Subgroups — C₂₃×#61680 #19209306

Order 5888.

2096 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3324	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3302	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3201	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3009	C₂	1	4	yes	maximal, complemented
15	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
19	C₂₃×#563	—	2	2	no	—
20	C₂₃×#559	—	2	1	no	—
21	Q₈²×C₂₃	—	2	1	no	—
22	C₂₃×#556	C₂²	1	2	yes	complemented
23	C₂₃×#556	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	C₂²	1	2	yes	—
28	C₂₃×#546	—	2	2	no	—
29	C₂₃×#546	C₂²	1	4	yes	—
30	D₄²×C₂₃	—	2	1	no	—
31	D₄²×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#542	—	2	2	no	—
33	C₂₃×#542	—	2	2	no	—
34	C₂₃×#537	C₂²	1	2	yes	—
35	C₂₃×#536	C₂²	1	4	yes	complemented
36	C₂₃×#534	—	2	2	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	—	2	2	no	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#497	C₂²	1	2	yes	complemented
44	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#489	C₂²	1	2	yes	complemented
47	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#485	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×#476	C₂²	1	2	yes	complemented
54	C₂₃×#474	C₂²	1	2	yes	complemented
55	C₂₃×#470	C₂²	1	4	yes	complemented
56	C₂₃×#468	C₂²	1	4	yes	complemented
57	C₂₃×#467	C₂²	1	4	yes	complemented
58	C₂₃×#465	C₂²	1	4	yes	complemented
59	C₂₃×#464	C₂²	1	4	yes	complemented
60	C₂₃×#462	C₂²	1	2	yes	complemented
61	C₂₃×#461	C₂²	1	2	yes	complemented
62	C₂₃×#461	C₂²	1	2	yes	complemented
63	C₂₃×#460	C₂²	1	2	yes	complemented
64	C₂₃×#452	C₂²	1	4	yes	complemented
65	C₂₃×#452	C₂²	1	4	yes	complemented
66	C₂₃×#452	C₂²	1	4	yes	complemented
67	C₂₃×#452	C₂²	1	4	yes	complemented
68	C₂₃×#451	C₂²	1	4	yes	complemented
69	C₂₃×#450	C₂²	1	2	yes	—
70	C₂₃×#450	C₂²	1	2	yes	—
71	C₂₃×#450	C₂²	1	4	yes	complemented
72	C₂₃×#450	C₂²	1	4	yes	complemented
73	C₂₃×#448	C₂²	1	4	yes	complemented
74	C₂₃×#440	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
77	C₂₃×#436	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#418	C₂²	1	4	yes	complemented
83	C₂₃×#416	C₂²	1	4	yes	complemented
84	C₂₃×#408	C₂²	1	4	yes	complemented
85	C₂₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	C₂³	1	4	yes	—
88	C₂×#41×C₂₃	C₂³	1	2	yes	—
89	C₂×#41×C₂₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₂₃	—	2	4	no	—
92	C₂²×D₄×C₂₃	—	2	2	no	—
93	C₂²×D₄×C₂₃	—	2	2	no	—
94	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
96	C₂³×C₄×C₂₃	—	2	1	no	—
97	C₂₃×#137	—	4	8	no	—
98	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₂₃	—	4	8	no	—
101	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
108	C₂₃×C₄⋊Q₈	—	2	4	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	—	2	2	no	—
111	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×#127	D₄	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#126	—	2	4	no	—
121	C₂₃×#125	—	2	1	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	—	2	2	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	D₄	1	2	yes	—
127	C₂₃×#124	C₂³	1	2	yes	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×#123	—	2	4	no	—
131	C₂₃×#123	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	1	no	—
134	C₂₃×C₂²⋊Q₈	—	2	1	no	—
