Subgroups — C₂₃×#10778 #19158404

Order 5888.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#421	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#568	—	2	2	no	—
10	C₂₃×#568	—	2	2	no	—
11	C₂₃×#568	—	2	2	no	—
12	C₂₃×#568	—	2	2	no	—
13	C₂×C₂₃×#131	—	2	2	no	—
14	C₂×C₂₃×#131	C₄	1	4	yes	complemented
15	C₂²×M₁₆×C₂₃	—	2	2	no	—
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
22	C₂₃×#421	—	2	2	no	—
23	C₂₃×#421	C₄	1	4	yes	complemented
24	C₂×C₂₃×#104	—	2	2	no	—
25	C₂₃×#419	C₄	1	2	yes	complemented
26	C₂₃×#418	C₄	1	2	yes	complemented
27	C₂₃×#417	—	2	2	no	—
28	C₂₃×#416	—	2	2	no	—
29	C₂₃×#344	—	2	2	no	—
30	C₂₃×#344	—	2	2	no	—
31	C₂₃×#341	—	2	2	no	—
32	C₂₃×#339	—	2	2	no	—
33	C₂×#41×C₂₃	—	2	1	no	—
34	C₂×#41×C₂₃	—	2	1	no	—
35	C₂×#41×C₂₃	—	2	1	no	—
36	C₂×#41×C₂₃	—	2	1	no	—
37	C₂×#41×C₂₃	—	2	1	no	—
38	C₂×#41×C₂₃	—	2	1	no	—
39	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
40	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
41	C₂×#41×C₂₃	D₄	1	2	yes	—
42	C₂×#41×C₂₃	D₄	1	2	yes	—
43	C₂×#41×C₂₃	D₄	1	2	yes	—
44	C₂×#41×C₂₃	Q₈	1	2	yes	—
45	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₂₃	—	2	1	no	—
47	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×#131	—	2	8	no	—
51	C₂₃×#131	—	2	8	no	—
52	C₂₃×#131	—	2	8	no	—
53	C₂₃×#131	—	2	8	no	—
54	C₂×M₁₆×C₂₃	—	2	8	no	—
55	C₂×M₁₆×C₂₃	—	2	8	no	—
56	C₂×M₁₆×C₂₃	—	2	1	no	—
57	C₂×M₁₆×C₂₃	—	2	1	no	—
58	C₂×M₁₆×C₂₃	—	2	1	no	—
59	C₂×M₁₆×C₂₃	—	2	1	no	—
60	C₂×M₁₆×C₂₃	—	2	1	no	—
61	C₂×M₁₆×C₂₃	—	2	1	no	—
62	C₂×M₁₆×C₂₃	—	2	1	no	—
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	—	2	1	no	—
65	C₂×M₁₆×C₂₃	—	2	4	no	—
66	C₂×M₁₆×C₂₃	—	2	1	no	—
67	C₂×M₁₆×C₂₃	—	2	1	no	—
68	C₂×M₁₆×C₂₃	—	2	1	no	—
69	C₂×M₁₆×C₂₃	—	2	1	no	—
70	C₂×M₁₆×C₂₃	—	2	1	no	—
71	C₂×M₁₆×C₂₃	—	2	1	no	—
72	C₂×M₁₆×C₂₃	—	2	1	no	—
73	C₂×M₁₆×C₂₃	—	2	1	no	—
74	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
75	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
76	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
78	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
79	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
80	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂²×C₈×C₂₃	—	2	4	no	—
83	C₂²×C₈×C₂₃	—	2	1	no	—
84	C₂²×C₈×C₂₃	—	2	1	no	—
85	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
86	C₂₃×#117	—	2	1	no	—
87	C₂₃×#117	—	2	1	no	—
88	C₂₃×#117	—	2	1	no	—
89	C₂₃×#117	—	2	1	no	—
90	C₂₃×#117	—	2	1	no	—
91	C₂₃×#117	—	2	1	no	—
92	C₂₃×#117	C₂×C₄	1	2	yes	—
93	C₂₃×#117	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
98	C₂×C₄²×C₂₃	—	2	1	no	—
99	C₂×C₄²×C₂₃	—	2	1	no	—
100	C₂₃×#104	—	2	8	no	—
101	C₂₃×#103	—	2	4	no	—
102	C₂₃×#102	—	2	4	no	—
103	C₂⁴×C₂₃	—	2	1	no	—
104	C₂⁴×C₂₃	#41	1	1	yes	characteristic
105	#41×C₂₃	—	2	2	no	—
106	#41×C₂₃	—	2	2	no	—
107	#41×C₂₃	—	2	2	no	—
108	#41×C₂₃	—	2	2	no	—
109	#41×C₂₃	—	2	2	no	—
110	#41×C₂₃	—	2	2	no	—
111	#41×C₂₃	—	2	2	no	—
112	#41×C₂₃	—	2	2	no	—
113	#41×C₂₃	—	2	2	no	—
114	#41×C₂₃	—	2	2	no	—
115	#41×C₂₃	—	2	2	no	—
116	#41×C₂₃	—	2	2	no	—
117	#41×C₂₃	C₂²⋊C₄	1	4	yes	—
