Subgroups — C₂₃×#60593 #19208219

Order 5888.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3126	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3119	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3115	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3112	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3010	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2949	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#559	—	2	1	no	—
22	C₂₃×#559	—	2	1	no	—
23	C₂₃×#550	—	2	1	no	—
24	C₂₃×#550	—	2	1	no	—
25	C₂₃×#546	—	2	2	no	—
26	C₂₃×#546	—	2	2	no	—
27	C₂₃×#540	C₂²	1	4	yes	—
28	C₂₃×#535	C₂²	1	2	yes	—
29	C₂₃×#533	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	2	yes	—
31	C₂₃×#532	C₂²	1	2	yes	—
32	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
33	C₂₃×#520	—	2	2	no	—
34	C₂₃×#520	—	2	1	no	—
35	C₂₃×#520	C₂²	1	1	yes	characteristic
36	C₂₃×#520	C₂²	1	1	yes	characteristic
37	C₂₃×#520	C₂²	1	2	yes	complemented
38	C₂₃×#519	—	2	1	no	—
39	C₂₃×#519	C₂²	1	1	yes	characteristic
40	C₂₃×#519	C₂²	1	2	yes	complemented
41	C₂₃×#518	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	—	2	2	no	—
43	C₄×#41×C₂₃	—	2	1	no	—
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
48	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
50	C₂₃×#482	C₂²	1	4	yes	complemented
51	C₂₃×#482	C₂²	1	4	yes	complemented
52	C₂₃×#481	C₂²	1	4	yes	complemented
53	C₂₃×#480	C₂²	1	4	yes	complemented
54	C₂₃×#479	C₂²	1	2	yes	complemented
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#478	C₂²	1	2	yes	complemented
57	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#477	C₂²	1	2	yes	complemented
59	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#475	C₂²	1	2	yes	complemented
62	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#460	C₂²	1	2	yes	—
64	C₂₃×#460	C₂²	1	2	yes	—
65	C₂₃×#460	C₂²	1	4	yes	—
66	C₂₃×#460	C₂²	1	2	yes	—
67	C₂₃×#460	C₂²	1	2	yes	—
68	C₂₃×#459	C₂²	1	2	yes	—
69	C₂₃×#459	C₂²	1	2	yes	—
70	C₂₃×#449	C₂²	1	4	yes	complemented
71	C₂₃×#449	C₂²	1	4	yes	complemented
72	C₂₃×#448	C₂²	1	4	yes	complemented
73	C₂₃×#448	C₂²	1	4	yes	complemented
74	C₂₃×#442	C₂²	1	4	yes	complemented
75	C₂₃×#440	C₂²	1	4	yes	complemented
76	C₂₃×#440	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×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	—
86	C₂₃×#427	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#418	C₂²	1	2	yes	—
91	C₂₃×#416	C₂²	1	2	yes	—
92	C₂×C₂₃×#102	C₂²	1	2	yes	—
93	C₂₃×#408	C₂²	1	2	yes	—
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂₃×2₋¹⁺⁴	—	2	4	no	—
96	C₂₃×2₋¹⁺⁴	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	1	no	—
99	C₂×#41×C₂₃	—	2	2	no	—
100	C₂×#41×C₂₃	—	2	2	no	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₂₃	—	2	1	no	—
105	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	—	2	1	no	—
108	C₂²×D₄×C₂₃	—	2	1	no	—
109	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
110	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂×SD₁₆×C₂₃	—	2	8	no	—
112	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×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	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×#127	—	2	2	no	—
121	C₂₃×#127	—	2	1	no	—
122	C₂₃×#127	—	2	1	no	—
