Subgroups — C₂×C₃×C₅×#394 #14275420

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 464 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	2	yes	maximal, complemented
4	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#394	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×D₄	—	2	8	no	—
10	C₂²×C₃×C₅×D₄	—	2	4	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
19	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
22	C₃×C₅×#95	C₂²	1	4	yes	complemented
23	C₂×C₃×#394	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
27	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
28	C₅×#394	C₂×C₃	1	8	yes	direct product factor
29	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	2	4	no	—
31	C₂⁴×C₃×C₅	—	2	4	no	—
32	C₂⁴×C₃×C₅	—	2	4	no	—
33	C₂⁴×C₃×C₅	—	2	4	no	—
34	C₂⁴×C₃×C₅	—	2	4	no	—
35	C₂⁴×C₃×C₅	—	2	4	no	—
36	C₂⁴×C₃×C₅	D₄	1	8	yes	—
37	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	32	no	—
40	C₂×C₃×C₅×D₄	—	2	16	no	—
41	C₂×C₃×C₅×D₄	—	2	8	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	—	2	4	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
51	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	8	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
59	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
60	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
62	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
63	C₃×#394	C₂×C₅	1	8	yes	direct product factor
64	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
66	C₂²×C₅×D₄	—	2	8	no	—
67	C₂²×C₅×D₄	—	2	4	no	—
68	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
69	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
70	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	—	2	4	no	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
75	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
79	C₅×#95	C₂²×C₃	1	4	yes	complemented
80	C₂×#394	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³×C₃×C₅	—	2	16	no	—
82	C₂³×C₃×C₅	—	2	16	no	—
83	C₂³×C₃×C₅	—	2	16	no	—
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	2	4	no	—
86	C₂³×C₃×C₅	—	2	4	no	—
87	C₂³×C₃×C₅	—	2	4	no	—
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	—	2	4	no	—
90	C₂³×C₃×C₅	—	4	8	no	—
91	C₂³×C₃×C₅	—	4	8	no	—
92	C₂³×C₃×C₅	—	4	8	no	—
93	C₂³×C₃×C₅	—	4	8	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
95	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
96	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
97	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
98	C₂³×C₃×C₅	#41	1	2	yes	—
99	C₂³×C₃×C₅	#41	1	4	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×D₄	—	2	32	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	—	2	8	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	4	8	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
116	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×D₄	—	2	8	no	—
118	C₂²×C₃×D₄	—	2	4	no	—
119	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
120	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
121	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	—	2	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
126	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
127	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
130	C₃×#95	C₂²×C₅	1	4	yes	complemented
131	C₂⁴×C₅	—	2	4	no	—
132	C₂⁴×C₅	—	2	4	no	—
133	C₂⁴×C₅	—	2	4	no	—
134	C₂⁴×C₅	—	2	4	no	—
135	C₂⁴×C₅	—	2	4	no	—
136	C₂⁴×C₅	—	2	4	no	—
137	C₂⁴×C₅	C₃×D₄	1	8	yes	—
138	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
139	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂×C₅×D₄	—	2	32	no	—
141	C₂×C₅×D₄	—	2	16	no	—
142	C₂×C₅×D₄	—	2	8	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	4	no	—
151	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
152	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₅×C₄⋊C₄	—	2	8	no	—
158	C₅×C₂²⋊C₄	—	2	16	no	—
159	C₅×C₂²⋊C₄	—	2	16	no	—
160	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic
161	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
162	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
163	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
164	#394	C₂×C₃×C₅	1	8	yes	direct product factor
165	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	—	2	8	no	—
167	C₂²×C₃×C₅	—	2	8	no	—
168	C₂²×C₃×C₅	—	2	8	no	—
169	C₂²×C₃×C₅	—	4	4	no	—
170	C₂²×C₃×C₅	—	4	4	no	—
171	C₂²×C₃×C₅	—	4	4	no	—
172	C₂²×C₃×C₅	—	4	4	no	—
173	C₂²×C₃×C₅	—	4	32	no	—
174	C₂²×C₃×C₅	#120	1	4	yes	—
175	C₂²×C₃×C₅	#121	1	4	yes	—
176	C₂²×C₃×C₅	#121	1	8	yes	—
177	C₂²×C₃×C₅	#123	1	8	yes	—
178	C₂²×C₃×C₅	#124	1	4	yes	—
179	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	2	4	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×C₄×C₅	—	4	4	no	—
188	C₂⁴×C₃	—	2	4	no	—
189	C₂⁴×C₃	—	2	4	no	—
190	C₂⁴×C₃	—	2	4	no	—
191	C₂⁴×C₃	—	2	4	no	—
192	C₂⁴×C₃	—	2	4	no	—
193	C₂⁴×C₃	—	2	4	no	—