135	C₂₃×C₂²⋊Q₈	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	—	2	4	no	—
137	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	4	no	—
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	D₄	1	2	yes	—
150	C₂₃×#121	D₄	1	2	yes	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₂₃×#120	—	2	4	no	—
153	C₂₃×#120	—	2	4	no	—
154	C₄×Q₈×C₂₃	—	2	2	no	—
155	C₄×Q₈×C₂₃	—	2	2	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₂₃×#117	—	2	1	no	—
171	C₂₃×#117	—	2	1	no	—
172	C₂₃×#117	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×#107	C₂³	1	4	yes	—
179	C₂₃×#106	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	2	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#103	C₂³	1	2	yes	—
186	C₂₃×#103	C₂³	1	2	yes	—
187	C₂₃×#103	C₂³	1	4	yes	—
188	C₂₃×#102	C₂³	1	2	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×#102	C₂³	1	2	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	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₂⁴×C₂₃	—	2	1	no	—
201	C₂⁴×C₂₃	—	2	4	no	—
202	#41×C₂₃	—	2	8	no	—
203	#41×C₂₃	—	4	4	no	—
204	#41×C₂₃	—	4	4	no	—
205	#41×C₂₃	—	4	4	no	—
206	#41×C₂₃	—	4	8	no	—
207	C₂×Q₈×C₂₃	—	2	1	no	—
208	C₂×Q₈×C₂₃	—	2	1	no	—
209	C₂×Q₈×C₂₃	—	2	4	no	—
210	C₂×Q₈×C₂₃	—	4	4	no	—
211	C₂×Q₈×C₂₃	—	4	4	no	—
212	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₂₃	—	2	4	no	—
217	C₂×D₄×C₂₃	—	2	8	no	—
218	C₂×D₄×C₂₃	—	2	4	no	—
219	C₂×D₄×C₂₃	—	2	2	no	—
220	C₂×D₄×C₂₃	—	2	4	no	—
221	C₂×D₄×C₂₃	—	2	1	no	—
222	C₂×D₄×C₂₃	—	2	1	no	—
223	C₂×D₄×C₂₃	—	2	4	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	—	4	4	no	—
226	C₂×D₄×C₂₃	—	4	8	no	—
227	C₂×D₄×C₂₃	—	4	16	no	—
228	C₂×D₄×C₂₃	—	8	4	no	—
229	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	4	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	2	2	no	—
239	C₂²×C₄×C₂₃	—	2	2	no	—
240	C₂²×C₄×C₂₃	—	2	2	no	—
241	C₂²×C₄×C₂₃	—	8	2	no	—
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
246	Q₁₆×C₂₃	—	4	4	no	—
247	Q₁₆×C₂₃	—	4	4	no	—
248	SD₁₆×C₂₃	—	2	4	no	—
249	SD₁₆×C₂₃	—	2	8	no	—
250	SD₁₆×C₂₃	—	2	4	no	—
251	SD₁₆×C₂₃	—	4	4	no	—
252	SD₁₆×C₂₃	—	4	4	no	—
253	M₁₆×C₂₃	—	4	4	no	—
254	C₂×C₈×C₂₃	—	4	4	no	—
255	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
257	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	4	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	2	no	—
281	C₂²⋊C₄×C₂₃	—	2	2	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
292	C₄²×C₂₃	—	2	2	no	—
293	C₄²×C₂₃	—	2	2	no	—
294	C₄²×C₂₃	—	2	4	no	—
295	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
298	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
299	#61680	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂³×C₂₃	—	2	4	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	—	4	8	no	—
304	C₂³×C₂₃	—	8	1	no	—
305	C₂³×C₂₃	—	8	1	no	—
306	C₂³×C₂₃	—	8	4	no	—
307	C₂³×C₂₃	—	8	4	no	—
308	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
309	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₂₃	—	2	2	no	—
311	Q₈×C₂₃	—	2	4	no	—
312	Q₈×C₂₃	—	2	2	no	—
313	Q₈×C₂₃	—	2	4	no	—
314	Q₈×C₂₃	—	4	2	no	—
315	Q₈×C₂₃	—	4	2	no	—
316	Q₈×C₂₃	—	4	2	no	—
317	Q₈×C₂₃	—	8	4	no	—
318	D₄×C₂₃	—	2	4	no	—
319	D₄×C₂₃	—	2	4	no	—
320	D₄×C₂₃	—	2	2	no	—
321	D₄×C₂₃	—	2	4	no	—
322	D₄×C₂₃	—	4	2	no	—
323	D₄×C₂₃	—	4	4	no	—
324	D₄×C₂₃	—	4	2	no	—