118	#41×C₂₃	C₂²⋊C₄	1	4	yes	—
119	#41×C₂₃	C₄⋊C₄	1	4	yes	—
120	#41×C₂₃	C₄⋊C₄	1	4	yes	—
121	C₂×Q₈×C₂₃	—	2	1	no	—
122	C₂×Q₈×C₂₃	—	2	1	no	—
123	C₂×Q₈×C₂₃	—	2	1	no	—
124	C₂×Q₈×C₂₃	C₄²	1	2	yes	—
125	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
126	C₂×Q₈×C₂₃	C₄⋊C₄	1	2	yes	—
127	C₂×D₄×C₂₃	—	2	2	no	—
128	C₂×D₄×C₂₃	—	2	2	no	—
129	C₂×D₄×C₂₃	—	2	2	no	—
130	C₂×D₄×C₂₃	—	2	2	no	—
131	C₂×D₄×C₂₃	—	2	2	no	—
132	C₂×D₄×C₂₃	—	2	2	no	—
133	C₂×D₄×C₂₃	—	2	1	no	—
134	C₂×D₄×C₂₃	—	2	1	no	—
135	C₂×D₄×C₂₃	—	2	1	no	—
136	C₂×D₄×C₂₃	C₄²	1	2	yes	—
137	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
138	C₂×D₄×C₂₃	C₄⋊C₄	1	2	yes	—
139	C₂²×C₄×C₂₃	—	2	1	no	—
140	C₂²×C₄×C₂₃	—	2	2	no	—
141	C₂²×C₄×C₂₃	—	2	2	no	—
142	C₂²×C₄×C₂₃	—	2	2	no	—
143	C₂²×C₄×C₂₃	—	2	2	no	—
144	C₂²×C₄×C₂₃	—	2	2	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	4	1	no	—
147	C₂²×C₄×C₂₃	—	4	1	no	—
148	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
159	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
161	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
162	M₁₆×C₂₃	—	2	16	no	—
163	M₁₆×C₂₃	—	2	2	no	—
164	M₁₆×C₂₃	—	2	2	no	—
165	M₁₆×C₂₃	—	2	2	no	—
166	M₁₆×C₂₃	—	2	2	no	—
167	M₁₆×C₂₃	—	2	2	no	—
168	M₁₆×C₂₃	—	2	2	no	—
169	M₁₆×C₂₃	—	2	2	no	—
170	M₁₆×C₂₃	—	2	2	no	—
171	M₁₆×C₂₃	—	2	2	no	—
172	M₁₆×C₂₃	—	2	2	no	—
173	M₁₆×C₂₃	—	2	2	no	—
174	M₁₆×C₂₃	—	4	1	no	—
175	M₁₆×C₂₃	—	4	1	no	—
176	M₁₆×C₂₃	—	4	1	no	—
177	M₁₆×C₂₃	—	4	1	no	—
178	M₁₆×C₂₃	C₂²⋊C₄	1	4	yes	—
179	C₂×C₈×C₂₃	—	2	16	no	—
180	C₂×C₈×C₂₃	—	2	2	no	—
181	C₂×C₈×C₂₃	—	2	2	no	—
182	C₂×C₈×C₂₃	—	2	2	no	—
183	C₂×C₈×C₂₃	—	2	2	no	—
184	C₂×C₈×C₂₃	—	2	2	no	—
185	C₂×C₈×C₂₃	—	2	2	no	—
186	C₂×C₈×C₂₃	—	2	2	no	—
187	C₂×C₈×C₂₃	—	4	1	no	—
188	C₂×C₈×C₂₃	—	4	1	no	—
189	C₂×C₈×C₂₃	—	4	1	no	—
190	C₂×C₈×C₂₃	—	4	1	no	—
191	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
192	C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₄⋊C₄×C₂₃	—	2	2	no	—
194	C₄⋊C₄×C₂₃	—	4	1	no	—
195	C₄⋊C₄×C₂₃	—	4	1	no	—
196	C₂²⋊C₄×C₂₃	—	2	2	no	—
197	C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂²⋊C₄×C₂₃	—	4	1	no	—
199	C₂²⋊C₄×C₂₃	—	4	1	no	—
200	C₄²×C₂₃	—	2	2	no	—
201	C₄²×C₂₃	—	2	2	no	—
202	C₄²×C₂₃	—	4	1	no	—
203	C₄²×C₂₃	—	4	1	no	—
204	#10778	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₂₃	—	2	2	no	—
206	C₂³×C₂₃	—	2	2	no	—
207	C₂³×C₂₃	—	2	2	no	—
208	C₂³×C₂₃	—	8	1	no	—
209	C₂³×C₂₃	—	8	2	no	—
210	C₂³×C₂₃	#117	1	1	yes	characteristic
211	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₂₃	#121	1	1	yes	characteristic
214	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂³×C₂₃	#123	1	1	yes	characteristic
216	C₂³×C₂₃	#123	1	1	yes	characteristic
217	Q₈×C₂₃	—	2	2	no	—
218	Q₈×C₂₃	—	2	2	no	—
219	Q₈×C₂₃	—	2	2	no	—
220	Q₈×C₂₃	#95	1	4	yes	—
221	D₄×C₂₃	—	2	4	no	—
222	D₄×C₂₃	—	2	4	no	—
223	D₄×C₂₃	—	2	4	no	—
224	D₄×C₂₃	—	2	4	no	—
225	D₄×C₂₃	—	2	2	no	—
226	D₄×C₂₃	—	2	2	no	—
227	D₄×C₂₃	—	2	2	no	—
228	D₄×C₂₃	#95	1	4	yes	—
229	C₂×C₄×C₂₃	—	2	2	no	—
230	C₂×C₄×C₂₃	—	2	2	no	—
231	C₂×C₄×C₂₃	—	2	2	no	—
232	C₂×C₄×C₂₃	—	2	4	no	—
233	C₂×C₄×C₂₃	—	2	4	no	—
