Subgroups — C₂×C₃×C₅×#466 #14276082

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#466	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	—	2	2	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	—	2	4	no	—
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
17	C₃×C₅×#121	—	2	4	no	—
18	C₃×C₅×#121	C₂²	1	8	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
21	C₃×C₅×#107	C₂²	1	4	yes	complemented
22	C₃×C₅×#102	C₂²	1	8	yes	complemented
23	C₂×C₃×#466	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂³×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
27	C₅×#466	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	8	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	4	8	no	—
37	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×D₈	—	2	8	no	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	—	2	8	no	—
48	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
54	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂³×C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
57	C₃×#466	C₂×C₅	1	8	yes	direct product factor
58	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
60	C₂²×C₅×D₄	—	2	2	no	—
61	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×D₈	—	2	4	no	—
64	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
65	C₂²×C₅×C₈	—	2	4	no	—
66	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	4	yes	complemented
69	C₅×#121	—	2	4	no	—
70	C₅×#121	C₂²×C₃	1	8	yes	complemented
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₅×#107	C₂²×C₃	1	4	yes	complemented
74	C₅×#102	C₂²×C₃	1	8	yes	complemented
75	C₂×#466	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	—	4	4	no	—
81	C₂³×C₃×C₅	—	4	4	no	—
82	C₂³×C₃×C₅	D₈	1	4	yes	complemented
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	2	4	no	—
87	C₃×C₅×D₄	—	4	16	no	—
88	C₃×C₅×D₄	—	4	4	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	4	4	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	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	2	no	—
101	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
102	C₂²×C₃×D₄	—	2	2	no	—
103	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
104	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×D₈	—	2	4	no	—
106	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
107	C₂²×C₃×C₈	—	2	4	no	—
108	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₂²×C₃×C₈	C₂²×C₅	1	4	yes	complemented
111	C₃×#121	—	2	4	no	—
112	C₃×#121	C₂²×C₅	1	8	yes	complemented
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
115	C₃×#107	C₂²×C₅	1	4	yes	complemented
116	C₃×#102	C₂²×C₅	1	8	yes	complemented
117	C₂⁴×C₅	—	2	2	no	—
118	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	8	no	—
120	C₂×C₅×D₄	—	2	4	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	4	8	no	—
124	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₅×D₈	—	2	8	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	8	no	—
135	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
136	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
137	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
140	C₅×C₂²⋊C₄	—	2	8	no	—
141	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
142	C₂³×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
143	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
144	#466	C₂×C₃×C₅	1	8	yes	direct product factor
145	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	8	no	—
150	C₂²×C₃×C₅	—	4	4	no	—
151	C₂²×C₃×C₅	—	4	4	no	—
152	C₂²×C₃×C₅	—	4	4	no	—
153	C₂²×C₃×C₅	—	8	8	no	—
154	C₂²×C₃×C₅	#121	1	2	yes	—
155	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
156	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
157	C₂²×C₃×C₅	#135	1	2	yes	—
158	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	4	4	no	—
161	C₃×C₄×C₅	#121	1	2	yes	—
162	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
164	C₂⁴×C₃	—	2	2	no	—
165	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
166	C₂×C₃×D₄	—	2	8	no	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	4	8	no	—
171	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	2	2	no	—
175	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₃×D₈	—	2	8	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	8	no	—
182	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
183	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
184	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
187	C₃×C₂²⋊C₄	—	2	8	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	—	4	4	no	—
192	C₂³×C₅	—	4	4	no	—
193	C₂³×C₅	—	4	4	no	—
194	C₂³×C₅	C₃×D₈	1	4	yes	complemented
195	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
196	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	—	2	4	no	—
199	C₅×D₄	—	4	16	no	—
200	C₅×D₄	—	4	4	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₃×#41	1	2	yes	—
211	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
216	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂²×C₃×C₅	1	4	yes	complemented
223	#121	—	2	4	no	—
224	#121	C₂²×C₃×C₅	1	8	yes	complemented
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	#107	C₂²×C₃×C₅	1	4	yes	complemented
228	#102	C₂²×C₃×C₅	1	8	yes	complemented
229	C₂×C₃×C₅	—	2	4	no	—
230	C₂×C₃×C₅	—	8	4	no	—
231	C₂×C₃×C₅	#466	1	4	yes	direct product factor
232	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	4	4	no	—
239	C₂³×C₃	—	4	4	no	—
240	C₂³×C₃	—	4	4	no	—
241	C₂³×C₃	C₅×D₈	1	4	yes	complemented
242	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
243	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	4	16	no	—
247	C₃×D₄	—	4	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	4	4	no	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₅×#41	1	2	yes	—
258	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	8	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	—	4	4	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	8	8	no	—
