Subgroups — C₂₃×#61417 #19209043

Order 5888.

1974 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3399	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#559	C₂²	1	4	yes	complemented
30	C₂₃×#559	C₂²	1	4	yes	complemented
31	C₂₃×#556	C₂²	1	4	yes	complemented
32	C₂₃×#551	—	2	4	no	—
33	C₂₃×#550	C₂²	1	4	yes	complemented
34	C₂₃×#546	—	2	4	no	—
35	C₂₃×#542	—	2	2	no	—
36	C₂₃×#540	—	2	2	no	—
37	C₂₃×#536	C₂²	1	1	yes	characteristic
38	C₂₃×#535	C₂²	1	1	yes	characteristic
39	C₂₃×#535	C₂²	1	1	yes	characteristic
40	C₂₃×#535	C₂²	1	1	yes	characteristic
41	C₂₃×#533	C₂²	1	1	yes	characteristic
42	C₂₃×#532	—	2	2	no	—
43	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
44	C₂₃×#529	—	2	2	no	—
45	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
46	C₂₃×#519	C₂²	1	1	yes	characteristic
47	C₂₃×#518	C₂²	1	1	yes	characteristic
48	C₂₃×#518	C₂²	1	1	yes	characteristic
49	C₂₃×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
51	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
52	C₂₃×#497	C₂²	1	2	yes	complemented
53	C₂₃×#496	C₂²	1	4	yes	—
54	C₂₃×#496	C₂²	1	4	yes	—
55	C₂₃×#496	C₂²	1	2	yes	complemented
56	C₂₃×#496	C₂²	1	2	yes	complemented
57	C₂₃×#496	C₂²	1	2	yes	complemented
58	C₂₃×#495	C₂²	1	2	yes	complemented
59	C₂₃×#495	C₂²	1	2	yes	complemented
60	C₂₃×#493	C₂²	1	2	yes	complemented
61	C₂₃×#492	C₂²	1	2	yes	complemented
62	C₂₃×#464	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	complemented
64	C₂₃×#463	C₂²	1	4	yes	complemented
65	C₂₃×#463	C₂²	1	4	yes	complemented
66	C₂₃×#463	C₂²	1	4	yes	complemented
67	C₂₃×#463	C₂²	1	4	yes	complemented
68	C₂₃×#461	C₂²	1	4	yes	complemented
69	C₂₃×#460	C₂²	1	4	yes	complemented
70	C₂₃×#460	C₂²	1	4	yes	complemented
71	C₂₃×#459	C₂²	1	4	yes	complemented
72	C₂₃×#459	C₂²	1	4	yes	complemented
73	C₂₃×#459	C₂²	1	4	yes	complemented
74	C₂₃×#446	C₂²	1	4	yes	complemented
75	C₂₃×#446	C₂²	1	4	yes	complemented
76	C₂₃×#442	C₂²	1	2	yes	complemented
77	C₂₃×#442	C₂²	1	4	yes	complemented
78	C₂₃×#441	C₂²	1	2	yes	complemented
79	C₂₃×#440	C₂²	1	2	yes	complemented
80	C₂₃×#440	C₂²	1	2	yes	complemented
81	C₂₃×#440	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
83	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
84	C₂₃×#427	C₂²	1	1	yes	characteristic
85	C₂₃×#424	C₂²	1	1	yes	characteristic
86	C₂₃×#424	C₂²	1	1	yes	characteristic
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂₃×#419	C₂²	1	1	yes	characteristic
89	C₂₃×#418	C₂²	1	1	yes	characteristic
90	C₂₃×#418	C₂²	1	1	yes	characteristic
91	C₂₃×#418	C₂²	1	1	yes	characteristic
92	C₂₃×#416	C₂²	1	1	yes	characteristic
93	C₂₃×#416	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	1	yes	characteristic
95	C₂₃×#405	C₂²	1	1	yes	characteristic
96	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
97	C₂×#41×C₂₃	—	2	4	no	—
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₂₃	—	2	2	no	—
102	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂₃×#137	—	4	2	no	—
106	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
107	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
108	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
109	C₂₃×#135	—	2	4	no	—
110	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₂₃	—	2	4	no	—
113	C₂×SD₁₆×C₂₃	—	4	2	no	—
