Subgroups — C₂₃×#61205 #19208831

Order 5888.

2214 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3309	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3058	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3008	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
21	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
22	C₂₃×#559	—	2	2	no	—
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#555	C₂²	1	2	yes	complemented
25	C₂₃×#553	C₂²	1	4	yes	complemented
26	C₂₃×#550	—	2	1	no	—
27	C₂₃×#550	C₂²	1	2	yes	complemented
28	C₂₃×#550	C₂²	1	2	yes	complemented
29	C₂₃×#547	C₂²	1	2	yes	complemented
30	D₄²×C₂₃	—	2	2	no	—
31	D₄²×C₂₃	—	2	2	no	—
32	D₄²×C₂₃	C₂²	1	2	yes	complemented
33	D₄²×C₂₃	C₂²	1	2	yes	complemented
34	C₂₃×#538	—	2	2	no	—
35	C₂₃×#535	—	2	2	no	—
36	C₂₃×#535	C₂²	1	2	yes	—
37	C₂₃×#535	C₂²	1	2	yes	complemented
38	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#532	—	2	1	no	—
40	C₂₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#127	—	2	1	no	—
42	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
43	C₂₃×#525	—	2	2	no	—
44	C₂₃×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#490	C₂²	1	4	yes	complemented
48	C₂₃×#486	C₂²	1	2	yes	complemented
49	C₂₃×#486	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×#478	C₂²	1	2	yes	complemented
56	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#469	C₂²	1	4	yes	complemented
61	C₂₃×#469	C₂²	1	4	yes	complemented
62	C₂₃×#466	C₂²	1	4	yes	complemented
63	C₂₃×#466	C₂²	1	4	yes	complemented
64	C₂₃×#459	C₂²	1	2	yes	complemented
65	C₂₃×#459	C₂²	1	4	yes	complemented
66	C₂₃×#459	C₂²	1	2	yes	complemented
67	C₂₃×#449	C₂²	1	4	yes	complemented
68	C₂₃×#449	C₂²	1	4	yes	complemented
69	C₂₃×#447	C₂²	1	4	yes	complemented
70	C₂₃×#447	C₂²	1	4	yes	complemented
71	C₂₃×#442	C₂²	1	2	yes	complemented
72	C₂₃×#440	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
74	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂₃×#436	C₂²	1	2	yes	complemented
76	C₂₃×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
78	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#427	C₂²	1	2	yes	complemented
80	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#418	C₂²	1	2	yes	complemented
83	C₂₃×#418	C₂²	1	2	yes	complemented
84	C₂₃×#418	C₂²	1	4	yes	complemented
85	C₂₃×#417	C₂²	1	1	yes	characteristic
86	C₂₃×#417	C₂²	1	4	yes	complemented
87	C₂₃×#416	C₂²	1	2	yes	—
88	C₂₃×#416	C₂²	1	4	yes	complemented
89	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
90	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
91	C₂₃×#408	C₂²	1	2	yes	complemented
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×H(5,𝔽₂)	—	2	8	no	—
94	C₂₃×H(5,𝔽₂)	—	4	4	no	—
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	C₂³	1	4	yes	—
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₂₃	—	2	2	no	—
101	C₂²×D₄×C₂₃	—	2	4	no	—
102	C₂²×D₄×C₂₃	—	2	2	no	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	—	2	1	no	—
106	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
108	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
109	C₂³×C₄×C₂₃	—	2	1	no	—
110	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
111	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×D₈×C₂₃	—	4	4	no	—
113	C₂×D₈×C₂₃	C₂³	1	2	yes	—
114	C₂×D₈×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	4	yes	—
116	C₂₃×#131	—	4	4	no	—
117	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
