Subgroups — C₂₃×#60700 #19208326

Order 5888.

2256 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3184	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3182	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3180	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3171	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3169	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3167	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3055	C₂	1	4	yes	maximal, complemented
14	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
18	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
19	C₂₃×#533	C₂²	1	1	yes	characteristic
20	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#532	—	2	1	no	—
23	C₂₃×#532	—	2	1	no	—
24	C₂₃×#532	—	2	1	no	—
25	C₂₃×#532	—	2	1	no	—
26	C₂₃×#532	C₂²	1	1	yes	characteristic
27	C₂₃×#532	C₂²	1	2	yes	—
28	C₂₃×#532	C₂²	1	2	yes	—
29	C₂₃×#532	C₂²	1	2	yes	—
30	C₂₃×#532	C₂²	1	2	yes	—
31	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
35	C₂₃×#529	—	2	1	no	—
36	C₂₃×#529	—	2	1	no	—
37	C₂₃×#529	—	2	1	no	—
38	C₂₃×#529	—	2	1	no	—
39	C₂₃×#529	C₂²	1	2	yes	complemented
40	C₂₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#124	—	2	1	no	—
42	C₂₃×#525	—	2	1	no	—
43	C₂₃×#525	—	2	1	no	—
44	C₂₃×#525	C₂²	1	2	yes	—
45	C₂×C₂₃×#121	—	2	1	no	—
46	C₂×C₂₃×#121	C₂²	1	2	yes	—
47	C₄×#41×C₂₃	—	2	1	no	—
48	C₄×#41×C₂₃	—	2	1	no	—
49	C₄×#41×C₂₃	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₂₃	—	2	1	no	—
51	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
52	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
53	C₂₃×#501	C₂²	1	4	yes	complemented
54	C₂₃×#500	C₂²	1	2	yes	complemented
55	C₂₃×#498	C₂²	1	2	yes	complemented
56	C₂₃×#496	C₂²	1	4	yes	complemented
57	C₂₃×#493	C₂²	1	2	yes	complemented
58	C₂₃×#492	C₂²	1	2	yes	complemented
59	C₂₃×#490	C₂²	1	4	yes	complemented
60	C₂₃×#489	C₂²	1	4	yes	complemented
61	C₂₃×#487	C₂²	1	2	yes	complemented
62	C₂₃×#486	C₂²	1	2	yes	complemented
63	C₂₃×#486	C₂²	1	2	yes	complemented
64	C₂₃×#486	C₂²	1	2	yes	complemented
65	C₂₃×#469	C₂²	1	8	yes	complemented
66	C₂₃×#468	C₂²	1	8	yes	complemented
67	C₂₃×#466	C₂²	1	8	yes	complemented
68	C₂₃×#465	C₂²	1	8	yes	complemented
69	C₂₃×#442	C₂²	1	8	yes	complemented
70	C₂₃×#440	C₂²	1	8	yes	complemented
71	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
72	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
73	C₂₃×#428	C₂²	1	4	yes	—
74	C₂₃×#418	C₂²	1	4	yes	—
75	C₂₃×#417	C₂²	1	4	yes	—
76	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
77	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
78	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
79	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
80	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
81	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
82	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
83	C₂×#41×C₂₃	—	2	2	no	—
84	C₂×#41×C₂₃	—	2	2	no	—
85	C₂×#41×C₂₃	—	2	2	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	—	2	1	no	—
88	C₂×#41×C₂₃	—	2	1	no	—
89	C₂×#41×C₂₃	—	4	8	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂²×Q₈×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	—	2	2	no	—