123	C₂₃×#127	C₂³	1	2	yes	—
124	C₂₃×#127	C₂³	1	2	yes	—
125	C₂₃×#125	C₂³	1	2	yes	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×#123	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	1	no	—
132	C₂₃×C₂²⋊Q₈	—	2	1	no	—
133	C₂₃×#121	—	2	2	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	C₂³	1	4	yes	—
138	C₂₃×#121	C₂³	1	4	yes	—
139	C₂₃×#120	—	2	4	no	—
140	C₄×Q₈×C₂₃	—	2	1	no	—
141	C₄×Q₈×C₂₃	—	2	1	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	1	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	1	no	—
146	C₄×Q₈×C₂₃	—	2	1	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	1	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	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₃	D₄	1	2	yes	—
176	C₄×D₄×C₂₃	D₄	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	4	yes	—
179	C₄×D₄×C₂₃	C₂³	1	4	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	1	no	—
188	C₂₃×#117	—	2	2	no	—
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂₃×#117	C₂³	1	1	yes	characteristic
191	C₂₃×#117	C₂³	1	2	yes	—
192	C₂₃×#117	C₂³	1	1	yes	characteristic
193	C₂₃×#117	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
201	C₂×C₄²×C₂₃	—	2	1	no	—
202	C₂×C₄²×C₂₃	—	2	2	no	—
203	C₂×C₄²×C₂₃	—	2	1	no	—
204	C₂×C₄²×C₂₃	—	2	2	no	—
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
207	C₂₃×#107	C₂³	1	2	yes	—
208	C₂₃×#107	C₂³	1	2	yes	—
209	C₂₃×#107	C₂³	1	4	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	2	yes	—
212	C₂₃×#106	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#103	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
227	C₂₃×#102	C₂³	1	4	yes	—
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₂₃×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₂₃	C₂³	1	4	yes	—
232	C₂⁴×C₂₃	—	2	2	no	—
233	#41×C₂₃	—	2	16	no	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	2	4	no	—
236	#41×C₂₃	—	2	4	no	—
237	#41×C₂₃	—	2	2	no	—
238	#41×C₂₃	—	2	2	no	—
239	#41×C₂₃	—	2	2	no	—
240	#41×C₂₃	—	8	4	no	—
241	#41×C₂₃	—	8	4	no	—
242	#41×C₂₃	#41	1	4	yes	complemented
243	C₂×Q₈×C₂₃	—	2	8	no	—
244	C₂×Q₈×C₂₃	—	2	4	no	—
245	C₂×Q₈×C₂₃	—	2	4	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	1	no	—
248	C₂×Q₈×C₂₃	—	2	1	no	—
249	C₂×Q₈×C₂₃	—	2	1	no	—
250	C₂×Q₈×C₂₃	—	2	2	no	—
251	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
253	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	2	1	no	—
257	C₂×D₄×C₂₃	—	2	4	no	—
258	C₂×D₄×C₂₃	—	2	4	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	2	2	no	—
261	C₂×D₄×C₂₃	—	2	2	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	4	no	—
265	C₂×D₄×C₂₃	—	2	4	no	—
266	C₂×D₄×C₂₃	—	8	2	no	—
267	C₂×D₄×C₂₃	—	8	2	no	—
268	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
271	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	1	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	1	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	1	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	1	no	—
281	C₂²×C₄×C₂₃	—	2	4	no	—
282	C₂²×C₄×C₂₃	—	2	4	no	—
283	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	SD₁₆×C₂₃	—	2	8	no	—
290	SD₁₆×C₂₃	—	2	8	no	—
291	SD₁₆×C₂₃	—	2	8	no	—
292	D₈×C₂₃	—	2	8	no	—
293	M₁₆×C₂₃	—	2	4	no	—
294	C₂×C₈×C₂₃	—	2	4	no	—
