Subgroups — C₃×C₅×#2547 #14275581

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#380	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2547	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
13	C₃×C₅×#124	—	2	8	no	—
14	C₃×C₄×C₅×D₄	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	8	yes	—
25	C₃×#2547	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#124	C₂×C₃	1	2	yes	—
28	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
29	C₅×#397	C₂×C₃	1	4	yes	complemented
30	C₅×#391	C₂×C₃	1	2	yes	complemented
31	C₅×#380	C₂×C₃	1	4	yes	complemented
32	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	8	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	D₄	1	4	yes	—
56	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×C₃×#124	C₂×C₅	1	2	yes	—
58	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
59	C₃×#397	C₂×C₅	1	4	yes	complemented
60	C₃×#391	C₂×C₅	1	2	yes	complemented
61	C₃×#380	C₂×C₅	1	4	yes	complemented
62	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
64	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
66	C₅×C₄⋊Q₈	—	2	4	no	—
67	C₅×#124	—	2	8	no	—
68	C₄×C₅×D₄	—	2	4	no	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×#95	C₂²×C₃	1	2	yes	—
78	C₅×#95	C₂²×C₃	1	8	yes	—
79	#2547	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₃×C₅×Q₈	—	4	8	no	—
87	C₃×C₅×D₄	—	2	8	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	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	—	4	8	no	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
105	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
106	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
107	C₃×C₄⋊Q₈	—	2	4	no	—
108	C₃×#124	—	2	8	no	—
109	C₃×C₄×D₄	—	2	4	no	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
116	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
118	C₃×#95	C₂²×C₅	1	2	yes	—
119	C₃×#95	C₂²×C₅	1	8	yes	—
120	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
121	C₂×C₅×Q₈	—	2	4	no	—
122	C₂×C₅×Q₈	—	2	4	no	—
123	C₂×C₅×Q₈	—	2	4	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	2	no	—
126	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	8	no	—
129	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₂²⋊C₄	—	2	16	no	—
140	C₅×C₂²⋊C₄	—	2	4	no	—
141	C₄²×C₅	—	2	4	no	—
142	C₄²×C₅	C₃×D₄	1	4	yes	—
143	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
144	C₂×#124	C₂×C₃×C₅	1	2	yes	—
145	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
146	#397	C₂×C₃×C₅	1	4	yes	complemented
147	#391	C₂×C₃×C₅	1	2	yes	complemented
148	#380	C₂×C₃×C₅	1	4	yes	complemented
149	C₄×C₄⋊C₄	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	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	4	no	—
155	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
159	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
160	C₃×C₄×C₅	—	2	2	no	—
161	C₃×C₄×C₅	—	4	4	no	—
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	—	4	4	no	—
164	C₃×C₄×C₅	#121	1	4	yes	—
165	C₃×C₄×C₅	#124	1	4	yes	complemented
166	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
167	C₂×C₃×Q₈	—	2	4	no	—
168	C₂×C₃×Q₈	—	2	4	no	—
169	C₂×C₃×Q₈	—	2	4	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	8	no	—
175	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₂²⋊C₄	—	2	16	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	C₅×D₄	1	4	yes	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
194	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
195	C₅×Q₈	—	4	8	no	—
196	C₅×D₄	—	2	8	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	4	8	no	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₃×#41	1	2	yes	—
212	C₂×C₄×C₅	C₃×#41	1	4	yes	—
213	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
214	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
216	C₄⋊Q₈	—	2	4	no	—
217	#124	—	2	8	no	—
218	C₄×D₄	—	2	4	no	—
219	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
225	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
227	#95	C₂²×C₃×C₅	1	2	yes	—
228	#95	C₂²×C₃×C₅	1	8	yes	—
229	C₂×C₃×C₅	—	4	4	no	—
230	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
231	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
232	C₂×C₃×C₅	#536	1	1	yes	characteristic
233	C₂×C₃×C₅	#547	1	2	yes	—
234	C₂×C₃×C₅	#556	1	2	yes	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
240	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
241	C₃×Q₈	—	4	8	no	—
242	C₃×D₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	4	8	no	—
