Subgroups — C₃×C₅×#3080 #14276114

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#428	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#417	C₂	1	2	yes	maximal
8	C₅×#3080	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
11	C₃×C₅×#125	—	2	1	no	—
12	C₃×C₅×#125	—	2	1	no	—
13	C₃×C₅×#125	C₂²	1	4	yes	—
14	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	—	2	2	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₅×#117	—	2	1	no	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#107	C₂²	1	4	yes	—
24	C₃×C₅×#106	C₂²	1	4	yes	—
25	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	—
26	C₃×C₅×#103	C₂²	1	4	yes	—
27	C₃×C₅×#102	C₂²	1	4	yes	—
28	C₃×#3080	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
30	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
31	C₅×#479	C₂×C₃	1	4	yes	complemented
32	C₅×#478	C₂×C₃	1	4	yes	complemented
33	C₅×#428	C₂×C₃	1	2	yes	complemented
34	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#417	C₂×C₃	1	2	yes	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	Q₈	1	4	yes	—
38	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×M₁₆	—	2	4	no	—
47	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	2	no	—
58	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	2	yes	—
61	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
63	C₃×#479	C₂×C₅	1	4	yes	complemented
64	C₃×#478	C₂×C₅	1	4	yes	complemented
65	C₃×#428	C₂×C₅	1	2	yes	complemented
66	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#417	C₂×C₅	1	2	yes	—
68	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
70	C₅×#125	—	2	1	no	—
71	C₅×#125	—	2	1	no	—
72	C₅×#125	C₂²×C₃	1	4	yes	—
73	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
74	C₄×C₅×D₄	—	2	2	no	—
75	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
76	C₅×#117	—	2	1	no	—
77	C₅×#117	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×#107	C₂²×C₃	1	4	yes	—
83	C₅×#106	C₂²×C₃	1	4	yes	—
84	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	—
85	C₅×#103	C₂²×C₃	1	4	yes	—
86	C₅×#102	C₂²×C₃	1	4	yes	—
87	#3080	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂³×C₃×C₅	—	2	1	no	—
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₃×C₅×Q₈	—	2	1	no	—
91	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
92	C₃×C₅×D₄	—	2	4	no	—
93	C₃×C₅×D₄	—	2	1	no	—
94	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	2	no	—
100	C₂×C₃×C₄×C₅	—	4	4	no	—
101	C₂×C₃×C₄×C₅	—	4	4	no	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₅×C₈	—	2	4	no	—
109	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
111	C₃×#125	—	2	1	no	—
112	C₃×#125	—	2	1	no	—
113	C₃×#125	C₂²×C₅	1	4	yes	—
114	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
115	C₃×C₄×D₄	—	2	2	no	—
116	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
117	C₃×#117	—	2	1	no	—
118	C₃×#117	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₄²	—	2	1	no	—
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₃×#107	C₂²×C₅	1	4	yes	—
124	C₃×#106	C₂²×C₅	1	4	yes	—
125	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	—
126	C₃×#103	C₂²×C₅	1	4	yes	—
127	C₃×#102	C₂²×C₅	1	4	yes	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	C₃×Q₈	1	4	yes	—
130	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₅×M₁₆	—	2	4	no	—
139	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
145	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	1	no	—
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
151	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
152	C₄²×C₅	C₂³×C₃	1	2	yes	—
153	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
154	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic
155	#479	C₂×C₃×C₅	1	4	yes	complemented
156	#478	C₂×C₃×C₅	1	4	yes	complemented
157	#428	C₂×C₃×C₅	1	2	yes	complemented
158	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	#417	C₂×C₃×C₅	1	2	yes	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
164	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
165	C₃×C₄×C₅	—	2	2	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
171	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
173	C₃×#41	—	2	2	no	—
174	C₃×#41	C₅×Q₈	1	4	yes	—
175	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₃×M₁₆	—	2	4	no	—
184	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
190	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₂²⋊C₄	—	2	2	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
196	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
