Subgroups — C₂×C₃×C₅×#475 #14276107

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 332 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
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#475	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#106	C₂	1	2	yes	maximal
5	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal
7	C₂×C₅×#475	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	—	2	1	no	—
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	—	2	1	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#106	C₂²	1	8	yes	—
22	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	—
23	C₃×C₅×#103	C₂²	1	8	yes	—
24	C₂×C₃×#475	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
27	C₅×#475	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₅×#106	C₂×C₃	1	2	yes	—
29	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#103	C₂×C₃	1	2	yes	—
31	C₂×C₃×C₅×Q₈	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	4	4	no	—
35	C₂×C₃×C₅×Q₈	Q₈	1	4	yes	complemented
36	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	4	no	—
44	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
50	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
51	C₃×C₄²×C₅	—	2	4	no	—
52	C₃×C₄²×C₅	D₄	1	2	yes	—
53	C₃×C₄²×C₅	C₂³	1	2	yes	—
54	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
55	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
56	C₃×#475	C₂×C₅	1	8	yes	direct product factor
57	C₂×C₃×#106	C₂×C₅	1	2	yes	—
58	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×#103	C₂×C₅	1	2	yes	—
60	C₂²×C₅×Q₈	—	2	1	no	—
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
63	C₅×C₄⋊Q₈	—	2	2	no	—
64	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#106	C₂²×C₃	1	8	yes	—
74	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	—
75	C₅×#103	C₂²×C₃	1	8	yes	—
76	C₂×#475	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
78	C₃×C₅×Q₈	—	2	4	no	—
79	C₃×C₅×Q₈	—	2	2	no	—
80	C₃×C₅×Q₈	—	4	8	no	—
81	C₃×C₅×Q₈	C₂×Q₈	1	4	yes	complemented
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	4	4	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₃×C₅×C₈	—	2	4	no	—
97	C₂²×C₃×Q₈	—	2	1	no	—
98	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
99	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
100	C₃×C₄⋊Q₈	—	2	2	no	—
101	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
102	C₃×C₄×Q₈	—	2	2	no	—
103	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄²	—	2	1	no	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₃×#106	C₂²×C₅	1	8	yes	—
111	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	—
112	C₃×#103	C₂²×C₅	1	8	yes	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	4	4	no	—
117	C₂×C₅×Q₈	C₃×Q₈	1	4	yes	complemented
118	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂×C₅×C₈	—	2	4	no	—
126	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
132	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
133	C₄²×C₅	—	2	4	no	—
134	C₄²×C₅	C₃×D₄	1	2	yes	—
135	C₄²×C₅	C₂³×C₃	1	2	yes	—
136	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
137	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
138	#475	C₂×C₃×C₅	1	8	yes	direct product factor
139	C₂×#106	C₂×C₃×C₅	1	2	yes	—
140	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
141	C₂×#103	C₂×C₃×C₅	1	2	yes	—
142	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
143	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
144	C₂²×C₃×C₅	#137	1	2	yes	—
145	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
146	C₃×C₄×C₅	—	2	4	no	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	4	4	no	—
149	C₃×C₄×C₅	—	4	2	no	—
150	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
151	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	—
152	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
154	C₂×C₃×Q₈	—	2	1	no	—
155	C₂×C₃×Q₈	—	2	4	no	—
156	C₂×C₃×Q₈	—	2	2	no	—
157	C₂×C₃×Q₈	—	4	4	no	—
158	C₂×C₃×Q₈	C₅×Q₈	1	4	yes	complemented
159	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	2	2	no	—
163	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
173	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
174	C₃×C₄²	—	2	4	no	—
175	C₃×C₄²	C₅×D₄	1	2	yes	—
176	C₃×C₄²	C₂³×C₅	1	2	yes	—
177	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
178	C₅×Q₈	—	2	4	no	—
179	C₅×Q₈	—	2	2	no	—
180	C₅×Q₈	—	4	8	no	—
181	C₅×Q₈	C₂×C₃×Q₈	1	4	yes	complemented
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	4	4	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	—
190	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
194	C₂×C₄×C₅	C₃×#41	1	2	yes	—
195	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
196	C₅×C₈	—	2	4	no	—
197	C₂²×Q₈	—	2	1	no	—
198	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
200	C₄⋊Q₈	—	2	2	no	—
201	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
204	C₂×C₄⋊C₄	—	2	1	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₄²	—	2	1	no	—
209	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