114	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×D₈×C₂₃	—	2	4	no	—
124	C₂×D₈×C₂₃	—	4	2	no	—
125	C₂×D₈×C₂₃	C₂³	1	2	yes	—
126	C₂×D₈×C₂₃	C₂³	1	2	yes	—
127	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₂₃	C₂³	1	4	yes	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	2	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×#127	—	2	1	no	—
139	C₂₃×#127	—	2	1	no	—
140	C₂₃×#127	C₂³	1	2	yes	—
141	C₂₃×#127	C₂³	1	2	yes	—
142	C₂₃×#127	C₂³	1	4	yes	—
143	C₂₃×#127	C₂³	1	2	yes	—
144	C₂₃×#126	—	2	4	no	—
145	C₂₃×#126	—	2	4	no	—
146	C₂₃×#125	D₄	1	2	yes	—
147	C₂₃×#124	—	2	4	no	—
148	C₂₃×#124	—	2	4	no	—
149	C₂₃×#124	—	2	1	no	—
150	C₂₃×#124	—	2	1	no	—
151	C₂₃×#124	C₂³	1	2	yes	—
152	C₂₃×#124	C₂³	1	4	yes	—
153	C₂₃×#124	C₂³	1	2	yes	—
154	C₂₃×#124	C₂³	1	2	yes	—
155	C₂₃×#124	C₂³	1	2	yes	—
156	C₂₃×#123	—	2	4	no	—
157	C₂₃×#123	—	2	4	no	—
158	C₂₃×#123	—	2	4	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×C₂²⋊Q₈	—	2	4	no	—
162	C₂₃×C₂²⋊Q₈	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	—
164	C₂₃×#121	—	2	4	no	—
165	C₂₃×#121	—	2	4	no	—
166	C₂₃×#121	—	2	4	no	—
167	C₂₃×#121	—	2	2	no	—
168	C₂₃×#121	—	2	2	no	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#120	—	2	2	no	—
171	C₂₃×#120	—	2	2	no	—
172	C₂₃×#120	—	2	2	no	—
173	C₄×Q₈×C₂₃	—	2	2	no	—
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
176	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
177	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	4	no	—
181	C₄×D₄×C₂₃	—	2	4	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	2	no	—
184	C₄×D₄×C₂₃	—	2	2	no	—
185	C₄×D₄×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂³	1	4	yes	—
187	C₄×D₄×C₂₃	C₂³	1	4	yes	—
188	C₄×D₄×C₂₃	C₂³	1	4	yes	—
189	C₄×D₄×C₂₃	C₂³	1	2	yes	—
190	C₂₃×#117	—	2	4	no	—
191	C₂₃×#117	—	2	2	no	—
192	C₂₃×#117	—	2	1	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	C₂³	1	1	yes	characteristic
195	C₂₃×#117	C₂³	1	1	yes	characteristic
196	C₂₃×#117	C₂³	1	1	yes	characteristic
197	C₂₃×#117	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
202	C₂×C₄²×C₂₃	—	2	1	no	—
203	C₂×C₄²×C₂₃	—	2	1	no	—
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂₃×#107	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	2	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₂₃×#103	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#102	C₂³	1	2	yes	—
214	C₂₃×#102	C₂³	1	2	yes	—
215	C₂₃×#102	C₂³	1	4	yes	—
216	C₂₃×#102	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#97	C₂³	1	2	yes	—
219	C₂₃×#97	C₂³	1	2	yes	—
220	C₂₃×#97	C₂³	1	2	yes	—
221	C₂₃×#97	C₂³	1	2	yes	—
222	C₄×C₈×C₂₃	C₂³	1	2	yes	—
223	C₄×C₈×C₂₃	C₂³	1	2	yes	—
224	C₂⁴×C₂₃	—	2	1	no	—
225	C₂⁴×C₂₃	—	2	1	no	—
226	C₂⁴×C₂₃	—	2	1	no	—
227	#41×C₂₃	—	2	2	no	—
228	#41×C₂₃	—	2	2	no	—
229	#41×C₂₃	—	2	2	no	—
230	#41×C₂₃	—	2	2	no	—
231	#41×C₂₃	—	8	8	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
236	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₂₃	—	2	1	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	1	no	—
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	2	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	—	8	4	no	—
256	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	4	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	2	4	no	—
