Subgroups — C₂₃×#61262 #19208888

Order 5888.

1884 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3347	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3345	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3341	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3339	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3334	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#555	C₂²	1	4	yes	complemented
22	C₂₃×#553	C₂²	1	4	yes	complemented
23	C₂₃×#553	C₂²	1	4	yes	complemented
24	C₂₃×#551	—	2	4	no	—
25	C₂₃×#547	C₂²	1	4	yes	complemented
26	C₂₃×#546	—	2	4	no	—
27	C₂₃×#544	C₂²	1	2	yes	—
28	C₂₃×#542	—	2	2	no	—
29	C₂₃×#540	—	2	2	no	—
30	C₂₃×#535	C₂²	1	2	yes	—
31	C₂₃×#532	—	2	2	no	—
32	C₂₃×#529	—	2	2	no	—
33	C₂₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	2	yes	—
35	C₂₃×#520	C₂²	1	2	yes	—
36	C₂₃×#518	C₂²	1	2	yes	—
37	C₂×C₂₃×#117	C₂²	1	2	yes	—
38	C₂₃×#501	C₂²	1	4	yes	complemented
39	C₂₃×#500	C₂²	1	2	yes	complemented
40	C₂₃×#499	C₂²	1	2	yes	complemented
41	C₂₃×#482	C₂²	1	4	yes	complemented
42	C₂₃×#482	C₂²	1	4	yes	complemented
43	C₂₃×#482	C₂²	1	4	yes	complemented
44	C₂₃×#482	C₂²	1	4	yes	complemented
45	C₂₃×#481	C₂²	1	4	yes	complemented
46	C₂₃×#481	C₂²	1	4	yes	complemented
47	C₂₃×#480	C₂²	1	4	yes	complemented
48	C₂₃×#480	C₂²	1	4	yes	complemented
49	C₂₃×#478	C₂²	1	4	yes	complemented
50	C₂₃×#478	C₂²	1	4	yes	complemented
51	C₂₃×#476	C₂²	1	4	yes	complemented
52	C₂₃×#474	C₂²	1	4	yes	complemented
53	C₂₃×#469	C₂²	1	4	yes	complemented
54	C₂₃×#466	C₂²	1	2	yes	—
55	C₂₃×#466	C₂²	1	2	yes	—
56	C₂₃×#466	C₂²	1	2	yes	—
57	C₂₃×#466	C₂²	1	2	yes	—
58	C₂₃×#466	C₂²	1	2	yes	complemented
59	C₂₃×#466	C₂²	1	2	yes	complemented
60	C₂₃×#442	C₂²	1	4	yes	complemented
61	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
62	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
66	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
67	C₂₃×#428	C₂²	1	2	yes	—
68	C₂₃×#428	C₂²	1	2	yes	—
69	C₂₃×#428	C₂²	1	4	yes	complemented
70	C₂₃×#427	C₂²	1	1	yes	characteristic
71	C₂₃×#427	C₂²	1	1	yes	characteristic
72	C₂₃×#427	C₂²	1	2	yes	—
73	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#427	C₂²	1	2	yes	complemented
76	C₂₃×#427	C₂²	1	2	yes	complemented
77	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
78	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
81	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
82	C₂₃×#424	C₂²	1	1	yes	characteristic
83	C₂₃×#418	C₂²	1	2	yes	—
84	C₂₃×#418	C₂²	1	2	yes	—
85	C₂×C₂₃×#102	C₂²	1	2	yes	—
86	C₂₃×#408	C₂²	1	1	yes	characteristic
87	C₂₃×#407	C₂²	1	1	yes	characteristic
88	C₂₃×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₂₃	—	2	4	no	—
90	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₂₃	—	2	2	no	—
92	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×D₈×C₂₃	—	2	4	no	—
