Subgroups — C₃×C₅×#2627 #14275661

Order 1920.

1016 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	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#398	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	2	yes	maximal
7	C₃×C₅×#381	C₂	1	2	yes	maximal
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
9	C₅×#2627	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2627	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#400	C₂×C₃	1	2	yes	complemented
32	C₅×#398	C₂×C₃	1	4	yes	complemented
33	C₅×#395	C₂×C₃	1	2	yes	complemented
34	C₅×#385	C₂×C₃	1	2	yes	—
35	C₅×#381	C₂×C₃	1	2	yes	—
36	C₅×#380	C₂×C₃	1	1	yes	characteristic
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	4	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	4	2	no	—
44	C₂²×C₃×C₄×C₅	—	4	2	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
46	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	4	2	no	—
59	C₃×C₅×C₄⋊C₄	—	4	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
63	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
64	C₃×#400	C₂×C₅	1	2	yes	complemented
65	C₃×#398	C₂×C₅	1	4	yes	complemented
66	C₃×#395	C₂×C₅	1	2	yes	complemented
67	C₃×#385	C₂×C₅	1	2	yes	—
68	C₃×#381	C₂×C₅	1	2	yes	—
69	C₃×#380	C₂×C₅	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×C₂²⋊Q₈	—	2	4	no	—
75	C₂×C₅×C₄⋊C₄	—	2	4	no	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	4	yes	—
86	C₅×#95	C₂²×C₃	1	4	yes	—
87	C₅×#95	C₂²×C₃	1	4	yes	—
88	#2627	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
92	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
93	C₂³×C₃×C₅	#41	1	2	yes	—
94	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	4	4	no	—
96	C₂×C₃×C₄×C₅	—	2	8	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	4	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	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	4	4	no	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
115	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
119	C₃×C₂²⋊Q₈	—	2	4	no	—
120	C₂×C₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
129	C₃×#95	C₂²×C₅	1	2	yes	—
130	C₃×#95	C₂²×C₅	1	4	yes	—
131	C₃×#95	C₂²×C₅	1	4	yes	—
132	C₃×#95	C₂²×C₅	1	4	yes	—
133	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₅×Q₈	—	2	2	no	—
135	C₂×C₅×Q₈	—	4	2	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	—	4	2	no	—
141	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
142	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	2	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	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	4	no	—
151	C₅×C₄⋊C₄	—	2	4	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	—	4	4	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	2	4	no	—
158	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
159	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
160	#400	C₂×C₃×C₅	1	2	yes	complemented
161	#398	C₂×C₃×C₅	1	4	yes	complemented
162	#395	C₂×C₃×C₅	1	2	yes	complemented
163	#385	C₂×C₃×C₅	1	2	yes	—
164	#381	C₂×C₃×C₅	1	2	yes	—
165	#380	C₂×C₃×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	2	4	no	—
169	C₂²×C₃×C₅	—	2	4	no	—
170	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
174	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
175	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
176	C₃×C₄×C₅	—	2	4	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	4	2	no	—
180	C₃×C₄×C₅	—	4	2	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×C₄×C₅	—	4	4	no	—
183	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
184	C₂×C₃×Q₈	—	2	2	no	—
185	C₂×C₃×Q₈	—	4	2	no	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	—	2	2	no	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	4	2	no	—
190	C₂²×C₃×C₄	—	4	2	no	—
191	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
192	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
193	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
200	C₃×C₄⋊C₄	—	2	4	no	—
201	C₃×C₄⋊C₄	—	2	4	no	—
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₄⋊C₄	—	4	2	no	—
205	C₃×C₄⋊C₄	—	4	4	no	—
206	C₃×C₂²⋊C₄	—	2	4	no	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
211	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
212	C₂³×C₅	C₃×#41	1	2	yes	—
213	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₅×Q₈	—	4	4	no	—
215	C₂×C₄×C₅	—	2	8	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	4	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	—	2	4	no	—
229	C₂×C₄×C₅	—	4	4	no	—
230	C₂×C₄×C₅	—	4	4	no	—
231	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
