Subgroups — C₂₃×#61699 #19209325

Order 5888.

1854 conjugacy classes of subgroups.

The subgroup lattice has 868 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, complemented
2	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3339	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3337	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3301	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3297	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#481	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	—	2	2	no	—
18	C₂₃×#553	—	2	2	no	—
19	C₂₃×#553	C₂²	1	4	yes	—
20	C₂₃×#553	C₂²	1	4	yes	complemented
21	C₂₃×#553	C₂²	1	2	yes	complemented
22	C₂₃×#552	C₂²	1	2	yes	complemented
23	C₂₃×#551	—	2	2	no	—
24	C₂₃×#548	C₂²	1	2	yes	complemented
25	C₂₃×#546	C₂²	1	2	yes	complemented
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	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#525	C₂²	1	2	yes	—
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#121	—	2	1	no	—
36	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#518	—	2	1	no	—
40	C₂×C₄×D₄×C₂₃	—	2	1	no	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
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×#484	C₂²	1	2	yes	complemented
49	C₂₃×#484	C₂²	1	4	yes	complemented
50	C₂₃×#484	C₂²	1	2	yes	complemented
51	C₂₃×#483	C₂²	1	2	yes	complemented
52	C₂₃×#482	C₂²	1	4	yes	complemented
53	C₂₃×#482	C₂²	1	4	yes	complemented
54	C₂₃×#481	C₂²	1	2	yes	—
55	C₂₃×#481	C₂²	1	2	yes	—
56	C₂₃×#481	C₂²	1	2	yes	complemented
57	C₂₃×#481	C₂²	1	4	yes	complemented
58	C₂₃×#480	C₂²	1	2	yes	—
59	C₂₃×#480	C₂²	1	2	yes	complemented
60	C₂₃×#479	C₂²	1	4	yes	complemented
61	C₂₃×#478	C₂²	1	4	yes	complemented
62	C₂₃×#478	C₂²	1	4	yes	complemented
63	C₂₃×#466	C₂²	1	4	yes	complemented
64	C₂₃×#466	C₂²	1	4	yes	complemented
65	C₂₃×#465	C₂²	1	4	yes	complemented
66	C₂₃×#465	C₂²	1	4	yes	complemented
67	C₂₃×#463	C₂²	1	4	yes	complemented
68	C₂₃×#450	C₂²	1	2	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#448	C₂²	1	2	yes	complemented
71	C₂₃×#447	C₂²	1	2	yes	—
72	C₂₃×#447	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
74	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
75	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
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×D₄×C₂₃	—	2	1	no	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	—	2	1	no	—
96	C₂³×C₄×C₂₃	—	2	1	no	—
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×D₈×C₂₃	C₂³	1	4	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
104	C₂₃×#126	—	2	2	no	—
105	C₂₃×#126	—	2	4	no	—
106	C₂₃×#126	—	2	4	no	—
107	C₂₃×#126	—	2	2	no	—
108	C₂₃×#126	—	2	2	no	—
109	C₂₃×#125	—	2	2	no	—
110	C₂₃×#125	—	2	2	no	—
111	C₂₃×#125	C₂³	1	2	yes	—
112	C₂₃×#125	C₂³	1	4	yes	—
113	C₂₃×#124	—	2	2	no	—
114	C₂₃×#124	C₂³	1	2	yes	—
115	C₂₃×#123	—	2	2	no	—
116	C₂₃×#123	—	2	2	no	—
117	C₂₃×#123	—	2	2	no	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	4	no	—
121	C₂₃×#123	—	2	4	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	C₂³	1	2	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	—	2	4	no	—