325	D₄×C₂₃	—	4	8	no	—
326	D₄×C₂₃	—	4	8	no	—
327	D₄×C₂₃	—	4	4	no	—
328	D₄×C₂₃	—	4	2	no	—
329	D₄×C₂₃	—	8	1	no	—
330	D₄×C₂₃	—	8	4	no	—
331	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	4	no	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	8	no	—
344	C₂×C₄×C₂₃	—	4	4	no	—
345	C₂×C₄×C₂₃	—	4	4	no	—
346	C₂×C₄×C₂₃	—	8	2	no	—
347	C₂×C₄×C₂₃	—	8	1	no	—
348	C₂×C₄×C₂₃	—	8	4	no	—
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
356	C₈×C₂₃	—	2	2	no	—
357	C₈×C₂₃	—	2	4	no	—
358	C₈×C₂₃	—	2	2	no	—
359	#3550	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#3496	C₂×C₂₃	1	1	yes	characteristic
361	#3324	C₂×C₂₃	1	2	yes	complemented
362	#3311	C₂×C₂₃	1	4	yes	complemented
363	#3302	C₂×C₂₃	1	2	yes	complemented
364	D₄×SD₁₆	C₂×C₂₃	1	2	yes	complemented
365	#3276	C₂×C₂₃	1	2	yes	complemented
366	#3266	C₂×C₂₃	1	4	yes	complemented
367	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#3210	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#3201	C₂×C₂₃	1	4	yes	complemented
370	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#3009	C₂×C₂₃	1	4	yes	complemented
373	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂²×C₂₃	—	2	1	no	—
375	C₂²×C₂₃	—	2	4	no	—
376	C₂²×C₂₃	—	2	4	no	—
377	C₂²×C₂₃	—	2	1	no	—
378	C₂²×C₂₃	—	2	4	no	—
379	C₂²×C₂₃	—	2	1	no	—
380	C₂²×C₂₃	—	2	4	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	2	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	—	4	2	no	—
386	C₂²×C₂₃	—	8	4	no	—
387	C₂²×C₂₃	—	16	8	no	—
388	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₂₃	—	2	1	no	—
390	C₄×C₂₃	—	2	1	no	—
391	C₄×C₂₃	—	2	1	no	—
392	C₄×C₂₃	—	2	4	no	—
393	C₄×C₂₃	—	2	1	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	—	4	2	no	—
396	C₄×C₂₃	—	4	2	no	—
397	C₄×C₂₃	—	4	2	no	—
398	C₄×C₂₃	—	4	2	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	#577	1	2	yes	—
401	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
402	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
403	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
404	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
405	#563	—	2	2	no	—
406	#559	—	2	1	no	—
407	Q₈²	—	2	1	no	—
408	#556	C₂²×C₂₃	1	2	yes	complemented
409	#556	C₂²×C₂₃	1	2	yes	complemented
410	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
411	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
412	#547	—	2	1	no	—
413	#547	C₂²×C₂₃	1	2	yes	—
414	#546	—	2	2	no	—
415	#546	C₂²×C₂₃	1	4	yes	—
416	D₄²	—	2	1	no	—
417	D₄²	C₂²×C₂₃	1	2	yes	—
418	#542	—	2	2	no	—
419	#542	—	2	2	no	—
420	#537	C₂²×C₂₃	1	2	yes	—
421	#536	C₂²×C₂₃	1	4	yes	complemented
422	#534	—	2	2	no	—
423	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
424	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#532	C₂²×C₂₃	1	1	yes	characteristic
426	#532	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#121	—	2	2	no	—
428	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
429	#497	C₂²×C₂₃	1	2	yes	complemented
430	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#489	C₂²×C₂₃	1	2	yes	complemented
433	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#485	C₂²×C₂₃	1	4	yes	complemented
436	#484	C₂²×C₂₃	1	2	yes	complemented
437	#483	C₂²×C₂₃	1	2	yes	complemented
438	#482	C₂²×C₂₃	1	4	yes	complemented
439	#476	C₂²×C₂₃	1	2	yes	complemented
