Subgroups — C₂₃×#60578 #19208204

Order 5888.

2274 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3122	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3118	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3114	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3109	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2948	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#555	—	2	1	no	—
22	C₂₃×#553	—	2	1	no	—
23	C₂₃×#553	—	2	1	no	—
24	C₂₃×#551	—	2	2	no	—
25	C₂₃×#547	—	2	1	no	—
26	C₂₃×#546	—	2	2	no	—
27	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#542	C₂²	1	2	yes	complemented
29	C₂₃×#540	C₂²	1	2	yes	complemented
30	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#532	C₂²	1	2	yes	complemented
32	C₂₃×#529	C₂²	1	2	yes	complemented
33	C₂₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#518	—	2	2	no	—
37	C₂₃×#518	—	2	1	no	—
38	C₂₃×#518	—	2	1	no	—
39	C₂₃×#518	C₂²	1	2	yes	—
40	C₂₃×#518	C₂²	1	2	yes	—
41	C₂₃×#518	C₂²	1	4	yes	complemented
42	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₂₃	—	2	1	no	—
44	C₂×C₄×D₄×C₂₃	—	2	1	no	—
45	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₂₃	—	2	2	no	—
50	C₂₃×#485	C₂²	1	2	yes	complemented
51	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#482	C₂²	1	2	yes	complemented
54	C₂₃×#482	C₂²	1	4	yes	complemented
55	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#481	C₂²	1	2	yes	complemented
57	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#480	C₂²	1	2	yes	complemented
59	C₂₃×#478	C₂²	1	4	yes	complemented
60	C₂₃×#478	C₂²	1	4	yes	complemented
61	C₂₃×#476	C₂²	1	4	yes	complemented
62	C₂₃×#474	C₂²	1	4	yes	complemented
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#463	C₂²	1	4	yes	complemented
65	C₂₃×#459	C₂²	1	4	yes	complemented
66	C₂₃×#459	C₂²	1	4	yes	complemented
67	C₂₃×#450	C₂²	1	2	yes	complemented
68	C₂₃×#450	C₂²	1	2	yes	complemented
69	C₂₃×#447	C₂²	1	2	yes	—
70	C₂₃×#447	C₂²	1	2	yes	—
71	C₂₃×#447	C₂²	1	4	yes	—
72	C₂₃×#447	C₂²	1	2	yes	complemented
73	C₂₃×#447	C₂²	1	2	yes	complemented
74	C₂₃×#442	C₂²	1	4	yes	complemented
75	C₂₃×#442	C₂²	1	4	yes	complemented
76	C₂₃×#442	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
79	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
80	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
81	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
82	C₂₃×#433	C₂²	1	4	yes	complemented
83	C₂₃×#432	C₂²	1	2	yes	complemented
84	C₂₃×#431	C₂²	1	2	yes	complemented
85	C₂₃×#428	C₂²	1	2	yes	complemented
86	C₂₃×#427	C₂²	1	2	yes	complemented
87	C₂₃×#424	C₂²	1	2	yes	complemented
88	C₂₃×#418	C₂²	1	2	yes	—
89	C₂₃×#418	C₂²	1	2	yes	complemented
90	C₂₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₂₃×#102	C₂²	1	2	yes	—
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	—	2	8	no	—
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	—	2	1	no	—
103	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₂₃	—	2	2	no	—
108	C₂³×C₄×C₂₃	—	2	2	no	—
109	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×D₈×C₂₃	—	2	8	no	—
113	C₂×D₈×C₂₃	C₂³	1	4	yes	—
114	C₂×D₈×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	4	yes	—
116	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	—	2	1	no	—
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
120	C₂₃×#127	C₂³	1	2	yes	complemented
