Subgroups — C₃×C₅×#2536 #14275570

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 436 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	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal
6	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
9	C₅×#2536	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
14	C₃×C₄×C₅×Q₈	—	2	4	no	—
15	C₃×C₄×C₅×D₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×#2536	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
31	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
33	C₅×#398	C₂×C₃	1	2	yes	complemented
34	C₅×#394	C₂×C₃	1	2	yes	—
35	C₅×#388	C₂×C₃	1	4	yes	complemented
36	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#380	C₂×C₃	1	2	yes	complemented
38	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	4	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	—	2	2	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	—	2	8	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
62	C₃×C₄²×C₅	—	2	4	no	—
63	C₃×C₄²×C₅	D₄	1	4	yes	—
64	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
65	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
67	C₃×#398	C₂×C₅	1	2	yes	complemented
68	C₃×#394	C₂×C₅	1	2	yes	—
69	C₃×#388	C₂×C₅	1	4	yes	complemented
70	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#380	C₂×C₅	1	2	yes	complemented
72	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
75	C₅×C₂²⋊Q₈	—	2	8	no	—
76	C₄×C₅×Q₈	—	2	4	no	—
77	C₄×C₅×D₄	—	2	4	no	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
86	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₅×#95	C₂²×C₃	1	4	yes	—
89	C₅×#95	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	#2536	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	#41	1	4	yes	—
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×Q₈	—	2	8	no	—
101	C₃×C₅×D₄	—	2	8	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	4	8	no	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	#41	1	2	yes	—
121	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
124	C₃×C₂²⋊Q₈	—	2	8	no	—
125	C₃×C₄×Q₈	—	2	4	no	—
126	C₃×C₄×D₄	—	2	4	no	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×#95	C₂²×C₅	1	4	yes	—
138	C₃×#95	C₂²×C₅	1	2	yes	—
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	8	no	—
161	C₅×C₂²⋊C₄	—	2	8	no	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	2	8	no	—
164	C₄²×C₅	—	2	4	no	—
165	C₄²×C₅	C₃×D₄	1	4	yes	—
166	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
167	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
169	#398	C₂×C₃×C₅	1	2	yes	complemented
170	#394	C₂×C₃×C₅	1	2	yes	—
171	#388	C₂×C₃×C₅	1	4	yes	complemented
172	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
173	#380	C₂×C₃×C₅	1	2	yes	complemented
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	2	4	no	—
176	C₂²×C₃×C₅	—	2	4	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
185	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
186	C₃×C₄×C₅	—	2	4	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	4	no	—
192	C₃×C₄×C₅	#121	1	4	yes	—
193	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
194	C₂×C₃×Q₈	—	2	2	no	—
195	C₂×C₃×Q₈	—	2	2	no	—
196	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₃×C₄⋊C₄	—	2	2	no	—
210	C₃×C₄⋊C₄	—	2	4	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	8	no	—
214	C₃×C₂²⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₄²	—	2	4	no	—
218	C₃×C₄²	C₅×D₄	1	4	yes	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	C₃×#41	1	4	yes	—
226	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₅×Q₈	—	2	8	no	—
228	C₅×D₄	—	2	8	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	4	8	no	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₃×#41	1	2	yes	—
248	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
251	C₂²⋊Q₈	—	2	8	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×D₄	—	2	4	no	—
254	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
262	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
263	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
264	#95	C₂²×C₃×C₅	1	4	yes	—
265	#95	C₂²×C₃×C₅	1	2	yes	—
266	#95	C₂²×C₃×C₅	1	2	yes	—
267	C₂×C₃×C₅	—	4	4	no	—
268	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
269	C₂×C₃×C₅	#525	1	1	yes	characteristic
270	C₂×C₃×C₅	#536	1	1	yes	characteristic
271	C₂×C₃×C₅	#548	1	2	yes	—
272	C₂×C₃×C₅	#552	1	2	yes	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	C₅×#41	1	4	yes	—
280	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
281	C₃×Q₈	—	2	8	no	—
282	C₃×D₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	4	8	no	—
296	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂×C₃×C₄	C₅×#41	1	2	yes	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	2	4	no	—
304	C₂²×C₅	—	2	4	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	—	4	2	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
311	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
312	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
313	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
314	C₄×C₅	—	2	4	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	4	no	—
320	C₄×C₅	C₃×#121	1	4	yes	—
321	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
331	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
332	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
333	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
336	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₄²	—	2	4	no	—
346	C₄²	C₃×C₅×D₄	1	4	yes	—
347	C₃×C₅	#2536	1	1	yes	characteristic, direct product factor, Hall
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
358	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
359	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	4	no	—
366	C₃×C₄	C₅×#121	1	4	yes	—
367	C₂×C₅	—	4	4	no	—
368	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
369	C₂×C₅	C₃×#525	1	1	yes	characteristic
370	C₂×C₅	C₃×#536	1	1	yes	characteristic
371	C₂×C₅	C₃×#548	1	2	yes	—
372	C₂×C₅	C₃×#552	1	2	yes	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	C₃×C₅×#41	1	4	yes	—
380	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
381	Q₈	—	2	8	no	—
382	D₄	—	2	8	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
397	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
398	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
400	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
401	C₂×C₄	C₃×C₅×#41	1	2	yes	—
402	C₂×C₃	—	4	4	no	—
403	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
404	C₂×C₃	C₅×#525	1	1	yes	characteristic
405	C₂×C₃	C₅×#536	1	1	yes	characteristic
406	C₂×C₃	C₅×#548	1	2	yes	—
407	C₂×C₃	C₅×#552	1	2	yes	—
408	C₅	C₃×#2536	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
418	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
419	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
420	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	C₃×C₅×#121	1	4	yes	—
428	C₃	C₅×#2536	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	4	4	no	—
430	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
431	C₂	C₃×C₅×#525	1	1	yes	characteristic
432	C₂	C₃×C₅×#536	1	1	yes	characteristic
433	C₂	C₃×C₅×#548	1	2	yes	—
434	C₂	C₃×C₅×#552	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
8. C₃×C₅×#380	C₂	semidirect
9. C₅×#2536	C₃	direct (N × H)
29. C₃×#2536	C₅	direct (N × H)
30. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
31. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
33. C₅×#398	C₂×C₃	semidirect
35. C₅×#388	C₂×C₃	semidirect
36. C₅×#382	C₂×C₃	semidirect
37. C₅×#380	C₂×C₃	semidirect
41. C₂×C₃×C₅×Q₈	D₄	semidirect
64. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
65. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
67. C₃×#398	C₂×C₅	semidirect
69. C₃×#388	C₂×C₅	semidirect
70. C₃×#382	C₂×C₅	semidirect
71. C₃×#380	C₂×C₅	semidirect
91. #2536	C₃×C₅	direct (N × H)
143. C₂×C₅×Q₈	C₃×D₄	semidirect
166. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
167. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
169. #398	C₂×C₃×C₅	semidirect
171. #388	C₂×C₃×C₅	semidirect
172. #382	C₂×C₃×C₅	semidirect
173. #380	C₂×C₃×C₅	semidirect
196. C₂×C₃×Q₈	C₅×D₄	semidirect
324. C₂×Q₈	C₃×C₅×D₄	semidirect
347. C₃×C₅	#2536	direct (N × H)
408. C₅	C₃×#2536	direct (N × H)
428. C₃	C₅×#2536	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
C₂×C₃×C₄×C₅×Q₈	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#398	2
C₃×C₅×#394	2
C₃×C₅×#388	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₅×#2536	3
C₃×#2536	5

Subgroups — C3×C5×#2536 #14275570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2536 #14275570