Subgroups — C₄×C₂₃×#380 #19161397

Order 5888.

2782 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#380	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal
5	C₂₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1434	C₂	1	2	yes	maximal, complemented
7	C₂₃×C₂²⋊#95	C₂	1	2	yes	maximal
8	C₄×C₂₃×#95	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
14	C₂²×C₄²×C₂₃	—	2	8	no	—
15	C₂²×C₄²×C₂₃	C₄	1	8	yes	complemented
16	C₂²×C₄²×C₂₃	C₂²	1	4	yes	—
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#380	C₄	1	16	yes	direct product factor
22	C₄×C₄⋊C₄×C₂₃	—	2	8	no	—
23	C₄×C₂²⋊C₄×C₂₃	—	2	8	no	—
24	C₂×C₂₃×#95	C₂²	1	4	yes	—
25	C₂×C₂₃×#95	C₂²	1	4	yes	—
26	C₂×C₂₃×#95	C₂²	1	4	yes	—
27	C₂×C₂₃×#95	C₂²	1	4	yes	—
28	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	—	2	4	no	—
30	C₂³×C₄×C₂₃	—	2	4	no	—
31	C₂³×C₄×C₂₃	—	2	4	no	—
32	C₂³×C₄×C₂₃	—	2	4	no	—
33	C₂³×C₄×C₂₃	—	2	4	no	—
34	C₂³×C₄×C₂₃	—	2	4	no	—
35	C₂³×C₄×C₂₃	—	2	4	no	—
36	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	—
38	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₂₃	D₄	1	4	yes	—
41	C₂³×C₄×C₂₃	Q₈	1	4	yes	—
42	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
43	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
52	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
53	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	—
55	C₂×C₄²×C₂₃	—	2	4	no	—
56	C₂×C₄²×C₂₃	—	2	4	no	—
57	C₂×C₄²×C₂₃	—	2	4	no	—
58	C₂×C₄²×C₂₃	—	2	32	no	—
59	C₂×C₄²×C₂₃	—	2	8	no	—
60	C₂×C₄²×C₂₃	—	2	8	no	—
61	C₂×C₄²×C₂₃	—	2	8	no	—
62	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₂₃	D₄	1	8	yes	—
67	C₂₃×#95	—	2	8	no	—
68	C₂₃×#95	—	2	8	no	—
69	C₂₃×#95	—	2	8	no	—
70	C₂₃×#95	C₂×C₄	1	16	yes	complemented
71	C₂⁴×C₂₃	—	2	2	no	—
72	C₂⁴×C₂₃	—	2	2	no	—
73	C₂⁴×C₂₃	—	2	2	no	—
74	C₂⁴×C₂₃	—	2	2	no	—
75	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
76	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
78	C₂⁴×C₂₃	C₂×Q₈	1	2	yes	—
79	C₂⁴×C₂₃	#41	1	4	yes	—
80	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	—	2	32	no	—
82	C₂²×C₄×C₂₃	—	2	8	no	—
83	C₂²×C₄×C₂₃	—	2	2	no	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	2	no	—
86	C₂²×C₄×C₂₃	—	2	2	no	—
87	C₂²×C₄×C₂₃	—	2	2	no	—
88	C₂²×C₄×C₂₃	—	2	2	no	—
89	C₂²×C₄×C₂₃	—	2	2	no	—
90	C₂²×C₄×C₂₃	—	2	2	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	—	2	8	no	—
94	C₂²×C₄×C₂₃	—	2	8	no	—
95	C₂²×C₄×C₂₃	—	2	8	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	32	no	—
98	C₂²×C₄×C₂₃	—	2	16	no	—
99	C₂²×C₄×C₂₃	—	2	16	no	—
100	C₂²×C₄×C₂₃	—	2	8	no	—
101	C₂²×C₄×C₂₃	—	2	8	no	—
102	C₂²×C₄×C₂₃	—	2	8	no	—
103	C₂²×C₄×C₂₃	—	2	8	no	—
104	C₂²×C₄×C₂₃	—	2	8	no	—
105	C₂²×C₄×C₂₃	—	2	8	no	—
106	C₂²×C₄×C₂₃	C₄²	1	16	yes	complemented
107	C₂²×C₄×C₂₃	C₄⋊C₄	1	16	yes	complemented