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#125	—	2	1	no	—
124	C₂₃×#125	C₂³	1	2	yes	complemented
125	C₂₃×#124	—	2	2	no	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	C₂³	1	2	yes	complemented
128	C₂₃×#123	—	2	2	no	—
129	C₂₃×#123	—	2	1	no	—
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	—	2	2	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	1	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	C₂³	1	2	yes	—
145	C₂₃×#121	C₂³	1	2	yes	—
146	C₂₃×#121	C₂³	1	1	yes	characteristic
147	C₂₃×#121	C₂³	1	1	yes	characteristic
148	C₂₃×#120	—	2	1	no	—
149	C₂₃×#120	—	2	2	no	—
150	C₄×Q₈×C₂₃	C₂³	1	2	yes	complemented
151	C₄×D₄×C₂₃	—	2	1	no	—
152	C₄×D₄×C₂₃	—	2	1	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	1	no	—
155	C₄×D₄×C₂₃	—	2	1	no	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	4	no	—
161	C₄×D₄×C₂₃	—	2	4	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	C₂³	1	4	yes	—
169	C₄×D₄×C₂₃	C₂³	1	4	yes	—
170	C₄×D₄×C₂₃	C₂³	1	4	yes	—
171	C₄×D₄×C₂₃	C₂³	1	4	yes	—
172	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
173	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
174	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
175	C₂₃×#117	—	2	1	no	—
176	C₂₃×#117	—	2	1	no	—
177	C₂₃×#117	—	2	1	no	—
178	C₂₃×#117	—	2	2	no	—
179	C₂₃×#117	D₄	1	2	yes	—
180	C₂₃×#117	D₄	1	1	yes	characteristic
181	C₂₃×#117	D₄	1	1	yes	characteristic
182	C₂₃×#117	C₂³	1	2	yes	—
183	C₂₃×#117	C₂³	1	1	yes	characteristic
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂₃×#117	C₂³	1	1	yes	characteristic
186	C₂₃×#117	C₂³	1	1	yes	characteristic
187	C₂₃×#117	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
201	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
202	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
203	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
204	C₂×C₄²×C₂₃	—	2	1	no	—
205	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
206	C₂₃×#107	C₂³	1	2	yes	complemented
207	C₂₃×#107	C₂³	1	2	yes	complemented
208	C₂₃×#107	C₂³	1	4	yes	complemented
209	C₂₃×#106	C₂³	1	2	yes	complemented
210	C₂₃×#106	C₂³	1	2	yes	complemented
211	C₂₃×#106	C₂³	1	4	yes	complemented
212	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
213	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
214	C₂₃×#103	C₂³	1	2	yes	complemented
215	C₂₃×#103	C₂³	1	2	yes	complemented
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	complemented
221	C₂₃×#102	C₂³	1	2	yes	complemented
222	C₂₃×#102	C₂³	1	4	yes	complemented
223	C₂₃×#102	C₂³	1	4	yes	complemented
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₂₃×#97	C₂³	1	4	yes	complemented
230	C₄×C₈×C₂₃	C₂³	1	4	yes	complemented
231	C₂⁴×C₂₃	—	2	8	no	—
232	C₂⁴×C₂₃	—	2	2	no	—
233	C₂⁴×C₂₃	—	2	2	no	—
234	C₂⁴×C₂₃	—	2	2	no	—
235	C₂⁴×C₂₃	—	2	1	no	—
236	C₂⁴×C₂₃	—	8	2	no	—
237	C₂⁴×C₂₃	—	8	2	no	—
238	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
239	#41×C₂₃	—	2	4	no	—
240	#41×C₂₃	—	8	4	no	—
241	C₂×Q₈×C₂₃	—	2	2	no	—
242	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₂₃	—	2	8	no	—
244	C₂×D₄×C₂₃	—	2	8	no	—
245	C₂×D₄×C₂₃	—	2	8	no	—
246	C₂×D₄×C₂₃	—	2	8	no	—
247	C₂×D₄×C₂₃	—	2	8	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	—	2	2	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	2	1	no	—