130	C₂₃×#121	—	2	4	no	—
131	C₂₃×#121	—	2	2	no	—
132	C₂₃×#121	—	2	1	no	—
133	C₂₃×#121	—	2	1	no	—
134	C₂₃×#121	—	2	1	no	—
135	C₂₃×#121	—	2	2	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	4	yes	—
141	C₂₃×#121	C₂³	1	2	yes	—
142	C₂₃×#121	C₂³	1	2	yes	—
143	C₂₃×#121	C₂³	1	2	yes	—
144	C₂₃×#120	—	2	2	no	—
145	C₂₃×#120	—	2	2	no	—
146	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	—	2	4	no	—
152	C₄×D₄×C₂₃	—	2	4	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	D₄	1	2	yes	—
156	C₄×D₄×C₂₃	D₄	1	2	yes	—
157	C₄×D₄×C₂₃	C₂³	1	4	yes	—
158	C₄×D₄×C₂₃	C₂³	1	2	yes	—
159	C₄×D₄×C₂₃	C₂³	1	2	yes	—
160	C₄×D₄×C₂₃	C₂³	1	2	yes	—
161	C₂₃×#117	—	2	2	no	—
162	C₂₃×#117	—	2	2	no	—
163	C₂₃×#117	—	2	2	no	—
164	C₂₃×#117	C₂³	1	2	yes	—
165	C₂₃×#117	C₂³	1	4	yes	—
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	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	no	—
186	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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×#102	C₂³	1	4	yes	—
202	C₂₃×#102	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	—	2	1	no	—
214	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
216	#41×C₂₃	—	4	4	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	4	2	no	—
219	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
220	C₂×D₄×C₂₃	—	2	4	no	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	2	2	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	4	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	4	2	no	—
231	C₂×D₄×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	4	no	—
233	C₂×D₄×C₂₃	—	4	4	no	—
234	C₂×D₄×C₂₃	—	8	2	no	—
235	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	4	2	no	—
251	C₂²×C₄×C₂₃	—	4	2	no	—
252	C₂²×C₄×C₂₃	—	8	2	no	—
253	C₂²×C₄×C₂₃	—	8	2	no	—
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	SD₁₆×C₂₃	—	4	4	no	—
266	D₈×C₂₃	—	4	4	no	—
267	C₂×C₈×C₂₃	—	4	2	no	—
268	C₂×C₈×C₂₃	—	4	4	no	—
269	C₂×C₈×C₂₃	—	4	2	no	—
270	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
271	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	2	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	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	4	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	2	no	—
306	C₂²⋊C₄×C₂₃	—	2	2	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
313	C₄²×C₂₃	—	2	4	no	—
314	C₄²×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	C₂×D₄	1	2	yes	—
317	C₄²×C₂₃	C₂⁴	1	2	yes	—
318	#61699	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₂₃	—	2	2	no	—
320	C₂³×C₂₃	—	2	2	no	—
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	4	1	no	—
323	C₂³×C₂₃	—	4	1	no	—
324	C₂³×C₂₃	—	4	1	no	—
325	C₂³×C₂₃	—	4	1	no	—
326	C₂³×C₂₃	—	4	2	no	—
327	C₂³×C₂₃	—	4	2	no	—
328	C₂³×C₂₃	—	4	2	no	—
329	C₂³×C₂₃	—	4	2	no	—
330	C₂³×C₂₃	—	8	1	no	—
331	C₂³×C₂₃	—	8	1	no	—
332	C₂³×C₂₃	#135	1	4	yes	—
333	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
336	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₂₃	—	2	4	no	—