210	#106	C₂²×C₃×C₅	1	8	yes	—
211	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	—
212	#103	C₂²×C₃×C₅	1	8	yes	—
213	C₂×C₃×C₅	#475	1	4	yes	direct product factor
214	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
217	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
218	C₃×Q₈	—	2	4	no	—
219	C₃×Q₈	—	2	2	no	—
220	C₃×Q₈	—	4	8	no	—
221	C₃×Q₈	C₂×C₅×Q₈	1	4	yes	complemented
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	4	4	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	—
230	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
234	C₂×C₃×C₄	C₅×#41	1	2	yes	—
235	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
236	C₃×C₈	—	2	4	no	—
237	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
238	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
239	C₂²×C₅	C₃×#137	1	2	yes	—
240	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	2	4	no	—
243	C₄×C₅	—	4	4	no	—
244	C₄×C₅	—	4	2	no	—
245	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
246	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	—
247	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
248	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
249	C₂×Q₈	—	2	1	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	C₃×C₅×Q₈	1	4	yes	complemented
254	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
268	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₄²	—	2	4	no	—
270	C₄²	C₃×C₅×D₄	1	2	yes	—
271	C₄²	C₂³×C₃×C₅	1	2	yes	—
272	C₃×C₅	C₂×#475	1	1	yes	characteristic, direct product factor, Hall
273	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
274	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
275	C₂²×C₃	C₅×#137	1	2	yes	—
276	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
277	C₃×C₄	—	2	4	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	4	4	no	—
280	C₃×C₄	—	4	2	no	—
281	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
282	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	—
283	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
284	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
285	C₂×C₅	C₃×#475	1	4	yes	direct product factor
286	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
287	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
288	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
289	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
290	Q₈	—	2	4	no	—
291	Q₈	—	2	2	no	—
292	Q₈	—	4	8	no	—
293	Q₈	C₂×C₃×C₅×Q₈	1	4	yes	complemented
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	—
302	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
303	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
304	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
305	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
306	C₂×C₄	C₃×C₅×#41	1	2	yes	—
307	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
308	C₈	—	2	4	no	—
309	C₂×C₃	C₅×#475	1	4	yes	direct product factor
310	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
311	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
312	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
313	C₅	C₂×C₃×#475	1	1	yes	characteristic, direct product factor, Sylow
314	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
315	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
316	C₂²	C₃×C₅×#137	1	2	yes	—
317	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
318	C₄	—	2	4	no	—
319	C₄	—	2	2	no	—
320	C₄	—	4	4	no	—
321	C₄	—	4	2	no	—
322	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
323	C₄	C₂×C₃×C₅×SD₁₆	1	4	yes	—
324	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
325	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
326	C₃	C₂×C₅×#475	1	1	yes	characteristic, direct product factor, Sylow
327	C₂	C₃×C₅×#475	1	4	yes	direct product factor
328	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
329	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
330	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#475	C₂	direct (N × H)
7. C₂×C₅×#475	C₃	direct (N × H)
24. C₂×C₃×#475	C₅	direct (N × H)
27. C₅×#475	C₂×C₃	direct (N × H)
35. C₂×C₃×C₅×Q₈	Q₈	semidirect
56. C₃×#475	C₂×C₅	direct (N × H)
76. C₂×#475	C₃×C₅	direct (N × H)
81. C₃×C₅×Q₈	C₂×Q₈	semidirect
117. C₂×C₅×Q₈	C₃×Q₈	semidirect
138. #475	C₂×C₃×C₅	direct (N × H)
158. C₂×C₃×Q₈	C₅×Q₈	semidirect
181. C₅×Q₈	C₂×C₃×Q₈	semidirect
213. C₂×C₃×C₅	#475	direct (N × H)
221. C₃×Q₈	C₂×C₅×Q₈	semidirect
253. C₂×Q₈	C₃×C₅×Q₈	semidirect
272. C₃×C₅	C₂×#475	direct (N × H)
285. C₂×C₅	C₃×#475	direct (N × H)
293. Q₈	C₂×C₃×C₅×Q₈	semidirect
309. C₂×C₃	C₅×#475	direct (N × H)
313. C₅	C₂×C₃×#475	direct (N × H)
326. C₃	C₂×C₅×#475	direct (N × H)
327. C₂	C₃×C₅×#475	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×C₄×C₅×Q₈	2
C₃×C₅×#475	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×#103	2
C₂×C₅×#475	3
C₂×C₃×#475	5

Subgroups — C2×C3×C5×#475 #14276107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#475 #14276107