Subgroups — C₂₃×#25188 #19172814

Order 5888.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#537	C₂²	1	1	yes	characteristic
24	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
26	C₂₃×#520	C₂²	1	1	yes	characteristic
27	C₂₃×#469	—	2	1	no	—
28	C₂₃×#468	—	2	1	no	—
29	C₂₃×#466	—	2	1	no	—
30	C₂₃×#465	—	2	1	no	—
31	C₂₃×#464	—	2	1	no	—
32	C₂₃×#463	—	2	1	no	—
33	C₂₃×#460	—	2	1	no	—
34	C₂₃×#459	—	2	1	no	—
35	C₂₃×#453	—	2	4	no	—
36	C₂₃×#452	—	2	1	no	—
37	C₂₃×#450	—	2	1	no	—
38	C₂₃×#449	—	2	1	no	—
39	C₂₃×#447	—	2	1	no	—
40	C₂₃×#443	—	2	4	no	—
41	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#418	—	2	1	no	—
48	C₂₃×#418	C₂²	1	1	yes	characteristic
49	C₂₃×#417	—	2	1	no	—
50	C₂₃×#417	C₂²	1	1	yes	characteristic
51	C₂₃×#417	C₂²	1	1	yes	characteristic
52	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#416	—	2	1	no	—
54	C₂₃×#416	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#102	—	2	1	no	—
56	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#408	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×H(5,𝔽₂)	—	2	2	no	—
70	C₂₃×H(5,𝔽₂)	—	2	2	no	—
71	C₂₃×H(5,𝔽₂)	—	2	2	no	—
72	C₂₃×H(5,𝔽₂)	—	4	1	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	4	1	no	—
81	C₂²×D₄×C₂₃	—	4	1	no	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
85	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
89	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₂₃×#135	—	2	2	no	—
91	C₂₃×#135	—	2	2	no	—
92	C₂×Q₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
93	C₂×SD₁₆×C₂₃	—	2	1	no	—
94	C₂×SD₁₆×C₂₃	—	2	1	no	—
95	C₂×SD₁₆×C₂₃	—	2	1	no	—
96	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
97	C₂×SD₁₆×C₂₃	D₄	1	1	yes	characteristic, complemented
98	C₂×D₈×C₂₃	—	2	1	no	—
99	C₂×D₈×C₂₃	—	2	1	no	—
100	C₂×D₈×C₂₃	—	2	1	no	—
101	C₂×D₈×C₂₃	D₄	1	1	yes	characteristic, complemented
102	C₂₃×#131	—	2	2	no	—
103	C₂₃×#131	—	2	2	no	—
104	C₂₃×#131	—	4	1	no	—
105	C₂₃×#131	—	4	1	no	—
106	C₂×M₁₆×C₂₃	—	2	1	no	—
107	C₂×M₁₆×C₂₃	—	2	1	no	—
108	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	—	2	1	no	—
113	C₂²×C₈×C₂₃	—	2	1	no	—
114	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	1	no	—
117	C₂₃×#127	—	2	2	no	—
118	C₂₃×#127	—	2	2	no	—
119	C₂₃×#124	—	2	1	no	—
120	C₂₃×C₂²⋊Q₈	—	2	1	no	—
121	C₂₃×C₂²⋊Q₈	—	2	1	no	—
122	C₂₃×#121	—	2	1	no	—
123	C₂₃×#121	—	2	1	no	—
124	C₂₃×#121	—	2	1	no	—
125	C₂₃×#121	—	2	1	no	—
126	C₂₃×#121	—	4	1	no	—
127	C₂₃×#120	—	4	1	no	—
128	C₄×Q₈×C₂₃	—	2	1	no	—
129	C₄×D₄×C₂₃	—	2	1	no	—
130	C₄×D₄×C₂₃	—	4	1	no	—
131	C₂₃×#117	—	2	1	no	—
132	C₂₃×#117	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
138	C₂₃×#108	—	2	2	no	—
139	C₂₃×#107	—	2	1	no	—
140	C₂₃×#106	—	2	1	no	—
141	C₂₃×C₄⋊C₈	—	2	1	no	—
