Subgroups — C₂₃×#11137 #19158763

Order 5888.

854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#413	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂₃×#430	—	2	2	no	—
16	C₂₃×#430	—	2	2	no	—
17	C₂×C₂₃×#108	—	2	2	no	—
18	C₂₃×#413	—	2	2	no	—
19	C₂₃×#413	—	2	2	no	—
20	C₂×C₂₃×#101	C₄	1	2	yes	—
21	C₂×C₂₃×#100	C₄	1	2	yes	—
22	C₂₃×#408	—	2	2	no	—
23	C₂₃×#408	—	2	2	no	—
24	C₂₃×#408	—	2	2	no	—
25	C₂₃×#408	—	2	2	no	—
26	C₂₃×#407	—	2	2	no	—
27	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
28	C₂₃×#341	—	2	2	no	—
29	C₂₃×#341	—	2	2	no	—
30	C₂₃×#341	—	2	2	no	—
31	C₂×#41×C₂₃	—	2	1	no	—
32	C₂×#41×C₂₃	—	2	1	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	—	2	1	no	—
40	C₂×#41×C₂₃	—	2	1	no	—
41	C₂×#41×C₂₃	—	2	1	no	—
42	C₂×#41×C₂₃	—	2	1	no	—
43	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₂₃	Q₈	1	2	yes	—
46	C₂³×C₄×C₂₃	D₄	1	2	yes	—
47	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₂₃	—	2	1	no	—
49	C₂×M₁₆×C₂₃	—	2	1	no	—
50	C₂×M₁₆×C₂₃	—	2	1	no	—
51	C₂×M₁₆×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	1	no	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	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	1	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	C₂×C₄	1	2	yes	—
72	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
73	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
74	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
75	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
76	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
77	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
78	C₂²×C₈×C₂₃	—	2	1	no	—
79	C₂²×C₈×C₂₃	—	2	1	no	—
80	C₂²×C₈×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂²×C₈×C₂₃	—	2	1	no	—
83	C₂²×C₈×C₂₃	—	2	1	no	—
84	C₂²×C₈×C₂₃	—	2	1	no	—
85	C₂²×C₈×C₂₃	—	2	1	no	—
86	C₂²×C₈×C₂₃	—	2	1	no	—
87	C₂²×C₈×C₂₃	—	2	1	no	—
88	C₂²×C₈×C₂₃	—	2	1	no	—
89	C₂²×C₈×C₂₃	D₄	1	2	yes	—
90	C₂₃×#108	—	2	8	no	—
91	C₂₃×#101	—	2	4	no	—
92	C₂₃×#100	—	2	4	no	—
93	C₂₃×C₂²⋊C₈	—	2	8	no	—
94	C₂₃×C₂²⋊C₈	—	2	8	no	—
95	C₂⁴×C₂₃	C₄⋊C₄	1	2	yes	—
96	C₂⁴×C₂₃	C₂×Q₈	1	1	yes	characteristic
97	#41×C₂₃	—	4	1	no	—
98	#41×C₂₃	—	4	1	no	—
99	#41×C₂₃	—	4	1	no	—
100	#41×C₂₃	—	4	1	no	—
101	#41×C₂₃	—	4	1	no	—
102	#41×C₂₃	—	4	1	no	—
103	#41×C₂₃	—	4	1	no	—
104	#41×C₂₃	—	4	1	no	—
105	#41×C₂₃	—	4	1	no	—
106	#41×C₂₃	—	4	1	no	—
107	#41×C₂₃	—	4	1	no	—
108	#41×C₂₃	—	4	1	no	—
109	#41×C₂₃	—	4	1	no	—
110	#41×C₂₃	—	4	1	no	—
111	#41×C₂₃	—	4	1	no	—
112	#41×C₂₃	—	4	1	no	—
113	C₂×Q₈×C₂₃	—	2	1	no	—
114	C₂×Q₈×C₂₃	—	2	1	no	—
115	C₂×Q₈×C₂₃	—	2	1	no	—
116	C₂×Q₈×C₂₃	—	2	1	no	—
117	C₂×Q₈×C₂₃	—	2	1	no	—
118	C₂×Q₈×C₂₃	—	2	1	no	—
119	C₂×D₄×C₂₃	—	2	2	no	—
120	C₂×D₄×C₂₃	—	2	2	no	—
121	C₂×D₄×C₂₃	—	2	2	no	—
122	C₂×D₄×C₂₃	—	2	2	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	2	no	—
125	C₂×D₄×C₂₃	—	2	1	no	—
126	C₂×D₄×C₂₃	—	2	1	no	—
127	C₂×D₄×C₂₃	—	2	1	no	—
128	C₂×D₄×C₂₃	—	2	1	no	—
129	C₂×D₄×C₂₃	—	2	1	no	—
130	C₂×D₄×C₂₃	—	2	1	no	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	2	2	no	—
133	C₂²×C₄×C₂₃	—	2	2	no	—
134	C₂²×C₄×C₂₃	—	2	2	no	—
135	C₂²×C₄×C₂₃	—	2	2	no	—
136	C₂²×C₄×C₂₃	—	2	2	no	—
137	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
138	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
147	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
148	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
