Subgroups — C₂₃×#61696 #19209322

Order 5888.

1790 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3505	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3337	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3336	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3300	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3296	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#553	—	2	2	no	—
17	C₂₃×#553	C₂²	1	2	yes	—
18	C₂₃×#552	—	2	2	no	—
19	C₂₃×#552	—	2	2	no	—
20	C₂₃×#552	C₂²	1	4	yes	—
21	C₂₃×#552	C₂²	1	2	yes	—
22	C₂₃×#552	C₂²	1	4	yes	complemented
23	C₂₃×#551	—	2	2	no	—
24	C₂₃×#548	C₂²	1	2	yes	—
25	C₂₃×#546	C₂²	1	2	yes	—
26	C₂₃×#539	—	2	1	no	—
27	C₂₃×#538	—	2	1	no	—
28	C₂₃×#534	—	2	1	no	—
29	C₂₃×#529	C₂²	1	2	yes	—
30	C₂×C₂₃×#126	—	2	1	no	—
31	C₂×C₂₃×#125	—	2	1	no	—
32	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#525	C₂²	1	2	yes	—
34	C₂×C₂₃×#123	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂₃×#518	—	2	1	no	—
40	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#117	—	2	1	no	—
43	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#499	C₂²	1	4	yes	complemented
46	C₂₃×#488	C₂²	1	4	yes	complemented
47	C₂₃×#485	C₂²	1	4	yes	complemented
48	C₂₃×#485	C₂²	1	4	yes	complemented
49	C₂₃×#484	C₂²	1	2	yes	complemented
50	C₂₃×#484	C₂²	1	2	yes	complemented
51	C₂₃×#483	C₂²	1	2	yes	complemented
52	C₂₃×#483	C₂²	1	2	yes	complemented
53	C₂₃×#483	C₂²	1	4	yes	complemented
54	C₂₃×#483	C₂²	1	2	yes	complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#481	C₂²	1	2	yes	—
57	C₂₃×#480	C₂²	1	2	yes	—
58	C₂₃×#480	C₂²	1	2	yes	—
59	C₂₃×#480	C₂²	1	4	yes	complemented
60	C₂₃×#479	C₂²	1	4	yes	complemented
61	C₂₃×#479	C₂²	1	4	yes	complemented
62	C₂₃×#478	C₂²	1	4	yes	complemented
63	C₂₃×#467	C₂²	1	4	yes	complemented
64	C₂₃×#467	C₂²	1	4	yes	complemented
65	C₂₃×#465	C₂²	1	4	yes	complemented
66	C₂₃×#465	C₂²	1	4	yes	complemented
67	C₂₃×#464	C₂²	1	4	yes	complemented
68	C₂₃×#452	C₂²	1	4	yes	complemented
69	C₂₃×#451	C₂²	1	2	yes	complemented
70	C₂₃×#451	C₂²	1	2	yes	complemented
71	C₂₃×#450	C₂²	1	2	yes	complemented
72	C₂₃×#448	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
75	C₈×D₄×C₂₃	C₂²	1	4	yes	—
76	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
77	C₂₃×#431	C₂²	1	2	yes	complemented
78	C₂₃×#427	C₂²	1	4	yes	complemented
79	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
80	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
81	C₂₃×#416	C₂²	1	4	yes	complemented
82	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
84	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×#41×C₂₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	—	2	1	no	—
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
101	C₂₃×#126	—	2	2	no	—
102	C₂₃×#126	—	2	4	no	—
103	C₂₃×#126	—	2	4	no	—
104	C₂₃×#126	—	2	2	no	—
105	C₂₃×#126	—	2	2	no	—
106	C₂₃×#125	—	2	4	no	—
107	C₂₃×#125	—	2	4	no	—
108	C₂₃×#125	—	2	2	no	—
109	C₂₃×#125	—	2	2	no	—
110	C₂₃×#125	C₂³	1	4	yes	—
111	C₂₃×#125	C₂³	1	2	yes	—
112	C₂₃×#124	—	2	2	no	—
113	C₂₃×#124	C₂³	1	2	yes	—
114	C₂₃×#123	—	2	2	no	—
115	C₂₃×#123	—	2	4	no	—
116	C₂₃×#123	—	2	4	no	—
117	C₂₃×#123	—	2	2	no	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	1	no	—
122	C₂₃×C₂²⋊Q₈	—	2	1	no	—
123	C₂₃×C₂²⋊Q₈	—	2	1	no	—
124	C₂₃×C₂²⋊Q₈	—	2	2	no	—
