Subgroups — C₃×C₅×#2561 #14275595

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 444 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, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#393	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#381	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#379	C₂	1	2	yes	maximal
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2561	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	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	complemented
25	C₃×C₅×#95	C₂²	1	2	yes	complemented
26	C₃×C₅×#95	C₂²	1	4	yes	complemented
27	C₃×C₅×#95	C₂²	1	4	yes	complemented
28	C₃×#2561	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#397	C₂×C₃	1	2	yes	complemented
32	C₅×#393	C₂×C₃	1	2	yes	complemented
33	C₅×#388	C₂×C₃	1	4	yes	complemented
34	C₅×#381	C₂×C₃	1	2	yes	complemented
35	C₅×#379	C₂×C₃	1	2	yes	—
36	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	—	2	2	no	—
38	C₂⁴×C₃×C₅	—	2	4	no	—
39	C₂⁴×C₃×C₅	—	2	4	no	—
40	C₂⁴×C₃×C₅	—	4	2	no	—
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	4	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	4	2	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	4	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	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	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×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
63	C₃×C₄²×C₅	—	4	2	no	—
64	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
66	C₃×#397	C₂×C₅	1	2	yes	complemented
67	C₃×#393	C₂×C₅	1	2	yes	complemented
68	C₃×#388	C₂×C₅	1	4	yes	complemented
69	C₃×#381	C₂×C₅	1	2	yes	complemented
70	C₃×#379	C₂×C₅	1	2	yes	—
71	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×C₂²⋊Q₈	—	2	4	no	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	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	complemented
87	C₅×#95	C₂²×C₃	1	2	yes	complemented
88	C₅×#95	C₂²×C₃	1	4	yes	complemented
89	C₅×#95	C₂²×C₃	1	4	yes	complemented
90	#2561	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	4	no	—
98	C₂³×C₃×C₅	—	4	16	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	—	4	4	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	#41	1	4	yes	—
103	C₂³×C₃×C₅	#41	1	4	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	4	4	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	4	4	no	—
118	C₂×C₃×C₄×C₅	—	4	4	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
123	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
124	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₃×C₂²⋊Q₈	—	2	4	no	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
128	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	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	complemented
136	C₃×#95	C₂²×C₅	1	2	yes	complemented
137	C₃×#95	C₂²×C₅	1	4	yes	complemented
138	C₃×#95	C₂²×C₅	1	4	yes	complemented
139	C₂⁴×C₅	—	2	2	no	—
140	C₂⁴×C₅	—	2	4	no	—
141	C₂⁴×C₅	—	2	4	no	—
142	C₂⁴×C₅	—	4	2	no	—
143	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
144	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	4	2	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	4	2	no	—
150	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₂²⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	—	2	8	no	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₅×C₂²⋊C₄	—	4	4	no	—
165	C₄²×C₅	—	4	2	no	—
166	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
168	#397	C₂×C₃×C₅	1	2	yes	complemented
169	#393	C₂×C₃×C₅	1	2	yes	complemented
170	#388	C₂×C₃×C₅	1	4	yes	complemented
171	#381	C₂×C₃×C₅	1	2	yes	complemented
172	#379	C₂×C₃×C₅	1	2	yes	—
173	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	C₂²×C₃×C₅	—	2	2	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	8	no	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	2	8	no	—
179	C₂²×C₃×C₅	—	4	16	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	#124	1	4	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
186	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
187	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	4	no	—
194	C₂⁴×C₃	—	2	2	no	—
195	C₂⁴×C₃	—	2	4	no	—
196	C₂⁴×C₃	—	2	4	no	—
197	C₂⁴×C₃	—	4	2	no	—
198	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
199	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
200	C₂×C₃×Q₈	—	2	2	no	—
201	C₂×C₃×Q₈	—	4	2	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	4	no	—
204	C₂²×C₃×C₄	—	4	2	no	—
205	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	—	2	4	no	—
214	C₃×C₂²⋊C₄	—	2	4	no	—
215	C₃×C₂²⋊C₄	—	2	8	no	—
216	C₃×C₂²⋊C₄	—	2	4	no	—
217	C₃×C₂²⋊C₄	—	2	4	no	—
218	C₃×C₂²⋊C₄	—	2	4	no	—
219	C₃×C₂²⋊C₄	—	4	4	no	—
220	C₃×C₄²	—	4	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	8	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	2	4	no	—
227	C₂³×C₅	—	2	4	no	—
228	C₂³×C₅	—	4	16	no	—
229	C₂³×C₅	—	4	4	no	—
230	C₂³×C₅	—	4	4	no	—
231	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
232	C₂³×C₅	C₃×#41	1	4	yes	—
233	C₂³×C₅	C₃×#41	1	4	yes	—
234	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
235	C₅×Q₈	—	4	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	4	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	—	4	4	no	—
248	C₂×C₄×C₅	—	4	4	no	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
251	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
253	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
264	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
265	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
266	#95	C₂²×C₃×C₅	1	2	yes	complemented
267	#95	C₂²×C₃×C₅	1	4	yes	complemented
268	#95	C₂²×C₃×C₅	1	4	yes	complemented
269	C₂×C₃×C₅	—	2	4	no	—
270	C₂×C₃×C₅	—	4	4	no	—
271	C₂×C₃×C₅	#525	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