95	C₂×D₈×C₂₃	C₂³	1	2	yes	—
96	C₂×D₈×C₂₃	C₂³	1	2	yes	—
97	C₂₃×#131	—	2	4	no	—
98	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	—	2	4	no	—
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₂₃×#127	—	2	2	no	—
112	C₂₃×#126	—	2	4	no	—
113	C₂₃×#126	—	2	4	no	—
114	C₂₃×#125	—	2	2	no	—
115	C₂₃×#125	C₂³	1	4	yes	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#124	—	2	4	no	—
118	C₂₃×#124	—	2	4	no	—
119	C₂₃×#123	—	2	4	no	—
120	C₂₃×#123	—	2	4	no	—
121	C₂₃×#123	—	2	4	no	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×#123	D₄	1	2	yes	—
124	C₂₃×C₂²⋊Q₈	—	2	4	no	—
125	C₂₃×C₂²⋊Q₈	—	2	4	no	—
126	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₂₃×#121	—	2	4	no	—
129	C₂₃×#121	—	2	4	no	—
130	C₂₃×#121	—	2	4	no	—
131	C₂₃×#121	—	2	2	no	—
132	C₂₃×#121	—	2	2	no	—
133	C₂₃×#121	D₄	1	1	yes	characteristic
134	C₂₃×#121	D₄	1	1	yes	characteristic
135	C₂₃×#121	C₂³	1	4	yes	—
136	C₂₃×#121	C₂³	1	4	yes	—
137	C₂₃×#121	C₂³	1	4	yes	—
138	C₂₃×#121	C₂³	1	4	yes	—
139	C₂₃×#120	—	2	4	no	—
140	C₂₃×#120	D₄	1	2	yes	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×D₄×C₂₃	—	2	4	no	—
143	C₄×D₄×C₂₃	—	2	2	no	—
144	C₄×D₄×C₂₃	—	2	2	no	—
145	C₄×D₄×C₂₃	—	2	2	no	—
146	C₄×D₄×C₂₃	—	2	4	no	—
147	C₄×D₄×C₂₃	—	2	4	no	—
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	C₂₃×#117	—	2	2	no	—
153	C₂₃×#117	—	2	2	no	—
154	C₂₃×#117	—	2	4	no	—
155	C₂₃×#117	C₂³	1	2	yes	—
156	C₂₃×#117	C₂³	1	4	yes	—
157	C₂₃×#117	C₂³	1	2	yes	—
158	C₂₃×#117	C₂³	1	2	yes	—
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂₃×#117	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
166	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂×C₄²×C₂₃	—	2	2	no	—
169	C₂₃×#107	C₂³	1	2	yes	—
170	C₂₃×#107	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	1	yes	characteristic
172	C₂₃×#107	C₂³	1	1	yes	characteristic
173	C₂₃×#107	C₂³	1	1	yes	characteristic
174	C₂₃×#107	C₂³	1	1	yes	characteristic
175	C₂₃×#107	C₂³	1	2	yes	—
176	C₂₃×#107	C₂³	1	2	yes	—
177	C₂₃×#107	C₂³	1	4	yes	—
178	C₂₃×#107	C₂³	1	4	yes	—
179	C₂₃×#106	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	2	yes	—
181	C₂₃×#106	C₂³	1	2	yes	—
182	C₂₃×#106	C₂³	1	2	yes	—
183	C₂₃×#106	C₂³	1	4	yes	—
184	C₂₃×#106	C₂³	1	4	yes	—
185	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×#102	C₂³	1	4	yes	—
191	C₂₃×#102	C₂³	1	4	yes	—
192	C₂₃×#102	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	2	yes	—
199	C₂⁴×C₂₃	—	2	2	no	—
200	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
201	#41×C₂₃	—	2	2	no	—
202	#41×C₂₃	—	2	2	no	—
203	#41×C₂₃	—	8	8	no	—
204	C₂×Q₈×C₂₃	—	2	4	no	—
205	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	2	no	—
211	C₂×D₄×C₂₃	—	2	4	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	8	4	no	—
