Subgroups — C₂₃×#61431 #19209057

Order 5888.

2000 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3481	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3339	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3297	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3105	C₂	1	4	yes	maximal, complemented
15	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
20	C₂₃×#559	C₂²	1	2	yes	complemented
21	C₂₃×#554	C₂²	1	2	yes	—
22	C₂₃×#554	C₂²	1	2	yes	complemented
23	C₂₃×#553	—	2	2	no	—
24	C₂₃×#553	C₂²	1	4	yes	complemented
25	C₂₃×#551	—	2	4	no	—
26	C₂₃×#546	—	2	2	no	—
27	C₂₃×#546	C₂²	1	4	yes	complemented
28	D₄²×C₂₃	C₂²	1	2	yes	—
29	C₂₃×#532	C₂²	1	2	yes	complemented
30	C₂₃×#529	—	2	2	no	—
31	C₂₃×#529	C₂²	1	4	yes	complemented
32	C₂₃×#525	—	2	4	no	—
33	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₂₃	—	2	2	no	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
37	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#499	C₂²	1	2	yes	complemented
39	C₂₃×#495	C₂²	1	2	yes	complemented
40	C₂₃×#493	C₂²	1	1	yes	characteristic
41	C₂₃×#488	C₂²	1	4	yes	complemented
42	C₂₃×#486	C₂²	1	2	yes	complemented
43	C₂₃×#484	C₂²	1	4	yes	complemented
44	C₂₃×#482	C₂²	1	4	yes	complemented
45	C₂₃×#481	C₂²	1	4	yes	complemented
46	C₂₃×#478	C₂²	1	4	yes	complemented
47	C₂₃×#478	C₂²	1	4	yes	complemented
48	C₂₃×#477	C₂²	1	2	yes	complemented
49	C₂₃×#476	C₂²	1	2	yes	complemented
50	C₂₃×#467	C₂²	1	2	yes	complemented
51	C₂₃×#466	C₂²	1	2	yes	—
52	C₂₃×#466	C₂²	1	2	yes	complemented
53	C₂₃×#466	C₂²	1	2	yes	complemented
54	C₂₃×#465	C₂²	1	4	yes	complemented
55	C₂₃×#463	C₂²	1	4	yes	complemented
56	C₂₃×#463	C₂²	1	4	yes	complemented
57	C₂₃×#460	C₂²	1	2	yes	complemented
58	C₂₃×#459	C₂²	1	2	yes	—
59	C₂₃×#450	C₂²	1	4	yes	complemented
60	C₂₃×#449	C₂²	1	4	yes	complemented
61	C₂₃×#447	C₂²	1	4	yes	—
62	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
65	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
66	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
67	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
68	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
69	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
70	C₄×D₈×C₂₃	C₂²	1	2	yes	—
71	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
73	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
74	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
75	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
77	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
81	C₂₃×#431	C₂²	1	2	yes	complemented
82	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
85	C₂₃×#416	C₂²	1	2	yes	complemented
86	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
87	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₂₃	—	2	2	no	—
90	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
91	C₂×#41×C₂₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₂₃	—	2	2	no	—
93	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₂₃	—	2	4	no	—
95	C₂₃×#135	—	2	4	no	—
96	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	—	2	8	no	—
100	C₂×D₈×C₂₃	C₂³	1	4	yes	—
101	C₂×D₈×C₂₃	C₂³	1	2	yes	—
102	C₂×D₈×C₂₃	C₂³	1	2	yes	—