125	C₂₃×C₂²⋊Q₈	—	2	1	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₂₃×#121	—	2	2	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	1	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	C₂³	1	2	yes	—
139	C₂₃×#121	C₂³	1	2	yes	—
140	C₂₃×#121	C₂³	1	2	yes	—
141	C₂₃×#120	—	2	2	no	—
142	C₂₃×#120	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
146	C₄×D₄×C₂₃	—	2	2	no	—
147	C₄×D₄×C₂₃	—	2	2	no	—
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	D₄	1	2	yes	—
152	C₄×D₄×C₂₃	D₄	1	2	yes	—
153	C₄×D₄×C₂₃	C₂³	1	2	yes	—
154	C₄×D₄×C₂₃	C₂³	1	2	yes	—
155	C₄×D₄×C₂₃	C₂³	1	2	yes	—
156	C₂₃×#117	—	2	2	no	—
157	C₂₃×#117	—	2	2	no	—
158	C₂₃×#117	—	2	4	no	—
159	C₂₃×#117	—	2	4	no	—
160	C₂₃×#117	—	2	2	no	—
161	C₂₃×#117	C₂³	1	4	yes	—
162	C₂₃×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
164	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
166	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
167	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×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	4	yes	—
192	C₂₃×#107	C₂³	1	4	yes	—
193	C₂₃×#107	C₂³	1	4	yes	—
194	C₂₃×#106	C₂³	1	4	yes	—
195	C₂₃×#106	C₂³	1	4	yes	—
196	C₂₃×#106	C₂³	1	4	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₂₃×#103	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	4	yes	—
200	C₂₃×#103	C₂³	1	4	yes	—
201	C₂₃×#103	C₂³	1	4	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₂₃	C₂³	1	4	yes	—
212	C₂⁴×C₂₃	—	2	1	no	—
213	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
215	#41×C₂₃	—	4	4	no	—
216	C₂×Q₈×C₂₃	—	2	1	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	4	2	no	—
219	C₂×Q₈×C₂₃	—	4	2	no	—
220	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
222	C₂×D₄×C₂₃	—	2	4	no	—
223	C₂×D₄×C₂₃	—	2	2	no	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	2	no	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	1	no	—
228	C₂×D₄×C₂₃	—	4	2	no	—
229	C₂×D₄×C₂₃	—	4	4	no	—
230	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	2	no	—
239	C₂²×C₄×C₂₃	—	2	2	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	4	2	no	—
245	C₂²×C₄×C₂₃	—	4	2	no	—
246	C₂²×C₄×C₂₃	—	4	4	no	—
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	Q₁₆×C₂₃	—	4	4	no	—
259	SD₁₆×C₂₃	—	4	4	no	—
260	C₂×C₈×C₂₃	—	4	2	no	—
261	C₂×C₈×C₂₃	—	4	4	no	—
262	C₂×C₈×C₂₃	—	4	2	no	—
263	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	no	—
295	C₂²⋊C₄×C₂₃	—	2	2	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	—	2	2	no	—
299	C₂²⋊C₄×C₂₃	—	2	2	no	—
300	C₂²⋊C₄×C₂₃	—	2	2	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
306	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
308	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
309	C₄²×C₂₃	—	2	4	no	—
310	C₄²×C₂₃	—	2	4	no	—
311	C₄²×C₂₃	—	2	2	no	—
312	C₄²×C₂₃	—	2	2	no	—
313	C₄²×C₂₃	C₂×D₄	1	2	yes	—
314	C₄²×C₂₃	C₂⁴	1	2	yes	—
315	#61696	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂³×C₂₃	—	2	2	no	—
317	C₂³×C₂₃	—	2	2	no	—
318	C₂³×C₂₃	—	4	1	no	—
319	C₂³×C₂₃	—	4	1	no	—
320	C₂³×C₂₃	—	4	1	no	—
321	C₂³×C₂₃	—	4	1	no	—
322	C₂³×C₂₃	—	4	2	no	—
323	C₂³×C₂₃	—	8	1	no	—
324	C₂³×C₂₃	—	8	1	no	—
325	C₂³×C₂₃	#135	1	4	yes	—
326	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₂₃	—	2	4	no	—
331	Q₈×C₂₃	—	2	4	no	—
332	Q₈×C₂₃	—	4	2	no	—
333	Q₈×C₂₃	—	8	1	no	—
334	D₄×C₂₃	—	2	4	no	—
