Subgroups — C₂₃×#25439 #19173065

Order 5888.

960 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2003	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1887	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#536	C₂²	1	1	yes	characteristic
24	C₂₃×#535	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
27	C₂₃×#518	C₂²	1	1	yes	characteristic
28	C₂₃×#518	C₂²	1	1	yes	characteristic
29	C₂₃×#496	—	2	4	no	—
30	C₂₃×#472	—	2	4	no	—
31	C₂₃×#468	—	2	2	no	—
32	C₂₃×#465	—	2	2	no	—
33	C₂₃×#463	—	2	2	no	—
34	C₂₃×#463	—	2	2	no	—
35	C₂₃×#461	—	2	2	no	—
36	C₂₃×#459	—	2	2	no	—
37	C₂₃×#442	—	2	2	no	—
38	C₄×D₈×C₂₃	—	2	2	no	—
39	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
40	C₂₃×#427	C₂²	1	1	yes	characteristic
41	C₂₃×#424	C₂²	1	1	yes	characteristic
42	C₂₃×#424	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
44	C₂₃×#419	C₂²	1	1	yes	characteristic
45	C₂₃×#419	C₂²	1	1	yes	characteristic
46	C₂₃×#418	C₂²	1	1	yes	characteristic
47	C₂₃×#418	C₂²	1	1	yes	characteristic
48	C₂₃×#418	C₂²	1	1	yes	characteristic
49	C₂₃×#418	C₂²	1	1	yes	characteristic
50	C₂₃×#416	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
55	C₂₃×#405	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
57	C₂₃×#341	C₂²	1	1	yes	characteristic
58	C₂₃×#339	C₂²	1	1	yes	characteristic
59	C₂₃×#339	C₂²	1	1	yes	characteristic
60	C₂₃×#339	C₂²	1	1	yes	characteristic
61	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₃	—	4	1	no	—
64	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
68	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
69	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
70	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
71	C₂×SD₁₆×C₂₃	—	2	1	no	—
72	C₂×SD₁₆×C₂₃	—	2	1	no	—
73	C₂×SD₁₆×C₂₃	—	2	2	no	—
74	C₂×SD₁₆×C₂₃	—	2	2	no	—
75	C₂×SD₁₆×C₂₃	—	2	1	no	—
76	C₂×SD₁₆×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	2	no	—
78	C₂×SD₁₆×C₂₃	—	2	2	no	—
79	C₂×SD₁₆×C₂₃	—	4	1	no	—
80	C₂×D₈×C₂₃	—	2	2	no	—
81	C₂×D₈×C₂₃	—	2	1	no	—
82	C₂×D₈×C₂₃	—	2	1	no	—
83	C₂×D₈×C₂₃	—	2	1	no	—
84	C₂×D₈×C₂₃	—	2	1	no	—
85	C₂×D₈×C₂₃	—	2	2	no	—
86	C₂×D₈×C₂₃	—	2	2	no	—
87	C₂×D₈×C₂₃	—	4	1	no	—
88	C₂×D₈×C₂₃	D₄	1	4	yes	complemented
89	C₂₃×#131	—	2	2	no	—
90	C₂₃×#131	—	2	2	no	—
91	C₂×M₁₆×C₂₃	—	2	1	no	—
92	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	—	2	1	no	—
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂₃×C₄⋊Q₈	—	2	1	no	—
100	C₂₃×#127	—	2	1	no	—
101	C₂₃×#127	—	2	2	no	—
102	C₂₃×#127	—	2	2	no	—
103	C₂₃×#124	—	2	1	no	—
104	C₂₃×#124	—	2	1	no	—
105	C₂₃×#124	—	2	2	no	—
106	C₂₃×#124	—	2	2	no	—
107	C₂₃×#123	—	4	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	2	no	—
109	C₂₃×#121	—	2	2	no	—
110	C₂₃×#120	—	4	1	no	—
111	C₄×D₄×C₂₃	—	2	2	no	—
112	C₄×D₄×C₂₃	—	2	2	no	—
113	C₄×D₄×C₂₃	—	2	2	no	—