93	C₂²×D₄×C₂₃	—	2	1	no	—
94	C₂²×D₄×C₂₃	—	2	1	no	—
95	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₂₃	—	2	2	no	—
97	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
101	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
102	C₂×D₈×C₂₃	C₂³	1	8	yes	—
103	C₂×M₁₆×C₂₃	—	2	8	no	—
104	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×#127	—	2	1	no	—
116	C₂₃×#127	—	2	1	no	—
117	C₂₃×#127	C₂³	1	2	yes	—
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#127	C₂³	1	2	yes	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#125	—	2	1	no	—
124	C₂₃×#125	C₂³	1	2	yes	—
125	C₂₃×#124	—	2	2	no	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	1	no	—
130	C₂₃×#124	—	2	1	no	—
131	C₂₃×#124	C₂³	1	2	yes	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	1	no	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×#121	—	2	2	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	2	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	1	no	—
148	C₂₃×#121	—	2	1	no	—
149	C₂₃×#121	—	2	1	no	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₂₃×#121	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	4	yes	—
154	C₂₃×#121	C₂³	1	2	yes	—
155	C₂₃×#120	—	2	2	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	—	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	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	4	yes	—
180	C₄×D₄×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	—	2	1	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
191	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄²×C₂₃	—	2	2	no	—
193	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂₃×#107	C₂³	1	8	yes	—
206	C₂₃×#106	C₂³	1	8	yes	—
207	C₂₃×#103	C₂³	1	8	yes	—
208	C₂₃×#102	C₂³	1	8	yes	—
209	C₂₃×#102	C₂³	1	8	yes	—
210	C₂₃×#102	C₂³	1	8	yes	—
211	C₂₃×#97	C₂³	1	4	yes	—
212	C₂₃×#97	C₂³	1	2	yes	—
213	C₂₃×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₂₃	C₂³	1	4	yes	—
215	C₄×C₈×C₂₃	C₂³	1	2	yes	—
216	C₄×C₈×C₂₃	C₂³	1	2	yes	—
217	C₂⁴×C₂₃	—	2	2	no	—
218	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
219	#41×C₂₃	—	2	8	no	—
220	#41×C₂₃	—	4	4	no	—
221	#41×C₂₃	—	4	8	no	—
222	#41×C₂₃	—	4	8	no	—
223	#41×C₂₃	—	4	8	no	—
224	#41×C₂₃	—	4	4	no	—
225	#41×C₂₃	—	4	8	no	—
226	C₂×Q₈×C₂₃	—	2	1	no	—
227	C₂×Q₈×C₂₃	—	2	1	no	—
228	C₂×Q₈×C₂₃	—	2	2	no	—
229	C₂×Q₈×C₂₃	—	2	2	no	—
230	C₂×Q₈×C₂₃	—	4	4	no	—
231	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
232	C₂×D₄×C₂₃	—	2	2	no	—
233	C₂×D₄×C₂₃	—	2	2	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	2	1	no	—
238	C₂×D₄×C₂₃	—	2	1	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	8	no	—
245	C₂×D₄×C₂₃	—	4	4	no	—
246	C₂×D₄×C₂₃	—	4	4	no	—
247	C₂×D₄×C₂₃	—	4	8	no	—
248	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	4	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
258	C₂²×C₄×C₂₃	—	4	2	no	—
259	C₂²×C₄×C₂₃	—	4	8	no	—
260	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	SD₁₆×C₂₃	—	2	16	no	—
279	D₈×C₂₃	—	2	16	no	—
280	M₁₆×C₂₃	—	2	4	no	—
281	M₁₆×C₂₃	—	2	8	no	—
282	M₁₆×C₂₃	#41	1	8	yes	complemented
283	C₂×C₈×C₂₃	—	2	8	no	—
284	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	#60700	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	4	no	—