142	C₂₃×C₄⋊C₈	—	2	1	no	—
143	C₂₃×#104	—	2	2	no	—
144	C₂₃×#104	—	2	2	no	—
145	C₂₃×#104	D₄	1	4	yes	complemented
146	C₂₃×#103	—	2	1	no	—
147	C₂₃×#103	—	2	1	no	—
148	C₂₃×#103	—	2	1	no	—
149	C₂₃×#103	D₄	1	1	yes	characteristic, complemented
150	C₂₃×#103	D₄	1	1	yes	characteristic, complemented
151	C₂₃×#102	—	2	1	no	—
152	C₂₃×#102	—	2	1	no	—
153	C₂₃×#102	—	2	1	no	—
154	C₂₃×#102	—	2	1	no	—
155	C₂₃×#102	—	2	1	no	—
156	C₂₃×#102	—	2	1	no	—
157	C₂₃×#102	—	2	1	no	—
158	C₂₃×#102	—	2	1	no	—
159	C₂₃×#102	—	2	1	no	—
160	C₂₃×#102	—	2	1	no	—
161	C₂₃×#102	—	2	1	no	—
162	C₂₃×#102	—	2	1	no	—
163	C₂₃×#102	—	2	1	no	—
164	C₂₃×#102	D₄	1	1	yes	characteristic, complemented
165	C₂₃×#102	D₄	1	1	yes	characteristic, complemented
166	C₂₃×#100	—	2	2	no	—
167	C₂₃×#100	—	4	1	no	—
168	C₂₃×C₂²⋊C₈	—	2	1	no	—
169	C₂₃×C₂²⋊C₈	—	2	1	no	—
170	C₄×C₈×C₂₃	—	2	2	no	—
171	C₂⁴×C₂₃	—	2	1	no	—
172	C₂⁴×C₂₃	—	2	1	no	—
173	C₂⁴×C₂₃	—	4	1	no	—
174	#41×C₂₃	—	2	1	no	—
175	#41×C₂₃	—	2	1	no	—
176	#41×C₂₃	—	2	4	no	—
177	#41×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	2	1	no	—
179	#41×C₂₃	—	2	1	no	—
180	#41×C₂₃	—	2	1	no	—
181	#41×C₂₃	—	2	1	no	—
182	#41×C₂₃	—	2	1	no	—
183	#41×C₂₃	—	2	1	no	—
184	#41×C₂₃	—	2	1	no	—
185	#41×C₂₃	—	4	2	no	—
186	#41×C₂₃	—	4	2	no	—
187	#41×C₂₃	—	4	2	no	—
188	#41×C₂₃	C₂×D₄	1	2	yes	—
189	#41×C₂₃	#41	1	2	yes	—
190	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	4	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	1	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	4	2	no	—
209	C₂×D₄×C₂₃	—	4	1	no	—
210	C₂×D₄×C₂₃	—	4	1	no	—
211	C₂×D₄×C₂₃	—	4	4	no	—
212	C₂×D₄×C₂₃	—	4	1	no	—
213	C₂×D₄×C₂₃	—	4	1	no	—
214	C₂×D₄×C₂₃	—	4	2	no	—
215	C₂×D₄×C₂₃	—	4	4	no	—
216	C₂×D₄×C₂₃	—	4	4	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	—	4	1	no	—
219	C₂×D₄×C₂₃	—	8	2	no	—
220	C₂×D₄×C₂₃	—	8	2	no	—
221	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂×D₄×C₂₃	#41	1	2	yes	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	4	1	no	—
232	C₂²×C₄×C₂₃	—	4	1	no	—
233	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₂₃	—	2	2	no	—
235	SD₁₆×C₂₃	—	2	2	no	—
236	SD₁₆×C₂₃	—	2	2	no	—
237	SD₁₆×C₂₃	—	4	2	no	—
238	SD₁₆×C₂₃	—	4	2	no	—
239	SD₁₆×C₂₃	—	4	2	no	—
240	D₈×C₂₃	—	2	2	no	—
241	D₈×C₂₃	—	4	2	no	—
242	D₈×C₂₃	—	4	2	no	—
243	D₈×C₂₃	—	4	2	no	—
244	M₁₆×C₂₃	—	2	1	no	—
245	M₁₆×C₂₃	—	2	1	no	—
246	M₁₆×C₂₃	—	2	1	no	—
247	M₁₆×C₂₃	—	2	1	no	—
248	M₁₆×C₂₃	—	2	1	no	—
249	M₁₆×C₂₃	—	2	1	no	—
250	M₁₆×C₂₃	—	2	1	no	—
251	M₁₆×C₂₃	—	4	2	no	—
252	M₁₆×C₂₃	—	4	2	no	—
253	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×C₈×C₂₃	—	2	1	no	—
255	C₂×C₈×C₂₃	—	2	1	no	—
256	C₂×C₈×C₂₃	—	2	1	no	—
257	C₂×C₈×C₂₃	—	2	1	no	—
258	C₂×C₈×C₂₃	—	2	1	no	—
259	C₂×C₈×C₂₃	—	2	1	no	—