114	C₄×D₄×C₂₃	—	2	2	no	—
115	C₂₃×#117	C₂³	1	1	yes	characteristic
116	C₂₃×#117	C₂³	1	1	yes	characteristic
117	C₂₃×#117	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
121	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
122	C₂₃×#108	—	2	2	no	—
123	C₂₃×#107	D₄	1	2	yes	complemented
124	C₂₃×#106	D₄	1	2	yes	complemented
125	C₂₃×C₄⋊C₈	—	2	2	no	—
126	C₂₃×C₄⋊C₈	—	2	2	no	—
127	C₂₃×#104	—	2	2	no	—
128	C₂₃×#103	—	2	2	no	—
129	C₂₃×#103	—	2	2	no	—
130	C₂₃×#103	D₄	1	2	yes	complemented
131	C₂₃×#102	—	2	2	no	—
132	C₂₃×#102	—	2	2	no	—
133	C₂₃×#102	—	2	2	no	—
134	C₂₃×#102	—	2	2	no	—
135	C₂₃×#102	D₄	1	2	yes	complemented
136	C₂₃×#101	—	4	1	no	—
137	C₂₃×#100	—	2	2	no	—
138	C₂₃×#100	—	2	2	no	—
139	C₂₃×#100	—	4	1	no	—
140	C₂₃×#97	—	2	2	no	—
141	C₂₃×#97	—	2	1	no	—
142	C₄×C₈×C₂₃	—	2	1	no	—
143	C₂⁴×C₂₃	—	2	1	no	—
144	C₂⁴×C₂₃	—	2	1	no	—
145	C₂⁴×C₂₃	—	2	1	no	—
146	#41×C₂₃	—	2	1	no	—
147	#41×C₂₃	—	2	1	no	—
148	#41×C₂₃	—	2	1	no	—
149	#41×C₂₃	—	2	1	no	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	—	2	1	no	—
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	1	no	—
155	C₂×Q₈×C₂₃	—	2	1	no	—
156	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	1	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	1	no	—
169	C₂×D₄×C₂₃	—	2	1	no	—
170	C₂×D₄×C₂₃	—	2	1	no	—
171	C₂×D₄×C₂₃	—	2	1	no	—
172	C₂×D₄×C₂₃	—	2	1	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	4	4	no	—
175	C₂×D₄×C₂₃	—	4	2	no	—
176	C₂×D₄×C₂₃	—	8	4	no	—
177	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	2	no	—
185	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	SD₁₆×C₂₃	—	4	4	no	—
187	SD₁₆×C₂₃	—	4	2	no	—
188	SD₁₆×C₂₃	—	4	2	no	—
189	SD₁₆×C₂₃	—	4	2	no	—
190	SD₁₆×C₂₃	—	4	2	no	—
191	D₈×C₂₃	—	2	4	no	—
192	D₈×C₂₃	—	2	4	no	—
193	D₈×C₂₃	—	4	4	no	—
194	D₈×C₂₃	—	4	2	no	—
195	D₈×C₂₃	—	4	2	no	—
196	M₁₆×C₂₃	—	2	1	no	—
197	M₁₆×C₂₃	—	2	1	no	—
198	M₁₆×C₂₃	—	2	1	no	—
199	M₁₆×C₂₃	—	2	1	no	—
200	M₁₆×C₂₃	—	2	1	no	—
201	M₁₆×C₂₃	—	2	1	no	—
202	M₁₆×C₂₃	—	2	1	no	—
203	M₁₆×C₂₃	—	2	1	no	—
204	M₁₆×C₂₃	—	4	2	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	4	2	no	—
212	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₂₃	#41	1	2	yes	—
217	C₄⋊C₄×C₂₃	—	4	2	no	—
218	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
220	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
221	C₂²⋊C₄×C₂₃	—	2	1	no	—
222	C₂²⋊C₄×C₂₃	—	2	1	no	—
223	C₂²⋊C₄×C₂₃	—	2	1	no	—
224	C₂²⋊C₄×C₂₃	—	4	2	no	—
225	C₂²⋊C₄×C₂₃	—	4	2	no	—
226	C₂²⋊C₄×C₂₃	—	4	2	no	—
227	C₂²⋊C₄×C₂₃	—	4	4	no	—
228	C₂²⋊C₄×C₂₃	—	4	2	no	—
229	C₄²×C₂₃	—	2	1	no	—
230	C₄²×C₂₃	—	2	1	no	—
231	C₄²×C₂₃	—	2	1	no	—
232	C₄²×C₂₃	—	2	1	no	—
233	C₄²×C₂₃	#41	1	2	yes	—
234	#25439	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₂₃	—	2	1	no	—
236	C₂³×C₂₃	—	2	2	no	—
237	C₂³×C₂₃	—	2	2	no	—
238	C₂³×C₂₃	—	4	1	no	—