257	C₂×D₄×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	—	2	2	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	8	2	no	—
262	C₂×D₄×C₂₃	#41	1	8	yes	complemented
263	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
265	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₂₃	—	2	4	no	—
267	C₂²×C₄×C₂₃	—	2	1	no	—
268	C₂²×C₄×C₂₃	—	2	1	no	—
269	C₂²×C₄×C₂₃	—	2	1	no	—
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	—	2	4	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	2	no	—
278	C₂²×C₄×C₂₃	—	8	4	no	—
279	C₂²×C₄×C₂₃	—	8	4	no	—
280	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	SD₁₆×C₂₃	—	2	8	no	—
289	D₈×C₂₃	—	2	8	no	—
290	D₈×C₂₃	—	2	8	no	—
291	D₈×C₂₃	—	2	8	no	—
292	M₁₆×C₂₃	—	2	4	no	—
293	C₂×C₈×C₂₃	—	2	4	no	—
294	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
295	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	2	no	—
331	C₂²⋊C₄×C₂₃	—	2	2	no	—
332	C₂²⋊C₄×C₂₃	—	2	1	no	—
333	C₂²⋊C₄×C₂₃	—	2	2	no	—
334	C₂²⋊C₄×C₂₃	—	2	1	no	—
335	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	2	no	—
342	C₄²×C₂₃	—	2	1	no	—
343	C₄²×C₂₃	C₂×D₄	1	2	yes	—
344	C₄²×C₂₃	C₂×D₄	1	2	yes	—
345	C₄²×C₂₃	C₂⁴	1	2	yes	—
346	C₄²×C₂₃	C₂⁴	1	2	yes	—
347	#60578	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂³×C₂₃	—	2	8	no	—
349	C₂³×C₂₃	—	2	8	no	—
350	C₂³×C₂₃	—	2	2	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	4	no	—
353	C₂³×C₂₃	—	2	8	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	4	1	no	—
357	C₂³×C₂₃	—	4	4	no	—
358	C₂³×C₂₃	—	4	4	no	—
359	C₂³×C₂₃	—	4	2	no	—
360	C₂³×C₂₃	—	8	2	no	—
361	C₂³×C₂₃	—	8	2	no	—
362	C₂³×C₂₃	—	8	2	no	—
363	C₂³×C₂₃	—	8	2	no	—
364	C₂³×C₂₃	—	8	1	no	—
365	C₂³×C₂₃	—	8	1	no	—
366	C₂³×C₂₃	—	8	16	no	—
367	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
368	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	Q₈×C₂₃	—	2	2	no	—
371	Q₈×C₂₃	—	8	2	no	—
372	D₄×C₂₃	—	2	8	no	—
373	D₄×C₂₃	—	2	8	no	—
374	D₄×C₂₃	—	2	8	no	—
375	D₄×C₂₃	—	2	4	no	—
376	D₄×C₂₃	—	2	4	no	—
377	D₄×C₂₃	—	2	2	no	—
378	D₄×C₂₃	—	4	2	no	—
379	D₄×C₂₃	—	4	4	no	—
380	D₄×C₂₃	—	4	2	no	—
381	D₄×C₂₃	—	4	2	no	—
382	D₄×C₂₃	—	8	2	no	—
383	D₄×C₂₃	—	8	2	no	—
384	D₄×C₂₃	—	8	1	no	—
385	D₄×C₂₃	—	8	2	no	—
386	D₄×C₂₃	C₂×#41	1	8	yes	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	4	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	1	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	4	2	no	—
400	C₂×C₄×C₂₃	—	4	2	no	—
401	C₂×C₄×C₂₃	—	4	2	no	—
402	C₂×C₄×C₂₃	—	4	2	no	—
403	C₂×C₄×C₂₃	—	8	2	no	—
404	C₂×C₄×C₂₃	—	8	4	no	—
405	C₂×C₄×C₂₃	—	8	4	no	—
406	C₂×C₄×C₂₃	—	8	4	no	—
407	C₂×C₄×C₂₃	—	8	4	no	—
408	C₂×C₄×C₂₃	—	8	2	no	—
409	C₂×C₄×C₂₃	—	8	2	no	—
410	C₂×C₄×C₂₃	—	8	1	no	—
411	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
419	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₂₃	—	2	2	no	—
421	C₈×C₂₃	—	2	2	no	—
422	C₈×C₂₃	—	2	4	no	—
423	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
424	C₂×#518	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#3122	C₂×C₂₃	1	4	yes	complemented
426	#3118	C₂×C₂₃	1	4	yes	complemented
427	#3114	C₂×C₂₃	1	2	yes	complemented
428	#3109	C₂×C₂₃	1	2	yes	complemented
429	#3105	C₂×C₂₃	1	2	yes	complemented
430	#3100	C₂×C₂₃	1	2	yes	complemented
431	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
432	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#3081	C₂×C₂₃	1	2	yes	complemented
434	#3041	C₂×C₂₃	1	2	yes	complemented
