Subgroups — C₃×C₅×#2622 #14275656

Order 1920.

1404 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2622	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₃×C₅×#120	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
22	C₃×C₅×#95	C₂²	1	4	yes	complemented
23	C₃×C₅×#95	C₂²	1	4	yes	complemented
24	C₃×#2622	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×#397	C₂×C₃	1	4	yes	complemented
28	C₅×#394	C₂×C₃	1	4	yes	complemented
29	C₅×#386	C₂×C₃	1	2	yes	complemented
30	C₅×#385	C₂×C₃	1	2	yes	complemented
31	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	—	2	4	no	—
33	C₂⁴×C₃×C₅	—	4	4	no	—
34	C₂⁴×C₃×C₅	D₄	1	4	yes	—
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	4	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	4	4	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	4	4	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
54	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
55	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
56	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#397	C₂×C₅	1	4	yes	complemented
58	C₃×#394	C₂×C₅	1	4	yes	complemented
59	C₃×#386	C₂×C₅	1	2	yes	complemented
60	C₃×#385	C₂×C₅	1	2	yes	complemented
61	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
65	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
66	C₅×#120	—	2	4	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
68	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
75	C₅×#95	C₂²×C₃	1	4	yes	complemented
76	C₅×#95	C₂²×C₃	1	4	yes	complemented
77	#2622	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	8	no	—
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	—	2	1	no	—
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	—	2	4	no	—
86	C₂³×C₃×C₅	—	4	8	no	—
87	C₂³×C₃×C₅	—	4	16	no	—
88	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
89	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
90	C₂³×C₃×C₅	#41	1	4	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×D₄	—	4	8	no	—
93	C₃×C₅×D₄	—	4	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	4	8	no	—
105	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
108	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
109	C₃×#120	—	2	4	no	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
111	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
118	C₃×#95	C₂²×C₅	1	4	yes	complemented
119	C₃×#95	C₂²×C₅	1	4	yes	complemented
120	C₂⁴×C₅	—	2	4	no	—
121	C₂⁴×C₅	—	4	4	no	—
122	C₂⁴×C₅	C₃×D₄	1	4	yes	—
123	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
125	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	—	4	4	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	4	4	no	—
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	1	yes	characteristic
136	C₅×C₄⋊C₄	—	4	4	no	—
137	C₅×C₂²⋊C₄	—	2	8	no	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	4	no	—
141	C₅×C₂²⋊C₄	—	4	4	no	—
142	C₅×C₂²⋊C₄	—	4	4	no	—
143	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
144	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	#397	C₂×C₃×C₅	1	4	yes	complemented
146	#394	C₂×C₃×C₅	1	4	yes	complemented
147	#386	C₂×C₃×C₅	1	2	yes	complemented
148	#385	C₂×C₃×C₅	1	2	yes	complemented
149	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	—	2	4	no	—
153	C₂²×C₃×C₅	—	2	4	no	—
154	C₂²×C₃×C₅	—	2	4	no	—
155	C₂²×C₃×C₅	—	4	16	no	—
156	C₂²×C₃×C₅	—	4	8	no	—
157	C₂²×C₃×C₅	—	4	1	no	—
158	C₂²×C₃×C₅	—	4	2	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	#123	1	4	yes	—
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
163	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
164	C₃×C₄×C₅	—	4	1	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	—	4	4	no	—
168	C₂⁴×C₃	—	2	4	no	—
169	C₂⁴×C₃	—	4	4	no	—
170	C₂⁴×C₃	C₅×D₄	1	4	yes	—
171	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
172	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
173	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	4	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	4	4	no	—
180	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₃×C₄⋊C₄	—	4	4	no	—
185	C₃×C₂²⋊C₄	—	2	8	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	—	2	2	no	—
188	C₃×C₂²⋊C₄	—	2	4	no	—
189	C₃×C₂²⋊C₄	—	4	4	no	—
190	C₃×C₂²⋊C₄	—	4	4	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	2	8	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	2	4	no	—
199	C₂³×C₅	—	4	8	no	—
200	C₂³×C₅	—	4	16	no	—
201	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
202	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
203	C₂³×C₅	C₃×#41	1	4	yes	—
204	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
205	C₅×D₄	—	4	8	no	—
206	C₅×D₄	—	4	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	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	—	2	4	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	4	8	no	—
218	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
221	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
222	#120	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
224	C₂×C₂²⋊C₄	—	2	4	no	—
225	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
231	#95	C₂²×C₃×C₅	1	4	yes	complemented
232	#95	C₂²×C₃×C₅	1	4	yes	complemented