149	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
150	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
152	M₁₆×C₂₃	—	2	2	no	—
153	M₁₆×C₂₃	—	2	2	no	—
154	M₁₆×C₂₃	—	2	2	no	—
155	M₁₆×C₂₃	—	2	2	no	—
156	M₁₆×C₂₃	—	2	2	no	—
157	M₁₆×C₂₃	—	2	2	no	—
158	M₁₆×C₂₃	—	2	2	no	—
159	M₁₆×C₂₃	—	2	2	no	—
160	M₁₆×C₂₃	—	2	2	no	—
161	M₁₆×C₂₃	—	2	2	no	—
162	M₁₆×C₂₃	—	2	2	no	—
163	M₁₆×C₂₃	—	4	1	no	—
164	M₁₆×C₂₃	—	4	1	no	—
165	M₁₆×C₂₃	—	4	1	no	—
166	M₁₆×C₂₃	—	4	1	no	—
167	M₁₆×C₂₃	—	4	1	no	—
168	M₁₆×C₂₃	—	4	1	no	—
169	M₁₆×C₂₃	—	4	1	no	—
170	M₁₆×C₂₃	—	4	1	no	—
171	M₁₆×C₂₃	C₂²⋊C₄	1	4	yes	—
172	C₂×C₈×C₂₃	—	2	2	no	—
173	C₂×C₈×C₂₃	—	2	2	no	—
174	C₂×C₈×C₂₃	—	2	2	no	—
175	C₂×C₈×C₂₃	—	2	2	no	—
176	C₂×C₈×C₂₃	—	2	2	no	—
177	C₂×C₈×C₂₃	—	2	2	no	—
178	C₂×C₈×C₂₃	—	2	2	no	—
179	C₂×C₈×C₂₃	—	2	2	no	—
180	C₂×C₈×C₂₃	—	2	2	no	—
181	C₂×C₈×C₂₃	—	2	2	no	—
182	C₂×C₈×C₂₃	—	4	1	no	—
183	C₂×C₈×C₂₃	—	4	1	no	—
184	C₂×C₈×C₂₃	—	4	1	no	—
185	C₂×C₈×C₂₃	—	4	1	no	—
186	C₂×C₈×C₂₃	—	4	1	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	—	4	1	no	—
192	C₂×C₈×C₂₃	—	4	1	no	—
193	C₂×C₈×C₂₃	—	4	1	no	—
194	#11137	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₂₃	—	2	2	no	—
196	C₂³×C₂₃	—	2	2	no	—
197	C₂³×C₂₃	—	2	2	no	—
198	C₂³×C₂₃	—	4	2	no	—
199	C₂³×C₂₃	—	4	4	no	—
200	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
207	Q₈×C₂₃	—	4	1	no	—
208	Q₈×C₂₃	—	4	1	no	—
209	Q₈×C₂₃	—	4	1	no	—
210	Q₈×C₂₃	—	4	1	no	—
211	D₄×C₂₃	—	4	2	no	—
212	D₄×C₂₃	—	4	2	no	—
213	D₄×C₂₃	—	4	2	no	—
214	D₄×C₂₃	—	4	2	no	—
215	D₄×C₂₃	—	4	1	no	—
216	D₄×C₂₃	—	4	1	no	—
217	D₄×C₂₃	—	4	1	no	—
218	D₄×C₂₃	—	4	1	no	—
219	C₂×C₄×C₂₃	—	2	2	no	—
220	C₂×C₄×C₂₃	—	2	2	no	—
221	C₂×C₄×C₂₃	—	2	2	no	—
222	C₂×C₄×C₂₃	—	4	2	no	—
223	C₂×C₄×C₂₃	—	4	2	no	—
224	C₂×C₄×C₂₃	—	4	2	no	—
225	C₂×C₄×C₂₃	—	4	2	no	—
226	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
228	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
233	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
236	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
237	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
238	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
247	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
248	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
249	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
250	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
251	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
252	C₂×C₄×C₂₃	#126	1	1	yes	characteristic
253	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
254	C₈×C₂₃	—	2	4	no	—
255	C₈×C₂₃	—	4	2	no	—
256	C₈×C₂₃	—	4	2	no	—
257	C₈×C₂₃	—	4	2	no	—
258	C₈×C₂₃	—	4	2	no	—
259	C₈×C₂₃	—	4	2	no	—
260	C₂×#430	C₂×C₂₃	1	1	yes	characteristic, complemented
261	C₂×#413	C₂×C₂₃	1	1	yes	characteristic
262	#2879	C₂×C₂₃	1	1	yes	characteristic
263	C₂×#408	C₂×C₂₃	1	1	yes	characteristic
264	#1738	C₂×C₂₃	1	1	yes	characteristic, complemented
265	C₂×#341	C₂×C₂₃	1	1	yes	characteristic, complemented
266	C₂×#341	C₂×C₂₃	1	1	yes	characteristic, complemented
267	C₂²×C₂₃	—	2	2	no	—
268	C₂²×C₂₃	—	2	2	no	—
269	C₂²×C₂₃	—	2	2	no	—
270	C₂²×C₂₃	—	4	1	no	—
271	C₂²×C₂₃	—	4	1	no	—
272	C₂²×C₂₃	—	4	1	no	—
273	C₂²×C₂₃	—	4	1	no	—
274	C₂²×C₂₃	—	4	4	no	—
275	C₂²×C₂₃	—	4	4	no	—
276	C₂²×C₂₃	—	4	2	no	—
277	C₂²×C₂₃	—	8	2	no	—
278	C₂²×C₂₃	#380	1	1	yes	characteristic