197	C₃×C₄²	C₂³×C₅	1	2	yes	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	—
202	C₅×D₄	—	2	4	no	—
203	C₅×D₄	—	2	1	no	—
204	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	4	no	—
211	C₂×C₄×C₅	—	4	4	no	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
216	C₂×C₄×C₅	C₃×#41	1	2	yes	—
217	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
218	C₅×C₈	—	2	4	no	—
219	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
221	#125	—	2	1	no	—
222	#125	—	2	1	no	—
223	#125	C₂²×C₃×C₅	1	4	yes	—
224	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
227	#117	—	2	1	no	—
228	#117	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
233	#107	C₂²×C₃×C₅	1	4	yes	—
234	#106	C₂²×C₃×C₅	1	4	yes	—
235	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	—
236	#103	C₂²×C₃×C₅	1	4	yes	—
237	#102	C₂²×C₃×C₅	1	4	yes	—
238	C₂×C₃×C₅	—	2	2	no	—
239	C₂×C₃×C₅	—	4	2	no	—
240	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₃×C₅	#575	1	2	yes	—
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
244	C₃×Q₈	—	2	1	no	—
245	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	1	no	—
248	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	—	4	4	no	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
260	C₂×C₃×C₄	C₅×#41	1	2	yes	—
261	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
262	C₃×C₈	—	2	4	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
267	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	2	2	no	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	4	no	—
273	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
274	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
275	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
276	#41	—	2	2	no	—
277	#41	C₃×C₅×Q₈	1	4	yes	—
278	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
285	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
286	M₁₆	—	2	4	no	—
287	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
293	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
299	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
300	C₄²	C₂³×C₃×C₅	1	2	yes	—
301	C₃×C₅	#3080	1	1	yes	characteristic, direct product factor, Hall
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
306	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	4	no	—
312	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
313	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
314	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	4	2	no	—
317	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
318	C₂×C₅	C₃×#575	1	2	yes	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
321	Q₈	—	2	1	no	—
322	Q₈	C₂×C₃×C₅×Q₈	1	2	yes	—
323	D₄	—	2	4	no	—
324	D₄	—	2	1	no	—
325	D₄	C₂×C₃×C₅×Q₈	1	2	yes	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
335	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
337	C₂×C₄	C₃×C₅×#41	1	2	yes	—
338	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	4	2	no	—
342	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
343	C₂×C₃	C₅×#575	1	2	yes	—
344	C₅	C₃×#3080	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
349	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	4	no	—
355	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
356	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
357	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
358	C₃	C₅×#3080	1	1	yes	characteristic, direct product factor, Sylow
359	C₂	—	2	2	no	—
360	C₂	—	4	2	no	—
361	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂	C₃×C₅×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#428	C₂	semidirect
6. C₃×C₅×#423	C₂	semidirect
8. C₅×#3080	C₃	direct (N × H)
28. C₃×#3080	C₅	direct (N × H)
29. C₂×C₅×#125	C₂×C₃	semidirect
31. C₅×#479	C₂×C₃	semidirect
32. C₅×#478	C₂×C₃	semidirect
33. C₅×#428	C₂×C₃	semidirect
34. C₅×#423	C₂×C₃	semidirect
61. C₂×C₃×#125	C₂×C₅	semidirect
63. C₃×#479	C₂×C₅	semidirect
64. C₃×#478	C₂×C₅	semidirect
65. C₃×#428	C₂×C₅	semidirect
66. C₃×#423	C₂×C₅	semidirect
87. #3080	C₃×C₅	direct (N × H)
153. C₂×#125	C₂×C₃×C₅	semidirect
155. #479	C₂×C₃×C₅	semidirect
156. #478	C₂×C₃×C₅	semidirect
157. #428	C₂×C₃×C₅	semidirect
158. #423	C₂×C₃×C₅	semidirect
301. C₃×C₅	#3080	direct (N × H)
344. C₅	C₃×#3080	direct (N × H)
358. C₃	C₅×#3080	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×#125	2
C₃×C₄×C₅×#41	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#428	2
C₃×C₅×#423	2
C₃×C₅×#417	2
C₅×#3080	3
C₃×#3080	5

Subgroups — C3×C5×#3080 #14276114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3080 #14276114