Subgroups — C₂×C₃×C₅×#474 #14276104

Order 1920.

960 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#474	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal
7	C₂×C₅×#474	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
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×C₅×C₂²⋊C₄	—	2	1	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#107	C₂²	1	8	yes	complemented
22	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
23	C₃×C₅×#102	C₂²	1	8	yes	—
24	C₂×C₃×#474	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
27	C₅×#474	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₅×#107	C₂×C₃	1	2	yes	complemented
29	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#102	C₂×C₃	1	2	yes	—
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	—	4	4	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	2	no	—
36	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
37	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	4	4	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	—	2	4	no	—
46	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₄²×C₅	D₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂³	1	2	yes	—
55	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
57	C₃×#474	C₂×C₅	1	8	yes	direct product factor
58	C₂×C₃×#107	C₂×C₅	1	2	yes	complemented
59	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×C₃×#102	C₂×C₅	1	2	yes	—
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
65	C₅×C₄⋊Q₈	—	2	2	no	—
66	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
67	C₄×C₅×D₄	—	2	2	no	—
68	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×#107	C₂²×C₃	1	8	yes	complemented
75	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
76	C₅×#102	C₂²×C₃	1	8	yes	—
77	C₂×#474	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	4	8	no	—
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	—	4	4	no	—
92	C₂×C₃×C₄×C₅	—	4	8	no	—
93	C₂×C₃×C₄×C₅	D₈	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
98	C₂×C₃×C₄×C₅	#41	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×C₈	—	2	4	no	—
101	C₂²×C₃×Q₈	—	2	1	no	—
102	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₃×C₄	—	2	1	no	—
104	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
105	C₃×C₄⋊Q₈	—	2	2	no	—
106	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
107	C₃×C₄×D₄	—	2	2	no	—
108	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₃×#107	C₂²×C₅	1	8	yes	complemented
115	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
116	C₃×#102	C₂²×C₅	1	8	yes	—
117	C₂⁴×C₅	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	4	4	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
123	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	4	4	no	—
128	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₅×C₈	—	2	4	no	—
132	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
137	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₄²×C₅	C₃×D₄	1	2	yes	—
140	C₄²×C₅	C₂³×C₃	1	2	yes	—
141	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
142	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
143	#474	C₂×C₃×C₅	1	8	yes	direct product factor
144	C₂×#107	C₂×C₃×C₅	1	2	yes	complemented
145	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	C₂×#102	C₂×C₃×C₅	1	2	yes	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	2	no	—
150	C₂²×C₃×C₅	—	4	8	no	—
151	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
153	C₂²×C₃×C₅	#137	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	4	2	no	—
157	C₃×C₄×C₅	—	4	4	no	—
158	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
159	C₃×C₄×C₅	C₂×D₈	1	4	yes	—
160	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
162	C₂⁴×C₃	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	4	4	no	—
165	C₂×C₃×D₄	—	2	1	no	—
166	C₂×C₃×D₄	—	2	2	no	—
167	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
168	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	4	4	no	—
173	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
176	C₂×C₃×C₈	—	2	4	no	—
177	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
178	C₃×C₄⋊C₄	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
182	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₄²	C₅×D₄	1	2	yes	—
185	C₃×C₄²	C₂³×C₅	1	2	yes	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
191	C₅×Q₈	—	4	8	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	2	2	no	—
194	C₅×D₄	C₂×C₃×Q₈	1	4	yes	complemented
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	4	no	—
200	C₂×C₄×C₅	—	4	8	no	—
201	C₂×C₄×C₅	C₃×D₈	1	4	yes	—
202	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
203	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
206	C₂×C₄×C₅	C₃×#41	1	2	yes	—
207	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
208	C₅×C₈	—	2	4	no	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
213	C₄⋊Q₈	—	2	2	no	—
214	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
222	#107	C₂²×C₃×C₅	1	8	yes	complemented
223	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
224	#102	C₂²×C₃×C₅	1	8	yes	—
225	C₂×C₃×C₅	—	4	4	no	—
226	C₂×C₃×C₅	#474	1	4	yes	direct product factor
227	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	—	4	2	no	—
233	C₂³×C₃	—	4	2	no	—
234	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
235	C₃×Q₈	—	4	8	no	—
236	C₃×D₄	—	2	4	no	—
