Subgroups — C₂×C₃×C₅×#390 #14275326

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#390	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×D₄	—	2	4	no	—
9	C₂²×C₃×C₅×D₄	—	2	4	no	—
10	C₂²×C₃×C₅×D₄	C₄	1	8	yes	complemented
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	16	no	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
19	C₂×C₃×C₄²×C₅	—	2	4	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	complemented
21	C₂×C₃×#390	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
25	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#390	C₂×C₃	1	8	yes	direct product factor
27	C₂⁴×C₃×C₅	—	2	8	no	—
28	C₂⁴×C₃×C₅	—	2	4	no	—
29	C₂⁴×C₃×C₅	—	2	4	no	—
30	C₂⁴×C₃×C₅	—	2	8	no	—
31	C₂⁴×C₃×C₅	C₂×C₄	1	8	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	32	no	—
35	C₂×C₃×C₅×D₄	—	2	8	no	—
36	C₂×C₃×C₅×D₄	—	2	8	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	16	yes	complemented
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	8	no	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
44	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
45	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	32	no	—
51	C₃×C₄²×C₅	—	2	8	no	—
52	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
53	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
55	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×#390	C₂×C₅	1	8	yes	direct product factor
57	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
58	C₂²×C₅×D₄	—	2	4	no	—
59	C₂²×C₅×D₄	—	2	4	no	—
60	C₂²×C₅×D₄	C₃×C₄	1	8	yes	complemented
61	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
62	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
63	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	—	2	4	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
67	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
69	C₂×C₄²×C₅	—	2	4	no	—
70	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	complemented
71	C₂×#390	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	16	no	—
73	C₂³×C₃×C₅	—	2	32	no	—
74	C₂³×C₃×C₅	—	2	8	no	—
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	2	8	no	—
78	C₂³×C₃×C₅	—	4	16	no	—
79	C₂³×C₃×C₅	—	4	8	no	—
80	C₂³×C₃×C₅	—	4	8	no	—
81	C₂³×C₃×C₅	C₂²×C₄	1	8	yes	—
82	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
86	C₂³×C₃×C₅	#41	1	4	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₃×C₅×D₄	—	2	32	no	—
89	C₂×C₃×C₄×C₅	—	2	16	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	8	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	4	8	no	—
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
100	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
101	C₂²×C₃×D₄	—	2	4	no	—
102	C₂²×C₃×D₄	—	2	4	no	—
103	C₂²×C₃×D₄	C₄×C₅	1	8	yes	complemented
104	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
105	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
106	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
107	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
110	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	16	yes	complemented
112	C₂×C₃×C₄²	—	2	4	no	—
113	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	complemented
114	C₂⁴×C₅	—	2	8	no	—
115	C₂⁴×C₅	—	2	4	no	—
116	C₂⁴×C₅	—	2	4	no	—
117	C₂⁴×C₅	—	2	8	no	—
118	C₂⁴×C₅	C₂×C₃×C₄	1	8	yes	—
119	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
120	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂×C₅×D₄	—	2	32	no	—
122	C₂×C₅×D₄	—	2	8	no	—
123	C₂×C₅×D₄	—	2	8	no	—
124	C₂×C₅×D₄	C₂×C₃×C₄	1	16	yes	complemented
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	8	no	—
128	C₂²×C₄×C₅	—	2	4	no	—
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
130	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
131	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
132	C₂²×C₄×C₅	C₃×D₄	1	8	yes	complemented
133	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₅×C₄⋊C₄	—	2	8	no	—
137	C₅×C₂²⋊C₄	—	2	32	no	—
138	C₄²×C₅	—	2	8	no	—
139	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic
140	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
142	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
143	#390	C₂×C₃×C₅	1	8	yes	direct product factor
144	C₂²×C₃×C₅	—	2	8	no	—
145	C₂²×C₃×C₅	—	2	16	no	—
146	C₂²×C₃×C₅	—	4	8	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	4	32	no	—
150	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂²×C₃×C₅	C₄×D₄	1	8	yes	—
152	C₂²×C₃×C₅	#121	1	8	yes	—
153	C₂²×C₃×C₅	#124	1	4	yes	—
154	C₂²×C₃×C₅	#127	1	4	yes	—
155	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
159	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
160	C₃×C₄×C₅	—	2	8	no	—
161	C₃×C₄×C₅	—	4	4	no	—
162	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
163	C₂⁴×C₃	—	2	8	no	—
164	C₂⁴×C₃	—	2	4	no	—
165	C₂⁴×C₃	—	2	4	no	—
166	C₂⁴×C₃	—	2	8	no	—
167	C₂⁴×C₃	C₂×C₄×C₅	1	8	yes	—
168	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
169	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
170	C₂×C₃×D₄	—	2	32	no	—
171	C₂×C₃×D₄	—	2	8	no	—
172	C₂×C₃×D₄	—	2	8	no	—
173	C₂×C₃×D₄	C₂×C₄×C₅	1	16	yes	complemented