279	C₂²×C₂₃	#385	1	1	yes	characteristic
280	C₂²×C₂₃	#385	1	1	yes	characteristic
281	C₂²×C₂₃	#393	1	1	yes	characteristic
282	C₂²×C₂₃	#396	1	1	yes	characteristic
283	C₂²×C₂₃	#396	1	1	yes	characteristic
284	C₂²×C₂₃	#399	1	1	yes	characteristic
285	C₄×C₂₃	—	4	2	no	—
286	C₄×C₂₃	#386	1	1	yes	characteristic
287	C₄×C₂₃	#388	1	1	yes	characteristic
288	C₄×C₂₃	#388	1	1	yes	characteristic
289	C₄×C₂₃	#390	1	1	yes	characteristic
290	C₄×C₂₃	#392	1	1	yes	characteristic
291	C₄×C₂₃	#394	1	1	yes	characteristic
292	C₄×C₂₃	#394	1	1	yes	characteristic
293	C₄×C₂₃	#397	1	1	yes	characteristic
294	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
297	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
298	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
299	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
300	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
301	#430	—	2	2	no	—
302	#430	—	2	2	no	—
303	C₂×#108	—	2	2	no	—
304	#413	—	2	2	no	—
305	#413	—	2	2	no	—
306	C₂×#101	C₄×C₂₃	1	2	yes	—
307	C₂×#100	C₄×C₂₃	1	2	yes	—
308	#408	—	2	2	no	—
309	#408	—	2	2	no	—
310	#408	—	2	2	no	—
311	#408	—	2	2	no	—
312	#407	—	2	2	no	—
313	C₂×C₂²⋊C₈	—	2	2	no	—
314	#341	—	2	2	no	—
315	#341	—	2	2	no	—
316	#341	—	2	2	no	—
317	C₂×C₂₃	—	2	1	no	—
318	C₂×C₂₃	—	2	1	no	—
319	C₂×C₂₃	—	2	1	no	—
320	C₂×C₂₃	—	2	1	no	—
321	C₂×C₂₃	—	2	1	no	—
322	C₂×C₂₃	—	2	1	no	—
323	C₂×C₂₃	—	8	2	no	—
324	C₂×C₂₃	#1439	1	1	yes	characteristic
325	C₂×C₂₃	#1858	1	2	yes	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
339	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
340	C₂²×D₄	Q₈×C₂₃	1	2	yes	—
341	C₂³×C₄	D₄×C₂₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
367	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
368	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
369	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
370	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
371	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
372	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	D₄×C₂₃	1	2	yes	—
385	#108	—	2	8	no	—
386	#101	—	2	4	no	—
387	#100	—	2	4	no	—
388	C₂²⋊C₈	—	2	8	no	—
389	C₂²⋊C₈	—	2	8	no	—
390	C₂₃	#11137	1	1	yes	characteristic, direct product factor, Sylow
391	C₂⁴	C₄⋊C₄×C₂₃	1	2	yes	—
392	C₂⁴	C₂×Q₈×C₂₃	1	1	yes	characteristic
393	#41	—	4	1	no	—
394	#41	—	4	1	no	—
395	#41	—	4	1	no	—
396	#41	—	4	1	no	—
397	#41	—	4	1	no	—
398	#41	—	4	1	no	—
399	#41	—	4	1	no	—
400	#41	—	4	1	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	#41	—	4	1	no	—
405	#41	—	4	1	no	—
406	#41	—	4	1	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
434	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
442	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
443	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
444	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
445	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
446	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
447	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	4	1	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	C₂²⋊C₄×C₂₃	1	4	yes	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	—	4	1	no	—
489	C₂×C₈	—	4	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	4	no	—
495	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
496	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