237	C₃×D₄	—	2	2	no	—
238	C₃×D₄	C₂×C₅×Q₈	1	4	yes	complemented
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	—	4	8	no	—
245	C₂×C₃×C₄	C₅×D₈	1	4	yes	—
246	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
250	C₂×C₃×C₄	C₅×#41	1	2	yes	—
251	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
252	C₃×C₈	—	2	4	no	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	8	no	—
257	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
258	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
259	C₂²×C₅	C₃×#137	1	2	yes	—
260	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	4	2	no	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
265	C₄×C₅	C₂×C₃×D₈	1	4	yes	—
266	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
267	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₃×C₅×Q₈	1	4	yes	complemented
274	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
288	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
289	C₂²⋊C₄	—	2	4	no	—
290	C₄²	C₃×C₅×D₄	1	2	yes	—
291	C₄²	C₂³×C₃×C₅	1	2	yes	—
292	C₃×C₅	C₂×#474	1	1	yes	characteristic, direct product factor, Hall
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	4	8	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
298	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
299	C₂²×C₃	C₅×#137	1	2	yes	—
300	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	4	4	no	—
304	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
305	C₃×C₄	C₂×C₅×D₈	1	4	yes	—
306	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
307	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
308	C₂×C₅	—	4	4	no	—
309	C₂×C₅	C₃×#474	1	4	yes	direct product factor
310	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
311	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
312	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
313	C₂³	—	2	2	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
318	Q₈	—	4	8	no	—
319	D₄	—	2	4	no	—
320	D₄	—	2	2	no	—
321	D₄	C₂×C₃×C₅×Q₈	1	4	yes	complemented
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	C₃×C₅×D₈	1	4	yes	—
329	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
330	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
332	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
333	C₂×C₄	C₃×C₅×#41	1	2	yes	—
334	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₂×C₃	—	4	4	no	—
337	C₂×C₃	C₅×#474	1	4	yes	direct product factor
338	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
340	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
341	C₅	C₂×C₃×#474	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	2	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
347	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
348	C₂²	C₃×C₅×#137	1	2	yes	—
349	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	4	no	—
353	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
354	C₄	C₂×C₃×C₅×D₈	1	4	yes	—
355	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
356	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
357	C₃	C₂×C₅×#474	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	4	4	no	—
359	C₂	C₃×C₅×#474	1	4	yes	direct product factor
360	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
361	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
362	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#474	C₂	direct (N × H)
4. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
7. C₂×C₅×#474	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#107	C₂²	semidirect
22. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₂×C₃×#474	C₅	direct (N × H)
25. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
27. C₅×#474	C₂×C₃	direct (N × H)
28. C₂×C₅×#107	C₂×C₃	semidirect
29. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
36. C₂×C₃×C₅×D₄	Q₈	semidirect
55. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
57. C₃×#474	C₂×C₅	direct (N × H)
58. C₂×C₃×#107	C₂×C₅	semidirect
59. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
66. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
74. C₅×#107	C₂²×C₃	semidirect
75. C₅×C₄⋊C₈	C₂²×C₃	semidirect
77. C₂×#474	C₃×C₅	direct (N × H)
86. C₃×C₅×D₄	C₂×Q₈	semidirect
106. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
114. C₃×#107	C₂²×C₅	semidirect
115. C₃×C₄⋊C₈	C₂²×C₅	semidirect
122. C₂×C₅×D₄	C₃×Q₈	semidirect
141. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
143. #474	C₂×C₃×C₅	direct (N × H)
144. C₂×#107	C₂×C₃×C₅	semidirect
145. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
167. C₂×C₃×D₄	C₅×Q₈	semidirect
194. C₅×D₄	C₂×C₃×Q₈	semidirect
214. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
222. #107	C₂²×C₃×C₅	semidirect
223. C₄⋊C₈	C₂²×C₃×C₅	semidirect
226. C₂×C₃×C₅	#474	direct (N × H)
238. C₃×D₄	C₂×C₅×Q₈	semidirect
273. C₂×D₄	C₃×C₅×Q₈	semidirect
292. C₃×C₅	C₂×#474	direct (N × H)
309. C₂×C₅	C₃×#474	direct (N × H)
321. D₄	C₂×C₃×C₅×Q₈	semidirect
337. C₂×C₃	C₅×#474	direct (N × H)
341. C₅	C₂×C₃×#474	direct (N × H)
357. C₃	C₂×C₅×#474	direct (N × H)
359. C₂	C₃×C₅×#474	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×D₄	2
C₃×C₅×#474	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×#102	2
C₂×C₅×#474	3
C₂×C₃×#474	5

Subgroups — C2×C3×C5×#474 #14276104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#474 #14276104