Subgroups — C₃×C₅×#2639 #14275673

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 448 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	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#393	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2639	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	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
16	C₃×C₅×#121	—	2	4	no	—
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	1	yes	characteristic
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	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2639	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
31	C₅×#400	C₂×C₃	1	2	yes	complemented
32	C₅×#397	C₂×C₃	1	2	yes	complemented
33	C₅×#394	C₂×C₃	1	2	yes	complemented
34	C₅×#393	C₂×C₃	1	2	yes	complemented
35	C₅×#386	C₂×C₃	1	4	yes	complemented
36	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	4	2	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	8	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	4	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	4	2	no	—
47	C₂²×C₃×C₄×C₅	—	4	2	no	—
48	C₂²×C₃×C₄×C₅	—	4	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	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	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
63	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
65	C₃×#400	C₂×C₅	1	2	yes	complemented
66	C₃×#397	C₂×C₅	1	2	yes	complemented
67	C₃×#394	C₂×C₅	1	2	yes	complemented
68	C₃×#393	C₂×C₅	1	2	yes	complemented
69	C₃×#386	C₂×C₅	1	4	yes	complemented
70	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
73	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×C₂²⋊Q₈	—	2	4	no	—
77	C₅×#121	—	2	4	no	—
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	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	C₅×#95	C₂²×C₃	1	4	yes	—
88	C₅×#95	C₂²×C₃	1	4	yes	—
89	#2639	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
99	C₂³×C₃×C₅	#41	1	4	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	4	4	no	—
102	C₃×C₅×D₄	—	4	4	no	—
103	C₃×C₅×D₄	—	4	8	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	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
116	C₂×C₃×C₄×C₅	—	4	4	no	—
117	C₂×C₃×C₄×C₅	—	4	8	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
122	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
124	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₃×C₂²⋊Q₈	—	2	4	no	—
126	C₃×#121	—	2	4	no	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
134	C₃×#95	C₂²×C₅	1	2	yes	—
135	C₃×#95	C₂²×C₅	1	2	yes	—
136	C₃×#95	C₂²×C₅	1	4	yes	—
137	C₃×#95	C₂²×C₅	1	4	yes	—
138	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
139	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	—	4	2	no	—
142	C₂×C₅×D₄	—	2	4	no	—
143	C₂×C₅×D₄	—	2	8	no	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	4	2	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	4	2	no	—
148	C₂²×C₄×C₅	—	4	2	no	—
149	C₂²×C₄×C₅	—	4	2	no	—
150	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	4	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	2	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₅×C₂²⋊C₄	—	4	4	no	—
163	C₅×C₂²⋊C₄	—	4	4	no	—
164	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
166	#400	C₂×C₃×C₅	1	2	yes	complemented
167	#397	C₂×C₃×C₅	1	2	yes	complemented
168	#394	C₂×C₃×C₅	1	2	yes	complemented
169	#393	C₂×C₃×C₅	1	2	yes	complemented
170	#386	C₂×C₃×C₅	1	4	yes	complemented
171	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	2	2	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	2	4	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	4	no	—
180	C₂²×C₃×C₅	—	4	4	no	—
181	C₂²×C₃×C₅	#124	1	4	yes	—
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
184	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
185	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
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	2	no	—
192	C₃×C₄×C₅	—	4	4	no	—
193	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
194	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×Q₈	—	2	2	no	—
196	C₂×C₃×Q₈	—	4	2	no	—
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	2	8	no	—
199	C₂×C₃×D₄	—	2	2	no	—
200	C₂×C₃×D₄	—	4	2	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	4	2	no	—
203	C₂²×C₃×C₄	—	4	2	no	—
204	C₂²×C₃×C₄	—	4	2	no	—
205	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	2	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	2	no	—
214	C₃×C₄⋊C₄	—	2	4	no	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	C₃×C₂²⋊C₄	—	2	4	no	—
217	C₃×C₂²⋊C₄	—	4	4	no	—
218	C₃×C₂²⋊C₄	—	4	4	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
228	C₂³×C₅	C₃×#41	1	4	yes	—
229	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
230	C₅×Q₈	—	4	4	no	—
231	C₅×D₄	—	4	4	no	—
232	C₅×D₄	—	4	8	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	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	2	no	—
245	C₂×C₄×C₅	—	4	4	no	—
246	C₂×C₄×C₅	—	4	8	no	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
249	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