338	Q₈×C₂₃	—	8	1	no	—
339	D₄×C₂₃	—	2	4	no	—
340	D₄×C₂₃	—	2	4	no	—
341	D₄×C₂₃	—	2	4	no	—
342	D₄×C₂₃	—	2	4	no	—
343	D₄×C₂₃	—	4	2	no	—
344	D₄×C₂₃	—	4	4	no	—
345	D₄×C₂₃	—	4	4	no	—
346	D₄×C₂₃	—	4	4	no	—
347	D₄×C₂₃	—	4	4	no	—
348	D₄×C₂₃	—	8	1	no	—
349	D₄×C₂₃	—	8	2	no	—
350	D₄×C₂₃	—	8	4	no	—
351	D₄×C₂₃	—	8	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	4	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	4	2	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	1	no	—
368	C₂×C₄×C₂₃	—	4	1	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	2	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	8	2	no	—
374	C₂×C₄×C₂₃	—	8	4	no	—
375	C₂×C₄×C₂₃	—	8	2	no	—
376	C₂×C₄×C₂₃	—	8	1	no	—
377	C₂×C₄×C₂₃	—	8	2	no	—
378	C₂×C₄×C₂₃	—	8	2	no	—
379	C₂×C₄×C₂₃	—	8	1	no	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₂₃	—	2	4	no	—
388	C₈×C₂₃	—	2	4	no	—
389	#3505	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3339	C₂×C₂₃	1	4	yes	complemented
392	#3337	C₂×C₂₃	1	4	yes	complemented
393	#3301	C₂×C₂₃	1	4	yes	complemented
394	#3297	C₂×C₂₃	1	4	yes	complemented
395	#3232	C₂×C₂₃	1	2	yes	complemented
396	#3188	C₂×C₂₃	1	2	yes	complemented
397	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3105	C₂×C₂₃	1	2	yes	complemented
400	#3091	C₂×C₂₃	1	2	yes	complemented
401	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
402	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	1	no	—
406	C₂²×C₂₃	—	2	1	no	—
407	C₂²×C₂₃	—	2	1	no	—
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	4	4	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	8	2	no	—
421	C₂²×C₂₃	—	8	4	no	—
422	C₂²×C₂₃	—	16	2	no	—
423	C₂²×C₂₃	C₂×#135	1	2	yes	—
424	C₂²×C₂₃	C₂×#135	1	2	yes	—
425	C₂²×C₂₃	C₂×#135	1	2	yes	—
426	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	1	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	4	2	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	2	no	—
439	C₄×C₂₃	#585	1	2	yes	—
440	#553	—	2	2	no	—
441	#553	—	2	2	no	—
442	#553	—	2	2	no	—
443	#553	C₂²×C₂₃	1	4	yes	—
444	#553	C₂²×C₂₃	1	2	yes	complemented
445	#553	C₂²×C₂₃	1	4	yes	complemented
446	#552	C₂²×C₂₃	1	2	yes	complemented
447	#551	—	2	2	no	—
448	#548	C₂²×C₂₃	1	2	yes	complemented
449	#546	C₂²×C₂₃	1	2	yes	complemented
450	#539	—	2	1	no	—
451	#538	—	2	1	no	—
452	#534	—	2	1	no	—
453	#529	C₂²×C₂₃	1	2	yes	—
454	C₂×#126	—	2	1	no	—
455	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#525	C₂²×C₂₃	1	2	yes	—
457	C₂×#123	—	2	1	no	—
458	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#121	—	2	1	no	—
460	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	#518	—	2	1	no	—
464	C₂×C₄×D₄	—	2	1	no	—
465	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
469	#499	C₂²×C₂₃	1	4	yes	complemented
470	#488	C₂²×C₂₃	1	4	yes	complemented
471	#485	C₂²×C₂₃	1	4	yes	complemented
472	#484	C₂²×C₂₃	1	4	yes	complemented
473	#484	C₂²×C₂₃	1	2	yes	complemented
474	#484	C₂²×C₂₃	1	2	yes	complemented
475	#483	C₂²×C₂₃	1	2	yes	complemented
476	#482	C₂²×C₂₃	1	4	yes	complemented