295	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	1	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	1	no	—
307	C₄⋊C₄×C₂₃	—	2	1	no	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	1	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	1	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	1	no	—
328	C₂²⋊C₄×C₂₃	—	2	4	no	—
329	C₂²⋊C₄×C₂₃	—	2	4	no	—
330	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	1	no	—
335	C₄²×C₂₃	—	2	2	no	—
336	C₄²×C₂₃	—	2	1	no	—
337	C₄²×C₂₃	—	2	2	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	1	no	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	C₂×D₄	1	2	yes	—
344	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₂₃	C₂×D₄	1	2	yes	—
346	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₂₃	C₂⁴	1	2	yes	—
350	#60593	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₂³×C₂₃	—	2	1	no	—
352	C₂³×C₂₃	—	2	4	no	—
353	C₂³×C₂₃	—	4	4	no	—
354	C₂³×C₂₃	—	8	2	no	—
355	C₂³×C₂₃	—	8	2	no	—
356	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₂₃	—	2	8	no	—
359	Q₈×C₂₃	—	2	2	no	—
360	Q₈×C₂₃	—	2	4	no	—
361	Q₈×C₂₃	—	2	1	no	—
362	Q₈×C₂₃	—	2	2	no	—
363	Q₈×C₂₃	—	4	2	no	—
364	Q₈×C₂₃	—	4	2	no	—
365	Q₈×C₂₃	C₂×#41	1	2	yes	—
366	Q₈×C₂₃	C₂×#41	1	4	yes	—
367	D₄×C₂₃	—	2	8	no	—
368	D₄×C₂₃	—	2	4	no	—
369	D₄×C₂₃	—	2	4	no	—
370	D₄×C₂₃	—	2	2	no	—
371	D₄×C₂₃	—	2	1	no	—
372	D₄×C₂₃	—	2	4	no	—
373	D₄×C₂₃	—	2	4	no	—
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	4	4	no	—
376	D₄×C₂₃	—	4	4	no	—
377	D₄×C₂₃	—	8	2	no	—
378	D₄×C₂₃	—	8	2	no	—
379	D₄×C₂₃	—	8	4	no	—
380	D₄×C₂₃	—	8	4	no	—
381	D₄×C₂₃	C₂×#41	1	2	yes	—
382	C₂×C₄×C₂₃	—	2	8	no	—
383	C₂×C₄×C₂₃	—	2	8	no	—
384	C₂×C₄×C₂₃	—	2	4	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	4	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	4	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	1	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	4	1	no	—
398	C₂×C₄×C₂₃	—	4	2	no	—
399	C₂×C₄×C₂₃	—	4	2	no	—
400	C₂×C₄×C₂₃	—	8	2	no	—
401	C₂×C₄×C₂₃	—	8	1	no	—
402	C₂×C₄×C₂₃	—	8	4	no	—
403	C₂×C₄×C₂₃	—	8	4	no	—
404	C₂×C₄×C₂₃	—	8	1	no	—
405	C₂×C₄×C₂₃	—	8	2	no	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
415	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
417	C₈×C₂₃	—	2	2	no	—
418	C₈×C₂₃	—	2	2	no	—
419	C₈×C₂₃	—	2	4	no	—
420	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#3126	C₂×C₂₃	1	4	yes	complemented
423	#3119	C₂×C₂₃	1	4	yes	complemented
424	#3115	C₂×C₂₃	1	2	yes	complemented
425	#3112	C₂×C₂₃	1	2	yes	complemented
426	#3106	C₂×C₂₃	1	2	yes	complemented
427	#3103	C₂×C₂₃	1	2	yes	complemented
428	#3096	C₂×C₂₃	1	2	yes	complemented
429	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
431	#3038	C₂×C₂₃	1	1	yes	characteristic, complemented
432	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#3010	C₂×C₂₃	1	2	yes	complemented
434	#2949	C₂×C₂₃	1	2	yes	complemented
435	#2946	C₂×C₂₃	1	2	yes	complemented
436	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
437	C₂²×C₂₃	—	2	1	no	—
438	C₂²×C₂₃	—	2	1	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	2	no	—
441	C₂²×C₂₃	—	2	2	no	—
442	C₂²×C₂₃	—	2	2	no	—
443	C₂²×C₂₃	—	4	1	no	—
444	C₂²×C₂₃	—	4	1	no	—
445	C₂²×C₂₃	—	4	4	no	—
446	C₂²×C₂₃	—	4	4	no	—
447	C₂²×C₂₃	—	4	4	no	—
448	C₂²×C₂₃	—	16	4	no	—
449	C₂²×C₂₃	#525	1	2	yes	—