103	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₂₃×#127	C₂³	1	2	yes	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#126	—	2	4	no	—
112	C₂₃×#125	—	2	2	no	—
113	C₂₃×#125	C₂³	1	4	yes	—
114	C₂₃×#124	—	2	2	no	—
115	C₂₃×#124	—	2	2	no	—
116	C₂₃×#124	C₂³	1	4	yes	—
117	C₂₃×#123	—	2	4	no	—
118	C₂₃×#123	—	2	4	no	—
119	C₂₃×#123	—	2	4	no	—
120	C₂₃×#123	—	2	4	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	4	no	—
123	C₂₃×C₂²⋊Q₈	—	2	4	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×#121	—	2	4	no	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	4	no	—
129	C₂₃×#121	C₂³	1	4	yes	—
130	C₂₃×#121	C₂³	1	4	yes	—
131	C₂₃×#120	—	2	4	no	—
132	C₂₃×#120	—	2	4	no	—
133	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
134	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
135	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
136	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₂₃	—	2	2	no	—
138	C₄×D₄×C₂₃	—	2	2	no	—
139	C₄×D₄×C₂₃	—	2	4	no	—
140	C₄×D₄×C₂₃	—	2	2	no	—
141	C₄×D₄×C₂₃	—	2	2	no	—
142	C₄×D₄×C₂₃	—	2	4	no	—
143	C₄×D₄×C₂₃	—	2	4	no	—
144	C₄×D₄×C₂₃	—	2	2	no	—
145	C₄×D₄×C₂₃	—	2	4	no	—
146	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
147	C₄×D₄×C₂₃	D₄	1	2	yes	—
148	C₄×D₄×C₂₃	C₂³	1	4	yes	—
149	C₄×D₄×C₂₃	C₂³	1	4	yes	—
150	C₄×D₄×C₂₃	C₂³	1	2	yes	—
151	C₄×D₄×C₂₃	C₂³	1	2	yes	—
152	C₄×D₄×C₂₃	C₂³	1	4	yes	—
153	C₄×D₄×C₂₃	C₂³	1	2	yes	—
154	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂₃×#117	—	2	2	no	—
156	C₂₃×#117	—	2	4	no	—
157	C₂₃×#117	D₄	1	2	yes	—
158	C₂₃×#117	D₄	1	1	yes	characteristic
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
164	C₂×C₄²×C₂₃	—	2	2	no	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂₃×#107	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	2	yes	—
169	C₂₃×#107	C₂³	1	4	yes	—
170	C₂₃×#107	C₂³	1	1	yes	characteristic
171	C₂₃×#107	C₂³	1	2	yes	—
172	C₂₃×#106	C₂³	1	2	yes	—
173	C₂₃×#106	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×#103	C₂³	1	2	yes	—
179	C₂₃×#103	C₂³	1	2	yes	—
180	C₂₃×#103	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	2	yes	—
182	C₂₃×#102	C₂³	1	4	yes	—
183	C₂₃×#102	C₂³	1	4	yes	—
184	C₂₃×#102	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	2	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₂₃	C₂³	1	2	yes	—
193	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	2	yes	—
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	C₂⁴×C₂₃	—	2	4	no	—
199	#41×C₂₃	—	2	4	no	—
200	#41×C₂₃	—	2	4	no	—
201	#41×C₂₃	—	4	2	no	—
202	#41×C₂₃	—	8	4	no	—
203	C₂×Q₈×C₂₃	—	2	2	no	—
204	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₂₃	—	2	8	no	—
207	C₂×D₄×C₂₃	—	2	2	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	2	no	—
213	C₂×D₄×C₂₃	—	4	4	no	—
214	C₂×D₄×C₂₃	—	4	8	no	—
215	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
218	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	—	2	4	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	—	8	8	no	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₂₃	—	2	2	no	—
234	SD₁₆×C₂₃	—	2	4	no	—
235	SD₁₆×C₂₃	—	4	4	no	—
236	D₈×C₂₃	—	2	8	no	—
237	D₈×C₂₃	—	2	4	no	—
238	D₈×C₂₃	—	4	2	no	—
239	D₈×C₂₃	#41	1	4	yes	complemented
240	C₂×C₈×C₂₃	—	2	4	no	—