108	C₂²×C₄×C₂₃	C₂²×C₄	1	16	yes	—
109	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₂₃	#41	1	4	yes	—
125	C₂²×C₄×C₂₃	#41	1	4	yes	—
126	C₂²×C₄×C₂₃	#41	1	4	yes	—
127	C₄⋊C₄×C₂₃	—	2	32	no	—
128	C₂²⋊C₄×C₂₃	—	2	32	no	—
129	C₄²×C₂₃	—	2	8	no	—
130	C₄²×C₂₃	—	2	8	no	—
131	C₄²×C₂₃	—	2	8	no	—
132	C₄²×C₂₃	—	4	16	no	—
133	C₄²×C₂₃	C₂²⋊C₄	1	16	yes	complemented
134	C₄×#380	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₂₃	—	2	2	no	—
136	C₂³×C₂₃	—	2	2	no	—
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	2	2	no	—
139	C₂³×C₂₃	—	2	8	no	—
140	C₂³×C₂₃	—	2	8	no	—
141	C₂³×C₂₃	—	2	4	no	—
142	C₂³×C₂₃	—	2	4	no	—
143	C₂³×C₂₃	—	2	8	no	—
144	C₂³×C₂₃	—	2	8	no	—
145	C₂³×C₂₃	—	2	4	no	—
146	C₂³×C₂₃	—	2	4	no	—
147	C₂³×C₂₃	C₂×C₄²	1	4	yes	—
148	C₂³×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
149	C₂³×C₂₃	#117	1	4	yes	—
150	C₂³×C₂₃	C₄×D₄	1	8	yes	—
151	C₂³×C₂₃	C₄×Q₈	1	8	yes	—
152	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
154	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
155	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
156	C₂³×C₂₃	C₂²×Q₈	1	1	yes	characteristic
157	C₂³×C₂₃	C₂×#41	1	2	yes	—
158	C₂³×C₂₃	C₂×#41	1	2	yes	—
159	C₂³×C₂₃	C₂×#41	1	2	yes	—
160	C₂³×C₂₃	C₂×#41	1	2	yes	—
161	C₂×C₄×C₂₃	—	2	32	no	—
162	C₂×C₄×C₂₃	—	2	2	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	2	2	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	2	no	—
169	C₂×C₄×C₂₃	—	2	2	no	—
170	C₂×C₄×C₂₃	—	2	8	no	—
171	C₂×C₄×C₂₃	—	2	4	no	—
172	C₂×C₄×C₂₃	—	2	4	no	—
173	C₂×C₄×C₂₃	—	2	8	no	—
174	C₂×C₄×C₂₃	—	2	8	no	—
175	C₂×C₄×C₂₃	—	2	32	no	—
176	C₂×C₄×C₂₃	—	2	32	no	—
177	C₂×C₄×C₂₃	—	2	16	no	—
178	C₂×C₄×C₂₃	—	2	16	no	—
179	C₂×C₄×C₂₃	—	2	16	no	—
180	C₂×C₄×C₂₃	—	4	8	no	—
181	C₂×C₄×C₂₃	—	4	8	no	—
182	C₂×C₄×C₂₃	—	4	8	no	—
183	C₂×C₄×C₂₃	—	4	8	no	—
184	C₂×C₄×C₂₃	C₂×C₄²	1	4	yes	—
185	C₂×C₄×C₂₃	C₂×C₄²	1	4	yes	—
186	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
190	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
191	C₂×C₄×C₂₃	#117	1	4	yes	—
192	C₂×C₄×C₂₃	#117	1	4	yes	—
193	C₂×C₄×C₂₃	#117	1	4	yes	—
194	C₂×C₄×C₂₃	C₄×D₄	1	16	yes	—
195	C₂×C₄×C₂₃	#121	1	8	yes	—
196	C₂×C₄×C₂₃	C₂²⋊Q₈	1	8	yes	—
197	C₂³×C₄²	C₂×C₂₃	1	1	yes	characteristic
198	C₂×#380	C₂×C₂₃	1	2	yes	—
199	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
200	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	2	yes	—
201	C₄⋊#95	C₂×C₂₃	1	2	yes	complemented
202	#1434	C₂×C₂₃	1	2	yes	complemented
203	C₂²⋊#95	C₂×C₂₃	1	2	yes	—
204	C₄×#95	C₂×C₂₃	1	2	yes	complemented
205	C₂²×C₂₃	—	2	4	no	—
206	C₂²×C₂₃	—	2	4	no	—
207	C₂²×C₂₃	—	2	4	no	—
208	C₂²×C₂₃	—	2	4	no	—
209	C₂²×C₂₃	—	2	4	no	—
210	C₂²×C₂₃	—	2	4	no	—
211	C₂²×C₂₃	—	2	16	no	—
212	C₂²×C₂₃	—	2	16	no	—
213	C₂²×C₂₃	C₄×C₄⋊C₄	1	8	yes	complemented