194	C₂⁴×C₃	C₅×D₄	1	8	yes	—
195	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
196	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
197	C₂×C₃×D₄	—	2	32	no	—
198	C₂×C₃×D₄	—	2	16	no	—
199	C₂×C₃×D₄	—	2	8	no	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	4	no	—
204	C₂²×C₃×C₄	—	2	4	no	—
205	C₂²×C₃×C₄	—	2	4	no	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	4	no	—
208	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
209	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
210	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	2	16	no	—
216	C₃×C₂²⋊C₄	—	2	16	no	—
217	C₂³×C₅	—	2	16	no	—
218	C₂³×C₅	—	2	16	no	—
219	C₂³×C₅	—	2	16	no	—
220	C₂³×C₅	—	2	4	no	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	4	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	4	8	no	—
227	C₂³×C₅	—	4	8	no	—
228	C₂³×C₅	—	4	8	no	—
229	C₂³×C₅	—	4	8	no	—
230	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
231	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
232	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
234	C₂³×C₅	C₃×#41	1	2	yes	—
235	C₂³×C₅	C₃×#41	1	4	yes	—
236	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
237	C₅×D₄	—	2	32	no	—
238	C₂×C₄×C₅	—	2	8	no	—
239	C₂×C₄×C₅	—	2	8	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	4	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	4	4	no	—
249	C₂×C₄×C₅	—	4	8	no	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
252	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
253	C₂²×D₄	—	2	8	no	—
254	C₂²×D₄	—	2	4	no	—
255	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
256	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
262	C₂×C₂²⋊C₄	—	2	8	no	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
265	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
266	#95	C₂²×C₃×C₅	1	4	yes	complemented
267	C₂×C₃×C₅	—	4	8	no	—
268	C₂×C₃×C₅	#394	1	8	yes	direct product factor
269	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×#121	1	2	yes	—
272	C₂×C₃×C₅	C₂×#123	1	2	yes	—
273	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
274	C₂³×C₃	—	2	16	no	—
275	C₂³×C₃	—	2	16	no	—
276	C₂³×C₃	—	2	16	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	—	2	4	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	4	no	—
282	C₂³×C₃	—	2	4	no	—
283	C₂³×C₃	—	4	8	no	—
284	C₂³×C₃	—	4	8	no	—
285	C₂³×C₃	—	4	8	no	—
286	C₂³×C₃	—	4	8	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
288	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
289	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
290	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
291	C₂³×C₃	C₅×#41	1	2	yes	—
292	C₂³×C₃	C₅×#41	1	4	yes	—
293	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
294	C₃×D₄	—	2	32	no	—
295	C₂×C₃×C₄	—	2	8	no	—
296	C₂×C₃×C₄	—	2	8	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	4	no	—
305	C₂×C₃×C₄	—	4	4	no	—
306	C₂×C₃×C₄	—	4	8	no	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
308	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	—	2	8	no	—
311	C₂²×C₅	—	2	8	no	—
312	C₂²×C₅	—	4	32	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	—	4	4	no	—
315	C₂²×C₅	—	4	4	no	—
316	C₂²×C₅	—	4	4	no	—
317	C₂²×C₅	C₃×#120	1	4	yes	—
318	C₂²×C₅	C₃×#121	1	4	yes	—
319	C₂²×C₅	C₃×#121	1	8	yes	—
320	C₂²×C₅	C₃×#123	1	8	yes	—
321	C₂²×C₅	C₃×#124	1	4	yes	—
322	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
323	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
324	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
326	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	4	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	C₃×C₅×D₄	1	8	yes	—
338	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
339	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
340	C₂×D₄	—	2	32	no	—
341	C₂×D₄	—	2	16	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
352	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
353	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
354	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
355	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
356	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
357	C₄⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	2	16	no	—
359	C₂²⋊C₄	—	2	16	no	—
360	C₃×C₅	C₂×#394	1	1	yes	characteristic, direct product factor, Hall
361	C₂²×C₃	—	2	8	no	—
362	C₂²×C₃	—	2	8	no	—
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	—	4	32	no	—
365	C₂²×C₃	—	4	4	no	—
366	C₂²×C₃	—	4	4	no	—
367	C₂²×C₃	—	4	4	no	—
368	C₂²×C₃	—	4	4	no	—
369	C₂²×C₃	C₅×#120	1	4	yes	—
370	C₂²×C₃	C₅×#121	1	4	yes	—
371	C₂²×C₃	C₅×#121	1	8	yes	—
372	C₂²×C₃	C₅×#123	1	8	yes	—
373	C₂²×C₃	C₅×#124	1	4	yes	—
374	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
375	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
378	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