239	C₂³×C₂₃	—	4	1	no	—
240	C₂³×C₂₃	—	4	1	no	—
241	C₂³×C₂₃	—	4	1	no	—
242	C₂³×C₂₃	—	4	1	no	—
243	C₂³×C₂₃	—	4	1	no	—
244	C₂³×C₂₃	—	4	1	no	—
245	C₂³×C₂₃	—	8	2	no	—
246	C₂³×C₂₃	—	8	2	no	—
247	C₂³×C₂₃	—	8	2	no	—
248	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
249	Q₈×C₂₃	—	2	1	no	—
250	Q₈×C₂₃	—	2	1	no	—
251	Q₈×C₂₃	—	4	1	no	—
252	Q₈×C₂₃	—	4	1	no	—
253	Q₈×C₂₃	—	4	1	no	—
254	Q₈×C₂₃	—	4	1	no	—
255	D₄×C₂₃	—	2	2	no	—
256	D₄×C₂₃	—	2	2	no	—
257	D₄×C₂₃	—	2	1	no	—
258	D₄×C₂₃	—	2	1	no	—
259	D₄×C₂₃	—	2	2	no	—
260	D₄×C₂₃	—	2	2	no	—
261	D₄×C₂₃	—	4	1	no	—
262	D₄×C₂₃	—	4	1	no	—
263	D₄×C₂₃	—	4	1	no	—
264	D₄×C₂₃	—	4	1	no	—
265	D₄×C₂₃	—	4	1	no	—
266	D₄×C₂₃	—	4	1	no	—
267	D₄×C₂₃	—	4	1	no	—
268	D₄×C₂₃	—	4	1	no	—
269	D₄×C₂₃	—	4	1	no	—
270	D₄×C₂₃	—	4	1	no	—
271	D₄×C₂₃	—	8	8	no	—
272	D₄×C₂₃	—	16	2	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	1	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	4	2	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	16	2	no	—
285	C₂×C₄×C₂₃	—	16	2	no	—
286	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₈×C₂₃	—	2	2	no	—
293	C₈×C₂₃	—	4	1	no	—
294	C₈×C₂₃	—	4	1	no	—
295	C₈×C₂₃	—	4	1	no	—
296	C₈×C₂₃	—	4	1	no	—
297	C₈×C₂₃	#121	1	2	yes	—
298	C₈×C₂₃	#121	1	2	yes	—
299	C₂×#496	C₂×C₂₃	1	1	yes	characteristic, complemented
300	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
301	#3057	C₂×C₂₃	1	1	yes	characteristic, complemented
302	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
303	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
304	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
305	#2046	C₂×C₂₃	1	1	yes	characteristic, complemented
306	#2045	C₂×C₂₃	1	1	yes	characteristic, complemented
307	#2003	C₂×C₂₃	1	1	yes	characteristic, complemented
308	#2002	C₂×C₂₃	1	1	yes	characteristic, complemented
309	#1977	C₂×C₂₃	1	1	yes	characteristic, complemented
310	#1946	C₂×C₂₃	1	1	yes	characteristic, complemented
311	#1887	C₂×C₂₃	1	1	yes	characteristic, complemented
312	#1885	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#1765	C₂×C₂₃	1	1	yes	characteristic, complemented
314	C₂²×C₂₃	—	2	2	no	—
315	C₂²×C₂₃	—	4	1	no	—
316	C₂²×C₂₃	—	4	2	no	—
317	C₂²×C₂₃	—	4	2	no	—
318	C₂²×C₂₃	—	4	2	no	—
319	C₂²×C₂₃	—	8	2	no	—
320	C₂²×C₂₃	—	8	2	no	—
321	C₂²×C₂₃	—	8	2	no	—
322	C₂²×C₂₃	—	8	2	no	—
323	C₂²×C₂₃	—	8	2	no	—
324	C₂²×C₂₃	—	8	1	no	—
325	C₂²×C₂₃	—	8	2	no	—
326	C₂²×C₂₃	—	16	1	no	—
327	C₂²×C₂₃	—	16	1	no	—
328	C₂²×C₂₃	—	16	1	no	—
329	C₂²×C₂₃	#540	1	1	yes	characteristic
330	C₂²×C₂₃	D₄²	1	1	yes	characteristic
331	C₂²×C₂₃	#546	1	1	yes	characteristic
332	C₄×C₂₃	—	4	2	no	—
333	C₄×C₂₃	—	4	1	no	—
334	C₄×C₂₃	—	4	2	no	—
335	C₄×C₂₃	—	4	2	no	—
336	C₄×C₂₃	—	4	2	no	—
337	C₄×C₂₃	—	8	1	no	—
338	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
339	C₄×C₂₃	#532	1	1	yes	characteristic