477	#482	C₂²×C₂₃	1	4	yes	complemented
478	#481	C₂²×C₂₃	1	2	yes	—
479	#481	C₂²×C₂₃	1	2	yes	—
480	#481	C₂²×C₂₃	1	2	yes	complemented
481	#481	C₂²×C₂₃	1	4	yes	complemented
482	#480	C₂²×C₂₃	1	2	yes	—
483	#480	C₂²×C₂₃	1	2	yes	complemented
484	#479	C₂²×C₂₃	1	4	yes	complemented
485	#478	C₂²×C₂₃	1	4	yes	complemented
486	#478	C₂²×C₂₃	1	4	yes	complemented
487	#466	C₂²×C₂₃	1	4	yes	complemented
488	#466	C₂²×C₂₃	1	4	yes	complemented
489	#465	C₂²×C₂₃	1	4	yes	complemented
490	#465	C₂²×C₂₃	1	4	yes	complemented
491	#463	C₂²×C₂₃	1	4	yes	complemented
492	#450	C₂²×C₂₃	1	2	yes	complemented
493	#449	C₂²×C₂₃	1	4	yes	complemented
494	#448	C₂²×C₂₃	1	2	yes	complemented
495	#447	C₂²×C₂₃	1	2	yes	—
496	#447	C₂²×C₂₃	1	2	yes	complemented
497	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
498	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
499	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
500	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
501	#431	C₂²×C₂₃	1	2	yes	complemented
502	#427	C₂²×C₂₃	1	4	yes	complemented
503	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
504	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
505	#416	C₂²×C₂₃	1	4	yes	complemented
506	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
507	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
508	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
510	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
511	C₂×C₂₃	—	2	2	no	—
512	C₂×C₂₃	—	2	2	no	—
513	C₂×C₂₃	—	2	2	no	—
514	C₂×C₂₃	—	4	2	no	—
515	C₂×C₂₃	—	8	2	no	—
516	C₂×C₂₃	—	8	2	no	—
517	C₂×C₂₃	#3485	1	1	yes	characteristic
518	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
519	C₂×C₂₃	#3585	1	1	yes	characteristic
520	C₂×#41	C₂³×C₂₃	1	2	yes	—
521	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
533	C₂×D₈	C₂³×C₂₃	1	4	yes	—
534	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
535	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
536	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₂₃	1	4	yes	—
545	#125	C₂³×C₂₃	1	2	yes	—
546	#124	—	2	2	no	—
547	#124	C₂³×C₂₃	1	2	yes	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	4	no	—
553	#123	—	2	4	no	—
554	#123	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
559	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
560	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
561	#121	—	2	4	no	—
562	#121	—	2	4	no	—
563	#121	—	2	2	no	—
564	#121	—	2	2	no	—
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	C₂³×C₂₃	1	2	yes	—
572	#121	C₂³×C₂₃	1	2	yes	—
573	#121	C₂³×C₂₃	1	2	yes	—
574	#121	C₂³×C₂₃	1	2	yes	—
575	#121	C₂³×C₂₃	1	4	yes	—
576	#121	C₂³×C₂₃	1	2	yes	—
577	#120	—	2	2	no	—
578	#120	—	2	2	no	—
579	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	D₄×C₂₃	1	2	yes	—
589	C₄×D₄	D₄×C₂₃	1	2	yes	—
590	C₄×D₄	C₂³×C₂₃	1	4	yes	—
591	C₄×D₄	C₂³×C₂₃	1	2	yes	—
592	C₄×D₄	C₂³×C₂₃	1	2	yes	—
593	C₄×D₄	C₂³×C₂₃	1	2	yes	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	C₂³×C₂₃	1	4	yes	—