214	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₂₃	—	2	2	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	2	no	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	—	2	4	no	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	D₈×C₂₃	—	2	4	no	—
235	D₈×C₂₃	—	2	4	no	—
236	M₁₆×C₂₃	—	2	2	no	—
237	M₁₆×C₂₃	—	2	2	no	—
238	M₁₆×C₂₃	—	2	4	no	—
239	C₂×C₈×C₂₃	—	2	2	no	—
240	C₂×C₈×C₂₃	—	2	2	no	—
241	C₂×C₈×C₂₃	—	2	2	no	—
242	C₂×C₈×C₂₃	—	2	2	no	—
243	C₂×C₈×C₂₃	—	2	2	no	—
244	C₂×C₈×C₂₃	—	2	4	no	—
245	C₂×C₈×C₂₃	#41	1	4	yes	complemented
246	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₄⋊C₄×C₂₃	—	2	2	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	—	2	4	no	—
258	C₄⋊C₄×C₂₃	—	2	4	no	—
259	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	2	no	—
271	C₂²⋊C₄×C₂₃	—	2	2	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	—	2	4	no	—
276	C₂²⋊C₄×C₂₃	—	2	4	no	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₄²×C₂₃	—	2	2	no	—
285	C₄²×C₂₃	—	2	2	no	—
286	C₄²×C₂₃	—	2	2	no	—
287	C₄²×C₂₃	—	2	2	no	—
288	C₄²×C₂₃	—	2	4	no	—
289	C₄²×C₂₃	C₂⁴	1	2	yes	—
290	#61262	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂³×C₂₃	—	2	2	no	—
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	4	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	4	no	—
296	C₂³×C₂₃	—	8	2	no	—
297	C₂³×C₂₃	—	8	2	no	—
298	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
300	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₂₃	—	2	2	no	—
303	Q₈×C₂₃	—	8	4	no	—
304	D₄×C₂₃	—	2	4	no	—
305	D₄×C₂₃	—	2	4	no	—
306	D₄×C₂₃	—	2	2	no	—
307	D₄×C₂₃	—	2	4	no	—
308	D₄×C₂₃	—	2	4	no	—
309	D₄×C₂₃	—	4	2	no	—
310	D₄×C₂₃	—	4	8	no	—
311	D₄×C₂₃	—	4	4	no	—
312	D₄×C₂₃	—	8	4	no	—
313	D₄×C₂₃	—	8	4	no	—
314	D₄×C₂₃	—	8	4	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	4	no	—
329	C₂×C₄×C₂₃	—	4	4	no	—
330	C₂×C₄×C₂₃	—	8	4	no	—
331	C₂×C₄×C₂₃	—	8	4	no	—
332	C₂×C₄×C₂₃	—	8	2	no	—
333	C₂×C₄×C₂₃	—	8	2	no	—
334	C₂×C₄×C₂₃	—	8	4	no	—
335	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
342	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
343	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
344	C₈×C₂₃	—	2	1	no	—
345	C₈×C₂₃	—	2	1	no	—
346	C₈×C₂₃	—	2	2	no	—
347	C₈×C₂₃	—	2	2	no	—
348	C₈×C₂₃	C₂×#41	1	2	yes	—
349	C₈×C₂₃	C₂×#41	1	2	yes	—
350	#3494	C₂×C₂₃	1	2	yes	complemented
351	#3347	C₂×C₂₃	1	4	yes	complemented
352	#3345	C₂×C₂₃	1	4	yes	complemented
353	#3341	C₂×C₂₃	1	2	yes	complemented
354	#3339	C₂×C₂₃	1	2	yes	complemented
355	#3339	C₂×C₂₃	1	2	yes	complemented
356	#3334	C₂×C₂₃	1	2	yes	complemented
357	#3164	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#3096	C₂×C₂₃	1	2	yes	complemented
359	#3094	C₂×C₂₃	1	2	yes	complemented
360	#3081	C₂×C₂₃	1	2	yes	complemented
361	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2913	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂×#427	C₂×C₂₃	1	1	yes	characteristic, complemented