122	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₂₃×#127	—	2	2	no	—
126	C₂₃×#127	—	2	2	no	—
127	C₂₃×#127	—	2	2	no	—
128	C₂₃×#127	—	2	2	no	—
129	C₂₃×#127	—	2	1	no	—
130	C₂₃×#127	—	2	1	no	—
131	C₂₃×#127	D₄	1	1	yes	characteristic
132	C₂₃×#127	C₂³	1	2	yes	—
133	C₂₃×#127	C₂³	1	2	yes	—
134	C₂₃×#126	—	2	4	no	—
135	C₂₃×#125	C₂³	1	2	yes	—
136	C₂₃×#124	—	2	2	no	—
137	C₂₃×#124	—	2	2	no	—
138	C₂₃×#124	—	2	4	no	—
139	C₂₃×#124	D₄	1	2	yes	—
140	C₂₃×#123	—	2	4	no	—
141	C₂₃×#123	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	1	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×#121	—	2	4	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	4	no	—
150	C₂₃×#121	—	2	4	no	—
151	C₂₃×#121	D₄	1	2	yes	—
152	C₂₃×#121	D₄	1	2	yes	—
153	C₂₃×#121	C₂³	1	4	yes	—
154	C₂₃×#121	C₂³	1	4	yes	—
155	C₂₃×#121	C₂³	1	4	yes	—
156	C₂₃×#121	C₂³	1	4	yes	—
157	C₂₃×#120	—	2	4	no	—
158	C₂₃×#120	—	2	4	no	—
159	C₂₃×#120	—	2	4	no	—
160	C₂₃×#120	—	2	4	no	—
161	C₄×Q₈×C₂₃	—	2	2	no	—
162	C₄×Q₈×C₂₃	—	2	1	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	1	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	4	no	—
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	C₂³	1	4	yes	—
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂₃×#117	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄²×C₂₃	—	2	1	no	—
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂₃×#107	C₂³	1	2	yes	—
192	C₂₃×#107	C₂³	1	2	yes	—
193	C₂₃×#107	C₂³	1	2	yes	—
194	C₂₃×#106	C₂³	1	2	yes	—
195	C₂₃×#106	C₂³	1	2	yes	—
196	C₂₃×#106	C₂³	1	2	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₂₃×#103	C₂³	1	2	yes	—
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	2	yes	—
203	C₂₃×#102	C₂³	1	2	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	2	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	4	yes	—
208	C₂₃×#102	C₂³	1	2	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	2	yes	—
211	C₂₃×#102	C₂³	1	2	yes	—
212	C₂₃×#102	C₂³	1	4	yes	—
213	C₂₃×#102	C₂³	1	4	yes	—
214	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₂₃×#97	C₂³	1	2	yes	—
217	C₄×C₈×C₂₃	C₂³	1	2	yes	—
218	C₂⁴×C₂₃	—	2	1	no	—
219	C₂⁴×C₂₃	—	2	4	no	—
220	C₂⁴×C₂₃	—	2	2	no	—
221	#41×C₂₃	—	2	4	no	—
222	#41×C₂₃	—	2	4	no	—
223	#41×C₂₃	—	2	2	no	—
224	#41×C₂₃	—	2	8	no	—
225	#41×C₂₃	—	4	4	no	—
226	#41×C₂₃	—	4	8	no	—
227	#41×C₂₃	—	8	4	no	—
228	#41×C₂₃	#41	1	4	yes	complemented
229	C₂×Q₈×C₂₃	—	2	1	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
232	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	8	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	2	4	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	4	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	4	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	4	8	no	—
253	C₂×D₄×C₂₃	—	4	16	no	—
254	C₂×D₄×C₂₃	—	8	2	no	—
255	C₂×D₄×C₂₃	—	8	4	no	—
256	C₂×D₄×C₂₃	—	8	2	no	—
257	C₂×D₄×C₂₃	—	8	4	no	—
258	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
263	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	—	2	1	no	—
266	C₂²×C₄×C₂₃	—	2	1	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	2	1	no	—
269	C₂²×C₄×C₂₃	—	2	1	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	2	4	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	8	2	no	—
274	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	SD₁₆×C₂₃	—	2	4	no	—
279	D₈×C₂₃	—	2	4	no	—
280	D₈×C₂₃	—	4	4	no	—
281	D₈×C₂₃	—	4	4	no	—
282	M₁₆×C₂₃	—	2	2	no	—
283	M₁₆×C₂₃	—	2	2	no	—
284	M₁₆×C₂₃	—	4	4	no	—