450	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₂₃	—	2	1	no	—
452	C₄×C₂₃	—	2	2	no	—
453	C₄×C₂₃	—	2	1	no	—
454	C₄×C₂₃	—	2	4	no	—
455	C₄×C₂₃	—	2	2	no	—
456	C₄×C₂₃	—	2	2	no	—
457	C₄×C₂₃	—	2	2	no	—
458	C₄×C₂₃	—	2	1	no	—
459	C₄×C₂₃	—	4	2	no	—
460	C₄×C₂₃	—	4	1	no	—
461	C₄×C₂₃	—	4	2	no	—
462	C₄×C₂₃	—	4	1	no	—
463	C₄×C₂₃	—	4	2	no	—
464	C₄×C₂₃	#525	1	2	yes	—
465	C₄×C₂₃	#577	1	2	yes	—
466	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
467	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
468	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
470	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
471	#559	—	2	1	no	—
472	#559	—	2	1	no	—
473	#550	—	2	1	no	—
474	#550	—	2	1	no	—
475	#546	—	2	2	no	—
476	#546	—	2	2	no	—
477	#540	C₂²×C₂₃	1	4	yes	—
478	#535	C₂²×C₂₃	1	2	yes	—
479	#533	C₂²×C₂₃	1	1	yes	characteristic
480	#532	C₂²×C₂₃	1	2	yes	—
481	#532	C₂²×C₂₃	1	2	yes	—
482	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
483	#520	—	2	2	no	—
484	#520	—	2	1	no	—
485	#520	C₂²×C₂₃	1	1	yes	characteristic
486	#520	C₂²×C₂₃	1	1	yes	characteristic
487	#520	C₂²×C₂₃	1	2	yes	complemented
488	#519	—	2	1	no	—
489	#519	C₂²×C₂₃	1	1	yes	characteristic
490	#519	C₂²×C₂₃	1	2	yes	complemented
491	#518	C₂²×C₂₃	1	2	yes	—
492	C₄×#41	—	2	2	no	—
493	C₄×#41	—	2	1	no	—
494	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
495	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
496	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
497	C₂×C₄×Q₈	—	2	1	no	—
498	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
499	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
500	#482	C₂²×C₂₃	1	4	yes	complemented
501	#482	C₂²×C₂₃	1	4	yes	complemented
502	#481	C₂²×C₂₃	1	4	yes	complemented
503	#480	C₂²×C₂₃	1	4	yes	complemented
504	#479	C₂²×C₂₃	1	2	yes	complemented
505	#479	C₂²×C₂₃	1	4	yes	complemented
506	#478	C₂²×C₂₃	1	2	yes	complemented
507	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	#477	C₂²×C₂₃	1	2	yes	complemented
509	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#475	C₂²×C₂₃	1	2	yes	complemented
512	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	#460	C₂²×C₂₃	1	2	yes	—
514	#460	C₂²×C₂₃	1	2	yes	—
515	#460	C₂²×C₂₃	1	2	yes	—
516	#460	C₂²×C₂₃	1	4	yes	—
517	#460	C₂²×C₂₃	1	2	yes	—
518	#459	C₂²×C₂₃	1	2	yes	—
519	#459	C₂²×C₂₃	1	2	yes	—
520	#449	C₂²×C₂₃	1	4	yes	complemented
521	#449	C₂²×C₂₃	1	4	yes	complemented
522	#448	C₂²×C₂₃	1	4	yes	complemented
523	#448	C₂²×C₂₃	1	4	yes	complemented
524	#442	C₂²×C₂₃	1	4	yes	complemented
525	#440	C₂²×C₂₃	1	4	yes	complemented
526	#440	C₂²×C₂₃	1	4	yes	complemented
527	#440	C₂²×C₂₃	1	4	yes	complemented
528	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
529	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
530	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
531	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
532	#433	C₂²×C₂₃	1	4	yes	complemented
533	#432	C₂²×C₂₃	1	2	yes	complemented
534	#431	C₂²×C₂₃	1	2	yes	complemented
535	#428	C₂²×C₂₃	1	2	yes	—
536	#427	C₂²×C₂₃	1	2	yes	—
537	#423	C₂²×C₂₃	1	1	yes	characteristic
538	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
539	#419	C₂²×C₂₃	1	2	yes	—
540	#418	C₂²×C₂₃	1	2	yes	—
541	#416	C₂²×C₂₃	1	2	yes	—
