Subgroups — C₂×C₃×C₅×#397 #14275424

Order 1920.

1640 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#397	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#95	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#397	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₃×C₅×#95	C₂²	1	8	yes	complemented
20	C₃×C₅×#95	C₂²	1	4	yes	complemented
21	C₂×C₃×#397	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
24	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
25	C₅×#397	C₂×C₃	1	8	yes	direct product factor
26	C₂×C₅×#95	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₅	—	2	2	no	—
29	C₂⁴×C₃×C₅	—	2	2	no	—
30	C₂⁴×C₃×C₅	—	2	4	no	—
31	C₂⁴×C₃×C₅	—	2	4	no	—
32	C₂⁴×C₃×C₅	D₄	1	4	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
52	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
54	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
55	C₃×#397	C₂×C₅	1	8	yes	direct product factor
56	C₂×C₃×#95	C₂×C₅	1	2	yes	complemented
57	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
60	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
65	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
69	C₅×#95	C₂²×C₃	1	8	yes	complemented
70	C₅×#95	C₂²×C₃	1	4	yes	complemented
71	C₂×#397	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	8	no	—
73	C₂³×C₃×C₅	—	2	16	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	4	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	—	4	8	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	#41	1	2	yes	—
85	C₂³×C₃×C₅	#41	1	4	yes	—
86	C₂³×C₃×C₅	#41	1	4	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	—	2	8	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	4	8	no	—
99	C₂×C₃×C₄×C₅	—	4	8	no	—
100	C₂×C₃×C₄×C₅	—	4	4	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
102	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
104	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
106	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
109	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
110	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
113	C₃×#95	C₂²×C₅	1	8	yes	complemented
114	C₃×#95	C₂²×C₅	1	4	yes	complemented
115	C₂⁴×C₅	—	2	2	no	—
116	C₂⁴×C₅	—	2	2	no	—
117	C₂⁴×C₅	—	2	4	no	—
118	C₂⁴×C₅	—	2	4	no	—
119	C₂⁴×C₅	C₃×D₄	1	4	yes	—
120	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
121	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	4	no	—
129	C₂²×C₄×C₅	—	2	4	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₅×C₄⋊C₄	—	2	8	no	—
137	C₅×C₂²⋊C₄	—	2	16	no	—
138	C₅×C₂²⋊C₄	—	2	8	no	—
139	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
141	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
142	#397	C₂×C₃×C₅	1	8	yes	direct product factor
143	C₂×#95	C₂×C₃×C₅	1	2	yes	complemented
144	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₅	—	2	4	no	—
146	C₂²×C₃×C₅	—	2	8	no	—
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	4	no	—
150	C₂²×C₃×C₅	—	4	16	no	—
151	C₂²×C₃×C₅	#121	1	4	yes	—
152	C₂²×C₃×C₅	#123	1	4	yes	—
153	C₂²×C₃×C₅	#123	1	8	yes	—
154	C₂²×C₃×C₅	#124	1	4	yes	—
155	C₂²×C₃×C₅	#126	1	8	yes	—
156	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
160	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
161	C₃×C₄×C₅	—	2	4	no	—
162	C₃×C₄×C₅	—	4	4	no	—
163	C₃×C₄×C₅	—	4	4	no	—
164	C₃×C₄×C₅	—	4	2	no	—
165	C₂⁴×C₃	—	2	2	no	—
166	C₂⁴×C₃	—	2	2	no	—
167	C₂⁴×C₃	—	2	4	no	—
168	C₂⁴×C₃	—	2	4	no	—
169	C₂⁴×C₃	C₅×D₄	1	4	yes	—
170	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
171	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₃×C₄⋊C₄	—	2	8	no	—
187	C₃×C₂²⋊C₄	—	2	16	no	—
188	C₃×C₂²⋊C₄	—	2	8	no	—
189	C₂³×C₅	—	2	8	no	—
190	C₂³×C₅	—	2	16	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	4	4	no	—
196	C₂³×C₅	—	4	4	no	—
197	C₂³×C₅	—	4	8	no	—
198	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
199	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
201	C₂³×C₅	C₃×#41	1	2	yes	—
202	C₂³×C₅	C₃×#41	1	4	yes	—
203	C₂³×C₅	C₃×#41	1	4	yes	—
204	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	8	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	4	8	no	—
216	C₂×C₄×C₅	—	4	8	no	—
217	C₂×C₄×C₅	—	4	4	no	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
219	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
221	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
226	C₂×C₂²⋊C₄	—	2	8	no	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
230	#95	C₂²×C₃×C₅	1	8	yes	complemented
231	#95	C₂²×C₃×C₅	1	4	yes	complemented
232	C₂×C₃×C₅	—	4	4	no	—
233	C₂×C₃×C₅	#397	1	8	yes	direct product factor
234	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
236	C₂×C₃×C₅	C₂×#123	1	2	yes	—
237	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
238	C₂×C₃×C₅	C₂×#126	1	2	yes	—
239	C₂³×C₃	—	2	8	no	—
240	C₂³×C₃	—	2	16	no	—
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	4	4	no	—
246	C₂³×C₃	—	4	4	no	—
247	C₂³×C₃	—	4	8	no	—
248	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
249	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
250	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
251	C₂³×C₃	C₅×#41	1	2	yes	—
252	C₂³×C₃	C₅×#41	1	4	yes	—
253	C₂³×C₃	C₅×#41	1	4	yes	—
254	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	4	8	no	—
266	C₂×C₃×C₄	—	4	8	no	—
267	C₂×C₃×C₄	—	4	4	no	—
268	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	8	no	—