285	C₂×C₈×C₂₃	—	2	4	no	—
286	C₂×C₈×C₂₃	—	4	4	no	—
287	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
289	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
290	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	4	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
319	C₄²×C₂₃	—	2	1	no	—
320	C₄²×C₂₃	—	2	1	no	—
321	C₄²×C₂₃	—	2	1	no	—
322	C₄²×C₂₃	—	2	4	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#61205	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	4	no	—
332	C₂³×C₂₃	—	4	8	no	—
333	C₂³×C₂₃	—	4	2	no	—
334	C₂³×C₂₃	—	4	4	no	—
335	C₂³×C₂₃	—	8	1	no	—
336	C₂³×C₂₃	—	8	1	no	—
337	C₂³×C₂₃	—	8	2	no	—
338	C₂³×C₂₃	—	8	2	no	—
339	C₂³×C₂₃	—	8	4	no	—
340	C₂³×C₂₃	—	8	4	no	—
341	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
342	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₂₃	—	2	4	no	—
344	Q₈×C₂₃	—	2	1	no	—
345	Q₈×C₂₃	—	4	2	no	—
346	Q₈×C₂₃	—	8	1	no	—
347	Q₈×C₂₃	C₂×#41	1	2	yes	—
348	D₄×C₂₃	—	2	4	no	—
349	D₄×C₂₃	—	2	8	no	—
350	D₄×C₂₃	—	2	4	no	—
351	D₄×C₂₃	—	2	4	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	4	no	—
354	D₄×C₂₃	—	2	1	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	2	4	no	—
357	D₄×C₂₃	—	4	2	no	—
358	D₄×C₂₃	—	4	8	no	—
359	D₄×C₂₃	—	4	8	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	4	4	no	—
363	D₄×C₂₃	—	4	4	no	—
364	D₄×C₂₃	—	8	2	no	—
365	D₄×C₂₃	—	8	2	no	—
366	D₄×C₂₃	—	8	4	no	—
367	D₄×C₂₃	—	8	4	no	—
368	D₄×C₂₃	—	8	4	no	—
369	D₄×C₂₃	—	8	4	no	—
370	D₄×C₂₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	4	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	4	1	no	—
382	C₂×C₄×C₂₃	—	4	8	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	4	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	8	2	no	—
387	C₂×C₄×C₂₃	—	8	1	no	—
388	C₂×C₄×C₂₃	—	8	4	no	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
396	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
398	C₈×C₂₃	—	2	2	no	—
399	C₈×C₂₃	—	2	2	no	—
400	C₈×C₂₃	—	2	2	no	—
401	C₈×C₂₃	—	2	2	no	—
402	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3498	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3332	C₂×C₂₃	1	2	yes	complemented
405	#3325	C₂×C₂₃	1	2	yes	complemented
406	#3318	C₂×C₂₃	1	4	yes	complemented
407	#3309	C₂×C₂₃	1	4	yes	complemented
408	#3305	C₂×C₂₃	1	2	yes	complemented
409	#3294	C₂×C₂₃	1	2	yes	complemented
410	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3096	C₂×C₂₃	1	2	yes	complemented
412	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#3058	C₂×C₂₃	1	2	yes	complemented
414	C₂×#459	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#3008	C₂×C₂₃	1	2	yes	complemented
416	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2897	C₂×C₂₃	1	2	yes	complemented
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	4	no	—
422	C₂²×C₂₃	—	2	4	no	—
423	C₂²×C₂₃	—	2	2	no	—
424	C₂²×C₂₃	—	2	4	no	—
425	C₂²×C₂₃	—	4	1	no	—
426	C₂²×C₂₃	—	4	1	no	—
427	C₂²×C₂₃	—	4	4	no	—
428	C₂²×C₂₃	—	4	2	no	—
429	C₂²×C₂₃	—	4	4	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	4	4	no	—
433	C₂²×C₂₃	—	8	4	no	—
434	C₂²×C₂₃	—	16	4	no	—
435	C₂²×C₂₃	—	16	8	no	—
436	C₂²×C₂₃	#546	1	2	yes	—
437	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	2	no	—
441	C₄×C₂₃	—	2	4	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	4	1	no	—
444	C₄×C₂₃	—	4	2	no	—
445	C₄×C₂₃	—	4	2	no	—
446	C₄×C₂₃	—	4	1	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	#546	1	2	yes	—
449	C₄×C₂₃	#576	1	2	yes	—