335	D₄×C₂₃	—	2	4	no	—
336	D₄×C₂₃	—	2	4	no	—
337	D₄×C₂₃	—	4	4	no	—
338	D₄×C₂₃	—	4	4	no	—
339	D₄×C₂₃	—	8	1	no	—
340	D₄×C₂₃	—	8	2	no	—
341	D₄×C₂₃	—	8	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	4	2	no	—
355	C₂×C₄×C₂₃	—	4	1	no	—
356	C₂×C₄×C₂₃	—	4	1	no	—
357	C₂×C₄×C₂₃	—	4	1	no	—
358	C₂×C₄×C₂₃	—	4	1	no	—
359	C₂×C₄×C₂₃	—	4	1	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	2	no	—
362	C₂×C₄×C₂₃	—	4	2	no	—
363	C₂×C₄×C₂₃	—	4	2	no	—
364	C₂×C₄×C₂₃	—	4	4	no	—
365	C₂×C₄×C₂₃	—	4	4	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	—	8	2	no	—
368	C₂×C₄×C₂₃	—	8	2	no	—
369	C₂×C₄×C₂₃	—	8	1	no	—
370	C₂×C₄×C₂₃	—	8	1	no	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
378	C₈×C₂₃	—	2	4	no	—
379	C₈×C₂₃	—	2	4	no	—
380	#3505	C₂×C₂₃	1	1	yes	characteristic
381	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#3337	C₂×C₂₃	1	4	yes	complemented
383	#3336	C₂×C₂₃	1	4	yes	complemented
384	#3300	C₂×C₂₃	1	4	yes	complemented
385	#3296	C₂×C₂₃	1	4	yes	complemented
386	#3232	C₂×C₂₃	1	2	yes	complemented
387	#3190	C₂×C₂₃	1	2	yes	complemented
388	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#3108	C₂×C₂₃	1	2	yes	complemented
391	#3091	C₂×C₂₃	1	2	yes	complemented
392	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂²×C₂₃	—	2	1	no	—
396	C₂²×C₂₃	—	2	1	no	—
397	C₂²×C₂₃	—	2	1	no	—
398	C₂²×C₂₃	—	2	1	no	—
399	C₂²×C₂₃	—	2	1	no	—
400	C₂²×C₂₃	—	2	1	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	2	2	no	—
403	C₂²×C₂₃	—	2	2	no	—
404	C₂²×C₂₃	—	4	4	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	8	2	no	—
409	C₂²×C₂₃	—	16	2	no	—
410	C₂²×C₂₃	C₂×#135	1	2	yes	—
411	C₂²×C₂₃	C₂×#135	1	2	yes	—
412	C₂²×C₂₃	C₂×#135	1	2	yes	—
413	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
414	C₄×C₂₃	—	2	2	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	2	no	—
417	C₄×C₂₃	—	2	1	no	—
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	2	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	#585	1	2	yes	—
428	#553	—	2	2	no	—
429	#553	C₂²×C₂₃	1	2	yes	—
430	#552	—	2	2	no	—
431	#552	—	2	2	no	—
432	#552	C₂²×C₂₃	1	2	yes	—
433	#552	C₂²×C₂₃	1	4	yes	—
434	#552	C₂²×C₂₃	1	4	yes	complemented
435	#551	—	2	2	no	—
436	#548	C₂²×C₂₃	1	2	yes	—
437	#546	C₂²×C₂₃	1	2	yes	—
438	#539	—	2	1	no	—
439	#538	—	2	1	no	—
440	#534	—	2	1	no	—
441	#529	C₂²×C₂₃	1	2	yes	—
442	C₂×#126	—	2	1	no	—
443	C₂×#125	—	2	1	no	—
444	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#525	C₂²×C₂₃	1	2	yes	—
446	C₂×#123	—	2	1	no	—
447	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
451	#518	—	2	1	no	—
452	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#117	—	2	1	no	—
455	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
457	#499	C₂²×C₂₃	1	4	yes	complemented
458	#488	C₂²×C₂₃	1	4	yes	complemented
459	#485	C₂²×C₂₃	1	4	yes	complemented
460	#485	C₂²×C₂₃	1	4	yes	complemented
461	#484	C₂²×C₂₃	1	2	yes	complemented
462	#484	C₂²×C₂₃	1	2	yes	complemented
463	#483	C₂²×C₂₃	1	2	yes	complemented
464	#483	C₂²×C₂₃	1	4	yes	complemented
465	#483	C₂²×C₂₃	1	2	yes	complemented
466	#483	C₂²×C₂₃	1	2	yes	complemented
467	#482	C₂²×C₂₃	1	4	yes	complemented
468	#481	C₂²×C₂₃	1	2	yes	—
469	#480	C₂²×C₂₃	1	2	yes	—
470	#480	C₂²×C₂₃	1	2	yes	—
471	#480	C₂²×C₂₃	1	4	yes	complemented
472	#479	C₂²×C₂₃	1	4	yes	complemented