340	C₄×C₂₃	D₄²	1	1	yes	characteristic
341	C₄×C₂₃	#550	1	1	yes	characteristic
342	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
343	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
344	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
346	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
347	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
348	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
349	#536	C₂²×C₂₃	1	1	yes	characteristic
350	#535	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
352	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
353	#518	C₂²×C₂₃	1	1	yes	characteristic
354	#518	C₂²×C₂₃	1	1	yes	characteristic
355	#496	—	2	4	no	—
356	#472	—	2	4	no	—
357	#468	—	2	2	no	—
358	#465	—	2	2	no	—
359	#463	—	2	2	no	—
360	#463	—	2	2	no	—
361	#461	—	2	2	no	—
362	#459	—	2	2	no	—
363	#442	—	2	2	no	—
364	C₄×D₈	—	2	2	no	—
365	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
366	#427	C₂²×C₂₃	1	1	yes	characteristic
367	#424	C₂²×C₂₃	1	1	yes	characteristic
368	#424	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
370	#419	C₂²×C₂₃	1	1	yes	characteristic
371	#419	C₂²×C₂₃	1	1	yes	characteristic
372	#418	C₂²×C₂₃	1	1	yes	characteristic
373	#418	C₂²×C₂₃	1	1	yes	characteristic
374	#418	C₂²×C₂₃	1	1	yes	characteristic
375	#418	C₂²×C₂₃	1	1	yes	characteristic
376	#416	C₂²×C₂₃	1	1	yes	characteristic
377	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
381	#405	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
383	#341	C₂²×C₂₃	1	1	yes	characteristic
384	#339	C₂²×C₂₃	1	1	yes	characteristic
385	#339	C₂²×C₂₃	1	1	yes	characteristic
386	#339	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₂₃	—	2	1	no	—
388	C₂×C₂₃	—	2	1	no	—
389	C₂×C₂₃	—	8	1	no	—
390	C₂×C₂₃	—	8	2	no	—
391	C₂×C₂₃	—	8	2	no	—
392	C₂×C₂₃	—	16	1	no	—
393	C₂×C₂₃	#2428	1	1	yes	characteristic
394	C₂×C₂₃	#3288	1	2	yes	—
395	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
397	C₂²×D₄	—	4	1	no	—
398	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
401	AGL(1,ℤ/8)	—	2	2	no	—
402	AGL(1,ℤ/8)	—	2	2	no	—
403	AGL(1,ℤ/8)	—	4	1	no	—
404	AGL(1,ℤ/8)	—	4	1	no	—
405	C₂×SD₁₆	—	2	1	no	—
406	C₂×SD₁₆	—	2	1	no	—
407	C₂×SD₁₆	—	2	2	no	—
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×SD₁₆	—	2	1	no	—
410	C₂×SD₁₆	—	2	1	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	4	1	no	—
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	2	1	no	—
416	C₂×D₈	—	2	1	no	—
417	C₂×D₈	—	2	1	no	—
418	C₂×D₈	—	2	1	no	—
419	C₂×D₈	—	2	2	no	—
420	C₂×D₈	—	2	2	no	—
421	C₂×D₈	—	4	1	no	—
422	C₂×D₈	D₄×C₂₃	1	4	yes	complemented
423	#131	—	2	2	no	—
424	#131	—	2	2	no	—
425	C₂×M₁₆	—	2	1	no	—
426	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
427	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