271	C₂²×C₅	—	4	16	no	—
272	C₂²×C₅	—	4	2	no	—
273	C₂²×C₅	—	4	2	no	—
274	C₂²×C₅	—	4	4	no	—
275	C₂²×C₅	C₃×#121	1	4	yes	—
276	C₂²×C₅	C₃×#123	1	4	yes	—
277	C₂²×C₅	C₃×#123	1	8	yes	—
278	C₂²×C₅	C₃×#124	1	4	yes	—
279	C₂²×C₅	C₃×#126	1	8	yes	—
280	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
282	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
283	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
284	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
285	C₄×C₅	—	2	4	no	—
286	C₄×C₅	—	4	4	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	—	4	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	C₃×C₅×D₄	1	4	yes	—
294	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
295	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
306	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
307	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
308	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
309	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
310	C₄⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₂²⋊C₄	—	2	8	no	—
313	C₃×C₅	C₂×#397	1	1	yes	characteristic, direct product factor, Hall
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	2	8	no	—
316	C₂²×C₃	—	4	16	no	—
317	C₂²×C₃	—	4	2	no	—
318	C₂²×C₃	—	4	2	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	C₅×#121	1	4	yes	—
321	C₂²×C₃	C₅×#123	1	4	yes	—
322	C₂²×C₃	C₅×#123	1	8	yes	—
323	C₂²×C₃	C₅×#124	1	4	yes	—
324	C₂²×C₃	C₅×#126	1	8	yes	—
325	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
328	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
329	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	4	4	no	—
332	C₃×C₄	—	4	4	no	—
333	C₃×C₄	—	4	2	no	—
334	C₂×C₅	—	4	4	no	—
335	C₂×C₅	C₃×#397	1	8	yes	direct product factor
336	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
337	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
338	C₂×C₅	C₂×C₃×#123	1	2	yes	—
339	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
340	C₂×C₅	C₂×C₃×#126	1	2	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	16	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	8	no	—
350	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
351	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
352	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
353	C₂³	C₃×C₅×#41	1	2	yes	—
354	C₂³	C₃×C₅×#41	1	4	yes	—
355	C₂³	C₃×C₅×#41	1	4	yes	—
356	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
371	C₂×C₃	—	4	4	no	—
372	C₂×C₃	C₅×#397	1	8	yes	direct product factor
373	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
374	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
375	C₂×C₃	C₂×C₅×#123	1	2	yes	—
376	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
377	C₂×C₃	C₂×C₅×#126	1	2	yes	—
378	C₅	C₂×C₃×#397	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	16	no	—
385	C₂²	C₃×C₅×#121	1	4	yes	—
386	C₂²	C₃×C₅×#123	1	4	yes	—
387	C₂²	C₃×C₅×#123	1	8	yes	—
388	C₂²	C₃×C₅×#124	1	4	yes	—
389	C₂²	C₃×C₅×#126	1	8	yes	—
390	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
391	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
392	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
393	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
394	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	2	no	—
399	C₃	C₂×C₅×#397	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	4	4	no	—
401	C₂	C₃×C₅×#397	1	8	yes	direct product factor
402	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
403	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
404	C₂	C₂×C₃×C₅×#123	1	2	yes	—
405	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
406	C₂	C₂×C₃×C₅×#126	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×C₅×#397	C₂	direct (N × H)
5. C₂×C₃×C₅×#95	C₂	semidirect
6. C₂×C₃×C₅×#95	C₂	semidirect
7. C₂×C₅×#397	C₃	direct (N × H)
14. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₃×C₅×#95	C₂²	semidirect
20. C₃×C₅×#95	C₂²	semidirect
21. C₂×C₃×#397	C₅	direct (N × H)
22. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
25. C₅×#397	C₂×C₃	direct (N × H)
26. C₂×C₅×#95	C₂×C₃	semidirect
27. C₂×C₅×#95	C₂×C₃	semidirect
52. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
55. C₃×#397	C₂×C₅	direct (N × H)
56. C₂×C₃×#95	C₂×C₅	semidirect
57. C₂×C₃×#95	C₂×C₅	semidirect
64. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
69. C₅×#95	C₂²×C₃	semidirect
70. C₅×#95	C₂²×C₃	semidirect
71. C₂×#397	C₃×C₅	direct (N × H)
108. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
113. C₃×#95	C₂²×C₅	semidirect
114. C₃×#95	C₂²×C₅	semidirect
139. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
142. #397	C₂×C₃×C₅	direct (N × H)
143. C₂×#95	C₂×C₃×C₅	semidirect
144. C₂×#95	C₂×C₃×C₅	semidirect
225. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
230. #95	C₂²×C₃×C₅	semidirect
231. #95	C₂²×C₃×C₅	semidirect
233. C₂×C₃×C₅	#397	direct (N × H)
313. C₃×C₅	C₂×#397	direct (N × H)
335. C₂×C₅	C₃×#397	direct (N × H)
372. C₂×C₃	C₅×#397	direct (N × H)
378. C₅	C₂×C₃×#397	direct (N × H)
399. C₃	C₂×C₅×#397	direct (N × H)
401. C₂	C₃×C₅×#397	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#397	2
C₂×C₃×C₅×#95	2
C₂×C₅×#397	3
C₂×C₃×#397	5

Subgroups — C2×C3×C5×#397 #14275424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#397 #14275424