379	C₃×C₄	—	2	4	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	4	4	no	—
383	C₂×C₅	—	4	8	no	—
384	C₂×C₅	C₃×#394	1	8	yes	direct product factor
385	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
386	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
387	C₂×C₅	C₂×C₃×#121	1	2	yes	—
388	C₂×C₅	C₂×C₃×#123	1	2	yes	—
389	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
390	C₂³	—	2	16	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	16	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	16	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	8	no	—
402	C₂³	—	4	8	no	—
403	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
404	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
405	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
406	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
407	C₂³	C₃×C₅×#41	1	2	yes	—
408	C₂³	C₃×C₅×#41	1	4	yes	—
409	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
410	D₄	—	2	32	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
424	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	complemented
425	C₂×C₃	—	4	8	no	—
426	C₂×C₃	C₅×#394	1	8	yes	direct product factor
427	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
428	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
429	C₂×C₃	C₂×C₅×#121	1	2	yes	—
430	C₂×C₃	C₂×C₅×#123	1	2	yes	—
431	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
432	C₅	C₂×C₃×#394	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	8	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	32	no	—
441	C₂²	C₃×C₅×#120	1	4	yes	—
442	C₂²	C₃×C₅×#121	1	4	yes	—
443	C₂²	C₃×C₅×#121	1	8	yes	—
444	C₂²	C₃×C₅×#123	1	8	yes	—
445	C₂²	C₃×C₅×#124	1	4	yes	—
446	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
447	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
448	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
449	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
450	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	4	no	—
455	C₃	C₂×C₅×#394	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	4	8	no	—
457	C₂	C₃×C₅×#394	1	8	yes	direct product factor
458	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
459	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
460	C₂	C₂×C₃×C₅×#121	1	2	yes	—
461	C₂	C₂×C₃×C₅×#123	1	2	yes	—
462	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅×D₄	C₂
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
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
5. C₃×C₅×#394	C₂	direct (N × H)
6. C₂×C₃×C₅×#95	C₂	semidirect
7. C₂×C₅×#394	C₃	direct (N × H)
17. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₂×C₃×#394	C₅	direct (N × H)
25. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
26. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
27. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
28. C₅×#394	C₂×C₃	direct (N × H)
29. C₂×C₅×#95	C₂×C₃	semidirect
51. C₂²×C₃×C₄×C₅	D₄	semidirect
60. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
61. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
62. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
63. C₃×#394	C₂×C₅	direct (N × H)
64. C₂×C₃×#95	C₂×C₅	semidirect
74. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
77. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
78. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
79. C₅×#95	C₂²×C₃	semidirect
80. C₂×#394	C₃×C₅	direct (N × H)
115. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
125. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
128. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
129. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
130. C₃×#95	C₂²×C₅	semidirect
152. C₂²×C₄×C₅	C₃×D₄	semidirect
161. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
162. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
163. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
164. #394	C₂×C₃×C₅	direct (N × H)
165. C₂×#95	C₂×C₃×C₅	semidirect
209. C₂²×C₃×C₄	C₅×D₄	semidirect
251. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
261. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
264. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
265. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
266. #95	C₂²×C₃×C₅	semidirect
268. C₂×C₃×C₅	#394	direct (N × H)
308. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
352. C₂²×C₄	C₃×C₅×D₄	semidirect
360. C₃×C₅	C₂×#394	direct (N × H)
384. C₂×C₅	C₃×#394	direct (N × H)
424. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
426. C₂×C₃	C₅×#394	direct (N × H)
432. C₅	C₂×C₃×#394	direct (N × H)
455. C₃	C₂×C₅×#394	direct (N × H)
457. C₂	C₃×C₅×#394	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
C₃×C₅×#394	2
C₂×C₃×C₅×#95	2
C₂×C₅×#394	3
C₂×C₃×#394	5

Subgroups — C2×C3×C5×#394 #14275420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#394 #14275420