241	C₂×C₈×C₂₃	—	2	2	no	—
242	C₂×C₈×C₂₃	—	4	1	no	—
243	C₂×C₈×C₂₃	—	4	2	no	—
244	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₂₃	—	2	2	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	2	no	—
254	C₄⋊C₄×C₂₃	—	2	2	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	2	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄²×C₂₃	—	2	2	no	—
279	C₄²×C₂₃	—	2	2	no	—
280	C₄²×C₂₃	—	2	2	no	—
281	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₂₃	C₂×D₄	1	2	yes	—
283	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₂₃	C₂×D₄	1	2	yes	—
285	C₄²×C₂₃	C₂⁴	1	2	yes	—
286	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
288	#61431	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	2	4	no	—
291	C₂³×C₂₃	—	4	8	no	—
292	C₂³×C₂₃	—	4	8	no	—
293	C₂³×C₂₃	—	8	4	no	—
294	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
296	Q₈×C₂₃	—	2	2	no	—
297	Q₈×C₂₃	—	2	2	no	—
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	—	8	2	no	—
300	D₄×C₂₃	—	2	4	no	—
301	D₄×C₂₃	—	2	4	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	2	4	no	—
304	D₄×C₂₃	—	4	8	no	—
305	D₄×C₂₃	—	4	4	no	—
306	D₄×C₂₃	—	4	8	no	—
307	D₄×C₂₃	—	4	4	no	—
308	D₄×C₂₃	—	8	2	no	—
309	D₄×C₂₃	—	8	4	no	—
310	D₄×C₂₃	#135	1	4	yes	complemented
311	D₄×C₂₃	C₂×#41	1	4	yes	—
312	C₂×C₄×C₂₃	—	2	4	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	4	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	4	4	no	—
325	C₂×C₄×C₂₃	—	4	4	no	—
326	C₂×C₄×C₂₃	—	4	4	no	—
327	C₂×C₄×C₂₃	—	4	8	no	—
328	C₂×C₄×C₂₃	—	8	4	no	—
329	C₂×C₄×C₂₃	—	8	4	no	—
330	C₂×C₄×C₂₃	—	8	4	no	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
340	C₈×C₂₃	—	2	2	no	—
341	C₈×C₂₃	—	2	1	no	—
342	C₈×C₂₃	—	2	1	no	—
343	C₈×C₂₃	—	2	1	no	—
344	C₈×C₂₃	—	2	2	no	—
345	C₈×C₂₃	C₂×#41	1	2	yes	—
346	#3481	C₂×C₂₃	1	2	yes	complemented
347	#3396	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#3380	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#3361	C₂×C₂₃	1	2	yes	complemented
350	#3339	C₂×C₂₃	1	2	yes	complemented
351	#3338	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#3297	C₂×C₂₃	1	4	yes	complemented
353	#3295	C₂×C₂₃	1	2	yes	complemented
354	#3280	C₂×C₂₃	1	2	yes	complemented
355	D₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#3168	C₂×C₂₃	1	2	yes	complemented
358	#3106	C₂×C₂₃	1	2	yes	complemented
359	#3105	C₂×C₂₃	1	4	yes	complemented
360	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
361	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×C₄×D₈	C₂×C₂₃	1	2	yes	complemented
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	1	no	—
366	C₂²×C₂₃	—	2	4	no	—
367	C₂²×C₂₃	—	2	1	no	—
368	C₂²×C₂₃	—	2	1	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	4	no	—
372	C₂²×C₂₃	—	4	4	no	—
373	C₂²×C₂₃	—	4	4	no	—
374	C₂²×C₂₃	—	8	16	no	—
375	C₂²×C₂₃	C₂×#135	1	4	yes	—
376	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
377	C₄×C₂₃	—	2	1	no	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	2	1	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	—	2	2	no	—
382	C₄×C₂₃	—	2	1	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	4	no	—
387	C₄×C₂₃	C₂×#135	1	2	yes	—
388	C₄×C₂₃	#576	1	2	yes	—
389	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