232	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
234	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
235	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
236	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
243	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
246	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
248	#95	C₂²×C₃×C₅	1	2	yes	—
249	#95	C₂²×C₃×C₅	1	4	yes	—
250	#95	C₂²×C₃×C₅	1	4	yes	—
251	#95	C₂²×C₃×C₅	1	4	yes	—
252	C₂×C₃×C₅	—	2	4	no	—
253	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₃×C₅	#534	1	1	yes	characteristic
255	C₂×C₃×C₅	#536	1	1	yes	characteristic
256	C₂×C₃×C₅	#539	1	2	yes	—
257	C₂×C₃×C₅	#544	1	2	yes	—
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
261	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
262	C₂³×C₃	C₅×#41	1	2	yes	—
263	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
264	C₃×Q₈	—	4	4	no	—
265	C₂×C₃×C₄	—	2	8	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	4	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	—	2	4	no	—
279	C₂×C₃×C₄	—	4	4	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	2	4	no	—
287	C₂²×C₅	—	2	4	no	—
288	C₂²×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
289	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
290	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
291	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
292	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
293	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
294	C₄×C₅	—	2	4	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	4	no	—
301	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
310	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
311	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
312	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
313	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
314	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
315	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₃×C₅	#2627	1	1	yes	characteristic, direct product factor, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	4	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
332	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
335	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
336	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	4	no	—
344	C₂×C₅	—	2	4	no	—
345	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
346	C₂×C₅	C₃×#534	1	1	yes	characteristic
347	C₂×C₅	C₃×#536	1	1	yes	characteristic
348	C₂×C₅	C₃×#539	1	2	yes	—
349	C₂×C₅	C₃×#544	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
353	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
354	C₂³	C₃×C₅×#41	1	2	yes	—
355	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
374	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
375	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂×C₃	C₅×#534	1	1	yes	characteristic
379	C₂×C₃	C₅×#536	1	1	yes	characteristic
380	C₂×C₃	C₅×#539	1	2	yes	—
381	C₂×C₃	C₅×#544	1	2	yes	—
382	C₅	C₃×#2627	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
388	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
389	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
390	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
391	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
392	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	4	no	—
400	C₃	C₅×#2627	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	2	4	no	—
402	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
403	C₂	C₃×C₅×#534	1	1	yes	characteristic
404	C₂	C₃×C₅×#536	1	1	yes	characteristic
405	C₂	C₃×C₅×#539	1	2	yes	—
406	C₂	C₃×C₅×#544	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#395	C₂	semidirect
9. C₅×#2627	C₃	direct (N × H)
28. C₃×#2627	C₅	direct (N × H)
31. C₅×#400	C₂×C₃	semidirect
32. C₅×#398	C₂×C₃	semidirect
33. C₅×#395	C₂×C₃	semidirect
46. C₂²×C₃×C₄×C₅	Q₈	semidirect
64. C₃×#400	C₂×C₅	semidirect
65. C₃×#398	C₂×C₅	semidirect
66. C₃×#395	C₂×C₅	semidirect
88. #2627	C₃×C₅	direct (N × H)
142. C₂²×C₄×C₅	C₃×Q₈	semidirect
160. #400	C₂×C₃×C₅	semidirect
161. #398	C₂×C₃×C₅	semidirect
162. #395	C₂×C₃×C₅	semidirect
192. C₂²×C₃×C₄	C₅×Q₈	semidirect
310. C₂²×C₄	C₃×C₅×Q₈	semidirect
326. C₃×C₅	#2627	direct (N × H)
382. C₅	C₃×#2627	direct (N × H)
400. C₃	C₅×#2627	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×C₂²⋊Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₅×#2627	3
C₃×#2627	5

Subgroups — C3×C5×#2627 #14275661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2627 #14275661