269	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	Q₁₆×C₂₃	—	2	2	no	—
272	Q₁₆×C₂₃	—	4	2	no	—
273	SD₁₆×C₂₃	—	2	4	no	—
274	SD₁₆×C₂₃	—	2	4	no	—
275	SD₁₆×C₂₃	—	2	2	no	—
276	SD₁₆×C₂₃	—	2	2	no	—
277	SD₁₆×C₂₃	—	4	4	no	—
278	SD₁₆×C₂₃	—	4	2	no	—
279	SD₁₆×C₂₃	—	4	2	no	—
280	SD₁₆×C₂₃	—	4	2	no	—
281	SD₁₆×C₂₃	—	4	2	no	—
282	D₈×C₂₃	—	2	4	no	—
283	D₈×C₂₃	—	2	4	no	—
284	D₈×C₂₃	—	2	2	no	—
285	D₈×C₂₃	—	4	4	no	—
286	D₈×C₂₃	—	4	2	no	—
287	D₈×C₂₃	—	4	2	no	—
288	D₈×C₂₃	—	4	2	no	—
289	M₁₆×C₂₃	—	2	2	no	—
290	M₁₆×C₂₃	—	2	2	no	—
291	C₂×C₈×C₂₃	—	2	2	no	—
292	C₂×C₈×C₂₃	#41	1	4	yes	complemented
293	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
294	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
295	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	4	no	—
301	C₄⋊C₄×C₂₃	—	2	4	no	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂²⋊C₄×C₂₃	—	2	1	no	—
310	C₂²⋊C₄×C₂₃	—	2	1	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	2	4	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	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	—	2	4	no	—
320	C₂²⋊C₄×C₂₃	—	2	4	no	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
324	C₄²×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	1	no	—
326	C₄²×C₂₃	—	2	1	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	4	no	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	2	yes	—
332	C₄²×C₂₃	C₂⁴	1	2	yes	—
333	C₄²×C₂₃	C₂⁴	1	2	yes	—
334	#61417	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	1	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	1	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	8	2	no	—
344	C₂³×C₂₃	—	8	2	no	—
345	C₂³×C₂₃	—	8	2	no	—
346	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	1	no	—
349	Q₈×C₂₃	—	2	1	no	—
350	Q₈×C₂₃	—	2	1	no	—
351	Q₈×C₂₃	—	2	2	no	—
352	Q₈×C₂₃	—	2	1	no	—
353	Q₈×C₂₃	—	4	4	no	—
354	Q₈×C₂₃	—	4	2	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	2	2	no	—
357	D₄×C₂₃	—	2	1	no	—
358	D₄×C₂₃	—	2	1	no	—
359	D₄×C₂₃	—	2	2	no	—
360	D₄×C₂₃	—	2	1	no	—
361	D₄×C₂₃	—	2	2	no	—
362	D₄×C₂₃	—	2	2	no	—
363	D₄×C₂₃	—	2	1	no	—
364	D₄×C₂₃	—	2	2	no	—
365	D₄×C₂₃	—	4	8	no	—
366	D₄×C₂₃	—	4	2	no	—
367	D₄×C₂₃	—	4	2	no	—
368	D₄×C₂₃	—	4	2	no	—
369	D₄×C₂₃	—	4	2	no	—
370	D₄×C₂₃	—	4	2	no	—
371	D₄×C₂₃	—	8	4	no	—
372	D₄×C₂₃	—	8	4	no	—
373	D₄×C₂₃	—	8	4	no	—
374	D₄×C₂₃	—	8	4	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	4	2	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	2	no	—
385	C₂×C₄×C₂₃	—	8	2	no	—
386	C₂×C₄×C₂₃	—	8	4	no	—
387	C₂×C₄×C₂₃	—	8	4	no	—
388	C₂×C₄×C₂₃	—	8	4	no	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
392	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
395	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
397	C₈×C₂₃	—	2	2	no	—
398	C₈×C₂₃	—	2	2	no	—
399	C₈×C₂₃	—	2	2	no	—
400	C₈×C₂₃	C₂×#41	1	2	yes	—
401	C₈×C₂₃	C₂×#41	1	2	yes	—
402	#3510	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3403	C₂×C₂₃	1	4	yes	complemented
405	#3401	C₂×C₂₃	1	4	yes	complemented
406	#3399	C₂×C₂₃	1	4	yes	complemented
407	#3397	C₂×C₂₃	1	4	yes	complemented