390	C₄×C₂₃	#585	1	1	yes	characteristic
391	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
392	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
393	#559	C₂²×C₂₃	1	2	yes	complemented
394	#554	C₂²×C₂₃	1	2	yes	—
395	#554	C₂²×C₂₃	1	2	yes	complemented
396	#553	—	2	2	no	—
397	#553	C₂²×C₂₃	1	4	yes	complemented
398	#551	—	2	4	no	—
399	#546	—	2	2	no	—
400	#546	C₂²×C₂₃	1	4	yes	complemented
401	D₄²	C₂²×C₂₃	1	2	yes	—
402	#532	C₂²×C₂₃	1	2	yes	complemented
403	#529	—	2	2	no	—
404	#529	C₂²×C₂₃	1	4	yes	complemented
405	#525	—	2	4	no	—
406	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
407	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
408	C₂×C₄×D₄	—	2	2	no	—
409	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
410	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
411	#499	C₂²×C₂₃	1	2	yes	complemented
412	#495	C₂²×C₂₃	1	2	yes	complemented
413	#493	C₂²×C₂₃	1	1	yes	characteristic
414	#488	C₂²×C₂₃	1	4	yes	complemented
415	#486	C₂²×C₂₃	1	2	yes	complemented
416	#484	C₂²×C₂₃	1	4	yes	complemented
417	#482	C₂²×C₂₃	1	4	yes	complemented
418	#481	C₂²×C₂₃	1	4	yes	complemented
419	#478	C₂²×C₂₃	1	4	yes	complemented
420	#478	C₂²×C₂₃	1	4	yes	complemented
421	#477	C₂²×C₂₃	1	2	yes	complemented
422	#476	C₂²×C₂₃	1	2	yes	complemented
423	#467	C₂²×C₂₃	1	2	yes	complemented
424	#466	C₂²×C₂₃	1	2	yes	—
425	#466	C₂²×C₂₃	1	2	yes	complemented
426	#466	C₂²×C₂₃	1	2	yes	complemented
427	#465	C₂²×C₂₃	1	4	yes	complemented
428	#463	C₂²×C₂₃	1	4	yes	complemented
429	#463	C₂²×C₂₃	1	4	yes	complemented
430	#460	C₂²×C₂₃	1	2	yes	complemented
431	#459	C₂²×C₂₃	1	2	yes	—
432	#450	C₂²×C₂₃	1	4	yes	complemented
433	#449	C₂²×C₂₃	1	4	yes	complemented
434	#447	C₂²×C₂₃	1	4	yes	—
435	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
438	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
440	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
441	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
442	C₄×D₈	C₂²×C₂₃	1	2	yes	—
443	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
446	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
447	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
448	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
449	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
450	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
451	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
452	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
453	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
454	#431	C₂²×C₂₃	1	2	yes	complemented
455	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
458	#416	C₂²×C₂₃	1	2	yes	complemented
459	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
460	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
461	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	C₂×C₂₃	—	2	4	no	—
463	C₂×C₂₃	—	4	1	no	—
464	C₂×C₂₃	—	4	4	no	—
465	C₂×C₂₃	—	8	4	no	—
466	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
467	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
468	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
469	C₂×#41	—	2	2	no	—
470	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
