Subgroups — C₂×C₃×C₅×#391 #14275328

Order 1920.

1856 conjugacy classes of subgroups.

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

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#391	C₂	direct (N × H)
6. C₂×C₅×#391	C₃	direct (N × H)
9. C₂²×C₃×C₅×Q₈	C₄	semidirect
20. C₂×C₃×#391	C₅	direct (N × H)
24. C₅×#391	C₂×C₃	direct (N × H)
30. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
41. C₂²×C₃×C₄×C₅	Q₈	semidirect
51. C₃×#391	C₂×C₅	direct (N × H)
55. C₂²×C₅×Q₈	C₃×C₄	semidirect
66. C₂×#391	C₃×C₅	direct (N × H)
88. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
91. C₂²×C₃×Q₈	C₄×C₅	semidirect
106. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
117. C₂²×C₄×C₅	C₃×Q₈	semidirect
127. #391	C₂×C₃×C₅	direct (N × H)
147. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
158. C₂²×C₃×C₄	C₅×Q₈	semidirect
186. C₂×C₄×C₅	C₂×C₃×Q₈	semidirect
189. C₂²×Q₈	C₃×C₄×C₅	semidirect
200. C₂×C₃×C₅	#391	direct (N × H)
227. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
246. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
257. C₂²×C₄	C₃×C₅×Q₈	semidirect
264. C₃×C₅	C₂×#391	direct (N × H)
279. C₂×C₅	C₃×#391	direct (N × H)
306. C₂×C₄	C₂×C₃×C₅×Q₈	semidirect
307. C₂×C₃	C₅×#391	direct (N × H)
313. C₅	C₂×C₃×#391	direct (N × H)
328. C₃	C₂×C₅×#391	direct (N × H)
329. C₂	C₃×C₅×#391	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
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#391	2
C₂×C₃×C₅×#95	2
C₂×C₅×#391	3
C₂×C₃×#391	5

Subgroups — C2×C3×C5×#391 #14275328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#391 #14275328