Subgroups — C₃×C₅×#2632 #14275666

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#399	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal
6	C₃×C₅×#393	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2632	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₃×C₅×#124	—	2	4	no	—
14	C₃×C₄×C₅×Q₈	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
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	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2632	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#399	C₂×C₃	1	2	yes	complemented
32	C₅×#395	C₂×C₃	1	2	yes	complemented
33	C₅×#394	C₂×C₃	1	2	yes	—
34	C₅×#393	C₂×C₃	1	2	yes	complemented
35	C₅×#388	C₂×C₃	1	4	yes	complemented
36	C₅×#383	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	—	4	2	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	4	2	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₄⋊C₄	—	4	4	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
57	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₃×C₄²×C₅	D₄	1	4	yes	—
60	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
61	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#399	C₂×C₅	1	2	yes	complemented
63	C₃×#395	C₂×C₅	1	2	yes	complemented
64	C₃×#394	C₂×C₅	1	2	yes	—
65	C₃×#393	C₂×C₅	1	2	yes	complemented
66	C₃×#388	C₂×C₅	1	4	yes	complemented
67	C₃×#383	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₅×#124	—	2	4	no	—
72	C₄×C₅×Q₈	—	2	4	no	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	C₅×#95	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	4	yes	—
86	#2632	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	—	2	4	no	—
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	8	no	—
93	C₃×C₅×Q₈	—	4	4	no	—
94	C₃×C₅×D₄	—	4	4	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	4	yes	—
111	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
112	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
114	C₃×#124	—	2	4	no	—
115	C₃×C₄×Q₈	—	2	4	no	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
123	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
125	C₃×#95	C₂²×C₅	1	2	yes	—
126	C₃×#95	C₂²×C₅	1	2	yes	—
127	C₃×#95	C₂²×C₅	1	2	yes	—
128	C₃×#95	C₂²×C₅	1	4	yes	—
129	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	2	4	no	—
133	C₂×C₅×Q₈	—	4	2	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	4	2	no	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	4	4	no	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	2	8	no	—
149	C₅×C₂²⋊C₄	—	4	4	no	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	C₃×D₄	1	4	yes	—
152	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
154	#399	C₂×C₃×C₅	1	2	yes	complemented
155	#395	C₂×C₃×C₅	1	2	yes	complemented
156	#394	C₂×C₃×C₅	1	2	yes	—
157	#393	C₂×C₃×C₅	1	2	yes	complemented
158	#388	C₂×C₃×C₅	1	4	yes	complemented
159	#383	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	—	4	2	no	—
161	C₂²×C₃×C₅	—	4	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	—	4	8	no	—
164	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
167	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	4	no	—
170	C₃×C₄×C₅	—	2	2	no	—
171	C₃×C₄×C₅	—	2	2	no	—
172	C₃×C₄×C₅	—	4	2	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	4	no	—
175	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
176	C₂×C₃×Q₈	—	2	2	no	—
177	C₂×C₃×Q₈	—	2	2	no	—
178	C₂×C₃×Q₈	—	2	4	no	—
179	C₂×C₃×Q₈	—	4	2	no	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	4	2	no	—
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	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
189	C₃×C₄⋊C₄	—	2	4	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	4	4	no	—
192	C₃×C₂²⋊C₄	—	2	4	no	—
193	C₃×C₂²⋊C₄	—	2	4	no	—
194	C₃×C₂²⋊C₄	—	2	8	no	—
195	C₃×C₂²⋊C₄	—	4	4	no	—
196	C₃×C₄²	—	2	4	no	—
197	C₃×C₄²	C₅×D₄	1	4	yes	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	4	no	—
200	C₂³×C₅	—	2	4	no	—
201	C₂³×C₅	—	2	4	no	—
202	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₅×Q₈	—	2	8	no	—
204	C₅×Q₈	—	4	4	no	—
205	C₅×D₄	—	4	4	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	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	—	2	4	no	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₃×#41	1	4	yes	—
222	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	#124	—	2	4	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