471	C₂×#41	C₂³×C₂₃	1	2	yes	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
474	C₂³×C₄	—	2	4	no	—
475	#135	—	2	4	no	—
476	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
477	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
478	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
479	C₂×D₈	—	2	8	no	—
480	C₂×D₈	C₂³×C₂₃	1	4	yes	—
481	C₂×D₈	C₂³×C₂₃	1	2	yes	—
482	C₂×D₈	C₂³×C₂₃	1	2	yes	—
483	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
485	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
487	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
489	#127	C₂³×C₂₃	1	2	yes	—
490	#126	—	2	4	no	—
491	#126	—	2	4	no	—
492	#125	—	2	2	no	—
493	#125	C₂³×C₂₃	1	4	yes	—
494	#124	—	2	2	no	—
495	#124	—	2	2	no	—
496	#124	C₂³×C₂₃	1	4	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
505	#121	—	2	4	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	C₂³×C₂₃	1	4	yes	—
510	#121	C₂³×C₂₃	1	4	yes	—
511	#120	—	2	4	no	—
512	#120	—	2	4	no	—
513	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
514	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
516	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
527	C₄×D₄	D₄×C₂₃	1	2	yes	—
528	C₄×D₄	C₂³×C₂₃	1	2	yes	—
529	C₄×D₄	C₂³×C₂₃	1	4	yes	—
530	C₄×D₄	C₂³×C₂₃	1	4	yes	—
531	C₄×D₄	C₂³×C₂₃	1	4	yes	—
532	C₄×D₄	C₂³×C₂₃	1	2	yes	—
533	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₄×D₄	C₂³×C₂₃	1	2	yes	—
535	#117	—	2	2	no	—
536	#117	—	2	4	no	—
537	#117	D₄×C₂₃	1	2	yes	—
538	#117	D₄×C₂₃	1	1	yes	characteristic
539	#117	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₄²	—	2	2	no	—
545	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
547	#107	C₂³×C₂₃	1	1	yes	characteristic
548	#107	C₂³×C₂₃	1	2	yes	—
549	#107	C₂³×C₂₃	1	4	yes	—
550	#107	C₂³×C₂₃	1	1	yes	characteristic
551	#107	C₂³×C₂₃	1	2	yes	—
552	#106	C₂³×C₂₃	1	2	yes	—
553	#106	C₂³×C₂₃	1	4	yes	—
554	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
555	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
556	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
557	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
558	#103	C₂³×C₂₃	1	2	yes	—
559	#103	C₂³×C₂₃	1	2	yes	—
560	#103	C₂³×C₂₃	1	4	yes	—
561	#102	C₂³×C₂₃	1	2	yes	—
562	#102	C₂³×C₂₃	1	4	yes	—
563	#102	C₂³×C₂₃	1	4	yes	—
564	#102	C₂³×C₂₃	1	4	yes	—
565	#102	C₂³×C₂₃	1	2	yes	—
566	#102	C₂³×C₂₃	1	4	yes	—
567	#102	C₂³×C₂₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
571	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₂₃	1	2	yes	—
573	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₂₃	1	2	yes	—
577	C₄×C₈	C₂³×C₂₃	1	2	yes	—
578	C₂₃	#61431	1	1	yes	characteristic, direct product factor, Sylow
579	C₂⁴	—	2	4	no	—
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	#41	—	4	2	no	—
583	#41	—	8	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	8	no	—
596	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
598	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
599	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	8	8	no	—
608	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	SD₁₆	—	2	4	no	—
616	SD₁₆	—	4	4	no	—
617	D₈	—	2	8	no	—
618	D₈	—	2	4	no	—
619	D₈	—	4	2	no	—