598	#117	C₂³×C₂₃	1	2	yes	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄²	—	2	1	no	—
623	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
624	#107	C₂³×C₂₃	1	4	yes	—
625	#107	C₂³×C₂₃	1	4	yes	—
626	#107	C₂³×C₂₃	1	4	yes	—
627	#106	C₂³×C₂₃	1	4	yes	—
628	#106	C₂³×C₂₃	1	4	yes	—
629	#106	C₂³×C₂₃	1	4	yes	—
630	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
631	#103	C₂³×C₂₃	1	4	yes	—
632	#103	C₂³×C₂₃	1	4	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#102	C₂³×C₂₃	1	4	yes	—
635	#102	C₂³×C₂₃	1	4	yes	—
636	#102	C₂³×C₂₃	1	4	yes	—
637	#102	C₂³×C₂₃	1	4	yes	—
638	#102	C₂³×C₂₃	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
640	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
641	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
644	C₄×C₈	C₂³×C₂₃	1	4	yes	—
645	C₂₃	#61699	1	1	yes	characteristic, direct product factor, Sylow
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	1	no	—
648	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
650	#41	—	4	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	8	2	no	—
669	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
672	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	8	2	no	—
687	C₂²×C₄	—	8	2	no	—
688	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
699	SD₁₆	—	4	4	no	—
700	D₈	—	4	4	no	—
701	C₂×C₈	—	4	2	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	—	4	2	no	—
704	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
705	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	C₂×D₄×C₂₃	1	2	yes	—
751	C₄²	C₂⁴×C₂₃	1	2	yes	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	C₂₃×#135	1	4	yes	—
766	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
769	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	8	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	4	no	—
775	D₄	—	2	4	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	—	8	1	no	—
813	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
820	C₈	—	2	4	no	—
821	C₈	—	2	4	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	4	no	—
840	C₂²	—	16	2	no	—
841	C₂²	C₂×C₂₃×#135	1	2	yes	—
842	C₂²	C₂×C₂₃×#135	1	2	yes	—
843	C₂²	C₂×C₂₃×#135	1	2	yes	—
844	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	C₂₃×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂₃×#3485	1	1	yes	characteristic
865	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
866	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3505	C₂	semidirect
2. C₂×C₂₃×#553	C₂	semidirect
3. C₂₃×#3339	C₂	semidirect
4. C₂₃×#3337	C₂	semidirect
5. C₂₃×#3301	C₂	semidirect
6. C₂₃×#3297	C₂	semidirect
7. C₂₃×#3232	C₂	semidirect
8. C₂₃×#3188	C₂	semidirect
9. C₂₃×#3187	C₂	semidirect
10. C₂₃×#3186	C₂	semidirect
11. C₂₃×#3105	C₂	semidirect
12. C₂₃×#3091	C₂	semidirect
13. C₂×C₂₃×#484	C₂	semidirect
14. C₂×C₂₃×#481	C₂	semidirect
15. C₂₃×#2972	C₂	semidirect
20. C₂₃×#553	C₂²	semidirect
21. C₂₃×#553	C₂²	semidirect
22. C₂₃×#552	C₂²	semidirect
24. C₂₃×#548	C₂²	semidirect
25. C₂₃×#546	C₂²	semidirect
31. C₂×C₂₃×#125	C₂²	semidirect
38. C₂×C₂₃×#121	C₂²	semidirect