214	C₂²×C₂₃	C₂²×C₄²	1	1	yes	characteristic
215	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
218	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
219	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
220	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
221	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
222	C₂²×C₂₃	C₂×C₄×D₄	1	2	yes	—
223	C₂²×C₂₃	C₂×C₄×Q₈	1	2	yes	—
224	C₂²×C₂₃	C₄×#41	1	4	yes	—
225	C₂²×C₂₃	C₂×#121	1	2	yes	—
226	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	2	yes	—
227	C₂²×C₂₃	#525	1	4	yes	—
228	C₂²×C₂₃	#529	1	4	yes	—
229	C₂²×C₂₃	#532	1	2	yes	—
230	C₂²×C₂₃	#533	1	2	yes	—
231	C₄×C₂₃	—	2	4	no	—
232	C₄×C₂₃	—	2	4	no	—
233	C₄×C₂₃	—	2	4	no	—
234	C₄×C₂₃	—	2	4	no	—
235	C₄×C₂₃	—	4	16	no	—
236	C₄×C₂₃	C₄×C₂²⋊C₄	1	8	yes	complemented
237	C₄×C₂₃	#380	1	8	yes	direct product factor
238	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
240	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
243	C₂²×C₄²	—	2	8	no	—
244	C₂²×C₄²	C₄×C₂₃	1	8	yes	complemented
245	C₂²×C₄²	C₂²×C₂₃	1	4	yes	—
246	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
248	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
250	#380	C₄×C₂₃	1	16	yes	direct product factor
251	C₄×C₄⋊C₄	—	2	8	no	—
252	C₄×C₂²⋊C₄	—	2	8	no	—
253	C₂×#95	C₂²×C₂₃	1	4	yes	—
254	C₂×#95	C₂²×C₂₃	1	4	yes	—
255	C₂×#95	C₂²×C₂₃	1	4	yes	—
256	C₂×#95	C₂²×C₂₃	1	4	yes	—
257	C₂×C₂₃	—	2	8	no	—
258	C₂×C₂₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₂₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₂₃	C₄×#117	1	1	yes	characteristic
261	C₂×C₂₃	C₂×#380	1	1	yes	characteristic
262	C₂×C₂₃	#2280	1	1	yes	characteristic
263	C₂×C₂₃	#2283	1	1	yes	characteristic
264	C₂×C₂₃	#2285	1	1	yes	characteristic
265	C₂×C₂₃	C₄×#121	1	4	yes	—
266	C₂×C₂₃	C₄×C₂²⋊Q₈	1	4	yes	—
267	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	4	no	—
273	C₂³×C₄	—	2	4	no	—
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
276	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	—
277	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
278	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
279	C₂³×C₄	D₄×C₂₃	1	4	yes	—
280	C₂³×C₄	Q₈×C₂₃	1	4	yes	—
281	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
282	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	2	8	no	—
290	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
291	C₂×C₂²⋊C₄	—	2	8	no	—
292	C₂×C₂²⋊C₄	—	2	8	no	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	—
294	C₂×C₄²	—	2	4	no	—
295	C₂×C₄²	—	2	4	no	—
296	C₂×C₄²	—	2	4	no	—
297	C₂×C₄²	—	2	32	no	—
298	C₂×C₄²	—	2	8	no	—
299	C₂×C₄²	—	2	8	no	—
300	C₂×C₄²	—	2	8	no	—
301	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
302	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
