Subgroups — C₅×#8635 #11931355

Order 1280.

320 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2960	C₂	1	1	yes	maximal, characteristic
2	C₅×#1568	C₂	1	1	yes	maximal, characteristic
3	C₅×#1568	C₂	1	1	yes	maximal, characteristic
4	C₅×#1537	C₂	1	2	yes	maximal
5	C₅×#1307	C₂	1	2	yes	maximal
6	C₅×#533	C₂²	1	1	yes	characteristic
7	C₅×#446	—	2	1	no	—
8	C₅×#446	—	2	1	no	—
9	C₅×C₈×Q₈	—	2	1	no	—
10	C₅×C₈×Q₈	—	2	1	no	—
11	C₅×#432	C₂²	1	2	yes	—
12	C₅×#432	C₂²	1	2	yes	—
13	C₅×#424	C₄	1	2	yes	—
14	C₅×#423	C₂²	1	1	yes	characteristic
15	C₅×#405	C₄	1	2	yes	—
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#335	—	2	1	no	—
18	C₅×#335	—	2	1	no	—
19	C₅×#334	—	2	1	no	—
20	C₅×#334	—	2	1	no	—
21	C₅×#330	—	2	4	no	—
22	#8635	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
24	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₅×C₄⋊Q₈	Q₈	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	Q₈	1	1	yes	characteristic
28	C₅×#125	D₄	1	2	yes	—
29	C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₄×C₅×Q₈	—	2	1	no	—
32	C₄×C₅×Q₈	—	2	1	no	—
33	C₅×#117	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
35	C₅×C₄⋊C₈	—	2	2	no	—
36	C₅×C₄⋊C₈	—	2	2	no	—
37	C₅×C₄⋊C₈	—	2	1	no	—
38	C₅×C₄⋊C₈	—	2	1	no	—
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×C₄⋊C₈	—	2	2	no	—
41	C₅×C₂²⋊C₈	—	2	2	no	—
42	C₅×C₂²⋊C₈	—	2	2	no	—
43	C₅×#97	—	2	2	no	—
44	C₅×#97	—	2	2	no	—
45	C₅×#97	—	2	2	no	—
46	C₄×C₅×C₈	—	2	2	no	—
47	C₄×C₅×C₈	D₄	1	1	yes	characteristic
48	C₄×C₅×C₈	D₄	1	1	yes	characteristic
49	C₄×C₅×C₈	D₄	1	1	yes	characteristic
50	C₄×C₅×C₈	D₄	1	1	yes	characteristic
51	#2960	C₂×C₅	1	1	yes	characteristic
52	#1568	C₂×C₅	1	1	yes	characteristic
53	#1568	C₂×C₅	1	1	yes	characteristic
54	#1537	C₂×C₅	1	2	yes	—
55	#1307	C₂×C₅	1	2	yes	—
56	C₂×C₅×Q₈	—	2	1	no	—
57	C₂×C₅×Q₈	—	2	1	no	—
58	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₅	#41	1	1	yes	characteristic
60	C₂²×C₄×C₅	#41	1	1	yes	characteristic
61	C₅×M₁₆	—	4	2	no	—
62	C₂×C₅×C₈	—	2	2	no	—
63	C₂×C₅×C₈	—	2	2	no	—
64	C₂×C₅×C₈	—	4	1	no	—
65	C₂×C₅×C₈	—	4	2	no	—
66	C₂×C₅×C₈	—	4	2	no	—
67	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
71	C₅×C₄⋊C₄	—	2	2	no	—
72	C₅×C₄⋊C₄	—	2	2	no	—
73	C₅×C₄⋊C₄	—	2	1	no	—
74	C₅×C₄⋊C₄	—	2	1	no	—
75	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
76	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
77	C₅×C₂²⋊C₄	—	2	2	no	—
78	C₄²×C₅	—	2	2	no	—
79	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
83	#533	C₂²×C₅	1	1	yes	characteristic
84	#446	—	2	1	no	—
85	#446	—	2	1	no	—
86	C₈×Q₈	—	2	1	no	—
87	C₈×Q₈	—	2	1	no	—
88	#432	C₂²×C₅	1	2	yes	—
89	#432	C₂²×C₅	1	2	yes	—
90	#424	C₄×C₅	1	2	yes	—
91	#423	C₂²×C₅	1	1	yes	characteristic
92	#405	C₄×C₅	1	2	yes	—
93	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
94	#335	—	2	1	no	—
95	#335	—	2	1	no	—
96	#334	—	2	1	no	—
97	#334	—	2	1	no	—
98	#330	—	2	4	no	—
99	C₂³×C₅	#117	1	1	yes	characteristic
100	C₅×Q₈	—	4	2	no	—
101	C₅×Q₈	—	4	2	no	—
102	C₂×C₄×C₅	—	2	1	no	—
103	C₂×C₄×C₅	—	2	1	no	—
104	C₂×C₄×C₅	—	2	2	no	—
105	C₂×C₄×C₅	—	2	2	no	—
106	C₂×C₄×C₅	—	4	1	no	—
107	C₂×C₄×C₅	—	4	1	no	—
108	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₅	#121	1	1	yes	characteristic
111	C₂×C₄×C₅	#121	1	1	yes	characteristic
112	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