339	C₂³×C₂₃	—	4	1	no	—
340	C₂³×C₂₃	—	4	4	no	—
341	C₂³×C₂₃	—	4	4	no	—
342	C₂³×C₂₃	—	4	4	no	—
343	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₂₃	—	2	4	no	—
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	4	no	—
349	Q₈×C₂₃	—	4	2	no	—
350	Q₈×C₂₃	—	4	2	no	—
351	D₄×C₂₃	—	2	4	no	—
352	D₄×C₂₃	—	2	8	no	—
353	D₄×C₂₃	—	4	4	no	—
354	D₄×C₂₃	—	4	4	no	—
355	D₄×C₂₃	—	4	8	no	—
356	D₄×C₂₃	—	4	4	no	—
357	D₄×C₂₃	—	4	4	no	—
358	D₄×C₂₃	—	4	8	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	4	4	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	—	4	4	no	—
364	D₄×C₂₃	—	4	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	4	no	—
382	C₂×C₄×C₂₃	—	4	1	no	—
383	C₂×C₄×C₂₃	—	4	1	no	—
384	C₂×C₄×C₂₃	—	4	1	no	—
385	C₂×C₄×C₂₃	—	4	8	no	—
386	C₂×C₄×C₂₃	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	4	4	no	—
389	C₂×C₄×C₂₃	—	4	8	no	—
390	C₂×C₄×C₂₃	—	4	4	no	—
391	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
404	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
405	C₈×C₂₃	—	2	4	no	—
406	C₈×C₂₃	C₂×#41	1	8	yes	complemented
407	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
408	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3184	C₂×C₂₃	1	2	yes	complemented
410	#3182	C₂×C₂₃	1	2	yes	complemented
411	#3180	C₂×C₂₃	1	4	yes	complemented
412	#3171	C₂×C₂₃	1	4	yes	complemented
413	#3169	C₂×C₂₃	1	2	yes	complemented
414	#3167	C₂×C₂₃	1	2	yes	complemented
415	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3151	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3055	C₂×C₂₃	1	4	yes	complemented
420	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	4	yes	complemented
421	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
422	C₂²×C₂₃	—	2	1	no	—
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	1	no	—
426	C₂²×C₂₃	—	2	1	no	—
427	C₂²×C₂₃	—	2	1	no	—
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	4	4	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	4	no	—
432	C₂²×C₂₃	—	4	4	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	2	no	—
435	C₂²×C₂₃	—	4	4	no	—
436	C₂²×C₂₃	—	8	8	no	—
437	C₂²×C₂₃	#532	1	2	yes	—
438	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
439	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	2	1	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	1	no	—
445	C₄×C₂₃	—	2	1	no	—
446	C₄×C₂₃	—	2	1	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	4	4	no	—
449	C₄×C₂₃	—	4	2	no	—
450	C₄×C₂₃	—	4	2	no	—
451	C₄×C₂₃	#532	1	2	yes	—
452	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
453	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
454	C₄×C₂₃	#575	1	2	yes	—
455	C₄×C₂₃	C₂²×#41	1	2	yes	—
456	C₂²×#41	—	2	1	no	—
457	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	—
458	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
459	#533	C₂²×C₂₃	1	1	yes	characteristic
460	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#532	—	2	1	no	—
463	#532	—	2	1	no	—
464	#532	—	2	1	no	—
465	#532	—	2	1	no	—
466	#532	C₂²×C₂₃	1	1	yes	characteristic
467	#532	C₂²×C₂₃	1	2	yes	—
468	#532	C₂²×C₂₃	1	2	yes	—
469	#532	C₂²×C₂₃	1	2	yes	—
470	#532	C₂²×C₂₃	1	2	yes	—
471	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
475	#529	—	2	1	no	—