450	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
451	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
453	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
454	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
455	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
456	#559	—	2	2	no	—
457	#556	—	2	1	no	—
458	#555	C₂²×C₂₃	1	2	yes	complemented
459	#553	C₂²×C₂₃	1	4	yes	complemented
460	#550	—	2	1	no	—
461	#550	C₂²×C₂₃	1	2	yes	complemented
462	#550	C₂²×C₂₃	1	2	yes	complemented
463	#547	C₂²×C₂₃	1	2	yes	complemented
464	D₄²	—	2	2	no	—
465	D₄²	—	2	2	no	—
466	D₄²	C₂²×C₂₃	1	2	yes	complemented
467	D₄²	C₂²×C₂₃	1	2	yes	complemented
468	#538	—	2	2	no	—
469	#535	—	2	2	no	—
470	#535	C₂²×C₂₃	1	2	yes	—
471	#535	C₂²×C₂₃	1	2	yes	complemented
472	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#532	—	2	1	no	—
474	#532	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#127	—	2	1	no	—
476	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
477	#525	—	2	2	no	—
478	#520	C₂²×C₂₃	1	2	yes	complemented
479	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#490	C₂²×C₂₃	1	4	yes	complemented
482	#486	C₂²×C₂₃	1	2	yes	complemented
483	#486	C₂²×C₂₃	1	2	yes	complemented
484	#482	C₂²×C₂₃	1	4	yes	complemented
485	#482	C₂²×C₂₃	1	4	yes	complemented
486	#481	C₂²×C₂₃	1	4	yes	complemented
487	#480	C₂²×C₂₃	1	4	yes	complemented
488	#479	C₂²×C₂₃	1	2	yes	complemented
489	#478	C₂²×C₂₃	1	2	yes	complemented
490	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	#469	C₂²×C₂₃	1	4	yes	complemented
495	#469	C₂²×C₂₃	1	4	yes	complemented
496	#466	C₂²×C₂₃	1	4	yes	complemented
497	#466	C₂²×C₂₃	1	4	yes	complemented
498	#459	C₂²×C₂₃	1	2	yes	complemented
499	#459	C₂²×C₂₃	1	2	yes	complemented
500	#459	C₂²×C₂₃	1	4	yes	complemented
501	#449	C₂²×C₂₃	1	4	yes	complemented
502	#449	C₂²×C₂₃	1	4	yes	complemented
503	#447	C₂²×C₂₃	1	4	yes	complemented
504	#447	C₂²×C₂₃	1	4	yes	complemented
505	#442	C₂²×C₂₃	1	2	yes	complemented
506	#440	C₂²×C₂₃	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
508	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
509	#436	C₂²×C₂₃	1	2	yes	complemented
510	#435	C₂²×C₂₃	1	4	yes	complemented
511	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
512	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	#427	C₂²×C₂₃	1	2	yes	complemented
514	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	#418	C₂²×C₂₃	1	2	yes	complemented
516	#418	C₂²×C₂₃	1	2	yes	complemented
517	#418	C₂²×C₂₃	1	4	yes	complemented
518	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	#417	C₂²×C₂₃	1	1	yes	characteristic
520	#417	C₂²×C₂₃	1	4	yes	complemented
521	#416	C₂²×C₂₃	1	2	yes	—
522	#416	C₂²×C₂₃	1	4	yes	complemented
523	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
524	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
525	#408	C₂²×C₂₃	1	2	yes	complemented
526	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	C₂×C₂₃	—	2	2	no	—
528	C₂×C₂₃	—	4	4	no	—
529	C₂×C₂₃	—	4	2	no	—
530	C₂×C₂₃	—	8	2	no	—
531	C₂×C₂₃	—	8	4	no	—
532	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
533	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
534	C₂×C₂₃	#3585	1	1	yes	characteristic
535	H(5,𝔽₂)	—	2	8	no	—
536	H(5,𝔽₂)	—	4	4	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	C₂³×C₂₃	1	4	yes	—
540	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×#41	C₂³×C₂₃	1	2	yes	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	—	2	4	no	—