473	#479	C₂²×C₂₃	1	4	yes	complemented
474	#478	C₂²×C₂₃	1	4	yes	complemented
475	#467	C₂²×C₂₃	1	4	yes	complemented
476	#467	C₂²×C₂₃	1	4	yes	complemented
477	#465	C₂²×C₂₃	1	4	yes	complemented
478	#465	C₂²×C₂₃	1	4	yes	complemented
479	#464	C₂²×C₂₃	1	4	yes	complemented
480	#452	C₂²×C₂₃	1	4	yes	complemented
481	#451	C₂²×C₂₃	1	2	yes	complemented
482	#451	C₂²×C₂₃	1	2	yes	complemented
483	#450	C₂²×C₂₃	1	2	yes	complemented
484	#448	C₂²×C₂₃	1	2	yes	—
485	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
486	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
487	C₈×D₄	C₂²×C₂₃	1	4	yes	—
488	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
489	#431	C₂²×C₂₃	1	2	yes	complemented
490	#427	C₂²×C₂₃	1	4	yes	complemented
491	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
492	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
493	#416	C₂²×C₂₃	1	4	yes	complemented
494	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
495	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
496	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
499	C₂×C₂₃	—	2	2	no	—
500	C₂×C₂₃	—	2	2	no	—
501	C₂×C₂₃	—	2	2	no	—
502	C₂×C₂₃	—	4	2	no	—
503	C₂×C₂₃	—	8	2	no	—
504	C₂×C₂₃	#3485	1	1	yes	characteristic
505	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
506	C₂×C₂₃	#3586	1	1	yes	characteristic
507	C₂×#41	C₂³×C₂₃	1	2	yes	—
508	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
517	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
518	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
519	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
520	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
521	#126	—	2	2	no	—
522	#126	—	2	4	no	—
523	#126	—	2	4	no	—
524	#126	—	2	2	no	—
525	#126	—	2	2	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	C₂³×C₂₃	1	4	yes	—
531	#125	C₂³×C₂₃	1	2	yes	—
532	#124	—	2	2	no	—
533	#124	C₂³×C₂₃	1	2	yes	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	#123	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
548	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
549	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
550	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
552	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
553	#121	—	2	2	no	—
554	#121	—	2	2	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	2	no	—
558	#121	C₂³×C₂₃	1	2	yes	—
559	#121	C₂³×C₂₃	1	2	yes	—
560	#121	C₂³×C₂₃	1	2	yes	—
561	#120	—	2	2	no	—
562	#120	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
565	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	D₄×C₂₃	1	2	yes	—
572	C₄×D₄	D₄×C₂₃	1	2	yes	—
573	C₄×D₄	C₂³×C₂₃	1	2	yes	—
574	C₄×D₄	C₂³×C₂₃	1	2	yes	—
575	C₄×D₄	C₂³×C₂₃	1	2	yes	—
576	#117	—	2	2	no	—
577	#117	—	2	4	no	—
578	#117	—	2	4	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	C₂³×C₂₃	1	4	yes	—
582	#117	C₂³×C₂₃	1	2	yes	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	2	no	—
606	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	—	2	1	no	—
610	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
611	#107	C₂³×C₂₃	1	4	yes	—
612	#107	C₂³×C₂₃	1	4	yes	—
613	#107	C₂³×C₂₃	1	4	yes	—
614	#106	C₂³×C₂₃	1	4	yes	—
615	#106	C₂³×C₂₃	1	4	yes	—
616	#106	C₂³×C₂₃	1	4	yes	—
617	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
618	#103	C₂³×C₂₃	1	4	yes	—