260	C₂×C₈×C₂₃	—	2	1	no	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	4	2	no	—
263	C₂×C₈×C₂₃	—	4	2	no	—
264	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	4	1	no	—
273	C₄⋊C₄×C₂₃	—	4	1	no	—
274	C₄⋊C₄×C₂₃	—	8	2	no	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂²⋊C₄×C₂₃	—	2	1	no	—
278	C₂²⋊C₄×C₂₃	—	4	1	no	—
279	C₂²⋊C₄×C₂₃	—	4	1	no	—
280	C₂²⋊C₄×C₂₃	—	4	1	no	—
281	C₂²⋊C₄×C₂₃	—	4	1	no	—
282	C₂²⋊C₄×C₂₃	—	4	1	no	—
283	C₄²×C₂₃	—	2	1	no	—
284	C₄²×C₂₃	—	2	1	no	—
285	C₄²×C₂₃	—	4	1	no	—
286	C₄²×C₂₃	C₂×D₄	1	2	yes	—
287	#25188	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	1	no	—
290	C₂³×C₂₃	—	2	1	no	—
291	C₂³×C₂₃	—	2	2	no	—
292	C₂³×C₂₃	—	4	4	no	—
293	C₂³×C₂₃	—	4	1	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	1	no	—
296	C₂³×C₂₃	—	4	1	no	—
297	C₂³×C₂₃	—	4	1	no	—
298	C₂³×C₂₃	—	8	1	no	—
299	C₂³×C₂₃	—	8	1	no	—
300	C₂³×C₂₃	—	8	1	no	—
301	C₂³×C₂₃	—	8	1	no	—
302	C₂³×C₂₃	—	16	1	no	—
303	C₂³×C₂₃	—	16	1	no	—
304	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
305	Q₈×C₂₃	—	2	1	no	—
306	Q₈×C₂₃	—	2	1	no	—
307	Q₈×C₂₃	—	2	1	no	—
308	Q₈×C₂₃	—	2	1	no	—
309	Q₈×C₂₃	—	2	1	no	—
310	Q₈×C₂₃	#121	1	2	yes	—
311	D₄×C₂₃	—	2	2	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	2	1	no	—
314	D₄×C₂₃	—	2	1	no	—
315	D₄×C₂₃	—	2	2	no	—
316	D₄×C₂₃	—	2	1	no	—
317	D₄×C₂₃	—	2	1	no	—
318	D₄×C₂₃	—	2	1	no	—
319	D₄×C₂₃	—	2	2	no	—
320	D₄×C₂₃	—	4	4	no	—
321	D₄×C₂₃	—	4	4	no	—
322	D₄×C₂₃	—	4	1	no	—
323	D₄×C₂₃	—	4	1	no	—
324	D₄×C₂₃	—	4	1	no	—
325	D₄×C₂₃	—	4	1	no	—
326	D₄×C₂₃	—	4	1	no	—
327	D₄×C₂₃	—	4	1	no	—
328	D₄×C₂₃	—	4	1	no	—
329	D₄×C₂₃	—	4	1	no	—
330	D₄×C₂₃	—	4	1	no	—
331	D₄×C₂₃	—	4	1	no	—
332	D₄×C₂₃	—	8	8	no	—
333	D₄×C₂₃	—	16	1	no	—
334	D₄×C₂₃	—	16	1	no	—
335	D₄×C₂₃	—	16	1	no	—
336	D₄×C₂₃	#121	1	2	yes	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	1	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	4	4	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	1	no	—
354	C₂×C₄×C₂₃	—	8	1	no	—
355	C₂×C₄×C₂₃	—	8	1	no	—
356	C₂×C₄×C₂₃	—	16	1	no	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₂₃	—	2	1	no	—
364	C₈×C₂₃	—	2	1	no	—
365	C₈×C₂₃	—	2	1	no	—
366	C₈×C₂₃	—	2	1	no	—
367	C₈×C₂₃	—	2	2	no	—
368	C₈×C₂₃	—	4	1	no	—
369	C₈×C₂₃	—	4	1	no	—
370	C₈×C₂₃	—	4	1	no	—
371	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#453	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#443	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#2063	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#2051	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#2039	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2002	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#1957	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#1937	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#1907	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#1907	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#1859	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₂²×C₂₃	—	2	1	no	—