544	C₂²×D₄	—	2	2	no	—
545	C₂²×D₄	—	2	2	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
550	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
551	C₂³×C₄	—	2	1	no	—
552	AGL(1,ℤ/8)	—	2	4	no	—
553	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
554	C₂×D₈	—	4	4	no	—
555	C₂×D₈	C₂³×C₂₃	1	2	yes	—
556	C₂×D₈	C₂³×C₂₃	1	4	yes	—
557	C₂×D₈	C₂³×C₂₃	1	4	yes	—
558	#131	—	4	4	no	—
559	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
561	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
562	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
563	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
564	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
567	#127	—	2	2	no	—
568	#127	—	2	2	no	—
569	#127	—	2	2	no	—
570	#127	—	2	2	no	—
571	#127	—	2	1	no	—
572	#127	—	2	1	no	—
573	#127	D₄×C₂₃	1	1	yes	characteristic
574	#127	C₂³×C₂₃	1	2	yes	—
575	#127	C₂³×C₂₃	1	2	yes	—
576	#126	—	2	4	no	—
577	#125	C₂³×C₂₃	1	2	yes	—
578	#124	—	2	2	no	—
579	#124	—	2	2	no	—
580	#124	—	2	4	no	—
581	#124	D₄×C₂₃	1	2	yes	—
582	#123	—	2	4	no	—
583	#123	—	2	4	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	4	no	—
592	#121	—	2	4	no	—
593	#121	D₄×C₂₃	1	2	yes	—
594	#121	D₄×C₂₃	1	2	yes	—
595	#121	C₂³×C₂₃	1	4	yes	—
596	#121	C₂³×C₂₃	1	4	yes	—
597	#121	C₂³×C₂₃	1	4	yes	—
598	#121	C₂³×C₂₃	1	4	yes	—
599	#120	—	2	4	no	—
600	#120	—	2	4	no	—
601	#120	—	2	4	no	—
602	#120	—	2	4	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	C₂³×C₂₃	1	2	yes	—
618	C₄×D₄	C₂³×C₂₃	1	2	yes	—
619	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₂₃	1	2	yes	—
622	C₄×D₄	C₂³×C₂₃	1	2	yes	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	C₂³×C₂₃	1	1	yes	characteristic
626	#117	C₂³×C₂₃	1	2	yes	—
627	#117	C₂³×C₂₃	1	4	yes	—
628	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
633	#107	C₂³×C₂₃	1	2	yes	—
634	#107	C₂³×C₂₃	1	2	yes	—
635	#107	C₂³×C₂₃	1	2	yes	—
636	#106	C₂³×C₂₃	1	2	yes	—
637	#106	C₂³×C₂₃	1	2	yes	—
638	#106	C₂³×C₂₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
642	#103	C₂³×C₂₃	1	2	yes	—
643	#103	C₂³×C₂₃	1	2	yes	—
644	#103	C₂³×C₂₃	1	2	yes	—
645	#102	C₂³×C₂₃	1	2	yes	—
646	#102	C₂³×C₂₃	1	4	yes	—
647	#102	C₂³×C₂₃	1	2	yes	—
648	#102	C₂³×C₂₃	1	4	yes	—
649	#102	C₂³×C₂₃	1	4	yes	—
650	#102	C₂³×C₂₃	1	2	yes	—
651	#102	C₂³×C₂₃	1	4	yes	—
652	#102	C₂³×C₂₃	1	2	yes	—
653	#102	C₂³×C₂₃	1	2	yes	—
654	#102	C₂³×C₂₃	1	4	yes	—
655	#102	C₂³×C₂₃	1	4	yes	—
656	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
657	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
658	#97	C₂³×C₂₃	1	2	yes	—
659	C₄×C₈	C₂³×C₂₃	1	2	yes	—
660	C₂₃	#61205	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	2	2	no	—
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	2	2	no	—
667	#41	—	2	8	no	—
668	#41	—	4	4	no	—
669	#41	—	4	8	no	—
670	#41	—	8	4	no	—
671	#41	#41×C₂₃	1	4	yes	complemented
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	8	no	—
696	C₂×D₄	—	4	16	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	—	8	4	no	—
699	C₂×D₄	—	8	2	no	—
700	C₂×D₄	—	8	4	no	—
701	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
705	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
706	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
707	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	8	2	no	—
717	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	SD₁₆	—	2	4	no	—
722	D₈	—	2	4	no	—
723	D₈	—	4	4	no	—
724	D₈	—	4	4	no	—