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	2	8	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
179	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
180	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
181	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₂²⋊C₄	—	2	32	no	—
187	C₃×C₄²	—	2	8	no	—
188	C₂³×C₅	—	2	16	no	—
189	C₂³×C₅	—	2	32	no	—
190	C₂³×C₅	—	2	8	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	8	no	—
194	C₂³×C₅	—	4	16	no	—
195	C₂³×C₅	—	4	8	no	—
196	C₂³×C₅	—	4	8	no	—
197	C₂³×C₅	C₂²×C₃×C₄	1	8	yes	—
198	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
199	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
201	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
202	C₂³×C₅	C₃×#41	1	4	yes	—
203	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₅×D₄	—	2	32	no	—
205	C₂×C₄×C₅	—	2	16	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	8	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	4	8	no	—
211	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	complemented
216	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	C₃×C₄×C₅	1	8	yes	complemented
220	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
221	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
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	16	no	—
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	16	yes	complemented
228	C₂×C₄²	—	2	4	no	—
229	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	complemented
230	C₂×C₃×C₅	—	4	8	no	—
231	C₂×C₃×C₅	#390	1	8	yes	direct product factor
232	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
234	C₂×C₃×C₅	C₂×#121	1	2	yes	—
235	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
236	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
237	C₂³×C₃	—	2	16	no	—
238	C₂³×C₃	—	2	32	no	—
239	C₂³×C₃	—	2	8	no	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	8	no	—
243	C₂³×C₃	—	4	16	no	—
244	C₂³×C₃	—	4	8	no	—
245	C₂³×C₃	—	4	8	no	—
246	C₂³×C₃	C₂²×C₄×C₅	1	8	yes	—
247	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
248	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
249	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
250	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
251	C₂³×C₃	C₅×#41	1	4	yes	—
252	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
253	C₃×D₄	—	2	32	no	—
254	C₂×C₃×C₄	—	2	16	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	8	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	4	8	no	—
260	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
261	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
265	C₂²×C₅	—	2	8	no	—
266	C₂²×C₅	—	2	16	no	—
267	C₂²×C₅	—	4	32	no	—
268	C₂²×C₅	—	4	8	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	4	4	no	—
271	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
272	C₂²×C₅	C₃×C₄×D₄	1	8	yes	—
273	C₂²×C₅	C₃×#121	1	8	yes	—
274	C₂²×C₅	C₃×#124	1	4	yes	—
275	C₂²×C₅	C₃×#127	1	4	yes	—
276	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
277	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
279	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
280	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
281	C₄×C₅	—	2	8	no	—
282	C₄×C₅	—	4	4	no	—
283	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	8	yes	complemented
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	8	no	—
288	C₂⁴	C₂×C₃×C₄×C₅	1	8	yes	—
289	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
290	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
291	C₂×D₄	—	2	32	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
300	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
301	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
302	C₂²×C₄	C₃×C₅×D₄	1	8	yes	complemented
303	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
304	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
305	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
306	C₄⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	2	32	no	—
308	C₄²	—	2	8	no	—
309	C₃×C₅	C₂×#390	1	1	yes	characteristic, direct product factor, Hall
310	C₂²×C₃	—	2	8	no	—
311	C₂²×C₃	—	2	16	no	—
312	C₂²×C₃	—	4	32	no	—
313	C₂²×C₃	—	4	8	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	—	4	4	no	—
316	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
317	C₂²×C₃	C₄×C₅×D₄	1	8	yes	—
318	C₂²×C₃	C₅×#121	1	8	yes	—
319	C₂²×C₃	C₅×#124	1	4	yes	—
320	C₂²×C₃	C₅×#127	1	4	yes	—
321	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
322	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
325	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
326	C₃×C₄	—	2	8	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
329	C₂×C₅	—	4	8	no	—
330	C₂×C₅	C₃×#390	1	8	yes	direct product factor
331	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₅	C₂×C₃×C₄×D₄	1	2	yes	—
333	C₂×C₅	C₂×C₃×#121	1	2	yes	—
334	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
335	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
336	C₂³	—	2	16	no	—
337	C₂³	—	2	32	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	16	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	8	no	—