440	#474	C₂²×C₂₃	1	2	yes	complemented
441	#470	C₂²×C₂₃	1	4	yes	complemented
442	#468	C₂²×C₂₃	1	4	yes	complemented
443	#467	C₂²×C₂₃	1	4	yes	complemented
444	#465	C₂²×C₂₃	1	4	yes	complemented
445	#464	C₂²×C₂₃	1	4	yes	complemented
446	#462	C₂²×C₂₃	1	2	yes	complemented
447	#461	C₂²×C₂₃	1	2	yes	complemented
448	#461	C₂²×C₂₃	1	2	yes	complemented
449	#460	C₂²×C₂₃	1	2	yes	complemented
450	#452	C₂²×C₂₃	1	4	yes	complemented
451	#452	C₂²×C₂₃	1	4	yes	complemented
452	#452	C₂²×C₂₃	1	4	yes	complemented
453	#452	C₂²×C₂₃	1	4	yes	complemented
454	#451	C₂²×C₂₃	1	4	yes	complemented
455	#450	C₂²×C₂₃	1	2	yes	—
456	#450	C₂²×C₂₃	1	2	yes	—
457	#450	C₂²×C₂₃	1	4	yes	complemented
458	#450	C₂²×C₂₃	1	4	yes	complemented
459	#448	C₂²×C₂₃	1	4	yes	complemented
460	#440	C₂²×C₂₃	1	4	yes	complemented
461	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
462	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
463	#436	C₂²×C₂₃	1	2	yes	complemented
464	#435	C₂²×C₂₃	1	4	yes	complemented
465	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
466	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	#418	C₂²×C₂₃	1	4	yes	complemented
469	#416	C₂²×C₂₃	1	4	yes	complemented
470	#408	C₂²×C₂₃	1	4	yes	complemented
471	C₂×C₂₃	—	4	1	no	—
472	C₂×C₂₃	—	4	4	no	—
473	C₂×C₂₃	—	4	4	no	—
474	C₂×C₂₃	—	8	2	no	—
475	C₂×C₂₃	#3484	1	1	yes	characteristic
476	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
477	C₂×C₂₃	#3586	1	1	yes	characteristic
478	H(5,𝔽₂)	—	4	8	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	C₂³×C₂₃	1	4	yes	—
481	C₂×#41	C₂³×C₂₃	1	2	yes	—
482	C₂×#41	C₂³×C₂₃	1	2	yes	—
483	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
484	C₂²×D₄	—	2	4	no	—
485	C₂²×D₄	—	2	2	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
489	C₂³×C₄	—	2	1	no	—
490	#137	—	4	8	no	—
491	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
492	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
493	C₂×SD₁₆	—	4	8	no	—
494	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
498	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
499	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
500	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
501	C₄⋊Q₈	—	2	4	no	—
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
510	#127	D₄×C₂₃	1	1	yes	characteristic
511	#127	C₂³×C₂₃	1	1	yes	characteristic
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#124	—	2	4	no	—
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	#124	D₄×C₂₃	1	2	yes	—
520	#124	C₂³×C₂₃	1	2	yes	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
531	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
533	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
535	#121	—	2	4	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	1	no	—
539	#121	—	2	1	no	—
540	#121	—	2	2	no	—
541	#121	—	2	4	no	—
542	#121	D₄×C₂₃	1	2	yes	—
543	#121	D₄×C₂₃	1	2	yes	—
544	#121	C₂³×C₂₃	1	4	yes	—
545	#120	—	2	4	no	—
546	#120	—	2	4	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
552	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	C₂³×C₂₃	1	2	yes	—
560	C₄×D₄	C₂³×C₂₃	1	2	yes	—
561	C₄×D₄	C₂³×C₂₃	1	2	yes	—
562	C₄×D₄	C₂³×C₂₃	1	2	yes	—
563	#117	—	2	1	no	—
564	#117	—	2	1	no	—
565	#117	C₂³×C₂₃	1	4	yes	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