303	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
304	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
305	C₂×C₄²	D₄×C₂₃	1	8	yes	—
306	#95	—	2	8	no	—
307	#95	—	2	8	no	—
308	#95	—	2	8	no	—
309	#95	C₂×C₄×C₂₃	1	16	yes	complemented
310	C₂₃	C₄×#380	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
316	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
317	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
318	C₂⁴	C₂×Q₈×C₂₃	1	2	yes	—
319	C₂⁴	#41×C₂₃	1	4	yes	—
320	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
321	C₂²×C₄	—	2	32	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	32	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	C₄²×C₂₃	1	16	yes	complemented
347	C₂²×C₄	C₄⋊C₄×C₂₃	1	16	yes	complemented
348	C₂²×C₄	C₂²×C₄×C₂₃	1	16	yes	—
349	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
350	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
362	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
363	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
364	C₂²×C₄	#41×C₂₃	1	4	yes	—
365	C₂²×C₄	#41×C₂₃	1	4	yes	—
366	C₂²×C₄	#41×C₂₃	1	4	yes	—
367	C₄⋊C₄	—	2	32	no	—
368	C₂²⋊C₄	—	2	32	no	—
369	C₄²	—	2	8	no	—
370	C₄²	—	2	8	no	—
371	C₄²	—	2	8	no	—
372	C₄²	—	4	16	no	—
373	C₄²	C₂²⋊C₄×C₂₃	1	16	yes	complemented
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	C₂×C₄²×C₂₃	1	4	yes	—
387	C₂³	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
388	C₂³	C₂₃×#117	1	4	yes	—
389	C₂³	C₄×D₄×C₂₃	1	8	yes	—
390	C₂³	C₄×Q₈×C₂₃	1	8	yes	—
391	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
392	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
393	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
394	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
395	C₂³	C₂²×Q₈×C₂₃	1	1	yes	characteristic
396	C₂³	C₂×#41×C₂₃	1	2	yes	—
397	C₂³	C₂×#41×C₂₃	1	2	yes	—
398	C₂³	C₂×#41×C₂₃	1	2	yes	—
399	C₂³	C₂×#41×C₂₃	1	2	yes	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	32	no	—
415	C₂×C₄	—	2	32	no	—
416	C₂×C₄	—	2	16	no	—
417	C₂×C₄	—	2	16	no	—
418	C₂×C₄	—	2	16	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	C₂×C₄²×C₂₃	1	4	yes	—
424	C₂×C₄	C₂×C₄²×C₂₃	1	4	yes	—
425	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
428	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
429	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
430	C₂×C₄	C₂₃×#117	1	4	yes	—
431	C₂×C₄	C₂₃×#117	1	4	yes	—
432	C₂×C₄	C₂₃×#117	1	4	yes	—
433	C₂×C₄	C₄×D₄×C₂₃	1	16	yes	—
434	C₂×C₄	C₂₃×#121	1	8	yes	—
435	C₂×C₄	C₂₃×C₂²⋊Q₈	1	8	yes	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	16	no	—
443	C₂²	—	2	16	no	—
444	C₂²	C₄×C₄⋊C₄×C₂₃	1	8	yes	complemented
445	C₂²	C₂²×C₄²×C₂₃	1	1	yes	characteristic