273	C₂×C₃×C₅	#534	1	1	yes	characteristic
274	C₂×C₃×C₅	#551	1	4	yes	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	8	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	4	no	—
282	C₂³×C₃	—	4	16	no	—
283	C₂³×C₃	—	4	4	no	—
284	C₂³×C₃	—	4	4	no	—
285	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
286	C₂³×C₃	C₅×#41	1	4	yes	—
287	C₂³×C₃	C₅×#41	1	4	yes	—
288	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
289	C₃×Q₈	—	4	4	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	4	4	no	—
302	C₂×C₃×C₄	—	4	4	no	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	8	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	—	4	16	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	C₃×#124	1	4	yes	—
315	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
317	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
318	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	4	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	4	2	no	—
329	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
330	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
339	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
340	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
342	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₄²	—	4	2	no	—
352	C₃×C₅	#2561	1	1	yes	characteristic, direct product factor, Hall
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	8	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	8	no	—
358	C₂²×C₃	—	4	16	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	4	no	—
362	C₂²×C₃	C₅×#124	1	4	yes	—
363	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
365	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
366	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	—	4	2	no	—
372	C₃×C₄	—	4	4	no	—
373	C₂×C₅	—	2	4	no	—
374	C₂×C₅	—	4	4	no	—
375	C₂×C₅	C₃×#525	1	1	yes	characteristic
376	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
377	C₂×C₅	C₃×#534	1	1	yes	characteristic
378	C₂×C₅	C₃×#551	1	4	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	16	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	4	no	—
389	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
390	C₂³	C₃×C₅×#41	1	4	yes	—
391	C₂³	C₃×C₅×#41	1	4	yes	—
392	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
393	Q₈	—	4	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
408	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
409	C₂×C₃	—	2	4	no	—
410	C₂×C₃	—	4	4	no	—
411	C₂×C₃	C₅×#525	1	1	yes	characteristic
412	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
413	C₂×C₃	C₅×#534	1	1	yes	characteristic
414	C₂×C₃	C₅×#551	1	4	yes	—
415	C₅	C₃×#2561	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	4	16	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	4	no	—
425	C₂²	C₃×C₅×#124	1	4	yes	—
426	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
427	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
428	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
429	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	4	no	—
436	C₃	C₅×#2561	1	1	yes	characteristic, direct product factor, Sylow
437	C₂	—	2	4	no	—
438	C₂	—	4	4	no	—
439	C₂	C₃×C₅×#525	1	1	yes	characteristic
440	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
441	C₂	C₃×C₅×#534	1	1	yes	characteristic
442	C₂	C₃×C₅×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	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
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#393	C₂	semidirect
5. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#381	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₅×#2561	C₃	direct (N × H)
11. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₄²×C₅	C₂²	semidirect
25. C₃×C₅×#95	C₂²	semidirect
26. C₃×C₅×#95	C₂²	semidirect
27. C₃×C₅×#95	C₂²	semidirect
28. C₃×#2561	C₅	direct (N × H)
29. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
31. C₅×#397	C₂×C₃	semidirect
32. C₅×#393	C₂×C₃	semidirect
33. C₅×#388	C₂×C₃	semidirect
34. C₅×#381	C₂×C₃	semidirect
36. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
64. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
66. C₃×#397	C₂×C₅	semidirect
67. C₃×#393	C₂×C₅	semidirect
68. C₃×#388	C₂×C₅	semidirect
69. C₃×#381	C₂×C₅	semidirect
71. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
73. C₂²×C₅×Q₈	C₂²×C₃	semidirect
77. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
78. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
86. C₂×C₄²×C₅	C₂²×C₃	semidirect
87. C₅×#95	C₂²×C₃	semidirect
88. C₅×#95	C₂²×C₃	semidirect
89. C₅×#95	C₂²×C₃	semidirect
90. #2561	C₃×C₅	direct (N × H)
122. C₂²×C₃×Q₈	C₂²×C₅	semidirect
126. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
127. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
135. C₂×C₃×C₄²	C₂²×C₅	semidirect
136. C₃×#95	C₂²×C₅	semidirect
137. C₃×#95	C₂²×C₅	semidirect
138. C₃×#95	C₂²×C₅	semidirect
166. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
168. #397	C₂×C₃×C₅	semidirect
169. #393	C₂×C₃×C₅	semidirect
170. #388	C₂×C₃×C₅	semidirect
171. #381	C₂×C₃×C₅	semidirect
173. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
252. C₂²×Q₈	C₂²×C₃×C₅	semidirect
256. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
257. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
265. C₂×C₄²	C₂²×C₃×C₅	semidirect
266. #95	C₂²×C₃×C₅	semidirect
267. #95	C₂²×C₃×C₅	semidirect
268. #95	C₂²×C₃×C₅	semidirect
352. C₃×C₅	#2561	direct (N × H)
415. C₅	C₃×#2561	direct (N × H)
436. C₃	C₅×#2561	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×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#393	2
C₃×C₅×#388	2
C₃×C₅×#381	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2561	3
C₃×#2561	5

Subgroups — C3×C5×#2561 #14275595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2561 #14275595