435	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
436	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
437	#2948	C₂×C₂₃	1	2	yes	complemented
438	#2946	C₂×C₂₃	1	2	yes	complemented
439	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
440	C₂²×C₂₃	—	2	1	no	—
441	C₂²×C₂₃	—	2	1	no	—
442	C₂²×C₂₃	—	2	1	no	—
443	C₂²×C₂₃	—	2	1	no	—
444	C₂²×C₂₃	—	2	1	no	—
445	C₂²×C₂₃	—	2	1	no	—
446	C₂²×C₂₃	—	2	8	no	—
447	C₂²×C₂₃	—	2	1	no	—
448	C₂²×C₂₃	—	4	4	no	—
449	C₂²×C₂₃	—	4	16	no	—
450	C₂²×C₂₃	—	4	4	no	—
451	C₂²×C₂₃	—	4	4	no	—
452	C₂²×C₂₃	—	4	2	no	—
453	C₂²×C₂₃	—	4	1	no	—
454	C₂²×C₂₃	—	4	1	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	1	no	—
457	C₂²×C₂₃	—	4	2	no	—
458	C₂²×C₂₃	—	8	8	no	—
459	C₂²×C₂₃	—	8	8	no	—
460	C₂²×C₂₃	—	16	2	no	—
461	C₂²×C₂₃	#525	1	2	yes	—
462	C₂²×C₂₃	#576	1	2	yes	—
463	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	1	no	—
467	C₄×C₂₃	—	2	1	no	—
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	1	no	—
472	C₄×C₂₃	—	4	1	no	—
473	C₄×C₂₃	—	4	2	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	1	no	—
476	C₄×C₂₃	#525	1	2	yes	—
477	C₄×C₂₃	C₂²×#41	1	2	yes	—
478	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
480	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
481	#555	—	2	1	no	—
482	#553	—	2	1	no	—
483	#553	—	2	1	no	—
484	#551	—	2	2	no	—
485	#547	—	2	1	no	—
486	#546	—	2	2	no	—
487	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	#542	C₂²×C₂₃	1	2	yes	complemented
489	#540	C₂²×C₂₃	1	2	yes	complemented
490	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#532	C₂²×C₂₃	1	2	yes	complemented
492	#529	C₂²×C₂₃	1	2	yes	complemented
493	#525	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
495	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	#518	—	2	2	no	—
497	#518	—	2	1	no	—
498	#518	—	2	1	no	—
499	#518	C₂²×C₂₃	1	2	yes	—
500	#518	C₂²×C₂₃	1	2	yes	—
501	#518	C₂²×C₂₃	1	4	yes	complemented
502	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	C₂×C₄×D₄	—	2	1	no	—
504	C₂×C₄×D₄	—	2	1	no	—
505	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
506	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
507	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
509	C₂²×C₂²⋊C₄	—	2	2	no	—
510	#485	C₂²×C₂₃	1	2	yes	complemented
511	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	#482	C₂²×C₂₃	1	2	yes	complemented
514	#482	C₂²×C₂₃	1	4	yes	complemented
515	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	#481	C₂²×C₂₃	1	2	yes	complemented
517	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	#480	C₂²×C₂₃	1	2	yes	complemented
519	#478	C₂²×C₂₃	1	4	yes	complemented
520	#478	C₂²×C₂₃	1	4	yes	complemented
521	#476	C₂²×C₂₃	1	4	yes	complemented
522	#474	C₂²×C₂₃	1	4	yes	complemented
523	#463	C₂²×C₂₃	1	4	yes	complemented
524	#463	C₂²×C₂₃	1	4	yes	complemented
525	#459	C₂²×C₂₃	1	4	yes	complemented
526	#459	C₂²×C₂₃	1	4	yes	complemented
527	#450	C₂²×C₂₃	1	2	yes	complemented
528	#450	C₂²×C₂₃	1	2	yes	complemented
529	#447	C₂²×C₂₃	1	2	yes	—
530	#447	C₂²×C₂₃	1	2	yes	—
531	#447	C₂²×C₂₃	1	4	yes	—
532	#447	C₂²×C₂₃	1	2	yes	complemented
533	#447	C₂²×C₂₃	1	2	yes	complemented
534	#442	C₂²×C₂₃	1	4	yes	complemented
535	#442	C₂²×C₂₃	1	4	yes	complemented
536	#442	C₂²×C₂₃	1	4	yes	complemented
537	#440	C₂²×C₂₃	1	4	yes	complemented
538	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