408	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3154	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂×#496	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3043	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#3040	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3038	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#2943	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂²×C₂₃	—	2	2	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	4	no	—
424	C₂²×C₂₃	—	4	4	no	—
425	C₂²×C₂₃	—	4	2	no	—
426	C₂²×C₂₃	—	4	4	no	—
427	C₂²×C₂₃	—	4	1	no	—
428	C₂²×C₂₃	—	4	1	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	16	2	no	—
433	C₂²×C₂₃	—	16	2	no	—
434	C₂²×C₂₃	—	16	2	no	—
435	C₂²×C₂₃	#550	1	2	yes	—
436	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₂₃	—	2	2	no	—
438	C₄×C₂₃	—	2	2	no	—
439	C₄×C₂₃	—	2	4	no	—
440	C₄×C₂₃	—	2	4	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	1	no	—
444	C₄×C₂₃	—	4	1	no	—
445	C₄×C₂₃	—	4	2	no	—
446	C₄×C₂₃	#550	1	2	yes	—
447	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
448	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
454	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
455	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
456	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
457	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
458	#559	C₂²×C₂₃	1	4	yes	complemented
459	#559	C₂²×C₂₃	1	4	yes	complemented
460	#556	C₂²×C₂₃	1	4	yes	complemented
461	#551	—	2	4	no	—
462	#550	C₂²×C₂₃	1	4	yes	complemented
463	#546	—	2	4	no	—
464	#542	—	2	2	no	—
465	#540	—	2	2	no	—
466	#536	C₂²×C₂₃	1	1	yes	characteristic
467	#535	C₂²×C₂₃	1	1	yes	characteristic
468	#535	C₂²×C₂₃	1	1	yes	characteristic
469	#535	C₂²×C₂₃	1	1	yes	characteristic
470	#533	C₂²×C₂₃	1	1	yes	characteristic
471	#532	—	2	2	no	—
472	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
473	#529	—	2	2	no	—
474	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
475	#519	C₂²×C₂₃	1	1	yes	characteristic
476	#518	C₂²×C₂₃	1	1	yes	characteristic
477	#518	C₂²×C₂₃	1	1	yes	characteristic
478	#518	C₂²×C₂₃	1	1	yes	characteristic
479	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
480	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
481	#497	C₂²×C₂₃	1	2	yes	complemented
482	#496	C₂²×C₂₃	1	4	yes	—
483	#496	C₂²×C₂₃	1	4	yes	—
484	#496	C₂²×C₂₃	1	2	yes	complemented
485	#496	C₂²×C₂₃	1	2	yes	complemented
486	#496	C₂²×C₂₃	1	2	yes	complemented
487	#495	C₂²×C₂₃	1	2	yes	complemented
488	#495	C₂²×C₂₃	1	2	yes	complemented
489	#493	C₂²×C₂₃	1	2	yes	complemented
490	#492	C₂²×C₂₃	1	2	yes	complemented
491	#464	C₂²×C₂₃	1	4	yes	complemented
492	#464	C₂²×C₂₃	1	4	yes	complemented
493	#463	C₂²×C₂₃	1	4	yes	complemented
494	#463	C₂²×C₂₃	1	4	yes	complemented
495	#463	C₂²×C₂₃	1	4	yes	complemented
496	#463	C₂²×C₂₃	1	4	yes	complemented
497	#461	C₂²×C₂₃	1	4	yes	complemented
498	#460	C₂²×C₂₃	1	4	yes	complemented
499	#460	C₂²×C₂₃	1	4	yes	complemented
500	#459	C₂²×C₂₃	1	4	yes	complemented
501	#459	C₂²×C₂₃	1	4	yes	complemented
502	#459	C₂²×C₂₃	1	4	yes	complemented
503	#446	C₂²×C₂₃	1	4	yes	complemented
504	#446	C₂²×C₂₃	1	4	yes	complemented
505	#442	C₂²×C₂₃	1	2	yes	complemented
506	#442	C₂²×C₂₃	1	4	yes	complemented
507	#441	C₂²×C₂₃	1	2	yes	complemented
508	#440	C₂²×C₂₃	1	2	yes	complemented
509	#440	C₂²×C₂₃	1	4	yes	complemented
510	#440	C₂²×C₂₃	1	2	yes	complemented