234	C₂×C₄×C₂₃	—	2	4	no	—
235	C₂×C₄×C₂₃	—	2	4	no	—
236	C₂×C₄×C₂₃	—	4	2	no	—
237	C₂×C₄×C₂₃	—	4	2	no	—
238	C₂×C₄×C₂₃	—	8	2	no	—
239	C₂×C₄×C₂₃	—	8	2	no	—
240	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
250	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
257	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
258	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
260	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
262	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
263	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
267	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
268	C₈×C₂₃	—	2	4	no	—
269	C₈×C₂₃	—	2	4	no	—
270	C₈×C₂₃	—	4	2	no	—
271	C₈×C₂₃	—	4	2	no	—
272	C₂×#568	C₂×C₂₃	1	1	yes	characteristic
273	C₂×#421	C₂×C₂₃	1	1	yes	characteristic
274	#2896	C₂×C₂₃	1	1	yes	characteristic
275	C₂×#344	C₂×C₂₃	1	1	yes	characteristic, complemented
276	C₂×#344	C₂×C₂₃	1	1	yes	characteristic, complemented
277	#1738	C₂×C₂₃	1	1	yes	characteristic, complemented
278	#1733	C₂×C₂₃	1	1	yes	characteristic, complemented
279	C₂²×C₂₃	—	2	4	no	—
280	C₂²×C₂₃	—	4	1	no	—
281	C₂²×C₂₃	—	4	1	no	—
282	C₂²×C₂₃	—	4	1	no	—
283	C₂²×C₂₃	—	4	1	no	—
284	C₂²×C₂₃	—	4	1	no	—
285	C₂²×C₂₃	—	4	1	no	—
286	C₂²×C₂₃	—	4	1	no	—
287	C₂²×C₂₃	—	4	4	no	—
288	C₂²×C₂₃	—	8	2	no	—
289	C₂²×C₂₃	—	8	2	no	—
290	C₂²×C₂₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₂₃	#380	1	1	yes	characteristic
292	C₂²×C₂₃	#381	1	1	yes	characteristic
293	C₂²×C₂₃	#385	1	1	yes	characteristic
294	C₂²×C₂₃	#385	1	1	yes	characteristic
295	C₂²×C₂₃	#386	1	1	yes	characteristic
296	C₂²×C₂₃	#386	1	1	yes	characteristic
297	C₄×C₂₃	—	2	4	no	—
298	C₄×C₂₃	—	8	2	no	—
299	C₄×C₂₃	—	8	2	no	—
300	C₄×C₂₃	C₂×#95	1	1	yes	characteristic
301	C₄×C₂₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×C₂₃	#379	1	1	yes	characteristic
303	C₄×C₂₃	#380	1	1	yes	characteristic
304	C₄×C₂₃	#385	1	1	yes	characteristic
305	C₄×C₂₃	#385	1	1	yes	characteristic
306	C₄×C₂₃	#386	1	1	yes	characteristic
307	C₄×C₂₃	#386	1	1	yes	characteristic
308	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
309	#568	—	2	2	no	—
310	#568	—	2	2	no	—
311	#568	—	2	2	no	—
312	#568	—	2	2	no	—
313	C₂×#131	—	2	2	no	—
314	C₂×#131	C₄×C₂₃	1	4	yes	complemented
315	C₂²×M₁₆	—	2	2	no	—
316	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
320	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
321	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
322	#421	—	2	2	no	—
323	#421	C₄×C₂₃	1	4	yes	complemented
324	C₂×#104	—	2	2	no	—
325	#419	C₄×C₂₃	1	2	yes	complemented
326	#418	C₄×C₂₃	1	2	yes	complemented
327	#417	—	2	2	no	—
328	#416	—	2	2	no	—
329	#344	—	2	2	no	—
330	#344	—	2	2	no	—
331	#341	—	2	2	no	—
332	#339	—	2	2	no	—
333	C₂×C₂₃	—	2	1	no	—
334	C₂×C₂₃	—	2	1	no	—
335	C₂×C₂₃	—	2	1	no	—
336	C₂×C₂₃	—	2	1	no	—
337	C₂×C₂₃	—	2	1	no	—
338	C₂×C₂₃	—	2	1	no	—
339	C₂×C₂₃	—	2	1	no	—
340	C₂×C₂₃	—	4	4	no	—
341	C₂×C₂₃	C₂²⋊#95	1	1	yes	characteristic
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