367	C₂²×C₂₃	—	2	1	no	—
368	C₂²×C₂₃	—	2	1	no	—
369	C₂²×C₂₃	—	2	1	no	—
370	C₂²×C₂₃	—	2	1	no	—
371	C₂²×C₂₃	—	2	1	no	—
372	C₂²×C₂₃	—	2	2	no	—
373	C₂²×C₂₃	—	2	1	no	—
374	C₂²×C₂₃	—	2	2	no	—
375	C₂²×C₂₃	—	2	2	no	—
376	C₂²×C₂₃	—	2	1	no	—
377	C₂²×C₂₃	—	4	4	no	—
378	C₂²×C₂₃	—	4	4	no	—
379	C₂²×C₂₃	—	4	4	no	—
380	C₂²×C₂₃	—	4	4	no	—
381	C₂²×C₂₃	—	16	4	no	—
382	C₂²×C₂₃	#547	1	2	yes	—
383	C₂²×C₂₃	#576	1	2	yes	—
384	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₂₃	—	2	2	no	—
386	C₄×C₂₃	—	2	1	no	—
387	C₄×C₂₃	—	2	1	no	—
388	C₄×C₂₃	—	2	2	no	—
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	—	4	4	no	—
395	C₄×C₂₃	#547	1	2	yes	—
396	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
397	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
400	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
401	#555	C₂²×C₂₃	1	4	yes	complemented
402	#553	C₂²×C₂₃	1	4	yes	complemented
403	#553	C₂²×C₂₃	1	4	yes	complemented
404	#551	—	2	4	no	—
405	#547	C₂²×C₂₃	1	4	yes	complemented
406	#546	—	2	4	no	—
407	#544	C₂²×C₂₃	1	2	yes	—
408	#542	—	2	2	no	—
409	#540	—	2	2	no	—
410	#535	C₂²×C₂₃	1	2	yes	—
411	#532	—	2	2	no	—
412	#529	—	2	2	no	—
413	#525	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#121	C₂²×C₂₃	1	2	yes	—
415	#520	C₂²×C₂₃	1	2	yes	—
416	#518	C₂²×C₂₃	1	2	yes	—
417	C₂×#117	C₂²×C₂₃	1	2	yes	—
418	#501	C₂²×C₂₃	1	4	yes	complemented
419	#500	C₂²×C₂₃	1	2	yes	complemented
420	#499	C₂²×C₂₃	1	2	yes	complemented
421	#482	C₂²×C₂₃	1	4	yes	complemented
422	#482	C₂²×C₂₃	1	4	yes	complemented
423	#482	C₂²×C₂₃	1	4	yes	complemented
424	#482	C₂²×C₂₃	1	4	yes	complemented
425	#481	C₂²×C₂₃	1	4	yes	complemented
426	#481	C₂²×C₂₃	1	4	yes	complemented
427	#480	C₂²×C₂₃	1	4	yes	complemented
428	#480	C₂²×C₂₃	1	4	yes	complemented
429	#478	C₂²×C₂₃	1	4	yes	complemented
430	#478	C₂²×C₂₃	1	4	yes	complemented
431	#476	C₂²×C₂₃	1	4	yes	complemented
432	#474	C₂²×C₂₃	1	4	yes	complemented
433	#469	C₂²×C₂₃	1	4	yes	complemented
434	#466	C₂²×C₂₃	1	2	yes	—
435	#466	C₂²×C₂₃	1	2	yes	—
436	#466	C₂²×C₂₃	1	2	yes	—
437	#466	C₂²×C₂₃	1	2	yes	—
438	#466	C₂²×C₂₃	1	2	yes	complemented
439	#466	C₂²×C₂₃	1	2	yes	complemented
440	#442	C₂²×C₂₃	1	4	yes	complemented
441	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
442	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
443	#435	C₂²×C₂₃	1	2	yes	complemented
444	#435	C₂²×C₂₃	1	2	yes	complemented
445	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
446	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
447	#428	C₂²×C₂₃	1	2	yes	—
448	#428	C₂²×C₂₃	1	2	yes	—
449	#428	C₂²×C₂₃	1	4	yes	complemented
450	#427	C₂²×C₂₃	1	2	yes	—
451	#427	C₂²×C₂₃	1	1	yes	characteristic
452	#427	C₂²×C₂₃	1	1	yes	characteristic
453	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#427	C₂²×C₂₃	1	2	yes	complemented