233	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
234	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
235	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
236	#95	C₂²×C₃×C₅	1	2	yes	—
237	#95	C₂²×C₃×C₅	1	2	yes	—
238	#95	C₂²×C₃×C₅	1	2	yes	—
239	#95	C₂²×C₃×C₅	1	4	yes	—
240	C₂×C₃×C₅	—	8	2	no	—
241	C₂×C₃×C₅	#525	1	1	yes	characteristic
242	C₂×C₃×C₅	#535	1	1	yes	characteristic
243	C₂×C₃×C₅	#536	1	1	yes	characteristic
244	C₂×C₃×C₅	#542	1	4	yes	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
250	C₃×Q₈	—	2	8	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₃×D₄	—	4	4	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	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	C₂×C₅×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
267	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
268	C₂×C₃×C₄	C₅×#41	1	4	yes	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	8	no	—
273	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
275	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	4	4	no	—
284	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
292	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
293	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	8	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	C₃×C₅×D₄	1	4	yes	—
307	C₃×C₅	#2632	1	1	yes	characteristic, direct product factor, Hall
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	4	2	no	—
310	C₂²×C₃	—	4	2	no	—
311	C₂²×C₃	—	4	8	no	—
312	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
314	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
315	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	4	2	no	—
322	C₃×C₄	—	4	4	no	—
323	C₂×C₅	—	8	2	no	—
324	C₂×C₅	C₃×#525	1	1	yes	characteristic
325	C₂×C₅	C₃×#535	1	1	yes	characteristic
326	C₂×C₅	C₃×#536	1	1	yes	characteristic
327	C₂×C₅	C₃×#542	1	4	yes	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
333	Q₈	—	2	8	no	—
334	Q₈	—	4	4	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
349	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
350	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
351	C₂×C₄	C₃×C₅×#41	1	4	yes	—
352	C₂×C₃	—	8	2	no	—
353	C₂×C₃	C₅×#525	1	1	yes	characteristic
354	C₂×C₃	C₅×#535	1	1	yes	characteristic
355	C₂×C₃	C₅×#536	1	1	yes	characteristic
356	C₂×C₃	C₅×#542	1	4	yes	—
357	C₅	C₃×#2632	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	8	no	—
362	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
363	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
364	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
365	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
366	C₄	—	2	2	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	4	no	—
373	C₃	C₅×#2632	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	8	2	no	—
375	C₂	C₃×C₅×#525	1	1	yes	characteristic
376	C₂	C₃×C₅×#535	1	1	yes	characteristic
377	C₂	C₃×C₅×#536	1	1	yes	characteristic
378	C₂	C₃×C₅×#542	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#395	C₂	semidirect
6. C₃×C₅×#393	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#383	C₂	semidirect
9. C₅×#2632	C₃	direct (N × H)
28. C₃×#2632	C₅	direct (N × H)
30. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
31. C₅×#399	C₂×C₃	semidirect
32. C₅×#395	C₂×C₃	semidirect
34. C₅×#393	C₂×C₃	semidirect
35. C₅×#388	C₂×C₃	semidirect
36. C₅×#383	C₂×C₃	semidirect
61. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
62. C₃×#399	C₂×C₅	semidirect
63. C₃×#395	C₂×C₅	semidirect
65. C₃×#393	C₂×C₅	semidirect
66. C₃×#388	C₂×C₅	semidirect
67. C₃×#383	C₂×C₅	semidirect
86. #2632	C₃×C₅	direct (N × H)
153. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
154. #399	C₂×C₃×C₅	semidirect
155. #395	C₂×C₃×C₅	semidirect
157. #393	C₂×C₃×C₅	semidirect
158. #388	C₂×C₃×C₅	semidirect
159. #383	C₂×C₃×C₅	semidirect
307. C₃×C₅	#2632	direct (N × H)
357. C₅	C₃×#2632	direct (N × H)
373. C₃	C₅×#2632	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×#124	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#399	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#388	2
C₃×C₅×#383	2
C₅×#2632	3
C₃×#2632	5

Subgroups — C3×C5×#2632 #14275666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2632 #14275666