349	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
350	C₂×#41	D₄×C₂₃	1	2	yes	—
351	C₂×#41	D₄×C₂₃	1	2	yes	—
352	C₂×#41	D₄×C₂₃	1	2	yes	—
353	C₂×#41	Q₈×C₂₃	1	2	yes	—
354	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
359	#131	—	2	8	no	—
360	#131	—	2	8	no	—
361	#131	—	2	8	no	—
362	#131	—	2	8	no	—
363	C₂×M₁₆	—	2	8	no	—
364	C₂×M₁₆	—	2	8	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	4	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
384	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
385	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
386	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
387	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
388	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
389	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	4	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	C₂×C₄×C₂₃	1	2	yes	—
402	#117	C₂×C₄×C₂₃	1	2	yes	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	#104	—	2	8	no	—
410	#103	—	2	4	no	—
411	#102	—	2	4	no	—
412	C₂₃	#10778	1	1	yes	characteristic, direct product factor, Sylow
413	C₂⁴	—	2	1	no	—
414	C₂⁴	#41×C₂₃	1	1	yes	characteristic
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	C₂²⋊C₄×C₂₃	1	4	yes	—
428	#41	C₂²⋊C₄×C₂₃	1	4	yes	—
429	#41	C₄⋊C₄×C₂₃	1	4	yes	—
430	#41	C₄⋊C₄×C₂₃	1	4	yes	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₄²×C₂₃	1	2	yes	—
435	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
436	C₂×Q₈	C₄⋊C₄×C₂₃	1	2	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₄²×C₂₃	1	2	yes	—
447	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
448	C₂×D₄	C₄⋊C₄×C₂₃	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
469	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
470	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
471	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
472	M₁₆	—	2	16	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	1	no	—
485	M₁₆	—	4	1	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	C₂²⋊C₄×C₂₃	1	4	yes	—
489	C₂×C₈	—	2	16	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₂×C₈	—	4	1	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	8	1	no	—
518	C₂³	—	8	2	no	—
519	C₂³	C₂₃×#117	1	1	yes	characteristic
520	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
521	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
522	C₂³	C₂₃×#121	1	1	yes	characteristic
523	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
524	C₂³	C₂₃×#123	1	1	yes	characteristic
525	C₂³	C₂₃×#123	1	1	yes	characteristic
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	C₂₃×#95	1	4	yes	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	2	2	no	—
537	D₄	C₂₃×#95	1	4	yes	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
550	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
551	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
552	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
554	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
555	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