511	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
512	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
513	#427	C₂²×C₂₃	1	1	yes	characteristic
514	#424	C₂²×C₂₃	1	1	yes	characteristic
515	#424	C₂²×C₂₃	1	1	yes	characteristic
516	#423	C₂²×C₂₃	1	1	yes	characteristic
517	#419	C₂²×C₂₃	1	1	yes	characteristic
518	#418	C₂²×C₂₃	1	1	yes	characteristic
519	#418	C₂²×C₂₃	1	1	yes	characteristic
520	#418	C₂²×C₂₃	1	1	yes	characteristic
521	#416	C₂²×C₂₃	1	1	yes	characteristic
522	#416	C₂²×C₂₃	1	1	yes	characteristic
523	#405	C₂²×C₂₃	1	1	yes	characteristic
524	#405	C₂²×C₂₃	1	1	yes	characteristic
525	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
526	C₂×C₂₃	—	2	2	no	—
527	C₂×C₂₃	—	8	1	no	—
528	C₂×C₂₃	—	8	1	no	—
529	C₂×C₂₃	—	8	2	no	—
530	C₂×C₂₃	—	8	2	no	—
531	C₂×C₂₃	—	8	2	no	—
532	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
533	C₂×C₂₃	#3585	1	2	yes	—
534	C₂×#41	—	2	4	no	—
535	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
542	#137	—	4	2	no	—
543	AGL(1,ℤ/8)	—	4	2	no	—
544	AGL(1,ℤ/8)	—	4	2	no	—
545	AGL(1,ℤ/8)	—	4	2	no	—
546	#135	—	2	4	no	—
547	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
548	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
549	C₂×SD₁₆	—	2	4	no	—
550	C₂×SD₁₆	—	4	2	no	—
551	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
560	C₂×D₈	—	2	4	no	—
561	C₂×D₈	—	4	2	no	—
562	C₂×D₈	C₂³×C₂₃	1	2	yes	—
563	C₂×D₈	C₂³×C₂₃	1	2	yes	—
564	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×D₈	C₂³×C₂₃	1	4	yes	—
566	C₂×D₈	C₂³×C₂₃	1	2	yes	—
567	C₂×D₈	C₂³×C₂₃	1	2	yes	—
568	C₂×D₈	C₂³×C₂₃	1	2	yes	—
569	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
571	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
573	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
575	#127	—	2	1	no	—
576	#127	—	2	1	no	—
577	#127	C₂³×C₂₃	1	4	yes	—
578	#127	C₂³×C₂₃	1	2	yes	—
579	#127	C₂³×C₂₃	1	2	yes	—
580	#127	C₂³×C₂₃	1	2	yes	—
581	#126	—	2	4	no	—
582	#126	—	2	4	no	—
583	#125	D₄×C₂₃	1	2	yes	—
584	#124	—	2	4	no	—
585	#124	—	2	4	no	—
586	#124	—	2	1	no	—
587	#124	—	2	1	no	—
588	#124	C₂³×C₂₃	1	4	yes	—
589	#124	C₂³×C₂₃	1	2	yes	—
590	#124	C₂³×C₂₃	1	2	yes	—
591	#124	C₂³×C₂₃	1	2	yes	—
592	#124	C₂³×C₂₃	1	2	yes	—
593	#123	—	2	4	no	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	4	no	—
605	#121	—	2	4	no	—
606	#121	—	2	4	no	—
607	#120	—	2	2	no	—
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
612	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
613	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
614	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
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	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	C₂³×C₂₃	1	2	yes	—
623	C₄×D₄	C₂³×C₂₃	1	2	yes	—
624	C₄×D₄	C₂³×C₂₃	1	4	yes	—
625	C₄×D₄	C₂³×C₂₃	1	4	yes	—
626	C₄×D₄	C₂³×C₂₃	1	4	yes	—
627	#117	—	2	4	no	—
628	#117	—	2	2	no	—
629	#117	—	2	1	no	—
630	#117	—	2	1	no	—
631	#117	C₂³×C₂₃	1	1	yes	characteristic
632	#117	C₂³×C₂₃	1	1	yes	characteristic
633	#117	C₂³×C₂₃	1	1	yes	characteristic
634	#117	C₂³×C₂₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
642	#107	C₂³×C₂₃	1	2	yes	—
643	#106	C₂³×C₂₃	1	2	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
646	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	2	yes	—