476	#529	—	2	1	no	—
477	#529	—	2	1	no	—
478	#529	—	2	1	no	—
479	#529	C₂²×C₂₃	1	2	yes	complemented
480	#529	C₂²×C₂₃	1	2	yes	complemented
481	C₂×#124	—	2	1	no	—
482	#525	—	2	1	no	—
483	#525	—	2	1	no	—
484	#525	C₂²×C₂₃	1	2	yes	—
485	C₂×#121	—	2	1	no	—
486	C₂×#121	C₂²×C₂₃	1	2	yes	—
487	C₄×#41	—	2	1	no	—
488	C₄×#41	—	2	1	no	—
489	C₄×#41	C₂²×C₂₃	1	2	yes	—
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
492	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
493	#501	C₂²×C₂₃	1	4	yes	complemented
494	#500	C₂²×C₂₃	1	2	yes	complemented
495	#498	C₂²×C₂₃	1	2	yes	complemented
496	#496	C₂²×C₂₃	1	4	yes	complemented
497	#493	C₂²×C₂₃	1	2	yes	complemented
498	#492	C₂²×C₂₃	1	2	yes	complemented
499	#490	C₂²×C₂₃	1	4	yes	complemented
500	#489	C₂²×C₂₃	1	4	yes	complemented
501	#487	C₂²×C₂₃	1	2	yes	complemented
502	#486	C₂²×C₂₃	1	2	yes	complemented
503	#486	C₂²×C₂₃	1	2	yes	complemented
504	#486	C₂²×C₂₃	1	2	yes	complemented
505	#469	C₂²×C₂₃	1	8	yes	complemented
506	#468	C₂²×C₂₃	1	8	yes	complemented
507	#466	C₂²×C₂₃	1	8	yes	complemented
508	#465	C₂²×C₂₃	1	8	yes	complemented
509	#442	C₂²×C₂₃	1	8	yes	complemented
510	#440	C₂²×C₂₃	1	8	yes	complemented
511	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
512	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
513	#428	C₂²×C₂₃	1	4	yes	—
514	#418	C₂²×C₂₃	1	4	yes	—
515	#417	C₂²×C₂₃	1	4	yes	—
516	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
517	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
518	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
519	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
520	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
521	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
522	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	2	2	no	—
525	C₂×C₂₃	—	4	1	no	—
526	C₂×C₂₃	—	8	2	no	—
527	C₂×C₂₃	—	8	4	no	—
528	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
529	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	—	4	8	no	—
538	C₂×#41	C₂³×C₂₃	1	2	yes	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×D₄	—	2	2	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
544	C₂³×C₄	—	2	2	no	—
545	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
546	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
548	AGL(1,ℤ/8)	—	2	16	no	—
549	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
550	C₂×D₈	C₂³×C₂₃	1	8	yes	—
551	C₂×M₁₆	—	2	8	no	—
552	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
553	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
554	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
555	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	#127	—	2	1	no	—
564	#127	—	2	1	no	—
565	#127	C₂³×C₂₃	1	2	yes	—
566	#127	C₂³×C₂₃	1	2	yes	—
567	#127	C₂³×C₂₃	1	1	yes	characteristic
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	—	2	1	no	—
572	#125	C₂³×C₂₃	1	2	yes	—
573	#124	—	2	2	no	—
574	#124	—	2	2	no	—
575	#124	—	2	2	no	—
576	#124	—	2	2	no	—
577	#124	—	2	1	no	—
578	#124	—	2	1	no	—
579	#124	C₂³×C₂₃	1	2	yes	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
588	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	1	no	—
596	#121	—	2	1	no	—
597	#121	—	2	1	no	—