268	C₂²×C₅	C₃×#121	1	2	yes	—
269	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
270	C₂²×C₅	C₂×C₃×D₈	1	4	yes	complemented
271	C₂²×C₅	C₃×#135	1	2	yes	—
272	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	C₃×#121	1	2	yes	—
276	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
277	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
278	C₂⁴	—	2	2	no	—
279	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	4	8	no	—
285	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
290	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
291	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
292	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
293	D₈	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
297	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
298	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, direct product factor, Hall
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	4	4	no	—
307	C₂²×C₃	—	4	4	no	—
308	C₂²×C₃	—	4	4	no	—
309	C₂²×C₃	—	8	8	no	—
310	C₂²×C₃	C₅×#121	1	2	yes	—
311	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
312	C₂²×C₃	C₂×C₅×D₈	1	4	yes	complemented
313	C₂²×C₃	C₅×#135	1	2	yes	—
314	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	4	4	no	—
317	C₃×C₄	C₅×#121	1	2	yes	—
318	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
319	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	—	8	4	no	—
322	C₂×C₅	C₃×#466	1	4	yes	direct product factor
323	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
324	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
325	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	C₃×C₅×D₈	1	4	yes	complemented
333	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
334	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
335	D₄	—	2	4	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	16	no	—
338	D₄	—	4	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
347	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
348	C₂×C₄	C₃×C₅×#41	1	2	yes	—
349	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	C₂×C₃×C₅×D₄	1	4	yes	complemented
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	8	4	no	—
354	C₂×C₃	C₅×#466	1	4	yes	direct product factor
355	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
356	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
357	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
358	C₅	C₂×C₃×#466	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	8	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	8	8	no	—
366	C₂²	C₃×C₅×#121	1	2	yes	—
367	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
368	C₂²	C₂×C₃×C₅×D₈	1	4	yes	complemented
369	C₂²	C₃×C₅×#135	1	2	yes	—
370	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	4	4	no	—
373	C₄	C₃×C₅×#121	1	2	yes	—
374	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
375	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
376	C₃	C₂×C₅×#466	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	8	4	no	—
379	C₂	C₃×C₅×#466	1	4	yes	direct product factor
380	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
381	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
382	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂³×C₃×C₅×C₈	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₃×C₅×#466	C₂	direct (N × H)
5. C₂×C₃×C₅×#107	C₂	semidirect
6. C₂×C₃×C₅×#102	C₂	semidirect
7. C₂×C₅×#466	C₃	direct (N × H)
12. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×C₅×#121	C₂²	semidirect
21. C₃×C₅×#107	C₂²	semidirect
22. C₃×C₅×#102	C₂²	semidirect
23. C₂×C₃×#466	C₅	direct (N × H)
24. C₂²×C₅×D₈	C₂×C₃	semidirect
25. C₂³×C₅×C₈	C₂×C₃	semidirect
26. C₂×C₅×#121	C₂×C₃	semidirect
27. C₅×#466	C₂×C₃	direct (N × H)
28. C₂×C₅×#107	C₂×C₃	semidirect
29. C₂×C₅×#102	C₂×C₃	semidirect
48. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×D₈	C₂×C₅	semidirect
55. C₂³×C₃×C₈	C₂×C₅	semidirect
56. C₂×C₃×#121	C₂×C₅	semidirect
57. C₃×#466	C₂×C₅	direct (N × H)
58. C₂×C₃×#107	C₂×C₅	semidirect
59. C₂×C₃×#102	C₂×C₅	semidirect
64. C₂×C₅×D₈	C₂²×C₃	semidirect
68. C₂²×C₅×C₈	C₂²×C₃	semidirect
70. C₅×#121	C₂²×C₃	semidirect
73. C₅×#107	C₂²×C₃	semidirect
74. C₅×#102	C₂²×C₃	semidirect
75. C₂×#466	C₃×C₅	direct (N × H)
82. C₂³×C₃×C₅	D₈	semidirect
101. C₃×C₅×C₈	C₂×D₄	semidirect
106. C₂×C₃×D₈	C₂²×C₅	semidirect
110. C₂²×C₃×C₈	C₂²×C₅	semidirect
112. C₃×#121	C₂²×C₅	semidirect
115. C₃×#107	C₂²×C₅	semidirect
116. C₃×#102	C₂²×C₅	semidirect
135. C₂×C₅×C₈	C₃×D₄	semidirect
141. C₂²×D₈	C₂×C₃×C₅	semidirect
142. C₂³×C₈	C₂×C₃×C₅	semidirect
143. C₂×#121	C₂×C₃×C₅	semidirect
144. #466	C₂×C₃×C₅	direct (N × H)
145. C₂×#107	C₂×C₃×C₅	semidirect
146. C₂×#102	C₂×C₃×C₅	semidirect
156. C₂²×C₃×C₅	C₂×D₈	semidirect
182. C₂×C₃×C₈	C₅×D₄	semidirect
194. C₂³×C₅	C₃×D₈	semidirect
213. C₅×C₈	C₂×C₃×D₄	semidirect
218. C₂×D₈	C₂²×C₃×C₅	semidirect
222. C₂²×C₈	C₂²×C₃×C₅	semidirect
224. #121	C₂²×C₃×C₅	semidirect
227. #107	C₂²×C₃×C₅	semidirect
228. #102	C₂²×C₃×C₅	semidirect
231. C₂×C₃×C₅	#466	direct (N × H)
241. C₂³×C₃	C₅×D₈	semidirect
260. C₃×C₈	C₂×C₅×D₄	semidirect
270. C₂²×C₅	C₂×C₃×D₈	semidirect
296. C₂×C₈	C₃×C₅×D₄	semidirect
302. C₃×C₅	C₂×#466	direct (N × H)
312. C₂²×C₃	C₂×C₅×D₈	semidirect
322. C₂×C₅	C₃×#466	direct (N × H)
332. C₂³	C₃×C₅×D₈	semidirect
351. C₈	C₂×C₃×C₅×D₄	semidirect
354. C₂×C₃	C₅×#466	direct (N × H)
358. C₅	C₂×C₃×#466	direct (N × H)
368. C₂²	C₂×C₃×C₅×D₈	semidirect
376. C₃	C₂×C₅×#466	direct (N × H)
379. C₂	C₃×C₅×#466	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂³×C₃×C₅×C₈	2
C₂×C₃×C₅×#121	2
C₃×C₅×#466	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#102	2
C₂×C₅×#466	3
C₂×C₃×#466	5

Subgroups — C2×C3×C5×#466 #14276082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#466 #14276082