620	D₈	#41×C₂₃	1	4	yes	complemented
621	C₂×C₈	—	2	4	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	4	1	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
626	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
627	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
628	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
629	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
640	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
657	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
658	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₂₃	1	2	yes	—
665	C₄²	C₂×D₄×C₂₃	1	2	yes	—
666	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
667	C₄²	C₂⁴×C₂₃	1	2	yes	—
668	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	8	4	no	—
674	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
675	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	8	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	8	2	no	—
689	D₄	—	8	4	no	—
690	D₄	C₂₃×#135	1	4	yes	complemented
691	D₄	C₂×#41×C₂₃	1	4	yes	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
719	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	2	no	—
725	C₈	C₂×#41×C₂₃	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	8	16	no	—
738	C₂²	C₂×C₂₃×#135	1	4	yes	—
739	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	4	no	—
750	C₄	C₂×C₂₃×#135	1	2	yes	—
751	C₄	C₂₃×#576	1	2	yes	—
752	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
753	C₄	C₂₃×#585	1	1	yes	characteristic
754	C₂	—	2	4	no	—
755	C₂	—	4	1	no	—
756	C₂	—	4	4	no	—
757	C₂	—	8	4	no	—
758	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
759	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
760	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3481	C₂	semidirect
2. C₂₃×#3396	C₂	semidirect
3. C₂₃×#3380	C₂	semidirect
4. C₂₃×#3361	C₂	semidirect
5. C₂₃×#3339	C₂	semidirect
6. C₂₃×#3338	C₂	semidirect
7. C₂₃×#3297	C₂	semidirect
8. C₂₃×#3295	C₂	semidirect
9. C₂₃×#3280	C₂	semidirect
10. D₄×D₈×C₂₃	C₂	semidirect
11. C₂₃×#3169	C₂	semidirect
12. C₂₃×#3168	C₂	semidirect
13. C₂₃×#3106	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₈×#41×C₂₃	C₂	semidirect
16. C₄×C₂₃×#135	C₂	semidirect
17. C₂×C₄×D₈×C₂₃	C₂	semidirect
20. C₂₃×#559	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
24. C₂₃×#553	C₂²	semidirect
27. C₂₃×#546	C₂²	semidirect
29. C₂₃×#532	C₂²	semidirect
31. C₂₃×#529	C₂²	semidirect
34. C₄×#41×C₂₃	C₂²	semidirect
36. C₂×C₄×D₄×C₂₃	C₂²	semidirect
37. C₂₃×#500	C₂²	semidirect
38. C₂₃×#499	C₂²	semidirect
39. C₂₃×#495	C₂²	semidirect
41. C₂₃×#488	C₂²	semidirect
42. C₂₃×#486	C₂²	semidirect
43. C₂₃×#484	C₂²	semidirect
44. C₂₃×#482	C₂²	semidirect
45. C₂₃×#481	C₂²	semidirect
46. C₂₃×#478	C₂²	semidirect
47. C₂₃×#478	C₂²	semidirect
48. C₂₃×#477	C₂²	semidirect
49. C₂₃×#476	C₂²	semidirect
50. C₂₃×#467	C₂²	semidirect
52. C₂₃×#466	C₂²	semidirect
53. C₂₃×#466	C₂²	semidirect
54. C₂₃×#465	C₂²	semidirect
55. C₂₃×#463	C₂²	semidirect
56. C₂₃×#463	C₂²	semidirect
57. C₂₃×#460	C₂²	semidirect
59. C₂₃×#450	C₂²	semidirect
60. C₂₃×#449	C₂²	semidirect
62. C₈×Q₈×C₂₃	C₂²	semidirect
63. C₈×Q₈×C₂₃	C₂²	semidirect
64. C₄×Q₁₆×C₂₃	C₂²	semidirect