598	#121	—	2	1	no	—
599	#121	C₂³×C₂₃	1	4	yes	—
600	#121	C₂³×C₂₃	1	4	yes	—
601	#121	C₂³×C₂₃	1	2	yes	—
602	#121	C₂³×C₂₃	1	2	yes	—
603	#120	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
609	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	C₂³×C₂₃	1	4	yes	—
627	C₄×D₄	C₂³×C₂₃	1	4	yes	—
628	C₄×D₄	C₂³×C₂₃	1	2	yes	—
629	C₄×D₄	C₂³×C₂₃	1	2	yes	—
630	#117	—	2	1	no	—
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	C₂³×C₂₃	1	2	yes	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₄²	—	2	2	no	—
641	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
643	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
644	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
645	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
646	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
653	#107	C₂³×C₂₃	1	8	yes	—
654	#106	C₂³×C₂₃	1	8	yes	—
655	#103	C₂³×C₂₃	1	8	yes	—
656	#102	C₂³×C₂₃	1	8	yes	—
657	#102	C₂³×C₂₃	1	8	yes	—
658	#102	C₂³×C₂₃	1	8	yes	—
659	#97	C₂³×C₂₃	1	4	yes	—
660	#97	C₂³×C₂₃	1	2	yes	—
661	#97	C₂³×C₂₃	1	2	yes	—
662	C₄×C₈	C₂³×C₂₃	1	4	yes	—
663	C₄×C₈	C₂³×C₂₃	1	2	yes	—
664	C₄×C₈	C₂³×C₂₃	1	2	yes	—
665	C₂₃	#60700	1	1	yes	characteristic, direct product factor, Sylow
666	C₂⁴	—	2	2	no	—
667	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
668	#41	—	2	8	no	—
669	#41	—	4	8	no	—
670	#41	—	4	8	no	—
671	#41	—	4	8	no	—
672	#41	—	4	4	no	—
673	#41	—	4	8	no	—
674	#41	—	4	4	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	4	4	no	—
680	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	8	no	—
709	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	SD₁₆	—	2	16	no	—
728	D₈	—	2	16	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	2	8	no	—
731	M₁₆	#41×C₂₃	1	8	yes	complemented
732	C₂×C₈	—	2	8	no	—
733	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
734	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
793	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
794	Q₈	—	2	4	no	—
795	Q₈	—	4	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	8	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
840	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
851	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
852	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
853	C₈	—	2	4	no	—
854	C₈	C₂×#41×C₂₃	1	8	yes	complemented
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	4	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₂₃×#532	1	2	yes	—
871	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
872	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	4	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	C₂₃×#532	1	2	yes	—
885	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
886	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
887	C₄	C₂₃×#575	1	2	yes	—
888	C₄	C₂²×#41×C₂₃	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	4	no	—
893	C₂	—	8	2	no	—
894	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
895	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
896	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂×C₂₃×#532	C₂	semidirect
3. C₂₃×#3184	C₂	semidirect
4. C₂₃×#3182	C₂	semidirect
5. C₂₃×#3180	C₂	semidirect