251	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂²⋊Q₈	—	2	4	no	—
255	#121	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
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	4	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
263	#95	C₂²×C₃×C₅	1	2	yes	—
264	#95	C₂²×C₃×C₅	1	2	yes	—
265	#95	C₂²×C₃×C₅	1	4	yes	—
266	#95	C₂²×C₃×C₅	1	4	yes	—
267	C₂×C₃×C₅	—	2	4	no	—
268	C₂×C₃×C₅	—	8	2	no	—
269	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
270	C₂×C₃×C₅	#534	1	1	yes	characteristic
271	C₂×C₃×C₅	#537	1	1	yes	characteristic
272	C₂×C₃×C₅	#538	1	2	yes	—
273	C₂×C₃×C₅	#539	1	2	yes	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	1	no	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
283	C₂³×C₃	C₅×#41	1	4	yes	—
284	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
285	C₃×Q₈	—	4	4	no	—
286	C₃×D₄	—	4	4	no	—
287	C₃×D₄	—	4	8	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	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	4	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	2	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	2	no	—
300	C₂×C₃×C₄	—	4	4	no	—
301	C₂×C₃×C₄	—	4	8	no	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	4	no	—
307	C₂²×C₅	—	2	4	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	4	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	C₃×#124	1	4	yes	—
314	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
316	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
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	C₂³×C₃×C₅	1	2	yes	—
326	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	C₃×C₅×D₄	1	4	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	2	yes	—
342	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₃×C₅	#2639	1	1	yes	characteristic, direct product factor, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	4	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	4	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	C₅×#124	1	4	yes	—
362	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
364	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
365	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
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	—	8	2	no	—
375	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
376	C₂×C₅	C₃×#534	1	1	yes	characteristic
377	C₂×C₅	C₃×#537	1	1	yes	characteristic
378	C₂×C₅	C₃×#538	1	2	yes	—
379	C₂×C₅	C₃×#539	1	2	yes	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	2	no	—
388	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
389	C₂³	C₃×C₅×#41	1	4	yes	—
390	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
391	Q₈	—	4	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	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	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
409	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
410	C₂×C₃	—	2	4	no	—
411	C₂×C₃	—	8	2	no	—
412	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
413	C₂×C₃	C₅×#534	1	1	yes	characteristic
414	C₂×C₃	C₅×#537	1	1	yes	characteristic
415	C₂×C₃	C₅×#538	1	2	yes	—
416	C₂×C₃	C₅×#539	1	2	yes	—
417	C₅	C₃×#2639	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₃×C₅×#124	1	4	yes	—
428	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
429	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
430	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
431	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₃	C₅×#2639	1	1	yes	characteristic, direct product factor, Sylow
440	C₂	—	2	4	no	—
441	C₂	—	8	2	no	—
442	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
443	C₂	C₃×C₅×#534	1	1	yes	characteristic
444	C₂	C₃×C₅×#537	1	1	yes	characteristic
445	C₂	C₃×C₅×#538	1	2	yes	—
446	C₂	C₃×C₅×#539	1	2	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. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#393	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₂×C₃×C₅×#95	C₂	semidirect
9. C₅×#2639	C₃	direct (N × H)
28. C₃×#2639	C₅	direct (N × H)
29. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
31. C₅×#400	C₂×C₃	semidirect
32. C₅×#397	C₂×C₃	semidirect
33. C₅×#394	C₂×C₃	semidirect
34. C₅×#393	C₂×C₃	semidirect
35. C₅×#386	C₂×C₃	semidirect
36. C₂×C₅×#95	C₂×C₃	semidirect
63. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
65. C₃×#400	C₂×C₅	semidirect
66. C₃×#397	C₂×C₅	semidirect
67. C₃×#394	C₂×C₅	semidirect
68. C₃×#393	C₂×C₅	semidirect
69. C₃×#386	C₂×C₅	semidirect
70. C₂×C₃×#95	C₂×C₅	semidirect
89. #2639	C₃×C₅	direct (N × H)
164. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
166. #400	C₂×C₃×C₅	semidirect
167. #397	C₂×C₃×C₅	semidirect
168. #394	C₂×C₃×C₅	semidirect
169. #393	C₂×C₃×C₅	semidirect
170. #386	C₂×C₃×C₅	semidirect
171. C₂×#95	C₂×C₃×C₅	semidirect
351. C₃×C₅	#2639	direct (N × H)
417. C₅	C₃×#2639	direct (N × H)
439. C₃	C₅×#2639	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×C₅×#121	2
C₃×C₅×#400	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#386	2
C₂×C₃×C₅×#95	2
C₅×#2639	3
C₃×#2639	5

Subgroups — C3×C5×#2639 #14275673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2639 #14275673