387	C₂²×C₂₃	—	2	1	no	—
388	C₂²×C₂₃	—	2	2	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	1	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	1	no	—
394	C₂²×C₂₃	—	4	1	no	—
395	C₂²×C₂₃	—	4	1	no	—
396	C₂²×C₂₃	—	4	1	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	—	8	2	no	—
399	C₂²×C₂₃	—	8	2	no	—
400	C₂²×C₂₃	—	8	1	no	—
401	C₂²×C₂₃	—	8	1	no	—
402	C₂²×C₂₃	—	8	1	no	—
403	C₂²×C₂₃	—	8	1	no	—
404	C₂²×C₂₃	—	8	1	no	—
405	C₂²×C₂₃	—	16	1	no	—
406	C₂²×C₂₃	—	16	1	no	—
407	C₂²×C₂₃	—	16	4	no	—
408	C₂²×C₂₃	#538	1	1	yes	characteristic
409	C₂²×C₂₃	D₄²	1	1	yes	characteristic
410	C₂²×C₂₃	#546	1	1	yes	characteristic
411	C₄×C₂₃	—	2	4	no	—
412	C₄×C₂₃	—	2	2	no	—
413	C₄×C₂₃	—	4	1	no	—
414	C₄×C₂₃	—	4	1	no	—
415	C₄×C₂₃	—	4	1	no	—
416	C₄×C₂₃	—	4	1	no	—
417	C₄×C₂₃	—	8	1	no	—
418	C₄×C₂₃	—	8	1	no	—
419	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
420	C₄×C₂₃	#525	1	1	yes	characteristic
421	C₄×C₂₃	D₄²	1	1	yes	characteristic
422	C₄×C₂₃	#546	1	1	yes	characteristic
423	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	#537	C₂²×C₂₃	1	1	yes	characteristic
431	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
433	#520	C₂²×C₂₃	1	1	yes	characteristic
434	#469	—	2	1	no	—
435	#468	—	2	1	no	—
436	#466	—	2	1	no	—
437	#465	—	2	1	no	—
438	#464	—	2	1	no	—
439	#463	—	2	1	no	—
440	#460	—	2	1	no	—
441	#459	—	2	1	no	—
442	#453	—	2	4	no	—
443	#452	—	2	1	no	—
444	#450	—	2	1	no	—
445	#449	—	2	1	no	—
446	#447	—	2	1	no	—
447	#443	—	2	4	no	—
448	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#418	—	2	1	no	—
455	#418	C₂²×C₂₃	1	1	yes	characteristic
456	#417	—	2	1	no	—
457	#417	C₂²×C₂₃	1	1	yes	characteristic
458	#417	C₂²×C₂₃	1	1	yes	characteristic
459	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#416	—	2	1	no	—
461	#416	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#102	—	2	1	no	—
463	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
469	#408	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×C₂₃	—	2	1	no	—
477	C₂×C₂₃	—	2	1	no	—
478	C₂×C₂₃	—	4	2	no	—
479	C₂×C₂₃	—	8	1	no	—
480	C₂×C₂₃	—	8	1	no	—
481	C₂×C₂₃	—	8	2	no	—
482	C₂×C₂₃	—	16	1	no	—
483	C₂×C₂₃	#2424	1	1	yes	characteristic
484	C₂×C₂₃	#3291	1	1	yes	characteristic
485	C₂×C₂₃	#3292	1	1	yes	characteristic
486	H(5,𝔽₂)	—	2	2	no	—
487	H(5,𝔽₂)	—	2	2	no	—
488	H(5,𝔽₂)	—	2	2	no	—
489	H(5,𝔽₂)	—	4	1	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
493	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	AGL(1,ℤ/8)	—	2	2	no	—