497	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
498	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
499	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
500	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
501	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
522	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
523	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
524	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
525	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
526	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
527	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
528	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
529	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
530	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
531	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
532	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
533	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
534	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
535	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
536	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
537	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
538	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
539	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
540	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
541	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
542	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
543	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
544	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
545	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
546	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
547	C₂×C₄	C₂₃×#126	1	1	yes	characteristic
548	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₈	—	4	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	8	2	no	—
566	C₂²	C₂₃×#380	1	1	yes	characteristic
567	C₂²	C₂₃×#385	1	1	yes	characteristic
568	C₂²	C₂₃×#385	1	1	yes	characteristic
569	C₂²	C₂₃×#393	1	1	yes	characteristic
570	C₂²	C₂₃×#396	1	1	yes	characteristic
571	C₂²	C₂₃×#396	1	1	yes	characteristic
572	C₂²	C₂₃×#399	1	1	yes	characteristic
573	C₄	—	4	2	no	—
574	C₄	C₂₃×#386	1	1	yes	characteristic
575	C₄	C₂₃×#388	1	1	yes	characteristic
576	C₄	C₂₃×#388	1	1	yes	characteristic
577	C₄	C₂₃×#390	1	1	yes	characteristic
578	C₄	C₂₃×#392	1	1	yes	characteristic
579	C₄	C₂₃×#394	1	1	yes	characteristic
580	C₄	C₂₃×#394	1	1	yes	characteristic
581	C₄	C₂₃×#397	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	8	2	no	—
589	C₂	C₂₃×#1439	1	1	yes	characteristic
590	C₂	C₂₃×#1858	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	#385
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#430	C₂	semidirect
5. C₂₃×#1738	C₂	semidirect
6. C₂×C₂₃×#341	C₂	semidirect
7. C₂×C₂₃×#341	C₂	semidirect
194. #11137	C₂₃	direct (N × H)
260. C₂×#430	C₂×C₂₃	semidirect
264. #1738	C₂×C₂₃	semidirect
265. C₂×#341	C₂×C₂₃	semidirect
266. C₂×#341	C₂×C₂₃	semidirect
390. C₂₃	#11137	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×#430	2
C₂×C₂₃×#413	2
C₂₃×#2879	2
C₂×C₂₃×#408	2
C₂₃×#1738	2
C₂×C₂₃×#341	2
#11137	23

Subgroups — C23×#11137 #19158763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11137 #19158763