233	C₂×C₃×C₅	—	2	4	no	—
234	C₂×C₃×C₅	—	4	4	no	—
235	C₂×C₃×C₅	—	8	1	no	—
236	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
237	C₂×C₃×C₅	#534	1	2	yes	—
238	C₂×C₃×C₅	#538	1	4	yes	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	2	8	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	4	8	no	—
248	C₂³×C₃	—	4	16	no	—
249	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
250	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
251	C₂³×C₃	C₅×#41	1	4	yes	—
252	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
253	C₃×D₄	—	4	8	no	—
254	C₃×D₄	—	4	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	2	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	C₂²×C₅	—	2	4	no	—
267	C₂²×C₅	—	2	8	no	—
268	C₂²×C₅	—	2	4	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	4	no	—
271	C₂²×C₅	—	4	16	no	—
272	C₂²×C₅	—	4	8	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	4	2	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	C₃×#123	1	4	yes	—
277	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
279	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
280	C₄×C₅	—	4	1	no	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	4	4	no	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	4	4	no	—
286	C₂⁴	C₃×C₅×D₄	1	4	yes	—
287	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
288	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
289	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
299	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
300	C₄⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₃×C₅	#2622	1	1	yes	characteristic, direct product factor, Hall
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	2	4	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	4	16	no	—
314	C₂²×C₃	—	4	8	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	—	4	4	no	—
318	C₂²×C₃	C₅×#123	1	4	yes	—
319	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
321	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	4	4	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	4	4	no	—
326	C₂×C₅	—	2	4	no	—
327	C₂×C₅	—	4	4	no	—
328	C₂×C₅	—	8	1	no	—
329	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
330	C₂×C₅	C₃×#534	1	2	yes	—
331	C₂×C₅	C₃×#538	1	4	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	—	4	16	no	—
342	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
343	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
344	C₂³	C₃×C₅×#41	1	4	yes	—
345	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
346	D₄	—	4	8	no	—
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₃	—	2	4	no	—
360	C₂×C₃	—	4	4	no	—
361	C₂×C₃	—	8	1	no	—
362	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
363	C₂×C₃	C₅×#534	1	2	yes	—
364	C₂×C₃	C₅×#538	1	4	yes	—
365	C₅	C₃×#2622	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	4	16	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₃×C₅×#123	1	4	yes	—
377	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
378	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
379	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	4	no	—
384	C₃	C₅×#2622	1	1	yes	characteristic, direct product factor, Sylow
385	C₂	—	2	4	no	—
386	C₂	—	4	4	no	—
387	C₂	—	8	1	no	—
388	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
389	C₂	C₃×C₅×#534	1	2	yes	—
390	C₂	C₃×C₅×#538	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#386	C₂	semidirect
6. C₃×C₅×#385	C₂	semidirect
7. C₃×C₅×#379	C₂	semidirect
8. C₅×#2622	C₃	direct (N × H)
14. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₃×C₅×#95	C₂²	semidirect
24. C₃×#2622	C₅	direct (N × H)
26. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
27. C₅×#397	C₂×C₃	semidirect
28. C₅×#394	C₂×C₃	semidirect
29. C₅×#386	C₂×C₃	semidirect
30. C₅×#385	C₂×C₃	semidirect
31. C₅×#379	C₂×C₃	semidirect
56. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
57. C₃×#397	C₂×C₅	semidirect
58. C₃×#394	C₂×C₅	semidirect
59. C₃×#386	C₂×C₅	semidirect
60. C₃×#385	C₂×C₅	semidirect
61. C₃×#379	C₂×C₅	semidirect
67. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
74. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
75. C₅×#95	C₂²×C₃	semidirect
76. C₅×#95	C₂²×C₃	semidirect
77. #2622	C₃×C₅	direct (N × H)
110. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
117. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
118. C₃×#95	C₂²×C₅	semidirect
119. C₃×#95	C₂²×C₅	semidirect
144. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
145. #397	C₂×C₃×C₅	semidirect
146. #394	C₂×C₃×C₅	semidirect
147. #386	C₂×C₃×C₅	semidirect
148. #385	C₂×C₃×C₅	semidirect
149. #379	C₂×C₃×C₅	semidirect
223. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
230. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
231. #95	C₂²×C₃×C₅	semidirect
232. #95	C₂²×C₃×C₅	semidirect
307. C₃×C₅	#2622	direct (N × H)
365. C₅	C₃×#2622	direct (N × H)
384. C₃	C₅×#2622	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×C₃×C₅×#120	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#379	2
C₅×#2622	3
C₃×#2622	5

Subgroups — C3×C5×#2622 #14275656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2622 #14275656