542	C₂×#102	C₂²×C₂₃	1	2	yes	—
543	#408	C₂²×C₂₃	1	2	yes	—
544	#405	C₂²×C₂₃	1	2	yes	—
545	C₂×C₂₃	—	2	2	no	—
546	C₂×C₂₃	—	4	2	no	—
547	C₂×C₂₃	—	4	2	no	—
548	C₂×C₂₃	—	8	4	no	—
549	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
550	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
551	C₂×C₂₃	#3585	1	1	yes	characteristic
552	2₋¹⁺⁴	—	2	4	no	—
553	2₋¹⁺⁴	—	2	4	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	2	1	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	C₂³×C₂₃	1	2	yes	—
559	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
561	C₂²×Q₈	—	2	1	no	—
562	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
563	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
567	AGL(1,ℤ/8)	—	2	8	no	—
568	C₂×SD₁₆	—	2	8	no	—
569	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
572	C₂×D₈	C₂³×C₂₃	1	4	yes	—
573	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
574	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
577	#127	—	2	2	no	—
578	#127	—	2	1	no	—
579	#127	—	2	1	no	—
580	#127	C₂³×C₂₃	1	2	yes	—
581	#127	C₂³×C₂₃	1	2	yes	—
582	#125	C₂³×C₂₃	1	2	yes	—
583	#124	—	2	2	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#123	—	2	4	no	—
587	#123	—	2	4	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	—	2	4	no	—
594	#121	C₂³×C₂₃	1	4	yes	—
595	#121	C₂³×C₂₃	1	4	yes	—
596	#120	—	2	4	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
609	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
611	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
612	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
614	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
615	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	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	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	D₄×C₂₃	1	2	yes	—
631	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
632	C₄×D₄	D₄×C₂₃	1	2	yes	—
633	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₂₃	1	2	yes	—
637	C₄×D₄	C₂³×C₂₃	1	4	yes	—
638	C₄×D₄	C₂³×C₂₃	1	4	yes	—
639	#117	—	2	1	no	—
640	#117	—	2	2	no	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	—	2	2	no	—
644	#117	—	2	1	no	—
645	#117	—	2	2	no	—
646	#117	C₂³×C₂₃	1	1	yes	characteristic
647	#117	C₂³×C₂₃	1	2	yes	—
648	#117	C₂³×C₂₃	1	2	yes	—
649	#117	C₂³×C₂₃	1	1	yes	characteristic
650	#117	C₂³×C₂₃	1	2	yes	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	2	no	—
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₂²⋊C₄	—	2	4	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	2	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	2	no	—
662	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
664	#107	C₂³×C₂₃	1	2	yes	—
665	#107	C₂³×C₂₃	1	2	yes	—
666	#107	C₂³×C₂₃	1	4	yes	—
667	#106	C₂³×C₂₃	1	2	yes	—
668	#106	C₂³×C₂₃	1	2	yes	—
669	#106	C₂³×C₂₃	1	4	yes	—
670	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
671	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
672	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
673	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
674	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
675	#103	C₂³×C₂₃	1	2	yes	—
676	#103	C₂³×C₂₃	1	2	yes	—
677	#103	C₂³×C₂₃	1	4	yes	—
678	#103	C₂³×C₂₃	1	4	yes	—