725	M₁₆	—	2	2	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	4	4	no	—
728	C₂×C₈	—	2	4	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
733	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
761	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	4	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	C₂⁴×C₂₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	4	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	4	no	—
782	C₂³	—	8	4	no	—
783	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
784	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
785	Q₈	—	2	1	no	—
786	Q₈	—	2	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	1	no	—
789	Q₈	C₂×#41×C₂₃	1	2	yes	—
790	D₄	—	2	4	no	—
791	D₄	—	2	8	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	4	no	—
798	D₄	—	2	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	2	no	—
806	D₄	—	8	2	no	—
807	D₄	—	8	2	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	D₄	C₂×#41×C₂₃	1	2	yes	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
833	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
837	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
838	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
839	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
840	C₈	—	2	2	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	4	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	4	no	—
859	C₂²	—	16	4	no	—
860	C₂²	—	16	8	no	—
861	C₂²	C₂₃×#546	1	2	yes	—
862	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	C₂₃×#546	1	2	yes	—
874	C₄	C₂₃×#576	1	2	yes	—
875	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
876	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂	—	2	2	no	—
878	C₂	—	4	4	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	2	no	—
881	C₂	—	8	4	no	—
882	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
883	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
884	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 ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3506	C₂	semidirect
2. C₂₃×#3498	C₂	semidirect
3. C₂₃×#3332	C₂	semidirect
4. C₂₃×#3325	C₂	semidirect
5. C₂₃×#3318	C₂	semidirect
6. C₂₃×#3309	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3294	C₂	semidirect
9. C₂₃×#3138	C₂	semidirect
10. C₂₃×#3096	C₂	semidirect
11. C₂₃×#3076	C₂	semidirect
12. C₂₃×#3058	C₂	semidirect
13. C₂×C₂₃×#459	C₂	semidirect
14. C₂₃×#3008	C₂	semidirect
15. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
16. C₂₃×#2935	C₂	semidirect
17. C₂₃×#2897	C₂	semidirect
20. C₂²×D₈×C₂₃	C₂²	semidirect
21. C₂×C₂₃×#131	C₂²	semidirect
24. C₂₃×#555	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
27. C₂₃×#550	C₂²	semidirect
28. C₂₃×#550	C₂²	semidirect
29. C₂₃×#547	C₂²	semidirect
32. D₄²×C₂₃	C₂²	semidirect
33. D₄²×C₂₃	C₂²	semidirect
37. C₂₃×#535	C₂²	semidirect
38. C₂₃×#533	C₂²	semidirect
44. C₂₃×#520	C₂²	semidirect
46. C₂×C₄×D₄×C₂₃	C₂²	semidirect
47. C₂₃×#490	C₂²	semidirect
48. C₂₃×#486	C₂²	semidirect
49. C₂₃×#486	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×#478	C₂²	semidirect
56. C₂₃×#477	C₂²	semidirect
57. C₂₃×#476	C₂²	semidirect
58. C₂₃×#475	C₂²	semidirect
59. C₂₃×#474	C₂²	semidirect
60. C₂₃×#469	C₂²	semidirect
61. C₂₃×#469	C₂²	semidirect
62. C₂₃×#466	C₂²	semidirect
63. C₂₃×#466	C₂²	semidirect
64. C₂₃×#459	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
67. C₂₃×#449	C₂²	semidirect
68. C₂₃×#449	C₂²	semidirect
69. C₂₃×#447	C₂²	semidirect