502	AGL(1,ℤ/8)	—	2	2	no	—
503	AGL(1,ℤ/8)	—	2	2	no	—
504	AGL(1,ℤ/8)	—	2	2	no	—
505	AGL(1,ℤ/8)	—	4	1	no	—
506	AGL(1,ℤ/8)	—	4	1	no	—
507	#135	—	2	2	no	—
508	#135	—	2	2	no	—
509	C₂×Q₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
510	C₂×SD₁₆	—	2	1	no	—
511	C₂×SD₁₆	—	2	1	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
514	C₂×SD₁₆	D₄×C₂₃	1	1	yes	characteristic, complemented
515	C₂×D₈	—	2	1	no	—
516	C₂×D₈	—	2	1	no	—
517	C₂×D₈	—	2	1	no	—
518	C₂×D₈	D₄×C₂₃	1	1	yes	characteristic, complemented
519	#131	—	2	2	no	—
520	#131	—	2	2	no	—
521	#131	—	4	1	no	—
522	#131	—	4	1	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	—	2	1	no	—
525	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×C₈	—	2	1	no	—
530	C₂²×C₈	—	2	1	no	—
531	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
533	#127	—	2	1	no	—
534	#127	—	2	2	no	—
535	#127	—	2	2	no	—
536	#124	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	4	1	no	—
544	#120	—	4	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	4	1	no	—
548	#117	—	2	1	no	—
549	#117	C₂³×C₂₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	4	1	no	—
552	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
555	#108	—	2	2	no	—
556	#107	—	2	1	no	—
557	#106	—	2	1	no	—
558	C₄⋊C₈	—	2	1	no	—
559	C₄⋊C₈	—	2	1	no	—
560	#104	—	2	2	no	—
561	#104	—	2	2	no	—
562	#104	D₄×C₂₃	1	4	yes	complemented
563	#103	—	2	1	no	—
564	#103	—	2	1	no	—
565	#103	—	2	1	no	—
566	#103	D₄×C₂₃	1	1	yes	characteristic, complemented
567	#103	D₄×C₂₃	1	1	yes	characteristic, complemented
568	#102	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#102	—	2	1	no	—
577	#102	—	2	1	no	—
578	#102	—	2	1	no	—
579	#102	—	2	1	no	—
580	#102	—	2	1	no	—
581	#102	D₄×C₂₃	1	1	yes	characteristic, complemented
582	#102	D₄×C₂₃	1	1	yes	characteristic, complemented
583	#100	—	2	2	no	—
584	#100	—	4	1	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	—	2	1	no	—
587	C₄×C₈	—	2	2	no	—
588	C₂₃	#25188	1	1	yes	characteristic, direct product factor, Sylow
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	2	1	no	—
591	C₂⁴	—	4	1	no	—
592	#41	—	2	1	no	—
593	#41	—	2	1	no	—
594	#41	—	2	4	no	—
595	#41	—	2	1	no	—
596	#41	—	2	1	no	—
597	#41	—	2	1	no	—
598	#41	—	2	1	no	—
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	2	1	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	2	no	—
606	#41	C₂×D₄×C₂₃	1	2	yes	—
607	#41	#41×C₂₃	1	2	yes	—
608	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
609	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	8	2	no	—
638	C₂×D₄	—	8	2	no	—
639	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₂×D₄	#41×C₂₃	1	2	yes	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
