect
10. C₂₃×#3095	C₂	semidirect
11. C₂₃×#3091	C₂	semidirect
12. C₂₃×#3062	C₂	semidirect
13. C₂₃×#3057	C₂	semidirect
14. C₂₃×#3010	C₂	semidirect
15. C₂₃×#3003	C₂	semidirect
16. C₂×C₂₃×#450	C₂	semidirect
17. C₂₃×#2880	C₂	semidirect
18. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
21. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂²×SD₁₆×C₂₃	C₂²	semidirect
23. C₂×C₂₃×#131	C₂²	semidirect
30. C₂₃×#537	C₂²	semidirect
31. C₂₃×#537	C₂²	semidirect
32. C₂₃×#536	C₂²	semidirect
33. C₂₃×#536	C₂²	semidirect
43. C₂₃×#525	C₂²	semidirect
45. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
49. C₂₃×#520	C₂²	semidirect
51. C₂₃×#485	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#484	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
55. C₂₃×#483	C₂²	semidirect
56. C₂₃×#483	C₂²	semidirect
57. C₂₃×#482	C₂²	semidirect
58. C₂₃×#482	C₂²	semidirect
59. C₂₃×#482	C₂²	semidirect
60. C₂₃×#481	C₂²	semidirect
61. C₂₃×#481	C₂²	semidirect
62. C₂₃×#480	C₂²	semidirect
63. C₂₃×#480	C₂²	semidirect
64. C₂₃×#469	C₂²	semidirect
65. C₂₃×#468	C₂²	semidirect
66. C₂₃×#468	C₂²	semidirect
67. C₂₃×#468	C₂²	semidirect
68. C₂₃×#466	C₂²	semidirect
69. C₂₃×#465	C₂²	semidirect
70. C₂₃×#465	C₂²	semidirect
71. C₂₃×#465	C₂²	semidirect
75. C₂₃×#450	C₂²	semidirect
76. C₂₃×#450	C₂²	semidirect
77. C₂₃×#449	C₂²	semidirect
78. C₂₃×#449	C₂²	semidirect
79. C₂₃×#448	C₂²	semidirect
80. C₂₃×#448	C₂²	semidirect
82. C₂₃×#447	C₂²	semidirect
83. C₂₃×#428	C₂²	semidirect
84. C₂₃×#427	C₂²	semidirect
85. C₂₃×#419	C₂²	semidirect
86. C₂₃×#418	C₂²	semidirect
87. C₂₃×#416	C₂²	semidirect
88. C₂×C₂₃×#102	C₂²	semidirect
89. C₂₃×#408	C₂²	semidirect
90. C₂₃×#408	C₂²	semidirect
92. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
107. C₂×#41×C₂₃	C₂³	semidirect
111. C₂²×Q₈×C₂₃	C₂³	semidirect
133. C₂×M₁₆×C₂₃	C₂³	semidirect
135. C₂²×C₈×C₂₃	C₂³	semidirect
161. C₂₃×C₂²⋊Q₈	C₂³	semidirect
162. C₂₃×C₂²⋊Q₈	C₂³	semidirect
163. C₂₃×C₂²⋊Q₈	C₂³	semidirect
179. C₂₃×#121	C₂³	semidirect
198. C₂₃×#117	C₂³	semidirect
204. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
211. C₂₃×#107	C₂³	semidirect
212. C₂₃×#107	C₂³	semidirect
213. C₂₃×#107	C₂³	semidirect
214. C₂₃×#106	C₂³	semidirect
215. C₂₃×#106	C₂³	semidirect
216. C₂₃×#106	C₂³	semidirect
217. C₂₃×#103	C₂³	semidirect
218. C₂₃×#103	C₂³	semidirect
219. C₂₃×#103	C₂³	semidirect
220. C₂₃×#103	C₂³	semidirect
225. C₂₃×#102	C₂³	semidirect
226. C₂₃×#102	C₂³	semidirect
232. C₂₃×C₂²⋊C₈	C₂³	semidirect
233. C₂₃×C₂²⋊C₈	C₂³	semidirect
365. #60757	C₂₃	direct (N × H)
453. #3489	C₂×C₂₃	semidirect
454. C₂×#535	C₂×C₂₃	semidirect
455. #3200	C₂×C₂₃	semidirect
456. #3198	C₂×C₂₃	semidirect
457. #3194	C₂×C₂₃	semidirect
458. #3193	C₂×C₂₃	semidirect
459. #3188	C₂×C₂₃	semidirect
460. #3187	C₂×C₂₃	semidirect
461. #3096	C₂×C₂₃	semidirect
462. #3095	C₂×C₂₃	semidirect
463. #3091	C₂×C₂₃	semidirect
464. #3062	C₂×C₂₃	semidirect