571	#107	C₂³×C₂₃	1	4	yes	—
572	#106	C₂³×C₂₃	1	2	yes	—
573	#106	C₂³×C₂₃	1	2	yes	—
574	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
575	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
576	#103	C₂³×C₂₃	1	4	yes	—
577	#103	C₂³×C₂₃	1	4	yes	—
578	#103	C₂³×C₂₃	1	2	yes	—
579	#103	C₂³×C₂₃	1	2	yes	—
580	#103	C₂³×C₂₃	1	4	yes	—
581	#102	C₂³×C₂₃	1	2	yes	—
582	#102	C₂³×C₂₃	1	4	yes	—
583	#102	C₂³×C₂₃	1	2	yes	—
584	#102	C₂³×C₂₃	1	4	yes	—
585	#102	C₂³×C₂₃	1	4	yes	—
586	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
587	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
590	#97	C₂³×C₂₃	1	2	yes	—
591	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
593	C₂₃	#61680	1	1	yes	characteristic, direct product factor, Sylow
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	4	no	—
596	#41	—	2	8	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
609	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	8	no	—
621	C₂×D₄	—	4	16	no	—
622	C₂×D₄	—	8	4	no	—
623	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
625	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
628	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
640	Q₁₆	—	4	4	no	—
641	Q₁₆	—	4	4	no	—
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	8	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	M₁₆	—	4	4	no	—
648	C₂×C₈	—	4	4	no	—
649	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
650	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
651	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
685	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	4	no	—
689	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
702	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	4	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	2	no	—
722	D₄	—	8	1	no	—
723	D₄	—	8	4	no	—
724	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	2	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	16	8	no	—
766	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	C₂₃×#577	1	2	yes	—
779	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
780	C₂	—	4	1	no	—
781	C₂	—	4	4	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂₃×#3484	1	1	yes	characteristic
785	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
786	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×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3550	C₂	semidirect
3. C₂₃×#3324	C₂	semidirect
4. C₂₃×#3311	C₂	semidirect
5. C₂₃×#3302	C₂	semidirect
6. D₄×SD₁₆×C₂₃	C₂	semidirect
7. C₂₃×#3276	C₂	semidirect
8. C₂₃×#3266	C₂	semidirect
9. C₂₃×#3216	C₂	semidirect
10. C₂₃×#3210	C₂	semidirect
11. C₂₃×#3201	C₂	semidirect
12. C₂₃×#3110	C₂	semidirect
13. C₂₃×#3101	C₂	semidirect
14. C₂₃×#3009	C₂	semidirect
15. C₂₃×#2981	C₂	semidirect
17. C₂×C₂₃×#137	C₂²	semidirect
18. C₂²×SD₁₆×C₂₃	C₂²	semidirect
22. C₂₃×#556	C₂²	semidirect
23. C₂₃×#556	C₂²	semidirect
24. D₄×Q₈×C₂₃	C₂²	semidirect
25. D₄×Q₈×C₂₃	C₂²	semidirect
35. C₂₃×#536	C₂²	semidirect
37. C₂₃×#533	C₂²	semidirect
38. C₂₃×#533	C₂²	semidirect
43. C₂₃×#497	C₂²	semidirect
44. C₂₃×#494	C₂²	semidirect
45. C₂₃×#492	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#487	C₂²	semidirect
48. C₂₃×#486	C₂²	semidirect