679	#102	C₂³×C₂₃	1	4	yes	—
680	#102	C₂³×C₂₃	1	4	yes	—
681	#102	C₂³×C₂₃	1	2	yes	—
682	#102	C₂³×C₂₃	1	2	yes	—
683	#102	C₂³×C₂₃	1	4	yes	—
684	#102	C₂³×C₂₃	1	4	yes	—
685	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
686	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
687	#97	C₂³×C₂₃	1	4	yes	—
688	C₄×C₈	C₂³×C₂₃	1	4	yes	—
689	C₂₃	#60593	1	1	yes	characteristic, direct product factor, Sylow
690	C₂⁴	—	2	2	no	—
691	#41	—	2	16	no	—
692	#41	—	2	8	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	8	4	no	—
699	#41	—	8	4	no	—
700	#41	#41×C₂₃	1	4	yes	complemented
701	C₂×Q₈	—	2	8	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
710	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
711	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
728	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
729	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
747	SD₁₆	—	2	8	no	—
748	SD₁₆	—	2	8	no	—
749	SD₁₆	—	2	8	no	—
750	D₈	—	2	8	no	—
751	M₁₆	—	2	4	no	—
752	C₂×C₈	—	2	4	no	—
753	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
754	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
755	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	C₂×D₄×C₂₃	1	2	yes	—
802	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
803	C₄²	C₂×D₄×C₂₃	1	2	yes	—
804	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
805	C₄²	C₂⁴×C₂₃	1	2	yes	—
806	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
807	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
808	C₂³	—	2	1	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
814	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	2	1	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	C₂×#41×C₂₃	1	2	yes	—
823	Q₈	C₂×#41×C₂₃	1	4	yes	—
824	D₄	—	2	8	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	2	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	4	no	—
837	D₄	—	8	4	no	—
838	D₄	C₂×#41×C₂₃	1	2	yes	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	1	no	—
861	C₂×C₄	—	8	1	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
871	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
872	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
873	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
874	C₈	—	2	2	no	—
875	C₈	—	2	2	no	—
876	C₈	—	2	4	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	4	no	—
888	C₂²	—	16	4	no	—
889	C₂²	C₂₃×#525	1	2	yes	—
890	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	C₂₃×#525	1	2	yes	—
905	C₄	C₂₃×#577	1	2	yes	—
906	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
907	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
908	C₂	—	2	2	no	—
909	C₂	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	8	4	no	—
912	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
913	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
914	C₂	C₂₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3508	C₂	semidirect
2. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
3. C₂₃×#3126	C₂	semidirect
4. C₂₃×#3119	C₂	semidirect
5. C₂₃×#3115	C₂	semidirect
6. C₂₃×#3112	C₂	semidirect
7. C₂₃×#3106	C₂	semidirect
8. C₂₃×#3103	C₂	semidirect
9. C₂₃×#3096	C₂	semidirect
10. C₂₃×#3078	C₂	semidirect
11. C₂₃×#3076	C₂	semidirect
12. C₂₃×#3038	C₂	semidirect