556	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
558	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
559	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
560	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
561	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
562	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
563	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
564	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
565	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
566	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
567	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
568	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
569	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
570	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
571	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
572	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
573	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
574	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
575	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
576	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	2	4	no	—
579	C₈	—	4	2	no	—
580	C₈	—	4	2	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	8	2	no	—
591	C₂²	—	8	2	no	—
592	C₂²	C₄×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
593	C₂²	C₂₃×#380	1	1	yes	characteristic
594	C₂²	C₂₃×#381	1	1	yes	characteristic
595	C₂²	C₂₃×#385	1	1	yes	characteristic
596	C₂²	C₂₃×#385	1	1	yes	characteristic
597	C₂²	C₂₃×#386	1	1	yes	characteristic
598	C₂²	C₂₃×#386	1	1	yes	characteristic
599	C₄	—	2	4	no	—
600	C₄	—	8	2	no	—
601	C₄	—	8	2	no	—
602	C₄	C₂×C₂₃×#95	1	1	yes	characteristic
603	C₄	C₄×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
604	C₄	C₂₃×#379	1	1	yes	characteristic
605	C₄	C₂₃×#380	1	1	yes	characteristic
606	C₄	C₂₃×#385	1	1	yes	characteristic
607	C₄	C₂₃×#385	1	1	yes	characteristic
608	C₄	C₂₃×#386	1	1	yes	characteristic
609	C₄	C₂₃×#386	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	4	4	no	—
618	C₂	C₂₃×C₂²⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#379
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle	C₂×C₂₃	C₂²⋊#95
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₂₃×#344	C₂	semidirect
5. C₂×C₂₃×#344	C₂	semidirect
6. C₂₃×#1738	C₂	semidirect
7. C₂₃×#1733	C₂	semidirect
14. C₂×C₂₃×#131	C₄	semidirect
23. C₂₃×#421	C₄	semidirect
25. C₂₃×#419	C₄	semidirect
26. C₂₃×#418	C₄	semidirect
204. #10778	C₂₃	direct (N × H)
275. C₂×#344	C₂×C₂₃	semidirect
276. C₂×#344	C₂×C₂₃	semidirect
277. #1738	C₂×C₂₃	semidirect
278. #1733	C₂×C₂₃	semidirect
314. C₂×#131	C₄×C₂₃	semidirect
323. #421	C₄×C₂₃	semidirect
325. #419	C₄×C₂₃	semidirect
326. #418	C₄×C₂₃	semidirect
412. C₂₃	#10778	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×#568	2
C₂×C₂₃×#421	2
C₂₃×#2896	2
C₂×C₂₃×#344	2
C₂₃×#1738	2
C₂₃×#1733	2
#10778	23

Subgroups — C23×#10778 #19158404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10778 #19158404