49. C₂₃×#485	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
51. C₂₃×#483	C₂²	semidirect
52. C₂₃×#482	C₂²	semidirect
53. C₂₃×#476	C₂²	semidirect
54. C₂₃×#474	C₂²	semidirect
55. C₂₃×#470	C₂²	semidirect
56. C₂₃×#468	C₂²	semidirect
57. C₂₃×#467	C₂²	semidirect
58. C₂₃×#465	C₂²	semidirect
59. C₂₃×#464	C₂²	semidirect
60. C₂₃×#462	C₂²	semidirect
61. C₂₃×#461	C₂²	semidirect
62. C₂₃×#461	C₂²	semidirect
63. C₂₃×#460	C₂²	semidirect
64. C₂₃×#452	C₂²	semidirect
65. C₂₃×#452	C₂²	semidirect
66. C₂₃×#452	C₂²	semidirect
67. C₂₃×#452	C₂²	semidirect
68. C₂₃×#451	C₂²	semidirect
71. C₂₃×#450	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
73. C₂₃×#448	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₄×SD₁₆×C₂₃	C₂²	semidirect
76. C₄×SD₁₆×C₂₃	C₂²	semidirect
77. C₂₃×#436	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₂₃×#432	C₂²	semidirect
81. C₂₃×#431	C₂²	semidirect
82. C₂₃×#418	C₂²	semidirect
83. C₂₃×#416	C₂²	semidirect
84. C₂₃×#408	C₂²	semidirect
299. #61680	C₂₃	direct (N × H)
359. #3550	C₂×C₂₃	semidirect
361. #3324	C₂×C₂₃	semidirect
362. #3311	C₂×C₂₃	semidirect
363. #3302	C₂×C₂₃	semidirect
364. D₄×SD₁₆	C₂×C₂₃	semidirect
365. #3276	C₂×C₂₃	semidirect
366. #3266	C₂×C₂₃	semidirect
367. #3216	C₂×C₂₃	semidirect
368. #3210	C₂×C₂₃	semidirect
369. #3201	C₂×C₂₃	semidirect
370. #3110	C₂×C₂₃	semidirect
371. #3101	C₂×C₂₃	semidirect
372. #3009	C₂×C₂₃	semidirect
373. #2981	C₂×C₂₃	semidirect
403. C₂×#137	C₂²×C₂₃	semidirect
404. C₂²×SD₁₆	C₂²×C₂₃	semidirect
408. #556	C₂²×C₂₃	semidirect
409. #556	C₂²×C₂₃	semidirect
410. D₄×Q₈	C₂²×C₂₃	semidirect
411. D₄×Q₈	C₂²×C₂₃	semidirect
421. #536	C₂²×C₂₃	semidirect
423. #533	C₂²×C₂₃	semidirect
424. #533	C₂²×C₂₃	semidirect
429. #497	C₂²×C₂₃	semidirect
430. #494	C₂²×C₂₃	semidirect
431. #492	C₂²×C₂₃	semidirect
432. #489	C₂²×C₂₃	semidirect
433. #487	C₂²×C₂₃	semidirect
434. #486	C₂²×C₂₃	semidirect
435. #485	C₂²×C₂₃	semidirect
436. #484	C₂²×C₂₃	semidirect
437. #483	C₂²×C₂₃	semidirect
438. #482	C₂²×C₂₃	semidirect
439. #476	C₂²×C₂₃	semidirect
440. #474	C₂²×C₂₃	semidirect
441. #470	C₂²×C₂₃	semidirect
442. #468	C₂²×C₂₃	semidirect
443. #467	C₂²×C₂₃	semidirect
444. #465	C₂²×C₂₃	semidirect
445. #464	C₂²×C₂₃	semidirect
446. #462	C₂²×C₂₃	semidirect
447. #461	C₂²×C₂₃	semidirect
448. #461	C₂²×C₂₃	semidirect
449. #460	C₂²×C₂₃	semidirect
450. #452	C₂²×C₂₃	semidirect
451. #452	C₂²×C₂₃	semidirect
452. #452	C₂²×C₂₃	semidirect
453. #452	C₂²×C₂₃	semidirect
454. #451	C₂²×C₂₃	semidirect
457. #450	C₂²×C₂₃	semidirect
458. #450	C₂²×C₂₃	semidirect
459. #448	C₂²×C₂₃	semidirect
460. #440	C₂²×C₂₃	semidirect
461. C₄×SD₁₆	C₂²×C₂₃	semidirect
462. C₄×SD₁₆	C₂²×C₂₃	semidirect
463. #436	C₂²×C₂₃	semidirect
464. #435	C₂²×C₂₃	semidirect
465. C₈×D₄	C₂²×C₂₃	semidirect
466. #432	C₂²×C₂₃	semidirect
467. #431	C₂²×C₂₃	semidirect
468. #418	C₂²×C₂₃	semidirect
469. #416	C₂²×C₂₃	semidirect
470. #408	C₂²×C₂₃	semidirect
593. C₂₃	#61680	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×#3550	2
C₂₃×#3496	2
C₂₃×#3324	2
C₂₃×#3311	2
C₂₃×#3302	2
D₄×SD₁₆×C₂₃	2
C₂₃×#3276	2
C₂₃×#3266	2
C₂₃×#3216	2
C₂₃×#3210	2
C₂₃×#3201	2
C₂₃×#3110	2
C₂₃×#3101	2
C₂₃×#3009	2
C₂₃×#2981	2
#61680	23

Subgroups — C23×#61680 #19209306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61680 #19209306