652	Q₁₆	—	2	2	no	—
653	SD₁₆	—	2	2	no	—
654	SD₁₆	—	2	2	no	—
655	SD₁₆	—	4	2	no	—
656	SD₁₆	—	4	2	no	—
657	SD₁₆	—	4	2	no	—
658	D₈	—	2	2	no	—
659	D₈	—	4	2	no	—
660	D₈	—	4	2	no	—
661	D₈	—	4	2	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	4	2	no	—
670	M₁₆	—	4	2	no	—
671	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	4	2	no	—
681	C₂×C₈	—	4	2	no	—
682	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
684	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
685	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	8	2	no	—
693	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	4	1	no	—
698	C₂²⋊C₄	—	4	1	no	—
699	C₂²⋊C₄	—	4	1	no	—
700	C₂²⋊C₄	—	4	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	4	1	no	—
704	C₄²	C₂×D₄×C₂₃	1	2	yes	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	4	4	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	—	8	1	no	—
718	C₂³	—	8	1	no	—
719	C₂³	—	16	1	no	—
720	C₂³	—	16	1	no	—
721	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
722	Q₈	—	2	1	no	—
723	Q₈	—	2	1	no	—
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	C₂₃×#121	1	2	yes	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	1	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	8	8	no	—
750	D₄	—	16	1	no	—
751	D₄	—	16	1	no	—
752	D₄	—	16	1	no	—
753	D₄	C₂₃×#121	1	2	yes	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	16	1	no	—
774	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
777	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
778	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
779	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₈	—	2	1	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	—	2	1	no	—
784	C₈	—	2	2	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₈	—	4	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	8	2	no	—
801	C₂²	—	8	2	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	16	1	no	—
808	C₂²	—	16	1	no	—
809	C₂²	—	16	4	no	—
810	C₂²	C₂₃×#538	1	1	yes	characteristic
811	C₂²	D₄²×C₂₃	1	1	yes	characteristic
812	C₂²	C₂₃×#546	1	1	yes	characteristic
813	C₄	—	2	4	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	8	1	no	—
820	C₄	—	8	1	no	—
821	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
822	C₄	C₂₃×#525	1	1	yes	characteristic
823	C₄	D₄²×C₂₃	1	1	yes	characteristic
824	C₄	C₂₃×#546	1	1	yes	characteristic
825	C₂	—	2	1	no	—
826	C₂	—	2	1	no	—
827	C₂	—	4	2	no	—
828	C₂	—	8	1	no	—
829	C₂	—	8	1	no	—
830	C₂	—	8	2	no	—
831	C₂	—	16	1	no	—
832	C₂	C₂₃×#2424	1	1	yes	characteristic
833	C₂	C₂₃×#3291	1	1	yes	characteristic
834	C₂	C₂₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3062	C₂	semidirect
2. C₂₃×#3045	C₂	semidirect