253	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₅×#41	1	2	yes	—
258	C₂×C₃×C₄	C₅×#41	1	4	yes	—
259	C₂²×C₅	—	2	4	no	—
260	C₂²×C₅	—	2	8	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	4	no	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
266	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
268	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
269	C₄×C₅	—	2	2	no	—
270	C₄×C₅	—	4	4	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	4	no	—
273	C₄×C₅	C₃×#121	1	4	yes	—
274	C₄×C₅	C₃×#124	1	4	yes	complemented
275	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
285	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
286	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
287	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	16	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₄²	—	2	4	no	—
297	C₄²	C₃×C₅×D₄	1	4	yes	—
298	C₃×C₅	#2547	1	1	yes	characteristic, direct product factor, Hall
299	C₂²×C₃	—	2	4	no	—
300	C₂²×C₃	—	2	8	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	—	4	2	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
307	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
308	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	4	no	—
313	C₃×C₄	C₅×#121	1	4	yes	—
314	C₃×C₄	C₅×#124	1	4	yes	complemented
315	C₂×C₅	—	4	4	no	—
316	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
317	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
318	C₂×C₅	C₃×#536	1	1	yes	characteristic
319	C₂×C₅	C₃×#547	1	2	yes	—
320	C₂×C₅	C₃×#556	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
326	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
327	Q₈	—	4	8	no	—
328	D₄	—	2	8	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
340	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
341	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
342	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
343	C₂×C₄	C₃×C₅×#41	1	2	yes	—
344	C₂×C₄	C₃×C₅×#41	1	4	yes	—
345	C₂×C₃	—	4	4	no	—
346	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
347	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
348	C₂×C₃	C₅×#536	1	1	yes	characteristic
349	C₂×C₃	C₅×#547	1	2	yes	—
350	C₂×C₃	C₅×#556	1	2	yes	—
351	C₅	C₃×#2547	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	4	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	4	no	—
357	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
358	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
359	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
360	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
361	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	4	no	—
366	C₄	C₃×C₅×#121	1	4	yes	—
367	C₄	C₃×C₅×#124	1	4	yes	complemented
368	C₃	C₅×#2547	1	1	yes	characteristic, direct product factor, Sylow
369	C₂	—	4	4	no	—
370	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
371	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
372	C₂	C₃×C₅×#536	1	1	yes	characteristic
373	C₂	C₃×C₅×#547	1	2	yes	—
374	C₂	C₃×C₅×#556	1	2	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
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#380	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₅×#2547	C₃	direct (N × H)
25. C₃×#2547	C₅	direct (N × H)
26. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
29. C₅×#397	C₂×C₃	semidirect
30. C₅×#391	C₂×C₃	semidirect
31. C₅×#380	C₂×C₃	semidirect
32. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
56. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
59. C₃×#397	C₂×C₅	semidirect
60. C₃×#391	C₂×C₅	semidirect
61. C₃×#380	C₂×C₅	semidirect
62. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
79. #2547	C₃×C₅	direct (N × H)
143. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
146. #397	C₂×C₃×C₅	semidirect
147. #391	C₂×C₃×C₅	semidirect
148. #380	C₂×C₃×C₅	semidirect
149. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
165. C₃×C₄×C₅	#124	semidirect
274. C₄×C₅	C₃×#124	semidirect
298. C₃×C₅	#2547	direct (N × H)
314. C₃×C₄	C₅×#124	semidirect
351. C₅	C₃×#2547	direct (N × H)
367. C₄	C₃×C₅×#124	semidirect
368. C₃	C₅×#2547	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×C₄⋊Q₈	2
C₂×C₃×C₅×#124	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#397	2
C₃×C₅×#391	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2547	3
C₃×#2547	5

Subgroups — C3×C5×#2547 #14275581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2547 #14275581