648	#103	C₂³×C₂₃	1	2	yes	—
649	#103	C₂³×C₂₃	1	4	yes	—
650	#102	C₂³×C₂₃	1	2	yes	—
651	#102	C₂³×C₂₃	1	2	yes	—
652	#102	C₂³×C₂₃	1	4	yes	—
653	#102	C₂³×C₂₃	1	4	yes	—
654	#102	C₂³×C₂₃	1	4	yes	—
655	#97	C₂³×C₂₃	1	2	yes	—
656	#97	C₂³×C₂₃	1	2	yes	—
657	#97	C₂³×C₂₃	1	2	yes	—
658	#97	C₂³×C₂₃	1	2	yes	—
659	C₄×C₈	C₂³×C₂₃	1	2	yes	—
660	C₄×C₈	C₂³×C₂₃	1	2	yes	—
661	C₂₃	#61417	1	1	yes	characteristic, direct product factor, Sylow
662	C₂⁴	—	2	1	no	—
663	C₂⁴	—	2	1	no	—
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	2	2	no	—
669	#41	—	8	8	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
674	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	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	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	8	4	no	—
694	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
695	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
697	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
709	Q₁₆	—	2	2	no	—
710	Q₁₆	—	4	2	no	—
711	SD₁₆	—	2	4	no	—
712	SD₁₆	—	2	4	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	2	2	no	—
715	SD₁₆	—	4	4	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	SD₁₆	—	4	2	no	—
719	SD₁₆	—	4	2	no	—
720	D₈	—	2	4	no	—
721	D₈	—	2	4	no	—
722	D₈	—	2	2	no	—
723	D₈	—	4	4	no	—
724	D₈	—	4	2	no	—
725	D₈	—	4	2	no	—
726	D₈	—	4	2	no	—
727	M₁₆	—	2	2	no	—
728	M₁₆	—	2	2	no	—
729	C₂×C₈	—	2	2	no	—
730	C₂×C₈	#41×C₂₃	1	4	yes	complemented
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	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
741	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
744	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	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	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₄²	C₂⁴×C₂₃	1	2	yes	—
770	C₄²	C₂⁴×C₂₃	1	2	yes	—
771	C₄²	C₂⁴×C₂₃	1	2	yes	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	2	no	—
782	C₂³	—	8	2	no	—
783	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
827	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
830	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
831	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
832	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
833	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₈	—	2	2	no	—
837	C₈	C₂×#41×C₂₃	1	2	yes	—
838	C₈	C₂×#41×C₂₃	1	2	yes	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	16	2	no	—
851	C₂²	—	16	2	no	—
852	C₂²	—	16	2	no	—
853	C₂²	C₂₃×#550	1	2	yes	—
854	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	C₂₃×#550	1	2	yes	—
865	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
866	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	1	no	—
872	C₂	—	8	1	no	—
873	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
874	C₂	C₂₃×#3585	1	2	yes	—

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3510	C₂	semidirect
2. C₂₃×#3508	C₂	semidirect
3. C₂₃×#3403	C₂	semidirect
4. C₂₃×#3401	C₂	semidirect
5. C₂₃×#3399	C₂	semidirect
6. C₂₃×#3397	C₂	semidirect
7. C₂₃×#3155	C₂	semidirect
8. C₂₃×#3154	C₂	semidirect
9. C₂×C₂₃×#496	C₂	semidirect
10. C₂₃×#3043	C₂	semidirect
11. C₂₃×#3042	C₂	semidirect
12. C₂₃×#3041	C₂	semidirect
13. C₂₃×#3041	C₂	semidirect