539	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
540	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
541	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
542	#433	C₂²×C₂₃	1	4	yes	complemented
543	#432	C₂²×C₂₃	1	2	yes	complemented
544	#431	C₂²×C₂₃	1	2	yes	complemented
545	#428	C₂²×C₂₃	1	2	yes	complemented
546	#427	C₂²×C₂₃	1	2	yes	complemented
547	#424	C₂²×C₂₃	1	2	yes	complemented
548	#418	C₂²×C₂₃	1	2	yes	—
549	#418	C₂²×C₂₃	1	2	yes	complemented
550	#416	C₂²×C₂₃	1	2	yes	complemented
551	C₂×#102	C₂²×C₂₃	1	2	yes	—
552	#407	C₂²×C₂₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
554	#405	C₂²×C₂₃	1	2	yes	complemented
555	C₂×C₂₃	—	2	2	no	—
556	C₂×C₂₃	—	2	2	no	—
557	C₂×C₂₃	—	4	1	no	—
558	C₂×C₂₃	—	4	8	no	—
559	C₂×C₂₃	—	8	1	no	—
560	C₂×C₂₃	—	8	2	no	—
561	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
562	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
563	C₂×C₂₃	#3585	1	1	yes	characteristic
564	C₂⁵	—	2	1	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
567	C₂²×D₄	—	2	8	no	—
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	—	2	1	no	—
570	C₂²×D₄	—	2	1	no	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
574	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
576	C₂³×C₄	—	2	2	no	—
577	C₂³×C₄	—	2	2	no	—
578	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
579	AGL(1,ℤ/8)	—	2	8	no	—
580	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
581	C₂×D₈	—	2	8	no	—
582	C₂×D₈	C₂³×C₂₃	1	4	yes	—
583	C₂×D₈	C₂³×C₂₃	1	4	yes	—
584	C₂×D₈	C₂³×C₂₃	1	4	yes	—
585	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
586	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
587	C₄⋊Q₈	—	2	1	no	—
588	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
589	#127	C₂³×C₂₃	1	2	yes	complemented
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	1	no	—
593	#125	C₂³×C₂₃	1	2	yes	complemented
594	#124	—	2	2	no	—
595	#124	—	2	2	no	—
596	#124	C₂³×C₂₃	1	2	yes	complemented
597	#123	—	2	1	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
605	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	C₂³×C₂₃	1	2	yes	—
614	#121	C₂³×C₂₃	1	2	yes	—
615	#121	C₂³×C₂₃	1	1	yes	characteristic
616	#121	C₂³×C₂₃	1	1	yes	characteristic
617	#120	—	2	1	no	—
618	#120	—	2	2	no	—
619	C₄×Q₈	C₂³×C₂₃	1	2	yes	complemented
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	4	no	—
628	C₄×D₄	—	2	4	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	C₂³×C₂₃	1	4	yes	—
638	C₄×D₄	C₂³×C₂₃	1	4	yes	—
639	C₄×D₄	C₂³×C₂₃	1	4	yes	—
640	C₄×D₄	C₂³×C₂₃	1	4	yes	—
641	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
642	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
643	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
644	#117	—	2	1	no	—
645	#117	—	2	1	no	—
646	#117	—	2	1	no	—
647	#117	—	2	2	no	—
648	#117	D₄×C₂₃	1	2	yes	—
649	#117	D₄×C₂₃	1	1	yes	characteristic
650	#117	D₄×C₂₃	1	1	yes	characteristic
651	#117	C₂³×C₂₃	1	2	yes	—
652	#117	C₂³×C₂₃	1	2	yes	—
653	#117	C₂³×C₂₃	1	1	yes	characteristic
654	#117	C₂³×C₂₃	1	1	yes	characteristic
655	#117	C₂³×C₂₃	1	1	yes	characteristic
656	#117	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	4	no	—
668	C₂×C₂²⋊C₄	—	2	4	no	—
669	C₂×C₂²⋊C₄	—	2	4	no	—
670	C₂×C₂²⋊C₄	—	2	4	no	—
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
675	#107	C₂³×C₂₃	1	2	yes	complemented