428	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
429	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
430	C₂²×C₈	—	2	1	no	—
431	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
433	C₄⋊Q₈	—	2	1	no	—
434	#127	—	2	2	no	—
435	#127	—	2	1	no	—
436	#127	—	2	2	no	—
437	#124	—	2	1	no	—
438	#124	—	2	2	no	—
439	#124	—	2	1	no	—
440	#124	—	2	2	no	—
441	#123	—	4	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	#121	—	2	2	no	—
444	#120	—	4	1	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	#117	C₂³×C₂₃	1	1	yes	characteristic
450	#117	C₂³×C₂₃	1	1	yes	characteristic
451	#117	C₂³×C₂₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	—	4	1	no	—
453	C₂×C₂²⋊C₄	—	4	1	no	—
454	C₂×C₂²⋊C₄	—	4	1	no	—
455	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
456	#108	—	2	2	no	—
457	#107	D₄×C₂₃	1	2	yes	complemented
458	#106	D₄×C₂₃	1	2	yes	complemented
459	C₄⋊C₈	—	2	2	no	—
460	C₄⋊C₈	—	2	2	no	—
461	#104	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	D₄×C₂₃	1	2	yes	complemented
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	D₄×C₂₃	1	2	yes	complemented
470	#101	—	4	1	no	—
471	#100	—	2	2	no	—
472	#100	—	2	2	no	—
473	#100	—	4	1	no	—
474	#97	—	2	2	no	—
475	#97	—	2	1	no	—
476	C₄×C₈	—	2	1	no	—
477	C₂₃	#25439	1	1	yes	characteristic, direct product factor, Sylow
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	1	no	—
480	C₂⁴	—	2	1	no	—
481	#41	—	2	1	no	—
482	#41	—	2	1	no	—
483	#41	—	2	1	no	—
484	#41	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	8	4	no	—
512	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
513	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
514	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
521	SD₁₆	—	4	4	no	—
522	SD₁₆	—	4	2	no	—
523	SD₁₆	—	4	2	no	—
524	SD₁₆	—	4	2	no	—
525	SD₁₆	—	4	2	no	—
526	D₈	—	2	4	no	—
527	D₈	—	2	4	no	—
528	D₈	—	4	4	no	—
529	D₈	—	4	2	no	—
530	D₈	—	4	2	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	4	2	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	4	2	no	—
547	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
548	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
549	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
550	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
551	C₂×C₈	#41×C₂₃	1	2	yes	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
554	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
555	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	#41×C₂₃	1	2	yes	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	8	2	no	—
580	C₂³	—	8	2	no	—
581	C₂³	—	8	2	no	—
582	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
583	Q₈	—	2	1	no	—
584	Q₈	—	2	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	1	no	—
592	D₄	—	2	1	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	8	8	no	—