446	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
447	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
448	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
449	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
450	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
451	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
452	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
453	C₂²	C₂×C₄×D₄×C₂₃	1	2	yes	—
454	C₂²	C₂×C₄×Q₈×C₂₃	1	2	yes	—
455	C₂²	C₄×#41×C₂₃	1	4	yes	—
456	C₂²	C₂×C₂₃×#121	1	2	yes	—
457	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	2	yes	—
458	C₂²	C₂₃×#525	1	4	yes	—
459	C₂²	C₂₃×#529	1	4	yes	—
460	C₂²	C₂₃×#532	1	2	yes	—
461	C₂²	C₂₃×#533	1	2	yes	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	4	16	no	—
467	C₄	C₄×C₂²⋊C₄×C₂₃	1	8	yes	complemented
468	C₄	C₂₃×#380	1	8	yes	direct product factor
469	C₂	—	2	8	no	—
470	C₂	C₂×C₄×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
471	C₂	C₂×C₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
472	C₂	C₄×C₂₃×#117	1	1	yes	characteristic
473	C₂	C₂×C₂₃×#380	1	1	yes	characteristic
474	C₂	C₂₃×#2280	1	1	yes	characteristic
475	C₂	C₂₃×#2283	1	1	yes	characteristic
476	C₂	C₂₃×#2285	1	1	yes	characteristic
477	C₂	C₄×C₂₃×#121	1	4	yes	—
478	C₂	C₄×C₂₃×C₂²⋊Q₈	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₂₃	C₂³
commutator	C₂²	C₂²×C₄²×C₂₃
Frattini, cosocle	C₂⁴	C₂⁴×C₂₃
socle	C₂⁴×C₂₃	C₂⁴
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
5. C₂₃×C₄⋊#95	C₂	semidirect
6. C₂₃×#1434	C₂	semidirect
8. C₄×C₂₃×#95	C₂	semidirect
15. C₂²×C₄²×C₂₃	C₄	semidirect
21. C₂₃×#380	C₄	direct (N × H)
51. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
70. C₂₃×#95	C₂×C₄	semidirect
106. C₂²×C₄×C₂₃	C₄²	semidirect
107. C₂²×C₄×C₂₃	C₄⋊C₄	semidirect
133. C₄²×C₂₃	C₂²⋊C₄	semidirect
134. C₄×#380	C₂₃	direct (N × H)
199. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
201. C₄⋊#95	C₂×C₂₃	semidirect
202. #1434	C₂×C₂₃	semidirect
204. C₄×#95	C₂×C₂₃	semidirect
213. C₂²×C₂₃	C₄×C₄⋊C₄	semidirect
236. C₄×C₂₃	C₄×C₂²⋊C₄	semidirect
237. C₄×C₂₃	#380	direct (N × H)
244. C₂²×C₄²	C₄×C₂₃	semidirect
250. #380	C₄×C₂₃	direct (N × H)
290. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
309. #95	C₂×C₄×C₂₃	semidirect
310. C₂₃	C₄×#380	direct (N × H)
346. C₂²×C₄	C₄²×C₂₃	semidirect
347. C₂²×C₄	C₄⋊C₄×C₂₃	semidirect
373. C₄²	C₂²⋊C₄×C₂₃	semidirect
444. C₂²	C₄×C₄⋊C₄×C₂₃	semidirect
467. C₄	C₄×C₂²⋊C₄×C₂₃	semidirect
468. C₄	C₂₃×#380	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×C₄²×C₂₃	2
C₂×C₂₃×#380	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂₃×C₄⋊#95	2
C₂₃×#1434	2
C₂₃×C₂²⋊#95	2
C₄×C₂₃×#95	2
C₄×#380	23

Subgroups — C4×C23×#380 #19161397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#380 #19161397