619	#103	C₂³×C₂₃	1	4	yes	—
620	#103	C₂³×C₂₃	1	4	yes	—
621	#103	C₂³×C₂₃	1	4	yes	—
622	#103	C₂³×C₂₃	1	4	yes	—
623	#102	C₂³×C₂₃	1	4	yes	—
624	#102	C₂³×C₂₃	1	4	yes	—
625	#102	C₂³×C₂₃	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
627	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
628	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
629	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
630	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
631	C₄×C₈	C₂³×C₂₃	1	4	yes	—
632	C₂₃	#61696	1	1	yes	characteristic, direct product factor, Sylow
633	C₂⁴	—	2	1	no	—
634	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
635	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
636	#41	—	4	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	4	2	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
642	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
653	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	4	no	—
668	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
679	Q₁₆	—	4	4	no	—
680	SD₁₆	—	4	4	no	—
681	C₂×C₈	—	4	2	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	—	4	2	no	—
684	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
685	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
706	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
727	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
728	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	4	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	C₂×D₄×C₂₃	1	2	yes	—
735	C₄²	C₂⁴×C₂₃	1	2	yes	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	8	1	no	—
744	C₂³	—	8	1	no	—
745	C₂³	C₂₃×#135	1	4	yes	—
746	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
747	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
748	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
749	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
750	Q₈	—	2	4	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	8	1	no	—
754	D₄	—	2	4	no	—
755	D₄	—	2	4	no	—
756	D₄	—	2	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	D₄	—	8	1	no	—
760	D₄	—	8	2	no	—
761	D₄	—	8	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	1	no	—
791	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
792	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
798	C₈	—	2	4	no	—
799	C₈	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	2	no	—
814	C₂²	—	16	2	no	—
815	C₂²	C₂×C₂₃×#135	1	2	yes	—
816	C₂²	C₂×C₂₃×#135	1	2	yes	—
817	C₂²	C₂×C₂₃×#135	1	2	yes	—
818	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	C₂₃×#585	1	2	yes	—
833	C₂	—	2	2	no	—
834	C₂	—	2	2	no	—
835	C₂	—	2	2	no	—
836	C₂	—	4	2	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂₃×#3485	1	1	yes	characteristic
839	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
840	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#552	C₂	semidirect
3. C₂₃×#3337	C₂	semidirect
4. C₂₃×#3336	C₂	semidirect
5. C₂₃×#3300	C₂	semidirect
6. C₂₃×#3296	C₂	semidirect
7. C₂₃×#3232	C₂	semidirect
8. C₂₃×#3190	C₂	semidirect
9. C₂₃×#3189	C₂	semidirect
10. C₂₃×#3187	C₂	semidirect
11. C₂₃×#3108	C₂	semidirect
12. C₂₃×#3091	C₂	semidirect
13. C₂×C₂₃×#483	C₂	semidirect
14. C₂×C₂₃×#480	C₂	semidirect
15. C₂₃×#2972	C₂	semidirect
22. C₂₃×#552	C₂²	semidirect