65. C₄×Q₁₆×C₂₃	C₂²	semidirect
66. C₄×SD₁₆×C₂₃	C₂²	semidirect
67. C₄×SD₁₆×C₂₃	C₂²	semidirect
68. C₄×SD₁₆×C₂₃	C₂²	semidirect
72. C₄×D₈×C₂₃	C₂²	semidirect
73. C₄×D₈×C₂₃	C₂²	semidirect
74. C₄×D₈×C₂₃	C₂²	semidirect
75. C₄×D₈×C₂₃	C₂²	semidirect
76. C₄×D₈×C₂₃	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₈×D₄×C₂₃	C₂²	semidirect
81. C₂₃×#431	C₂²	semidirect
82. C₂₃×#431	C₂²	semidirect
83. C₂₃×#427	C₂²	semidirect
84. C₂×C₂₃×#107	C₂²	semidirect
85. C₂₃×#416	C₂²	semidirect
86. C₂×C₂₃×#102	C₂²	semidirect
87. C₂×C₄×C₈×C₂₃	C₂²	semidirect
88. C₂×C₄×C₈×C₂₃	C₂²	semidirect
239. D₈×C₂₃	#41	semidirect
288. #61431	C₂₃	direct (N × H)
310. D₄×C₂₃	#135	semidirect
346. #3481	C₂×C₂₃	semidirect
347. #3396	C₂×C₂₃	semidirect
348. #3380	C₂×C₂₃	semidirect
349. #3361	C₂×C₂₃	semidirect
350. #3339	C₂×C₂₃	semidirect
351. #3338	C₂×C₂₃	semidirect
352. #3297	C₂×C₂₃	semidirect
353. #3295	C₂×C₂₃	semidirect
354. #3280	C₂×C₂₃	semidirect
355. D₄×D₈	C₂×C₂₃	semidirect
356. #3169	C₂×C₂₃	semidirect
357. #3168	C₂×C₂₃	semidirect
358. #3106	C₂×C₂₃	semidirect
359. #3105	C₂×C₂₃	semidirect
360. C₈×#41	C₂×C₂₃	semidirect
361. C₄×#135	C₂×C₂₃	semidirect
362. C₂×C₄×D₈	C₂×C₂₃	semidirect
393. #559	C₂²×C₂₃	semidirect
395. #554	C₂²×C₂₃	semidirect
397. #553	C₂²×C₂₃	semidirect
400. #546	C₂²×C₂₃	semidirect
402. #532	C₂²×C₂₃	semidirect
404. #529	C₂²×C₂₃	semidirect
407. C₄×#41	C₂²×C₂₃	semidirect
409. C₂×C₄×D₄	C₂²×C₂₃	semidirect
410. #500	C₂²×C₂₃	semidirect
411. #499	C₂²×C₂₃	semidirect
412. #495	C₂²×C₂₃	semidirect
414. #488	C₂²×C₂₃	semidirect
415. #486	C₂²×C₂₃	semidirect
416. #484	C₂²×C₂₃	semidirect
417. #482	C₂²×C₂₃	semidirect
418. #481	C₂²×C₂₃	semidirect
419. #478	C₂²×C₂₃	semidirect
420. #478	C₂²×C₂₃	semidirect
421. #477	C₂²×C₂₃	semidirect
422. #476	C₂²×C₂₃	semidirect
423. #467	C₂²×C₂₃	semidirect
425. #466	C₂²×C₂₃	semidirect
426. #466	C₂²×C₂₃	semidirect
427. #465	C₂²×C₂₃	semidirect
428. #463	C₂²×C₂₃	semidirect
429. #463	C₂²×C₂₃	semidirect
430. #460	C₂²×C₂₃	semidirect
432. #450	C₂²×C₂₃	semidirect
433. #449	C₂²×C₂₃	semidirect
435. C₈×Q₈	C₂²×C₂₃	semidirect
436. C₈×Q₈	C₂²×C₂₃	semidirect
437. C₄×Q₁₆	C₂²×C₂₃	semidirect
438. C₄×Q₁₆	C₂²×C₂₃	semidirect
439. C₄×SD₁₆	C₂²×C₂₃	semidirect
440. C₄×SD₁₆	C₂²×C₂₃	semidirect
441. C₄×SD₁₆	C₂²×C₂₃	semidirect
445. C₄×D₈	C₂²×C₂₃	semidirect
446. C₄×D₈	C₂²×C₂₃	semidirect
447. C₄×D₈	C₂²×C₂₃	semidirect
448. C₄×D₈	C₂²×C₂₃	semidirect
449. C₄×D₈	C₂²×C₂₃	semidirect
452. C₈×D₄	C₂²×C₂₃	semidirect
453. C₈×D₄	C₂²×C₂₃	semidirect
454. #431	C₂²×C₂₃	semidirect
455. #431	C₂²×C₂₃	semidirect
456. #427	C₂²×C₂₃	semidirect
457. C₂×#107	C₂²×C₂₃	semidirect
458. #416	C₂²×C₂₃	semidirect
459. C₂×#102	C₂²×C₂₃	semidirect
460. C₂×C₄×C₈	C₂²×C₂₃	semidirect
461. C₂×C₄×C₈	C₂²×C₂₃	semidirect
578. C₂₃	#61431	direct (N × H)
620. D₈	#41×C₂₃	semidirect
690. D₄	C₂₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3481	2
C₂₃×#3396	2
C₂₃×#3380	2
C₂₃×#3361	2
C₂₃×#3339	2
C₂₃×#3338	2
C₂₃×#3297	2
C₂₃×#3295	2
C₂₃×#3280	2
D₄×D₈×C₂₃	2
C₂₃×#3169	2
C₂₃×#3168	2
C₂₃×#3106	2
C₂₃×#3105	2
C₈×#41×C₂₃	2
C₄×C₂₃×#135	2
C₂×C₄×D₈×C₂₃	2
#61431	23

Subgroups — C23×#61431 #19209057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61431 #19209057