345	C₂³	C₂²×C₃×C₄×C₅	1	8	yes	—
346	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
347	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
348	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
349	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
350	C₂³	C₃×C₅×#41	1	4	yes	—
351	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
352	D₄	—	2	32	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	16	yes	complemented
360	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
361	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
362	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
363	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	complemented
364	C₂×C₃	—	4	8	no	—
365	C₂×C₃	C₅×#390	1	8	yes	direct product factor
366	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₃	C₂×C₄×C₅×D₄	1	2	yes	—
368	C₂×C₃	C₂×C₅×#121	1	2	yes	—
369	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
370	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
371	C₅	C₂×C₃×#390	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	8	no	—
373	C₂²	—	2	16	no	—
374	C₂²	—	4	8	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	32	no	—
378	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	—
379	C₂²	C₃×C₄×C₅×D₄	1	8	yes	—
380	C₂²	C₃×C₅×#121	1	8	yes	—
381	C₂²	C₃×C₅×#124	1	4	yes	—
382	C₂²	C₃×C₅×#127	1	4	yes	—
383	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
384	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
385	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
386	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
387	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
388	C₄	—	2	8	no	—
389	C₄	—	4	4	no	—
390	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	8	yes	complemented
391	C₃	C₂×C₅×#390	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	—	4	8	no	—
393	C₂	C₃×C₅×#390	1	8	yes	direct product factor
394	C₂	C₂²×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂	C₂×C₃×C₄×C₅×D₄	1	2	yes	—
396	C₂	C₂×C₃×C₅×#121	1	2	yes	—
397	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
398	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₃×C₄²×C₅	C₂	semidirect
5. C₃×C₅×#390	C₂	direct (N × H)
6. C₂×C₅×#390	C₃	direct (N × H)
10. C₂²×C₃×C₅×D₄	C₄	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
20. C₂×C₃×C₄²×C₅	C₂²	semidirect
21. C₂×C₃×#390	C₅	direct (N × H)
23. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
24. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
25. C₂²×C₄²×C₅	C₂×C₃	semidirect
26. C₅×#390	C₂×C₃	direct (N × H)
37. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
45. C₂²×C₃×C₄×C₅	D₄	semidirect
53. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
54. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
55. C₂²×C₃×C₄²	C₂×C₅	semidirect
56. C₃×#390	C₂×C₅	direct (N × H)
60. C₂²×C₅×D₄	C₃×C₄	semidirect
66. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
68. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
70. C₂×C₄²×C₅	C₂²×C₃	semidirect
71. C₂×#390	C₃×C₅	direct (N × H)
95. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
99. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
103. C₂²×C₃×D₄	C₄×C₅	semidirect
109. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
111. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
113. C₂×C₃×C₄²	C₂²×C₅	semidirect
124. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
132. C₂²×C₄×C₅	C₃×D₄	semidirect
140. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
141. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
142. C₂²×C₄²	C₂×C₃×C₅	semidirect
143. #390	C₂×C₃×C₅	direct (N × H)
162. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
173. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
181. C₂²×C₃×C₄	C₅×D₄	semidirect
211. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
215. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
219. C₂²×D₄	C₃×C₄×C₅	semidirect
225. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
227. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
229. C₂×C₄²	C₂²×C₃×C₅	semidirect
231. C₂×C₃×C₅	#390	direct (N × H)
260. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
264. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
283. C₄×C₅	C₂×C₃×C₂²⋊C₄	semidirect
294. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
302. C₂²×C₄	C₃×C₅×D₄	semidirect
309. C₃×C₅	C₂×#390	direct (N × H)
328. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
330. C₂×C₅	C₃×#390	direct (N × H)
359. C₂×C₄	C₃×C₅×C₂²⋊C₄	semidirect
363. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
365. C₂×C₃	C₅×#390	direct (N × H)
371. C₅	C₂×C₃×#390	direct (N × H)
390. C₄	C₂×C₃×C₅×C₂²⋊C₄	semidirect
391. C₃	C₂×C₅×#390	direct (N × H)
393. C₂	C₃×C₅×#390	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×C₃×C₅×D₄	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#390	2
C₂×C₅×#390	3
C₂×C₃×#390	5

Subgroups — C2×C3×C5×#390 #14275326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#390 #14275326