42. C₂×C₄×D₄×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×#484	C₂²	semidirect
49. C₂₃×#484	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
51. C₂₃×#483	C₂²	semidirect
52. C₂₃×#482	C₂²	semidirect
53. C₂₃×#482	C₂²	semidirect
56. C₂₃×#481	C₂²	semidirect
57. C₂₃×#481	C₂²	semidirect
59. C₂₃×#480	C₂²	semidirect
60. C₂₃×#479	C₂²	semidirect
61. C₂₃×#478	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#466	C₂²	semidirect
64. C₂₃×#466	C₂²	semidirect
65. C₂₃×#465	C₂²	semidirect
66. C₂₃×#465	C₂²	semidirect
67. C₂₃×#463	C₂²	semidirect
68. C₂₃×#450	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#448	C₂²	semidirect
72. C₂₃×#447	C₂²	semidirect
73. C₄×SD₁₆×C₂₃	C₂²	semidirect
74. C₄×D₈×C₂₃	C₂²	semidirect
75. C₈×D₄×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
318. #61699	C₂₃	direct (N × H)
389. #3505	C₂×C₂₃	semidirect
390. C₂×#553	C₂×C₂₃	semidirect
391. #3339	C₂×C₂₃	semidirect
392. #3337	C₂×C₂₃	semidirect
393. #3301	C₂×C₂₃	semidirect
394. #3297	C₂×C₂₃	semidirect
395. #3232	C₂×C₂₃	semidirect
396. #3188	C₂×C₂₃	semidirect
397. #3187	C₂×C₂₃	semidirect
398. #3186	C₂×C₂₃	semidirect
399. #3105	C₂×C₂₃	semidirect
400. #3091	C₂×C₂₃	semidirect
401. C₂×#484	C₂×C₂₃	semidirect
402. C₂×#481	C₂×C₂₃	semidirect
403. #2972	C₂×C₂₃	semidirect
444. #553	C₂²×C₂₃	semidirect
445. #553	C₂²×C₂₃	semidirect
446. #552	C₂²×C₂₃	semidirect
448. #548	C₂²×C₂₃	semidirect
449. #546	C₂²×C₂₃	semidirect
455. C₂×#125	C₂²×C₂₃	semidirect
462. C₂×#121	C₂²×C₂₃	semidirect
466. C₂×C₄×D₄	C₂²×C₂₃	semidirect
467. C₂×#117	C₂²×C₂₃	semidirect
469. #499	C₂²×C₂₃	semidirect
470. #488	C₂²×C₂₃	semidirect
471. #485	C₂²×C₂₃	semidirect
472. #484	C₂²×C₂₃	semidirect
473. #484	C₂²×C₂₃	semidirect
474. #484	C₂²×C₂₃	semidirect
475. #483	C₂²×C₂₃	semidirect
476. #482	C₂²×C₂₃	semidirect
477. #482	C₂²×C₂₃	semidirect
480. #481	C₂²×C₂₃	semidirect
481. #481	C₂²×C₂₃	semidirect
483. #480	C₂²×C₂₃	semidirect
484. #479	C₂²×C₂₃	semidirect
485. #478	C₂²×C₂₃	semidirect
486. #478	C₂²×C₂₃	semidirect
487. #466	C₂²×C₂₃	semidirect
488. #466	C₂²×C₂₃	semidirect
489. #465	C₂²×C₂₃	semidirect
490. #465	C₂²×C₂₃	semidirect
491. #463	C₂²×C₂₃	semidirect
492. #450	C₂²×C₂₃	semidirect
493. #449	C₂²×C₂₃	semidirect
494. #448	C₂²×C₂₃	semidirect
496. #447	C₂²×C₂₃	semidirect
497. C₄×SD₁₆	C₂²×C₂₃	semidirect
498. C₄×D₈	C₂²×C₂₃	semidirect
499. C₈×D₄	C₂²×C₂₃	semidirect
500. C₈×D₄	C₂²×C₂₃	semidirect
501. #431	C₂²×C₂₃	semidirect
502. #427	C₂²×C₂₃	semidirect
503. C₂×#107	C₂²×C₂₃	semidirect
504. C₂×#106	C₂²×C₂₃	semidirect
505. #416	C₂²×C₂₃	semidirect
506. C₂×#103	C₂²×C₂₃	semidirect
507. C₂×#102	C₂²×C₂₃	semidirect
510. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
645. C₂₃	#61699	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×#553	2
C₂₃×#3339	2
C₂₃×#3337	2
C₂₃×#3301	2
C₂₃×#3297	2
C₂₃×#3232	2
C₂₃×#3188	2
C₂₃×#3187	2
C₂₃×#3186	2
C₂₃×#3105	2
C₂₃×#3091	2
C₂×C₂₃×#484	2
C₂×C₂₃×#481	2
C₂₃×#2972	2
#61699	23

Subgroups — C23×#61699 #19209325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61699 #19209325