676	#107	C₂³×C₂₃	1	2	yes	complemented
677	#107	C₂³×C₂₃	1	4	yes	complemented
678	#106	C₂³×C₂₃	1	2	yes	complemented
679	#106	C₂³×C₂₃	1	2	yes	complemented
680	#106	C₂³×C₂₃	1	4	yes	complemented
681	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
682	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
683	#103	C₂³×C₂₃	1	2	yes	complemented
684	#103	C₂³×C₂₃	1	2	yes	complemented
685	#102	C₂³×C₂₃	1	4	yes	—
686	#102	C₂³×C₂₃	1	4	yes	—
687	#102	C₂³×C₂₃	1	4	yes	—
688	#102	C₂³×C₂₃	1	4	yes	—
689	#102	C₂³×C₂₃	1	2	yes	complemented
690	#102	C₂³×C₂₃	1	2	yes	complemented
691	#102	C₂³×C₂₃	1	4	yes	complemented
692	#102	C₂³×C₂₃	1	4	yes	complemented
693	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
694	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
695	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
698	#97	C₂³×C₂₃	1	4	yes	complemented
699	C₄×C₈	C₂³×C₂₃	1	4	yes	complemented
700	C₂₃	#60578	1	1	yes	characteristic, direct product factor, Sylow
701	C₂⁴	—	2	8	no	—
702	C₂⁴	—	2	2	no	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	—	2	2	no	—
705	C₂⁴	—	2	1	no	—
706	C₂⁴	—	8	2	no	—
707	C₂⁴	—	8	2	no	—
708	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
709	#41	—	2	4	no	—
710	#41	—	8	4	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	8	2	no	—
732	C₂×D₄	#41×C₂₃	1	8	yes	complemented
733	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	8	4	no	—
749	C₂²×C₄	—	8	4	no	—
750	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
751	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
752	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
758	SD₁₆	—	2	8	no	—
759	D₈	—	2	8	no	—
760	D₈	—	2	8	no	—
761	D₈	—	2	8	no	—
762	M₁₆	—	2	4	no	—
763	C₂×C₈	—	2	4	no	—
764	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
765	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
766	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
781	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
808	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	C₂×D₄×C₂₃	1	2	yes	—
814	C₄²	C₂×D₄×C₂₃	1	2	yes	—
815	C₄²	C₂⁴×C₂₃	1	2	yes	—
816	C₄²	C₂⁴×C₂₃	1	2	yes	—
817	C₂³	—	2	8	no	—
818	C₂³	—	2	8	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	4	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	8	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	4	no	—
827	C₂³	—	4	4	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	8	2	no	—
830	C₂³	—	8	2	no	—
831	C₂³	—	8	2	no	—
832	C₂³	—	8	2	no	—
833	C₂³	—	8	1	no	—
834	C₂³	—	8	1	no	—
835	C₂³	—	8	16	no	—
836	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
837	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
838	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	8	2	no	—
841	D₄	—	2	8	no	—
842	D₄	—	2	8	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	4	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	8	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	2	no	—
853	D₄	—	8	2	no	—
854	D₄	—	8	1	no	—
855	D₄	C₂×#41×C₂₃	1	8	yes	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	8	4	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	2	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	1	no	—
880	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
887	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
888	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