113	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
114	C₅×C₈	—	2	1	no	—
115	C₅×C₈	—	2	1	no	—
116	C₅×C₈	—	2	1	no	—
117	C₅×C₈	—	4	2	no	—
118	C₅×C₈	—	8	2	no	—
119	C₅×C₈	—	8	2	no	—
120	C₅×C₈	#101	1	2	yes	—
121	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
122	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
123	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
124	C₄⋊Q₈	C₅×Q₈	1	1	yes	characteristic
125	C₄⋊Q₈	C₅×Q₈	1	1	yes	characteristic
126	#125	C₅×D₄	1	2	yes	—
127	C₂²⋊Q₈	—	2	1	no	—
128	C₂²⋊Q₈	—	2	1	no	—
129	C₄×Q₈	—	2	1	no	—
130	C₄×Q₈	—	2	1	no	—
131	#117	C₂×C₄×C₅	1	2	yes	—
132	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	2	1	no	—
136	C₄⋊C₈	—	2	1	no	—
137	C₄⋊C₈	—	2	2	no	—
138	C₄⋊C₈	—	2	2	no	—
139	C₂²⋊C₈	—	2	2	no	—
140	C₂²⋊C₈	—	2	2	no	—
141	#97	—	2	2	no	—
142	#97	—	2	2	no	—
143	#97	—	2	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	C₅×D₄	1	1	yes	characteristic
146	C₄×C₈	C₅×D₄	1	1	yes	characteristic
147	C₄×C₈	C₅×D₄	1	1	yes	characteristic
148	C₄×C₈	C₅×D₄	1	1	yes	characteristic
149	C₂²×C₅	—	2	1	no	—
150	C₂²×C₅	—	2	1	no	—
151	C₂²×C₅	—	2	1	no	—
152	C₂²×C₅	#380	1	1	yes	characteristic
153	C₄×C₅	—	2	1	no	—
154	C₄×C₅	—	2	1	no	—
155	C₄×C₅	—	2	1	no	—
156	C₄×C₅	—	2	1	no	—
157	C₄×C₅	—	2	1	no	—
158	C₄×C₅	—	4	2	no	—
159	C₄×C₅	—	4	2	no	—
160	C₄×C₅	C₂×#101	1	1	yes	characteristic
161	C₄×C₅	#413	1	1	yes	characteristic
162	C₂×Q₈	—	2	1	no	—
163	C₂×Q₈	—	2	1	no	—
164	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
165	C₂²×C₄	C₅×#41	1	1	yes	characteristic
166	C₂²×C₄	C₅×#41	1	1	yes	characteristic
167	M₁₆	—	4	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	1	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
182	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
186	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
187	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
188	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
189	C₂×C₅	—	4	1	no	—
190	C₂×C₅	#1801	1	1	yes	characteristic
191	C₂×C₅	#1814	1	1	yes	characteristic
192	C₂×C₅	#1814	1	1	yes	characteristic
193	C₂³	C₅×#117	1	1	yes	characteristic
194	Q₈	—	4	2	no	—
195	Q₈	—	4	2	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₅×#121	1	1	yes	characteristic
205	C₂×C₄	C₅×#121	1	1	yes	characteristic
206	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
208	C₈	—	2	1	no	—
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	4	2	no	—
212	C₈	—	8	2	no	—
213	C₈	—	8	2	no	—
214	C₈	C₅×#101	1	2	yes	—
215	C₅	#8635	1	1	yes	characteristic, direct product factor, Sylow
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	C₅×#380	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	4	2	no	—
226	C₄	—	4	2	no	—
227	C₄	C₂×C₅×#101	1	1	yes	characteristic
228	C₄	C₅×#413	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	C₅×#1801	1	1	yes	characteristic
231	C₂	C₅×#1814	1	1	yes	characteristic
232	C₂	C₅×#1814	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#380
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂³×C₅	#117
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
22. #8635	C₅	direct (N × H)
215. C₅	#8635	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#2960	2
C₅×#1568	2
C₅×#1537	2
C₅×#1307	2
#8635	5

Subgroups — C5×#8635 #11931355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8635 #11931355