32. C₂×C₂₃×#125	C₂²	semidirect
37. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
43. C₂×C₂₃×#117	C₂²	semidirect
45. C₂₃×#499	C₂²	semidirect
46. C₂₃×#488	C₂²	semidirect
47. C₂₃×#485	C₂²	semidirect
48. C₂₃×#485	C₂²	semidirect
49. C₂₃×#484	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
51. C₂₃×#483	C₂²	semidirect
52. C₂₃×#483	C₂²	semidirect
53. C₂₃×#483	C₂²	semidirect
54. C₂₃×#483	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
59. C₂₃×#480	C₂²	semidirect
60. C₂₃×#479	C₂²	semidirect
61. C₂₃×#479	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#467	C₂²	semidirect
64. C₂₃×#467	C₂²	semidirect
65. C₂₃×#465	C₂²	semidirect
66. C₂₃×#465	C₂²	semidirect
67. C₂₃×#464	C₂²	semidirect
68. C₂₃×#452	C₂²	semidirect
69. C₂₃×#451	C₂²	semidirect
70. C₂₃×#451	C₂²	semidirect
71. C₂₃×#450	C₂²	semidirect
73. C₄×Q₁₆×C₂₃	C₂²	semidirect
74. C₄×SD₁₆×C₂₃	C₂²	semidirect
76. C₈×D₄×C₂₃	C₂²	semidirect
77. C₂₃×#431	C₂²	semidirect
78. C₂₃×#427	C₂²	semidirect
79. C₂×C₂₃×#107	C₂²	semidirect
80. C₂×C₂₃×#106	C₂²	semidirect
81. C₂₃×#416	C₂²	semidirect
82. C₂×C₂₃×#103	C₂²	semidirect
83. C₂×C₂₃×#102	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
315. #61696	C₂₃	direct (N × H)
381. C₂×#552	C₂×C₂₃	semidirect
382. #3337	C₂×C₂₃	semidirect
383. #3336	C₂×C₂₃	semidirect
384. #3300	C₂×C₂₃	semidirect
385. #3296	C₂×C₂₃	semidirect
386. #3232	C₂×C₂₃	semidirect
387. #3190	C₂×C₂₃	semidirect
388. #3189	C₂×C₂₃	semidirect
389. #3187	C₂×C₂₃	semidirect
390. #3108	C₂×C₂₃	semidirect
391. #3091	C₂×C₂₃	semidirect
392. C₂×#483	C₂×C₂₃	semidirect
393. C₂×#480	C₂×C₂₃	semidirect
394. #2972	C₂×C₂₃	semidirect
434. #552	C₂²×C₂₃	semidirect
444. C₂×#125	C₂²×C₂₃	semidirect
449. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
452. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
455. C₂×#117	C₂²×C₂₃	semidirect
457. #499	C₂²×C₂₃	semidirect
458. #488	C₂²×C₂₃	semidirect
459. #485	C₂²×C₂₃	semidirect
460. #485	C₂²×C₂₃	semidirect
461. #484	C₂²×C₂₃	semidirect
462. #484	C₂²×C₂₃	semidirect
463. #483	C₂²×C₂₃	semidirect
464. #483	C₂²×C₂₃	semidirect
465. #483	C₂²×C₂₃	semidirect
466. #483	C₂²×C₂₃	semidirect
467. #482	C₂²×C₂₃	semidirect
471. #480	C₂²×C₂₃	semidirect
472. #479	C₂²×C₂₃	semidirect
473. #479	C₂²×C₂₃	semidirect
474. #478	C₂²×C₂₃	semidirect
475. #467	C₂²×C₂₃	semidirect
476. #467	C₂²×C₂₃	semidirect
477. #465	C₂²×C₂₃	semidirect
478. #465	C₂²×C₂₃	semidirect
479. #464	C₂²×C₂₃	semidirect
480. #452	C₂²×C₂₃	semidirect
481. #451	C₂²×C₂₃	semidirect
482. #451	C₂²×C₂₃	semidirect
483. #450	C₂²×C₂₃	semidirect
485. C₄×Q₁₆	C₂²×C₂₃	semidirect
486. C₄×SD₁₆	C₂²×C₂₃	semidirect
488. C₈×D₄	C₂²×C₂₃	semidirect
489. #431	C₂²×C₂₃	semidirect
490. #427	C₂²×C₂₃	semidirect
491. C₂×#107	C₂²×C₂₃	semidirect
492. C₂×#106	C₂²×C₂₃	semidirect
493. #416	C₂²×C₂₃	semidirect
494. C₂×#103	C₂²×C₂₃	semidirect
495. C₂×#102	C₂²×C₂₃	semidirect
498. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
632. C₂₃	#61696	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3505	2
C₂×C₂₃×#552	2
C₂₃×#3337	2
C₂₃×#3336	2
C₂₃×#3300	2
C₂₃×#3296	2
C₂₃×#3232	2
C₂₃×#3190	2
C₂₃×#3189	2
C₂₃×#3187	2
C₂₃×#3108	2
C₂₃×#3091	2
C₂×C₂₃×#483	2
C₂×C₂₃×#480	2
C₂₃×#2972	2
#61696	23

Subgroups — C23×#61696 #19209322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61696 #19209322