465. #3057	C₂×C₂₃	semidirect
466. #3010	C₂×C₂₃	semidirect
467. #3003	C₂×C₂₃	semidirect
468. C₂×#450	C₂×C₂₃	semidirect
469. #2880	C₂×C₂₃	semidirect
510. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
513. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
514. C₂²×SD₁₆	C₂²×C₂₃	semidirect
515. C₂×#131	C₂²×C₂₃	semidirect
522. #537	C₂²×C₂₃	semidirect
523. #537	C₂²×C₂₃	semidirect
524. #536	C₂²×C₂₃	semidirect
525. #536	C₂²×C₂₃	semidirect
535. #525	C₂²×C₂₃	semidirect
537. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
541. #520	C₂²×C₂₃	semidirect
543. #485	C₂²×C₂₃	semidirect
544. #485	C₂²×C₂₃	semidirect
545. #484	C₂²×C₂₃	semidirect
546. #484	C₂²×C₂₃	semidirect
547. #483	C₂²×C₂₃	semidirect
548. #483	C₂²×C₂₃	semidirect
549. #482	C₂²×C₂₃	semidirect
550. #482	C₂²×C₂₃	semidirect
551. #482	C₂²×C₂₃	semidirect
552. #481	C₂²×C₂₃	semidirect
553. #481	C₂²×C₂₃	semidirect
554. #480	C₂²×C₂₃	semidirect
555. #480	C₂²×C₂₃	semidirect
556. #469	C₂²×C₂₃	semidirect
557. #468	C₂²×C₂₃	semidirect
558. #468	C₂²×C₂₃	semidirect
559. #468	C₂²×C₂₃	semidirect
560. #466	C₂²×C₂₃	semidirect
561. #465	C₂²×C₂₃	semidirect
562. #465	C₂²×C₂₃	semidirect
563. #465	C₂²×C₂₃	semidirect
567. #450	C₂²×C₂₃	semidirect
568. #450	C₂²×C₂₃	semidirect
569. #449	C₂²×C₂₃	semidirect
570. #449	C₂²×C₂₃	semidirect
571. #448	C₂²×C₂₃	semidirect
572. #448	C₂²×C₂₃	semidirect
574. #447	C₂²×C₂₃	semidirect
575. #428	C₂²×C₂₃	semidirect
576. #427	C₂²×C₂₃	semidirect
577. #419	C₂²×C₂₃	semidirect
578. #418	C₂²×C₂₃	semidirect
579. #416	C₂²×C₂₃	semidirect
580. C₂×#102	C₂²×C₂₃	semidirect
581. #408	C₂²×C₂₃	semidirect
582. #408	C₂²×C₂₃	semidirect
584. #407	C₂²×C₂₃	semidirect
586. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
609. C₂×#41	C₂³×C₂₃	semidirect
613. C₂²×Q₈	C₂³×C₂₃	semidirect
635. C₂×M₁₆	C₂³×C₂₃	semidirect
637. C₂²×C₈	C₂³×C₂₃	semidirect
663. C₂²⋊Q₈	C₂³×C₂₃	semidirect
664. C₂²⋊Q₈	C₂³×C₂₃	semidirect
665. C₂²⋊Q₈	C₂³×C₂₃	semidirect
681. #121	C₂³×C₂₃	semidirect
700. #117	C₂³×C₂₃	semidirect
706. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
713. #107	C₂³×C₂₃	semidirect
714. #107	C₂³×C₂₃	semidirect
715. #107	C₂³×C₂₃	semidirect
716. #106	C₂³×C₂₃	semidirect
717. #106	C₂³×C₂₃	semidirect
718. #106	C₂³×C₂₃	semidirect
719. #103	C₂³×C₂₃	semidirect
720. #103	C₂³×C₂₃	semidirect
721. #103	C₂³×C₂₃	semidirect
722. #103	C₂³×C₂₃	semidirect
727. #102	C₂³×C₂₃	semidirect
728. #102	C₂³×C₂₃	semidirect
734. C₂²⋊C₈	C₂³×C₂₃	semidirect
735. C₂²⋊C₈	C₂³×C₂₃	semidirect
736. C₂₃	#60757	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×#3489	2
C₂×C₂₃×#535	2
C₂₃×#3200	2
C₂₃×#3198	2
C₂₃×#3194	2
C₂₃×#3193	2
C₂₃×#3188	2
C₂₃×#3187	2
C₂₃×#3096	2
C₂₃×#3095	2
C₂₃×#3091	2
C₂₃×#3062	2
C₂₃×#3057	2
C₂₃×#3010	2
C₂₃×#3003	2
C₂×C₂₃×#450	2
C₂₃×#2880	2
#60757	23

Subgroups — C23×#60757 #19208383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60757 #19208383