3. C₂×C₂₃×#453	C₂	semidirect
4. C₂₃×#3012	C₂	semidirect
5. C₂×C₂₃×#443	C₂	semidirect
6. C₂₃×#2897	C₂	semidirect
7. C₂₃×#2063	C₂	semidirect
8. C₂₃×#2051	C₂	semidirect
9. C₂₃×#2039	C₂	semidirect
10. C₂₃×#2002	C₂	semidirect
11. C₂₃×#1957	C₂	semidirect
12. C₂₃×#1937	C₂	semidirect
13. C₂₃×#1907	C₂	semidirect
14. C₂₃×#1907	C₂	semidirect
15. C₂₃×#1859	C₂	semidirect
22. C₂×C₂₃×#131	C₂²	semidirect
24. C₂₃×#535	C₂²	semidirect
41. C₂×C₂₃×#108	C₂²	semidirect
42. C₂₃×#428	C₂²	semidirect
43. C₂₃×#424	C₂²	semidirect
46. C₂×C₂₃×#104	C₂²	semidirect
52. C₂₃×#417	C₂²	semidirect
58. C₂×C₂₃×#102	C₂²	semidirect
59. C₂×C₂₃×#102	C₂²	semidirect
61. C₂×C₂₃×#100	C₂²	semidirect
63. C₂×C₄×C₈×C₂₃	C₂²	semidirect
64. C₂₃×#384	C₂²	semidirect
65. C₂₃×#343	C₂²	semidirect
66. C₂₃×#343	C₂²	semidirect
67. C₂₃×#341	C₂²	semidirect
68. C₂₃×#339	C₂²	semidirect
92. C₂×Q₁₆×C₂₃	D₄	semidirect
96. C₂×SD₁₆×C₂₃	D₄	semidirect
97. C₂×SD₁₆×C₂₃	D₄	semidirect
101. C₂×D₈×C₂₃	D₄	semidirect
145. C₂₃×#104	D₄	semidirect
149. C₂₃×#103	D₄	semidirect
150. C₂₃×#103	D₄	semidirect
164. C₂₃×#102	D₄	semidirect
165. C₂₃×#102	D₄	semidirect
287. #25188	C₂₃	direct (N × H)
371. #3062	C₂×C₂₃	semidirect
372. #3045	C₂×C₂₃	semidirect
373. C₂×#453	C₂×C₂₃	semidirect
374. #3012	C₂×C₂₃	semidirect
375. C₂×#443	C₂×C₂₃	semidirect
376. #2897	C₂×C₂₃	semidirect
377. #2063	C₂×C₂₃	semidirect
378. #2051	C₂×C₂₃	semidirect
379. #2039	C₂×C₂₃	semidirect
380. #2002	C₂×C₂₃	semidirect
381. #1957	C₂×C₂₃	semidirect
382. #1937	C₂×C₂₃	semidirect
383. #1907	C₂×C₂₃	semidirect
384. #1907	C₂×C₂₃	semidirect
385. #1859	C₂×C₂₃	semidirect
429. C₂×#131	C₂²×C₂₃	semidirect
431. #535	C₂²×C₂₃	semidirect
448. C₂×#108	C₂²×C₂₃	semidirect
449. #428	C₂²×C₂₃	semidirect
450. #424	C₂²×C₂₃	semidirect
453. C₂×#104	C₂²×C₂₃	semidirect
459. #417	C₂²×C₂₃	semidirect
465. C₂×#102	C₂²×C₂₃	semidirect
466. C₂×#102	C₂²×C₂₃	semidirect
468. C₂×#100	C₂²×C₂₃	semidirect
470. C₂×C₄×C₈	C₂²×C₂₃	semidirect
471. #384	C₂²×C₂₃	semidirect
472. #343	C₂²×C₂₃	semidirect
473. #343	C₂²×C₂₃	semidirect
474. #341	C₂²×C₂₃	semidirect
475. #339	C₂²×C₂₃	semidirect
509. C₂×Q₁₆	D₄×C₂₃	semidirect
513. C₂×SD₁₆	D₄×C₂₃	semidirect
514. C₂×SD₁₆	D₄×C₂₃	semidirect
518. C₂×D₈	D₄×C₂₃	semidirect
562. #104	D₄×C₂₃	semidirect
566. #103	D₄×C₂₃	semidirect
567. #103	D₄×C₂₃	semidirect
581. #102	D₄×C₂₃	semidirect
582. #102	D₄×C₂₃	semidirect
588. C₂₃	#25188	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×#3062	2
C₂₃×#3045	2
C₂×C₂₃×#453	2
C₂₃×#3012	2
C₂×C₂₃×#443	2
C₂₃×#2897	2
C₂₃×#2063	2
C₂₃×#2051	2
C₂₃×#2039	2
C₂₃×#2002	2
C₂₃×#1957	2
C₂₃×#1937	2
C₂₃×#1907	2
C₂₃×#1859	2
#25188	23

Subgroups — C23×#25188 #19172814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25188 #19172814