455	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#427	C₂²×C₂₃	1	2	yes	complemented
457	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
460	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
462	#424	C₂²×C₂₃	1	1	yes	characteristic
463	#418	C₂²×C₂₃	1	2	yes	—
464	#418	C₂²×C₂₃	1	2	yes	—
465	C₂×#102	C₂²×C₂₃	1	2	yes	—
466	#408	C₂²×C₂₃	1	1	yes	characteristic
467	#407	C₂²×C₂₃	1	1	yes	characteristic
468	#405	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×C₂₃	—	2	2	no	—
470	C₂×C₂₃	—	2	2	no	—
471	C₂×C₂₃	—	4	2	no	—
472	C₂×C₂₃	—	4	1	no	—
473	C₂×C₂₃	—	8	4	no	—
474	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
475	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
476	C₂×C₂₃	#3584	1	1	yes	characteristic
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
482	C₂×D₈	—	2	4	no	—
483	C₂×D₈	C₂³×C₂₃	1	2	yes	—
484	C₂×D₈	C₂³×C₂₃	1	2	yes	—
485	#131	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
488	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
489	C₂²×C₈	—	2	4	no	—
490	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
496	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
499	#127	—	2	2	no	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	2	no	—
503	#125	C₂³×C₂₃	1	4	yes	—
504	#124	—	2	2	no	—
505	#124	—	2	4	no	—
506	#124	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	D₄×C₂₃	1	2	yes	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
515	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
516	#121	—	2	4	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	D₄×C₂₃	1	1	yes	characteristic
522	#121	D₄×C₂₃	1	1	yes	characteristic
523	#121	C₂³×C₂₃	1	4	yes	—
524	#121	C₂³×C₂₃	1	4	yes	—
525	#121	C₂³×C₂₃	1	4	yes	—
526	#121	C₂³×C₂₃	1	4	yes	—
527	#120	—	2	4	no	—
528	#120	D₄×C₂₃	1	2	yes	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	C₂³×C₂₃	1	4	yes	—
537	C₄×D₄	C₂³×C₂₃	1	4	yes	—
538	C₄×D₄	C₂³×C₂₃	1	2	yes	—
539	C₄×D₄	C₂³×C₂₃	1	2	yes	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	2	4	no	—
543	#117	C₂³×C₂₃	1	2	yes	—
544	#117	C₂³×C₂₃	1	2	yes	—
545	#117	C₂³×C₂₃	1	2	yes	—
546	#117	C₂³×C₂₃	1	2	yes	—
547	#117	C₂³×C₂₃	1	4	yes	—
548	#117	C₂³×C₂₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
553	C₂×C₂²⋊C₄	—	2	2	no	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₄²	—	2	2	no	—
557	#107	C₂³×C₂₃	1	2	yes	—
558	#107	C₂³×C₂₃	1	2	yes	—
559	#107	C₂³×C₂₃	1	1	yes	characteristic
560	#107	C₂³×C₂₃	1	1	yes	characteristic
561	#107	C₂³×C₂₃	1	1	yes	characteristic
562	#107	C₂³×C₂₃	1	1	yes	characteristic
563	#107	C₂³×C₂₃	1	2	yes	—
564	#107	C₂³×C₂₃	1	2	yes	—
565	#107	C₂³×C₂₃	1	4	yes	—
566	#107	C₂³×C₂₃	1	4	yes	—
567	#106	C₂³×C₂₃	1	2	yes	—
568	#106	C₂³×C₂₃	1	2	yes	—
569	#106	C₂³×C₂₃	1	2	yes	—
570	#106	C₂³×C₂₃	1	2	yes	—
571	#106	C₂³×C₂₃	1	4	yes	—