14. C₂₃×#3040	C₂	semidirect
15. C₂₃×#3038	C₂	semidirect
16. C₂₃×#2961	C₂	semidirect
17. C₂₃×#2949	C₂	semidirect
18. C₂₃×#2948	C₂	semidirect
19. C₂₃×#2943	C₂	semidirect
29. C₂₃×#559	C₂²	semidirect
30. C₂₃×#559	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
33. C₂₃×#550	C₂²	semidirect
52. C₂₃×#497	C₂²	semidirect
55. C₂₃×#496	C₂²	semidirect
56. C₂₃×#496	C₂²	semidirect
57. C₂₃×#496	C₂²	semidirect
58. C₂₃×#495	C₂²	semidirect
59. C₂₃×#495	C₂²	semidirect
60. C₂₃×#493	C₂²	semidirect
61. C₂₃×#492	C₂²	semidirect
62. C₂₃×#464	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#463	C₂²	semidirect
65. C₂₃×#463	C₂²	semidirect
66. C₂₃×#463	C₂²	semidirect
67. C₂₃×#463	C₂²	semidirect
68. C₂₃×#461	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
70. C₂₃×#460	C₂²	semidirect
71. C₂₃×#459	C₂²	semidirect
72. C₂₃×#459	C₂²	semidirect
73. C₂₃×#459	C₂²	semidirect
74. C₂₃×#446	C₂²	semidirect
75. C₂₃×#446	C₂²	semidirect
76. C₂₃×#442	C₂²	semidirect
77. C₂₃×#442	C₂²	semidirect
78. C₂₃×#441	C₂²	semidirect
79. C₂₃×#440	C₂²	semidirect
80. C₂₃×#440	C₂²	semidirect
81. C₂₃×#440	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×D₈×C₂₃	C₂²	semidirect
292. C₂×C₈×C₂₃	#41	semidirect
334. #61417	C₂₃	direct (N × H)
402. #3510	C₂×C₂₃	semidirect
403. #3508	C₂×C₂₃	semidirect
404. #3403	C₂×C₂₃	semidirect
405. #3401	C₂×C₂₃	semidirect
406. #3399	C₂×C₂₃	semidirect
407. #3397	C₂×C₂₃	semidirect
408. #3155	C₂×C₂₃	semidirect
409. #3154	C₂×C₂₃	semidirect
410. C₂×#496	C₂×C₂₃	semidirect
411. #3043	C₂×C₂₃	semidirect
412. #3042	C₂×C₂₃	semidirect
413. #3041	C₂×C₂₃	semidirect
414. #3041	C₂×C₂₃	semidirect
415. #3040	C₂×C₂₃	semidirect
416. #3038	C₂×C₂₃	semidirect
417. #2961	C₂×C₂₃	semidirect
418. #2949	C₂×C₂₃	semidirect
419. #2948	C₂×C₂₃	semidirect
420. #2943	C₂×C₂₃	semidirect
458. #559	C₂²×C₂₃	semidirect
459. #559	C₂²×C₂₃	semidirect
460. #556	C₂²×C₂₃	semidirect
462. #550	C₂²×C₂₃	semidirect
481. #497	C₂²×C₂₃	semidirect
484. #496	C₂²×C₂₃	semidirect
485. #496	C₂²×C₂₃	semidirect
486. #496	C₂²×C₂₃	semidirect
487. #495	C₂²×C₂₃	semidirect
488. #495	C₂²×C₂₃	semidirect
489. #493	C₂²×C₂₃	semidirect
490. #492	C₂²×C₂₃	semidirect
491. #464	C₂²×C₂₃	semidirect
492. #464	C₂²×C₂₃	semidirect
493. #463	C₂²×C₂₃	semidirect
494. #463	C₂²×C₂₃	semidirect
495. #463	C₂²×C₂₃	semidirect
496. #463	C₂²×C₂₃	semidirect
497. #461	C₂²×C₂₃	semidirect
498. #460	C₂²×C₂₃	semidirect
499. #460	C₂²×C₂₃	semidirect
500. #459	C₂²×C₂₃	semidirect
501. #459	C₂²×C₂₃	semidirect
502. #459	C₂²×C₂₃	semidirect
503. #446	C₂²×C₂₃	semidirect
504. #446	C₂²×C₂₃	semidirect
505. #442	C₂²×C₂₃	semidirect
506. #442	C₂²×C₂₃	semidirect
507. #441	C₂²×C₂₃	semidirect
508. #440	C₂²×C₂₃	semidirect
509. #440	C₂²×C₂₃	semidirect
510. #440	C₂²×C₂₃	semidirect
511. C₄×SD₁₆	C₂²×C₂₃	semidirect
512. C₄×D₈	C₂²×C₂₃	semidirect
661. C₂₃	#61417	direct (N × H)
730. C₂×C₈	#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×#3510	2
C₂₃×#3508	2
C₂₃×#3403	2
C₂₃×#3401	2
C₂₃×#3399	2
C₂₃×#3397	2
C₂₃×#3155	2
C₂₃×#3154	2
C₂×C₂₃×#496	2
C₂₃×#3043	2
C₂₃×#3042	2
C₂₃×#3041	2
C₂₃×#3040	2
C₂₃×#3038	2
C₂₃×#2961	2
C₂₃×#2949	2
C₂₃×#2948	2
C₂₃×#2943	2
#61417	23

Subgroups — C23×#61417 #19209043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61417 #19209043