Subgroups — C₃×C₅×#2436 #14275470

Order 1920.

1704 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#393	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#386	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2436	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	8	no	—
10	C₂²×C₃×C₅×Q₈	—	2	4	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×#124	—	2	8	no	—
18	C₃×C₅×#121	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	8	yes	—
26	C₃×#2436	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
29	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
30	C₅×#393	C₂×C₃	1	4	yes	complemented
31	C₅×#391	C₂×C₃	1	2	yes	complemented
32	C₅×#386	C₂×C₃	1	4	yes	complemented
33	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₅×Q₈	—	2	32	no	—
37	C₂×C₃×C₅×Q₈	—	2	8	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	D₄	1	8	yes	complemented
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	8	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	8	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
59	C₃×C₄²×C₅	—	2	4	no	—
60	C₂³×C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
62	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
63	C₃×#393	C₂×C₅	1	4	yes	complemented
64	C₃×#391	C₂×C₅	1	2	yes	complemented
65	C₃×#386	C₂×C₅	1	4	yes	complemented
66	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×Q₈	—	2	8	no	—
68	C₂²×C₅×Q₈	—	2	4	no	—
69	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
70	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
71	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
72	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₅×#124	—	2	8	no	—
76	C₅×#121	—	2	4	no	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	C₅×#95	C₂²×C₃	1	8	yes	—
84	#2436	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	4	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	4	no	—
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
92	C₂³×C₃×C₅	#41	1	4	yes	—
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	16	no	—
95	C₃×C₅×Q₈	—	2	16	no	—
96	C₃×C₅×D₄	—	4	8	no	—
97	C₃×C₅×D₄	—	4	4	no	—
98	C₂×C₃×C₄×C₅	—	2	16	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂²×C₃×Q₈	—	2	8	no	—
113	C₂²×C₃×Q₈	—	2	4	no	—
114	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
115	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
116	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
119	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₃×#124	—	2	8	no	—
121	C₃×#121	—	2	4	no	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
126	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
127	C₃×#95	C₂²×C₅	1	2	yes	—
128	C₃×#95	C₂²×C₅	1	8	yes	—
129	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
130	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₅×Q₈	—	2	32	no	—
132	C₂×C₅×Q₈	—	2	8	no	—
133	C₂×C₅×Q₈	—	2	4	no	—
134	C₂×C₅×Q₈	—	2	4	no	—
135	C₂×C₅×Q₈	—	2	4	no	—
136	C₂×C₅×Q₈	C₃×D₄	1	8	yes	complemented
137	C₂×C₅×D₄	—	2	4	no	—
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	2	2	no	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	—	2	8	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	2	4	no	—
152	C₅×C₂²⋊C₄	—	2	4	no	—
153	C₅×C₂²⋊C₄	—	2	16	no	—
154	C₄²×C₅	—	2	4	no	—
155	C₂³×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
157	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
158	#393	C₂×C₃×C₅	1	4	yes	complemented
159	#391	C₂×C₃×C₅	1	2	yes	complemented
160	#386	C₂×C₃×C₅	1	4	yes	complemented
161	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	2	2	no	—
164	C₂²×C₃×C₅	—	2	8	no	—
165	C₂²×C₃×C₅	—	4	2	no	—
166	C₂²×C₃×C₅	—	4	2	no	—
167	C₂²×C₃×C₅	—	4	2	no	—
168	C₂²×C₃×C₅	—	4	8	no	—
169	C₂²×C₃×C₅	#124	1	4	yes	complemented
170	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
172	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
173	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
174	C₃×C₄×C₅	—	2	8	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	—	4	2	no	—
177	C₃×C₄×C₅	—	4	4	no	—
178	C₃×C₄×C₅	#120	1	4	yes	—
179	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
180	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
181	C₂×C₃×Q₈	—	2	32	no	—
182	C₂×C₃×Q₈	—	2	8	no	—
183	C₂×C₃×Q₈	—	2	4	no	—
184	C₂×C₃×Q₈	—	2	4	no	—
185	C₂×C₃×Q₈	—	2	4	no	—
186	C₂×C₃×Q₈	C₅×D₄	1	8	yes	complemented
187	C₂×C₃×D₄	—	2	4	no	—
188	C₂×C₃×D₄	—	2	8	no	—
189	C₂×C₃×D₄	—	2	2	no	—
190	C₂×C₃×D₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	—	2	8	no	—
193	C₂²×C₃×C₄	—	2	4	no	—
194	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
197	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
198	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₂²⋊C₄	—	2	4	no	—
202	C₃×C₂²⋊C₄	—	2	4	no	—
203	C₃×C₂²⋊C₄	—	2	16	no	—
204	C₃×C₄²	—	2	4	no	—
205	C₂³×C₅	—	2	2	no	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	2	4	no	—
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	2	4	no	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂³×C₅	C₃×#41	1	4	yes	—
213	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₅×Q₈	—	2	16	no	—
215	C₅×Q₈	—	2	16	no	—
216	C₅×D₄	—	4	8	no	—
217	C₅×D₄	—	4	4	no	—
218	C₂×C₄×C₅	—	2	16	no	—
219	C₂×C₄×C₅	—	2	4	no	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	8	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
229	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
231	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
232	C₂²×Q₈	—	2	8	no	—
233	C₂²×Q₈	—	2	4	no	—
234	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
235	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
236	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
238	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
239	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
240	#124	—	2	8	no	—