572	#106	C₂³×C₂₃	1	4	yes	—
573	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
574	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
575	#102	C₂³×C₂₃	1	4	yes	—
576	#102	C₂³×C₂₃	1	4	yes	—
577	#102	C₂³×C₂₃	1	4	yes	—
578	#102	C₂³×C₂₃	1	4	yes	—
579	#102	C₂³×C₂₃	1	4	yes	—
580	#102	C₂³×C₂₃	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
585	#97	C₂³×C₂₃	1	2	yes	—
586	C₄×C₈	C₂³×C₂₃	1	2	yes	—
587	C₂₃	#61262	1	1	yes	characteristic, direct product factor, Sylow
588	C₂⁴	—	2	2	no	—
589	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	8	4	no	—
603	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
604	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
605	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
606	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
607	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
623	D₈	—	2	4	no	—
624	D₈	—	2	4	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₂₃	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
656	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	C₂⁴×C₂₃	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	8	2	no	—
686	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
689	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
729	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
730	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	C₂×#41×C₂₃	1	2	yes	—
737	C₈	C₂×#41×C₂₃	1	2	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	16	4	no	—
753	C₂²	C₂₃×#547	1	2	yes	—
754	C₂²	C₂₃×#576	1	2	yes	—
755	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	C₂₃×#547	1	2	yes	—
767	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
768	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	4	no	—
774	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
775	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
776	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3347	C₂	semidirect
3. C₂₃×#3345	C₂	semidirect
4. C₂₃×#3341	C₂	semidirect
5. C₂₃×#3339	C₂	semidirect
6. C₂₃×#3339	C₂	semidirect
7. C₂₃×#3334	C₂	semidirect
8. C₂₃×#3164	C₂	semidirect
9. C₂₃×#3096	C₂	semidirect
10. C₂₃×#3094	C₂	semidirect
11. C₂₃×#3081	C₂	semidirect
12. C₂₃×#3058	C₂	semidirect
13. C₂×C₂₃×#466	C₂	semidirect
14. C₂₃×#2948	C₂	semidirect
15. C₂₃×#2929	C₂	semidirect
16. C₂₃×#2913	C₂	semidirect
17. C₂×C₂₃×#427	C₂	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#553	C₂²	semidirect
23. C₂₃×#553	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
38. C₂₃×#501	C₂²	semidirect
39. C₂₃×#500	C₂²	semidirect
40. C₂₃×#499	C₂²	semidirect
41. C₂₃×#482	C₂²	semidirect
42. C₂₃×#482	C₂²	semidirect
43. C₂₃×#482	C₂²	semidirect
44. C₂₃×#482	C₂²	semidirect
45. C₂₃×#481	C₂²	semidirect
46. C₂₃×#481	C₂²	semidirect
47. C₂₃×#480	C₂²	semidirect
48. C₂₃×#480	C₂²	semidirect