606	D₄	—	16	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	16	2	no	—
619	C₂×C₄	—	16	2	no	—
620	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
626	C₈	—	2	2	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	C₂₃×#121	1	2	yes	—
632	C₈	C₂₃×#121	1	2	yes	—
633	C₂²	—	2	2	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	8	2	no	—
639	C₂²	—	8	2	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	2	no	—
642	C₂²	—	8	2	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	2	no	—
645	C₂²	—	16	1	no	—
646	C₂²	—	16	1	no	—
647	C₂²	—	16	1	no	—
648	C₂²	C₂₃×#540	1	1	yes	characteristic
649	C₂²	D₄²×C₂₃	1	1	yes	characteristic
650	C₂²	C₂₃×#546	1	1	yes	characteristic
651	C₄	—	4	2	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	8	1	no	—
657	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
658	C₄	C₂₃×#532	1	1	yes	characteristic
659	C₄	D₄²×C₂₃	1	1	yes	characteristic
660	C₄	C₂₃×#550	1	1	yes	characteristic
661	C₂	—	2	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	8	1	no	—
664	C₂	—	8	2	no	—
665	C₂	—	8	2	no	—
666	C₂	—	16	1	no	—
667	C₂	C₂₃×#2428	1	1	yes	characteristic
668	C₂	C₂₃×#3288	1	2	yes	—

	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. C₂×C₂₃×#496	C₂	semidirect
2. C₂×C₂₃×#472	C₂	semidirect
3. C₂₃×#3057	C₂	semidirect
4. C₂₃×#3042	C₂	semidirect
5. C₂₃×#3041	C₂	semidirect
6. C₂₃×#2948	C₂	semidirect
7. C₂₃×#2046	C₂	semidirect
8. C₂₃×#2045	C₂	semidirect
9. C₂₃×#2003	C₂	semidirect
10. C₂₃×#2002	C₂	semidirect
11. C₂₃×#1977	C₂	semidirect
12. C₂₃×#1946	C₂	semidirect
13. C₂₃×#1887	C₂	semidirect
14. C₂₃×#1885	C₂	semidirect
15. C₂₃×#1765	C₂	semidirect
88. C₂×D₈×C₂₃	D₄	semidirect
123. C₂₃×#107	D₄	semidirect
124. C₂₃×#106	D₄	semidirect
130. C₂₃×#103	D₄	semidirect
135. C₂₃×#102	D₄	semidirect
234. #25439	C₂₃	direct (N × H)
299. C₂×#496	C₂×C₂₃	semidirect
300. C₂×#472	C₂×C₂₃	semidirect
301. #3057	C₂×C₂₃	semidirect
302. #3042	C₂×C₂₃	semidirect
303. #3041	C₂×C₂₃	semidirect
304. #2948	C₂×C₂₃	semidirect
305. #2046	C₂×C₂₃	semidirect
306. #2045	C₂×C₂₃	semidirect
307. #2003	C₂×C₂₃	semidirect
308. #2002	C₂×C₂₃	semidirect
309. #1977	C₂×C₂₃	semidirect
310. #1946	C₂×C₂₃	semidirect
311. #1887	C₂×C₂₃	semidirect
312. #1885	C₂×C₂₃	semidirect
313. #1765	C₂×C₂₃	semidirect
422. C₂×D₈	D₄×C₂₃	semidirect
457. #107	D₄×C₂₃	semidirect
458. #106	D₄×C₂₃	semidirect
464. #103	D₄×C₂₃	semidirect
469. #102	D₄×C₂₃	semidirect
477. C₂₃	#25439	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#496	2
C₂×C₂₃×#472	2
C₂₃×#3057	2
C₂₃×#3042	2
C₂₃×#3041	2
C₂₃×#2948	2
C₂₃×#2046	2
C₂₃×#2045	2
C₂₃×#2003	2
C₂₃×#2002	2
C₂₃×#1977	2
C₂₃×#1946	2
C₂₃×#1887	2
C₂₃×#1885	2
C₂₃×#1765	2
#25439	23

Subgroups — C23×#25439 #19173065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25439 #19173065