241	#121	—	2	4	no	—
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
245	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
246	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
247	#95	C₂²×C₃×C₅	1	2	yes	—
248	#95	C₂²×C₃×C₅	1	8	yes	—
249	C₂×C₃×C₅	—	2	4	no	—
250	C₂×C₃×C₅	—	8	2	no	—
251	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
252	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
253	C₂×C₃×C₅	#536	1	1	yes	characteristic
254	C₂×C₃×C₅	#548	1	4	yes	—
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
262	C₂³×C₃	C₅×#41	1	4	yes	—
263	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
264	C₃×Q₈	—	2	16	no	—
265	C₃×Q₈	—	2	16	no	—
266	C₃×D₄	—	4	8	no	—
267	C₃×D₄	—	4	4	no	—
268	C₂×C₃×C₄	—	2	16	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
279	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	8	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	—	4	8	no	—
289	C₂²×C₅	C₃×#124	1	4	yes	complemented
290	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
291	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
292	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
293	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
294	C₄×C₅	—	2	8	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	—	4	4	no	—
298	C₄×C₅	C₃×#120	1	4	yes	—
299	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
300	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
301	C₂×Q₈	—	2	32	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	C₃×C₅×D₄	1	8	yes	complemented
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
315	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
316	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
317	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
318	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
319	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	16	no	—
324	C₄²	—	2	4	no	—
325	C₃×C₅	#2436	1	1	yes	characteristic, direct product factor, Hall
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	8	no	—
329	C₂²×C₃	—	4	2	no	—
330	C₂²×C₃	—	4	2	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	4	8	no	—
333	C₂²×C₃	C₅×#124	1	4	yes	complemented
334	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
336	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
337	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
338	C₃×C₄	—	2	8	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	4	no	—
342	C₃×C₄	C₅×#120	1	4	yes	—
343	C₂×C₅	—	2	4	no	—
344	C₂×C₅	—	8	2	no	—
345	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
346	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
347	C₂×C₅	C₃×#536	1	1	yes	characteristic
348	C₂×C₅	C₃×#548	1	4	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	4	no	—
355	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
356	C₂³	C₃×C₅×#41	1	4	yes	—
357	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
358	Q₈	—	2	16	no	—
359	Q₈	—	2	16	no	—
360	D₄	—	4	8	no	—
361	D₄	—	4	4	no	—
362	C₂×C₄	—	2	16	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
373	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
374	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
375	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	8	2	no	—
378	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
379	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
380	C₂×C₃	C₅×#536	1	1	yes	characteristic
381	C₂×C₃	C₅×#548	1	4	yes	—
382	C₅	C₃×#2436	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	8	no	—
390	C₂²	C₃×C₅×#124	1	4	yes	complemented
391	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
392	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
393	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
394	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
395	C₄	—	2	8	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	C₃×C₅×#120	1	4	yes	—
400	C₃	C₅×#2436	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	2	4	no	—
402	C₂	—	8	2	no	—
403	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
404	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
405	C₂	C₃×C₅×#536	1	1	yes	characteristic
406	C₂	C₃×C₅×#548	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#121	C₂
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. C₂³×C₃×C₅×Q₈	C₂	semidirect
2. C₂×C₃×C₅×#124	C₂	semidirect
4. C₃×C₅×#393	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#386	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2436	C₃	direct (N × H)
26. C₃×#2436	C₅	direct (N × H)
27. C₂³×C₅×Q₈	C₂×C₃	semidirect
28. C₂×C₅×#124	C₂×C₃	semidirect
30. C₅×#393	C₂×C₃	semidirect
31. C₅×#391	C₂×C₃	semidirect
32. C₅×#386	C₂×C₃	semidirect
33. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
41. C₂×C₃×C₅×Q₈	D₄	semidirect
60. C₂³×C₃×Q₈	C₂×C₅	semidirect
61. C₂×C₃×#124	C₂×C₅	semidirect
63. C₃×#393	C₂×C₅	semidirect
64. C₃×#391	C₂×C₅	semidirect
65. C₃×#386	C₂×C₅	semidirect
66. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
84. #2436	C₃×C₅	direct (N × H)
136. C₂×C₅×Q₈	C₃×D₄	semidirect
155. C₂³×Q₈	C₂×C₃×C₅	semidirect
156. C₂×#124	C₂×C₃×C₅	semidirect
158. #393	C₂×C₃×C₅	semidirect
159. #391	C₂×C₃×C₅	semidirect
160. #386	C₂×C₃×C₅	semidirect
161. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
169. C₂²×C₃×C₅	#124	semidirect
186. C₂×C₃×Q₈	C₅×D₄	semidirect
289. C₂²×C₅	C₃×#124	semidirect
306. C₂×Q₈	C₃×C₅×D₄	semidirect
325. C₃×C₅	#2436	direct (N × H)
333. C₂²×C₃	C₅×#124	semidirect
382. C₅	C₃×#2436	direct (N × H)
390. C₂²	C₃×C₅×#124	semidirect
400. C₃	C₅×#2436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×Q₈	2
C₂×C₃×C₅×#124	2
C₂×C₃×C₅×#121	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2436	3
C₃×#2436	5

Subgroups — C3×C5×#2436 #14275470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2436 #14275470