70. C₂₃×#447	C₂²	semidirect
71. C₂₃×#442	C₂²	semidirect
72. C₂₃×#440	C₂²	semidirect
73. C₄×SD₁₆×C₂₃	C₂²	semidirect
74. C₄×D₈×C₂₃	C₂²	semidirect
75. C₂₃×#436	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₈×D₄×C₂₃	C₂²	semidirect
78. C₂₃×#428	C₂²	semidirect
79. C₂₃×#427	C₂²	semidirect
80. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
81. C₂₃×#418	C₂²	semidirect
82. C₂₃×#418	C₂²	semidirect
83. C₂₃×#418	C₂²	semidirect
84. C₂₃×#418	C₂²	semidirect
86. C₂₃×#417	C₂²	semidirect
88. C₂₃×#416	C₂²	semidirect
89. C₂×C₂₃×#102	C₂²	semidirect
90. C₂×C₂₃×#102	C₂²	semidirect
91. C₂₃×#408	C₂²	semidirect
92. C₄×M₁₆×C₂₃	C₂²	semidirect
228. #41×C₂₃	#41	semidirect
328. #61205	C₂₃	direct (N × H)
402. #3506	C₂×C₂₃	semidirect
403. #3498	C₂×C₂₃	semidirect
404. #3332	C₂×C₂₃	semidirect
405. #3325	C₂×C₂₃	semidirect
406. #3318	C₂×C₂₃	semidirect
407. #3309	C₂×C₂₃	semidirect
408. #3305	C₂×C₂₃	semidirect
409. #3294	C₂×C₂₃	semidirect
410. #3138	C₂×C₂₃	semidirect
411. #3096	C₂×C₂₃	semidirect
412. #3076	C₂×C₂₃	semidirect
413. #3058	C₂×C₂₃	semidirect
414. C₂×#459	C₂×C₂₃	semidirect
415. #3008	C₂×C₂₃	semidirect
416. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
417. #2935	C₂×C₂₃	semidirect
418. #2897	C₂×C₂₃	semidirect
454. C₂²×D₈	C₂²×C₂₃	semidirect
455. C₂×#131	C₂²×C₂₃	semidirect
458. #555	C₂²×C₂₃	semidirect
459. #553	C₂²×C₂₃	semidirect
461. #550	C₂²×C₂₃	semidirect
462. #550	C₂²×C₂₃	semidirect
463. #547	C₂²×C₂₃	semidirect
466. D₄²	C₂²×C₂₃	semidirect
467. D₄²	C₂²×C₂₃	semidirect
471. #535	C₂²×C₂₃	semidirect
472. #533	C₂²×C₂₃	semidirect
478. #520	C₂²×C₂₃	semidirect
480. C₂×C₄×D₄	C₂²×C₂₃	semidirect
481. #490	C₂²×C₂₃	semidirect
482. #486	C₂²×C₂₃	semidirect
483. #486	C₂²×C₂₃	semidirect
484. #482	C₂²×C₂₃	semidirect
485. #482	C₂²×C₂₃	semidirect
486. #481	C₂²×C₂₃	semidirect
487. #480	C₂²×C₂₃	semidirect
488. #479	C₂²×C₂₃	semidirect
489. #478	C₂²×C₂₃	semidirect
490. #477	C₂²×C₂₃	semidirect
491. #476	C₂²×C₂₃	semidirect
492. #475	C₂²×C₂₃	semidirect
493. #474	C₂²×C₂₃	semidirect
494. #469	C₂²×C₂₃	semidirect
495. #469	C₂²×C₂₃	semidirect
496. #466	C₂²×C₂₃	semidirect
497. #466	C₂²×C₂₃	semidirect
498. #459	C₂²×C₂₃	semidirect
499. #459	C₂²×C₂₃	semidirect
500. #459	C₂²×C₂₃	semidirect
501. #449	C₂²×C₂₃	semidirect
502. #449	C₂²×C₂₃	semidirect
503. #447	C₂²×C₂₃	semidirect
504. #447	C₂²×C₂₃	semidirect
505. #442	C₂²×C₂₃	semidirect
506. #440	C₂²×C₂₃	semidirect
507. C₄×SD₁₆	C₂²×C₂₃	semidirect
508. C₄×D₈	C₂²×C₂₃	semidirect
509. #436	C₂²×C₂₃	semidirect
510. #435	C₂²×C₂₃	semidirect
511. C₈×D₄	C₂²×C₂₃	semidirect
512. #428	C₂²×C₂₃	semidirect
513. #427	C₂²×C₂₃	semidirect
514. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
515. #418	C₂²×C₂₃	semidirect
516. #418	C₂²×C₂₃	semidirect
517. #418	C₂²×C₂₃	semidirect
518. #418	C₂²×C₂₃	semidirect
520. #417	C₂²×C₂₃	semidirect
522. #416	C₂²×C₂₃	semidirect
523. C₂×#102	C₂²×C₂₃	semidirect
524. C₂×#102	C₂²×C₂₃	semidirect
525. #408	C₂²×C₂₃	semidirect
526. C₄×M₁₆	C₂²×C₂₃	semidirect
660. C₂₃	#61205	direct (N × H)
671. #41	#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×#3506	2
C₂₃×#3498	2
C₂₃×#3332	2
C₂₃×#3325	2
C₂₃×#3318	2
C₂₃×#3309	2
C₂₃×#3305	2
C₂₃×#3294	2
C₂₃×#3138	2
C₂₃×#3096	2
C₂₃×#3076	2
C₂₃×#3058	2
C₂×C₂₃×#459	2
C₂₃×#3008	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#2935	2
C₂₃×#2897	2
#61205	23

Subgroups — C23×#61205 #19208831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61205 #19208831