6. C₂₃×#3171	C₂	semidirect
7. C₂₃×#3169	C₂	semidirect
8. C₂₃×#3167	C₂	semidirect
9. C₂₃×#3165	C₂	semidirect
10. C₂₃×#3151	C₂	semidirect
11. C₂₃×#3141	C₂	semidirect
12. C₂₃×#3138	C₂	semidirect
13. C₂₃×#3055	C₂	semidirect
14. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
20. C₂₃×#533	C₂²	semidirect
21. C₂₃×#533	C₂²	semidirect
31. C₂₃×#532	C₂²	semidirect
32. C₂₃×#532	C₂²	semidirect
39. C₂₃×#529	C₂²	semidirect
40. C₂₃×#529	C₂²	semidirect
53. C₂₃×#501	C₂²	semidirect
54. C₂₃×#500	C₂²	semidirect
55. C₂₃×#498	C₂²	semidirect
56. C₂₃×#496	C₂²	semidirect
57. C₂₃×#493	C₂²	semidirect
58. C₂₃×#492	C₂²	semidirect
59. C₂₃×#490	C₂²	semidirect
60. C₂₃×#489	C₂²	semidirect
61. C₂₃×#487	C₂²	semidirect
62. C₂₃×#486	C₂²	semidirect
63. C₂₃×#486	C₂²	semidirect
64. C₂₃×#486	C₂²	semidirect
65. C₂₃×#469	C₂²	semidirect
66. C₂₃×#468	C₂²	semidirect
67. C₂₃×#466	C₂²	semidirect
68. C₂₃×#465	C₂²	semidirect
69. C₂₃×#442	C₂²	semidirect
70. C₂₃×#440	C₂²	semidirect
71. C₄×SD₁₆×C₂₃	C₂²	semidirect
72. C₄×D₈×C₂₃	C₂²	semidirect
79. C₄×M₁₆×C₂₃	C₂²	semidirect
80. C₄×M₁₆×C₂₃	C₂²	semidirect
81. C₂×C₂₃×#97	C₂²	semidirect
82. C₂×C₄×C₈×C₂₃	C₂²	semidirect
282. M₁₆×C₂₃	#41	semidirect
334. #60700	C₂₃	direct (N × H)
391. C₂×C₄×C₂₃	AGL(1,ℤ/8)	semidirect
406. C₈×C₂₃	C₂×#41	semidirect
407. #3444	C₂×C₂₃	semidirect
408. C₂×#532	C₂×C₂₃	semidirect
409. #3184	C₂×C₂₃	semidirect
410. #3182	C₂×C₂₃	semidirect
411. #3180	C₂×C₂₃	semidirect
412. #3171	C₂×C₂₃	semidirect
413. #3169	C₂×C₂₃	semidirect
414. #3167	C₂×C₂₃	semidirect
415. #3165	C₂×C₂₃	semidirect
416. #3151	C₂×C₂₃	semidirect
417. #3141	C₂×C₂₃	semidirect
418. #3138	C₂×C₂₃	semidirect
419. #3055	C₂×C₂₃	semidirect
420. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
421. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
460. #533	C₂²×C₂₃	semidirect
461. #533	C₂²×C₂₃	semidirect
471. #532	C₂²×C₂₃	semidirect
472. #532	C₂²×C₂₃	semidirect
479. #529	C₂²×C₂₃	semidirect
480. #529	C₂²×C₂₃	semidirect
493. #501	C₂²×C₂₃	semidirect
494. #500	C₂²×C₂₃	semidirect
495. #498	C₂²×C₂₃	semidirect
496. #496	C₂²×C₂₃	semidirect
497. #493	C₂²×C₂₃	semidirect
498. #492	C₂²×C₂₃	semidirect
499. #490	C₂²×C₂₃	semidirect
500. #489	C₂²×C₂₃	semidirect
501. #487	C₂²×C₂₃	semidirect
502. #486	C₂²×C₂₃	semidirect
503. #486	C₂²×C₂₃	semidirect
504. #486	C₂²×C₂₃	semidirect
505. #469	C₂²×C₂₃	semidirect
506. #468	C₂²×C₂₃	semidirect
507. #466	C₂²×C₂₃	semidirect
508. #465	C₂²×C₂₃	semidirect
509. #442	C₂²×C₂₃	semidirect
510. #440	C₂²×C₂₃	semidirect
511. C₄×SD₁₆	C₂²×C₂₃	semidirect
512. C₄×D₈	C₂²×C₂₃	semidirect
519. C₄×M₁₆	C₂²×C₂₃	semidirect
520. C₄×M₁₆	C₂²×C₂₃	semidirect
521. C₂×#97	C₂²×C₂₃	semidirect
522. C₂×C₄×C₈	C₂²×C₂₃	semidirect
665. C₂₃	#60700	direct (N × H)
731. M₁₆	#41×C₂₃	semidirect
839. C₂×C₄	C₂₃×AGL(1,ℤ/8)	semidirect
854. C₈	C₂×#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×#3444	2
C₂×C₂₃×#532	2
C₂₃×#3184	2
C₂₃×#3182	2
C₂₃×#3180	2
C₂₃×#3171	2
C₂₃×#3169	2
C₂₃×#3167	2
C₂₃×#3165	2
C₂₃×#3151	2
C₂₃×#3141	2
C₂₃×#3138	2
C₂₃×#3055	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂×C₄×M₁₆×C₂₃	2
#60700	23

Subgroups — C23×#60700 #19208326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60700 #19208326