49. C₂₃×#478	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#476	C₂²	semidirect
52. C₂₃×#474	C₂²	semidirect
53. C₂₃×#469	C₂²	semidirect
58. C₂₃×#466	C₂²	semidirect
59. C₂₃×#466	C₂²	semidirect
60. C₂₃×#442	C₂²	semidirect
61. C₄×D₈×C₂₃	C₂²	semidirect
62. C₄×D₈×C₂₃	C₂²	semidirect
63. C₂₃×#435	C₂²	semidirect
64. C₂₃×#435	C₂²	semidirect
65. C₈×D₄×C₂₃	C₂²	semidirect
66. C₈×D₄×C₂₃	C₂²	semidirect
69. C₂₃×#428	C₂²	semidirect
73. C₂₃×#427	C₂²	semidirect
74. C₂₃×#427	C₂²	semidirect
75. C₂₃×#427	C₂²	semidirect
76. C₂₃×#427	C₂²	semidirect
78. C₂×C₂₃×#107	C₂²	semidirect
79. C₂×C₂₃×#107	C₂²	semidirect
80. C₂×C₂₃×#107	C₂²	semidirect
81. C₂×C₂₃×#106	C₂²	semidirect
245. C₂×C₈×C₂₃	#41	semidirect
290. #61262	C₂₃	direct (N × H)
350. #3494	C₂×C₂₃	semidirect
351. #3347	C₂×C₂₃	semidirect
352. #3345	C₂×C₂₃	semidirect
353. #3341	C₂×C₂₃	semidirect
354. #3339	C₂×C₂₃	semidirect
355. #3339	C₂×C₂₃	semidirect
356. #3334	C₂×C₂₃	semidirect
357. #3164	C₂×C₂₃	semidirect
358. #3096	C₂×C₂₃	semidirect
359. #3094	C₂×C₂₃	semidirect
360. #3081	C₂×C₂₃	semidirect
361. #3058	C₂×C₂₃	semidirect
362. C₂×#466	C₂×C₂₃	semidirect
363. #2948	C₂×C₂₃	semidirect
364. #2929	C₂×C₂₃	semidirect
365. #2913	C₂×C₂₃	semidirect
366. C₂×#427	C₂×C₂₃	semidirect
401. #555	C₂²×C₂₃	semidirect
402. #553	C₂²×C₂₃	semidirect
403. #553	C₂²×C₂₃	semidirect
405. #547	C₂²×C₂₃	semidirect
418. #501	C₂²×C₂₃	semidirect
419. #500	C₂²×C₂₃	semidirect
420. #499	C₂²×C₂₃	semidirect
421. #482	C₂²×C₂₃	semidirect
422. #482	C₂²×C₂₃	semidirect
423. #482	C₂²×C₂₃	semidirect
424. #482	C₂²×C₂₃	semidirect
425. #481	C₂²×C₂₃	semidirect
426. #481	C₂²×C₂₃	semidirect
427. #480	C₂²×C₂₃	semidirect
428. #480	C₂²×C₂₃	semidirect
429. #478	C₂²×C₂₃	semidirect
430. #478	C₂²×C₂₃	semidirect
431. #476	C₂²×C₂₃	semidirect
432. #474	C₂²×C₂₃	semidirect
433. #469	C₂²×C₂₃	semidirect
438. #466	C₂²×C₂₃	semidirect
439. #466	C₂²×C₂₃	semidirect
440. #442	C₂²×C₂₃	semidirect
441. C₄×D₈	C₂²×C₂₃	semidirect
442. C₄×D₈	C₂²×C₂₃	semidirect
443. #435	C₂²×C₂₃	semidirect
444. #435	C₂²×C₂₃	semidirect
445. C₈×D₄	C₂²×C₂₃	semidirect
446. C₈×D₄	C₂²×C₂₃	semidirect
449. #428	C₂²×C₂₃	semidirect
453. #427	C₂²×C₂₃	semidirect
454. #427	C₂²×C₂₃	semidirect
455. #427	C₂²×C₂₃	semidirect
456. #427	C₂²×C₂₃	semidirect
458. C₂×#107	C₂²×C₂₃	semidirect
459. C₂×#107	C₂²×C₂₃	semidirect
460. C₂×#107	C₂²×C₂₃	semidirect
461. C₂×#106	C₂²×C₂₃	semidirect
587. C₂₃	#61262	direct (N × H)
634. 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×#3494	2
C₂₃×#3347	2
C₂₃×#3345	2
C₂₃×#3341	2
C₂₃×#3339	2
C₂₃×#3334	2
C₂₃×#3164	2
C₂₃×#3096	2
C₂₃×#3094	2
C₂₃×#3081	2
C₂₃×#3058	2
C₂×C₂₃×#466	2
C₂₃×#2948	2
C₂₃×#2929	2
C₂₃×#2913	2
C₂×C₂₃×#427	2
#61262	23

Subgroups — C23×#61262 #19208888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61262 #19208888