889	C₈	—	2	2	no	—
890	C₈	—	2	2	no	—
891	C₈	—	2	4	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	8	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	4	4	no	—
901	C₂²	—	4	16	no	—
902	C₂²	—	4	4	no	—
903	C₂²	—	4	4	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	8	8	no	—
911	C₂²	—	8	8	no	—
912	C₂²	—	16	2	no	—
913	C₂²	C₂₃×#525	1	2	yes	—
914	C₂²	C₂₃×#576	1	2	yes	—
915	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	C₂₃×#525	1	2	yes	—
929	C₄	C₂²×#41×C₂₃	1	2	yes	—
930	C₂	—	2	2	no	—
931	C₂	—	2	2	no	—
932	C₂	—	4	1	no	—
933	C₂	—	4	8	no	—
934	C₂	—	8	2	no	—
935	C₂	—	8	1	no	—
936	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
937	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
938	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 ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂×C₂₃×#518	C₂	semidirect
3. C₂₃×#3122	C₂	semidirect
4. C₂₃×#3118	C₂	semidirect
5. C₂₃×#3114	C₂	semidirect
6. C₂₃×#3109	C₂	semidirect
7. C₂₃×#3105	C₂	semidirect
8. C₂₃×#3100	C₂	semidirect
9. C₂₃×#3094	C₂	semidirect
10. C₂₃×#3091	C₂	semidirect
11. C₂₃×#3081	C₂	semidirect
12. C₂₃×#3041	C₂	semidirect
13. C₂₃×#3003	C₂	semidirect
14. C₂×C₂₃×#447	C₂	semidirect
15. C₂₃×#2948	C₂	semidirect
16. C₂₃×#2946	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
27. C₂₃×#544	C₂²	semidirect
28. C₂₃×#542	C₂²	semidirect
29. C₂₃×#540	C₂²	semidirect
30. C₂₃×#535	C₂²	semidirect
31. C₂₃×#532	C₂²	semidirect
32. C₂₃×#529	C₂²	semidirect
35. C₂₃×#520	C₂²	semidirect
41. C₂₃×#518	C₂²	semidirect
42. C₂₃×#518	C₂²	semidirect
45. C₂×C₄×D₄×C₂₃	C₂²	semidirect
46. C₂×C₄×D₄×C₂₃	C₂²	semidirect
50. C₂₃×#485	C₂²	semidirect
51. C₂₃×#484	C₂²	semidirect
52. C₂₃×#483	C₂²	semidirect
53. C₂₃×#482	C₂²	semidirect
54. C₂₃×#482	C₂²	semidirect
55. C₂₃×#481	C₂²	semidirect
56. C₂₃×#481	C₂²	semidirect
57. C₂₃×#480	C₂²	semidirect
58. C₂₃×#480	C₂²	semidirect
59. C₂₃×#478	C₂²	semidirect
60. C₂₃×#478	C₂²	semidirect
61. C₂₃×#476	C₂²	semidirect
62. C₂₃×#474	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#463	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
67. C₂₃×#450	C₂²	semidirect
68. C₂₃×#450	C₂²	semidirect
72. C₂₃×#447	C₂²	semidirect
73. C₂₃×#447	C₂²	semidirect
74. C₂₃×#442	C₂²	semidirect
75. C₂₃×#442	C₂²	semidirect
76. C₂₃×#442	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
78. C₄×SD₁₆×C₂₃	C₂²	semidirect
79. C₄×D₈×C₂₃	C₂²	semidirect
80. C₄×D₈×C₂₃	C₂²	semidirect
81. C₄×D₈×C₂₃	C₂²	semidirect
82. C₂₃×#433	C₂²	semidirect
83. C₂₃×#432	C₂²	semidirect
84. C₂₃×#431	C₂²	semidirect
85. C₂₃×#428	C₂²	semidirect
86. C₂₃×#427	C₂²	semidirect
87. C₂₃×#424	C₂²	semidirect
89. C₂₃×#418	C₂²	semidirect
90. C₂₃×#416	C₂²	semidirect
94. C₂₃×#405	C₂²	semidirect
119. C₂₃×C₄⋊Q₈	C₂³	semidirect
120. C₂₃×#127	C₂³	semidirect
124. C₂₃×#125	C₂³	semidirect
127. C₂₃×#124	C₂³	semidirect
150. C₄×Q₈×C₂₃	C₂³	semidirect
172. C₄×D₄×C₂₃	C₂³	semidirect
173. C₄×D₄×C₂₃	C₂³	semidirect
174. C₄×D₄×C₂₃	C₂³	semidirect
206. C₂₃×#107	C₂³	semidirect
207. C₂₃×#107	C₂³	semidirect
208. C₂₃×#107	C₂³	semidirect
209. C₂₃×#106	C₂³	semidirect
210. C₂₃×#106	C₂³	semidirect
211. C₂₃×#106	C₂³	semidirect
212. C₂₃×C₄⋊C₈	C₂³	semidirect
213. C₂₃×C₄⋊C₈	C₂³	semidirect
214. C₂₃×#103	C₂³	semidirect
215. C₂₃×#103	C₂³	semidirect
220. C₂₃×#102	C₂³	semidirect
221. C₂₃×#102	C₂³	semidirect