13. C₂×C₂₃×#460	C₂	semidirect
14. C₂₃×#3010	C₂	semidirect
15. C₂₃×#2949	C₂	semidirect
16. C₂₃×#2946	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
37. C₂₃×#520	C₂²	semidirect
40. C₂₃×#519	C₂²	semidirect
46. C₄×#41×C₂₃	C₂²	semidirect
49. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
50. C₂₃×#482	C₂²	semidirect
51. C₂₃×#482	C₂²	semidirect
52. C₂₃×#481	C₂²	semidirect
53. C₂₃×#480	C₂²	semidirect
54. C₂₃×#479	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#478	C₂²	semidirect
57. C₂₃×#477	C₂²	semidirect
58. C₂₃×#477	C₂²	semidirect
59. C₂₃×#476	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#475	C₂²	semidirect
62. C₂₃×#474	C₂²	semidirect
70. C₂₃×#449	C₂²	semidirect
71. C₂₃×#449	C₂²	semidirect
72. C₂₃×#448	C₂²	semidirect
73. C₂₃×#448	C₂²	semidirect
74. C₂₃×#442	C₂²	semidirect
75. C₂₃×#440	C₂²	semidirect
76. C₂₃×#440	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
78. C₄×SD₁₆×C₂₃	C₂²	semidirect
79. C₄×SD₁₆×C₂₃	C₂²	semidirect
80. C₄×SD₁₆×C₂₃	C₂²	semidirect
81. C₄×D₈×C₂₃	C₂²	semidirect
82. C₂₃×#433	C₂²	semidirect
83. C₂₃×#432	C₂²	semidirect
84. C₂₃×#431	C₂²	semidirect
242. #41×C₂₃	#41	semidirect
252. C₂×Q₈×C₂₃	#41	semidirect
350. #60593	C₂₃	direct (N × H)
420. #3508	C₂×C₂₃	semidirect
421. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
422. #3126	C₂×C₂₃	semidirect
423. #3119	C₂×C₂₃	semidirect
424. #3115	C₂×C₂₃	semidirect
425. #3112	C₂×C₂₃	semidirect
426. #3106	C₂×C₂₃	semidirect
427. #3103	C₂×C₂₃	semidirect
428. #3096	C₂×C₂₃	semidirect
429. #3078	C₂×C₂₃	semidirect
430. #3076	C₂×C₂₃	semidirect
431. #3038	C₂×C₂₃	semidirect
432. C₂×#460	C₂×C₂₃	semidirect
433. #3010	C₂×C₂₃	semidirect
434. #2949	C₂×C₂₃	semidirect
435. #2946	C₂×C₂₃	semidirect
436. #2925	C₂×C₂₃	semidirect
487. #520	C₂²×C₂₃	semidirect
490. #519	C₂²×C₂₃	semidirect
496. C₄×#41	C₂²×C₂₃	semidirect
499. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
500. #482	C₂²×C₂₃	semidirect
501. #482	C₂²×C₂₃	semidirect
502. #481	C₂²×C₂₃	semidirect
503. #480	C₂²×C₂₃	semidirect
504. #479	C₂²×C₂₃	semidirect
505. #479	C₂²×C₂₃	semidirect
506. #478	C₂²×C₂₃	semidirect
507. #477	C₂²×C₂₃	semidirect
508. #477	C₂²×C₂₃	semidirect
509. #476	C₂²×C₂₃	semidirect
510. #475	C₂²×C₂₃	semidirect
511. #475	C₂²×C₂₃	semidirect
512. #474	C₂²×C₂₃	semidirect
520. #449	C₂²×C₂₃	semidirect
521. #449	C₂²×C₂₃	semidirect
522. #448	C₂²×C₂₃	semidirect
523. #448	C₂²×C₂₃	semidirect
524. #442	C₂²×C₂₃	semidirect
525. #440	C₂²×C₂₃	semidirect
526. #440	C₂²×C₂₃	semidirect
527. #440	C₂²×C₂₃	semidirect
528. C₄×SD₁₆	C₂²×C₂₃	semidirect
529. C₄×SD₁₆	C₂²×C₂₃	semidirect
530. C₄×SD₁₆	C₂²×C₂₃	semidirect
531. C₄×D₈	C₂²×C₂₃	semidirect
532. #433	C₂²×C₂₃	semidirect
533. #432	C₂²×C₂₃	semidirect
534. #431	C₂²×C₂₃	semidirect
689. C₂₃	#60593	direct (N × H)
700. #41	#41×C₂₃	semidirect
710. C₂×Q₈	#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×#3508	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3126	2
C₂₃×#3119	2
C₂₃×#3115	2
C₂₃×#3112	2
C₂₃×#3106	2
C₂₃×#3103	2
C₂₃×#3096	2
C₂₃×#3078	2
C₂₃×#3076	2
C₂₃×#3038	2
C₂×C₂₃×#460	2
C₂₃×#3010	2
C₂₃×#2949	2
C₂₃×#2946	2
C₂₃×#2925	2
#60593	23

Subgroups — C23×#60593 #19208219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60593 #19208219