222. C₂₃×#102	C₂³	semidirect
223. C₂₃×#102	C₂³	semidirect
229. C₂₃×#97	C₂³	semidirect
230. C₄×C₈×C₂₃	C₂³	semidirect
262. C₂×D₄×C₂₃	#41	semidirect
347. #60578	C₂₃	direct (N × H)
423. #3494	C₂×C₂₃	semidirect
424. C₂×#518	C₂×C₂₃	semidirect
425. #3122	C₂×C₂₃	semidirect
426. #3118	C₂×C₂₃	semidirect
427. #3114	C₂×C₂₃	semidirect
428. #3109	C₂×C₂₃	semidirect
429. #3105	C₂×C₂₃	semidirect
430. #3100	C₂×C₂₃	semidirect
431. #3094	C₂×C₂₃	semidirect
432. #3091	C₂×C₂₃	semidirect
433. #3081	C₂×C₂₃	semidirect
434. #3041	C₂×C₂₃	semidirect
435. #3003	C₂×C₂₃	semidirect
436. C₂×#447	C₂×C₂₃	semidirect
437. #2948	C₂×C₂₃	semidirect
438. #2946	C₂×C₂₃	semidirect
439. #2924	C₂×C₂₃	semidirect
487. #544	C₂²×C₂₃	semidirect
488. #542	C₂²×C₂₃	semidirect
489. #540	C₂²×C₂₃	semidirect
490. #535	C₂²×C₂₃	semidirect
491. #532	C₂²×C₂₃	semidirect
492. #529	C₂²×C₂₃	semidirect
495. #520	C₂²×C₂₃	semidirect
501. #518	C₂²×C₂₃	semidirect
502. #518	C₂²×C₂₃	semidirect
505. C₂×C₄×D₄	C₂²×C₂₃	semidirect
506. C₂×C₄×D₄	C₂²×C₂₃	semidirect
510. #485	C₂²×C₂₃	semidirect
511. #484	C₂²×C₂₃	semidirect
512. #483	C₂²×C₂₃	semidirect
513. #482	C₂²×C₂₃	semidirect
514. #482	C₂²×C₂₃	semidirect
515. #481	C₂²×C₂₃	semidirect
516. #481	C₂²×C₂₃	semidirect
517. #480	C₂²×C₂₃	semidirect
518. #480	C₂²×C₂₃	semidirect
519. #478	C₂²×C₂₃	semidirect
520. #478	C₂²×C₂₃	semidirect
521. #476	C₂²×C₂₃	semidirect
522. #474	C₂²×C₂₃	semidirect
523. #463	C₂²×C₂₃	semidirect
524. #463	C₂²×C₂₃	semidirect
525. #459	C₂²×C₂₃	semidirect
526. #459	C₂²×C₂₃	semidirect
527. #450	C₂²×C₂₃	semidirect
528. #450	C₂²×C₂₃	semidirect
532. #447	C₂²×C₂₃	semidirect
533. #447	C₂²×C₂₃	semidirect
534. #442	C₂²×C₂₃	semidirect
535. #442	C₂²×C₂₃	semidirect
536. #442	C₂²×C₂₃	semidirect
537. #440	C₂²×C₂₃	semidirect
538. C₄×SD₁₆	C₂²×C₂₃	semidirect
539. C₄×D₈	C₂²×C₂₃	semidirect
540. C₄×D₈	C₂²×C₂₃	semidirect
541. C₄×D₈	C₂²×C₂₃	semidirect
542. #433	C₂²×C₂₃	semidirect
543. #432	C₂²×C₂₃	semidirect
544. #431	C₂²×C₂₃	semidirect
545. #428	C₂²×C₂₃	semidirect
546. #427	C₂²×C₂₃	semidirect
547. #424	C₂²×C₂₃	semidirect
549. #418	C₂²×C₂₃	semidirect
550. #416	C₂²×C₂₃	semidirect
554. #405	C₂²×C₂₃	semidirect
588. C₄⋊Q₈	C₂³×C₂₃	semidirect
589. #127	C₂³×C₂₃	semidirect
593. #125	C₂³×C₂₃	semidirect
596. #124	C₂³×C₂₃	semidirect
619. C₄×Q₈	C₂³×C₂₃	semidirect
641. C₄×D₄	C₂³×C₂₃	semidirect
642. C₄×D₄	C₂³×C₂₃	semidirect
643. C₄×D₄	C₂³×C₂₃	semidirect
675. #107	C₂³×C₂₃	semidirect
676. #107	C₂³×C₂₃	semidirect
677. #107	C₂³×C₂₃	semidirect
678. #106	C₂³×C₂₃	semidirect
679. #106	C₂³×C₂₃	semidirect
680. #106	C₂³×C₂₃	semidirect
681. C₄⋊C₈	C₂³×C₂₃	semidirect
682. C₄⋊C₈	C₂³×C₂₃	semidirect
683. #103	C₂³×C₂₃	semidirect
684. #103	C₂³×C₂₃	semidirect
689. #102	C₂³×C₂₃	semidirect
690. #102	C₂³×C₂₃	semidirect
691. #102	C₂³×C₂₃	semidirect
692. #102	C₂³×C₂₃	semidirect
698. #97	C₂³×C₂₃	semidirect
699. C₄×C₈	C₂³×C₂₃	semidirect
700. C₂₃	#60578	direct (N × H)
732. C₂×D₄	#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×#3494	2
C₂×C₂₃×#518	2
C₂₃×#3122	2
C₂₃×#3118	2
C₂₃×#3114	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3100	2
C₂₃×#3094	2
C₂₃×#3091	2
C₂₃×#3081	2
C₂₃×#3041	2
C₂₃×#3003	2
C₂×C₂₃×#447	2
C₂₃×#2948	2
C₂₃×#2946	2
C₂₃×#2924	2
#60578	23

Subgroups — C23×#60578 #19208204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60578 #19208204