Subgroups — C₂×#91393 #11754281

Order 960.

660 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#6712	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#685	C₂	1	1	yes	maximal, characteristic
5	C₂×#6669	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#6665	C₂	1	1	yes	maximal, characteristic
7	C₂×Dic₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	#91393	C₂	1	8	yes	maximal, direct product factor
9	C₂×#4018	—	3	1	no	maximal, Hall
10	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
17	C₂×D₅×Dic₃	C₄	1	8	yes	complemented
18	C₂×D₅×Dic₃	C₂²	1	4	yes	—
19	#6712	C₂²	1	4	yes	complemented
20	C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
21	C₃×#685	C₂²	1	4	yes	—
22	#6669	C₂²	1	4	yes	complemented
23	#6665	C₂²	1	4	yes	—
24	Dic₃×Dic₅	C₂²	1	4	yes	complemented
25	C₂×#877	—	5	1	no	maximal, Hall
26	C₂²×C₄×D₅	—	3	1	no	—
27	C₂×C₄²×C₅	—	3	1	no	—
28	C₂×#685	—	3	1	no	—
29	C₂×#685	D₃	1	1	yes	characteristic
30	C₂×#683	—	3	1	no	—
31	C₂×#683	—	3	1	no	—
32	C₂×C₄×Dic₅	—	3	1	no	—
33	#4018	—	3	8	no	—
34	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₃×D₅	—	2	2	no	—
36	C₂²×C₃×D₅	—	2	2	no	—
37	C₂²×C₃×D₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×D₅	C₂³	1	2	yes	—
39	C₂×C₃×C₄×C₅	—	2	2	no	—
40	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂×Dic₁₅	—	2	2	no	—
42	C₂×Dic₁₅	C₂×C₄	1	4	yes	—
43	C₂×Dic₁₅	C₂³	1	2	yes	—
44	C₂×Dic₁₅	C₂³	1	2	yes	—
45	C₂×C₅×Dic₃	—	2	2	no	—
46	C₂×C₅×Dic₃	C₂×C₄	1	4	yes	—
47	C₂×C₅×Dic₃	C₂³	1	2	yes	—
48	C₂×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂×C₃×Dic₅	—	2	2	no	—
50	C₂×C₃×Dic₅	C₂³	1	2	yes	—
51	D₅×Dic₃	C₂×C₄	1	16	yes	complemented
52	C₂³×Dic₃	—	5	1	no	—
53	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
54	C₂×#217	—	5	1	no	—
55	C₂×Dic₃⋊C₄	—	5	1	no	—
56	C₂×Dic₃⋊C₄	—	5	1	no	—
57	C₂×C₄×Dic₃	—	5	1	no	—
58	C₂×C₄×Dic₃	D₅	1	1	yes	characteristic, complemented
59	#877	—	5	8	no	—
60	C₂³×D₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₄×C₅	—	3	1	no	—
62	C₂²×C₄×C₅	—	3	1	no	—
63	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂²×Dic₅	—	3	1	no	—
65	C₂²×Dic₅	—	3	1	no	—
66	C₂²×Dic₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₄×D₅	—	3	8	no	—
68	C₂×C₄×D₅	—	3	4	no	—
69	C₄²×C₅	—	3	4	no	—
70	#685	—	3	4	no	—
71	#685	C₂×D₃	1	4	yes	—
72	#683	—	3	4	no	—
73	#683	—	3	4	no	—
74	C₄×Dic₅	—	3	4	no	—
75	C₂×#117	—	15	1	no	Sylow
76	C₂²×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂²×C₃×C₅	#41	1	2	yes	—
78	C₂²×C₃×C₅	#41	1	2	yes	—
79	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₂×C₃×D₅	—	2	8	no	—
81	C₂×C₃×D₅	—	2	2	no	—
82	C₂×C₃×D₅	—	2	2	no	—
83	C₂×C₃×D₅	C₂²×C₄	1	4	yes	—
84	C₃×C₄×C₅	—	2	2	no	—
85	Dic₁₅	—	2	2	no	—
86	Dic₁₅	C₂²×C₄	1	4	yes	—
87	C₃×Dic₅	—	2	2	no	—
88	C₅×Dic₃	—	2	2	no	—
89	C₅×Dic₃	C₂²×C₄	1	4	yes	—
90	C₂⁴×C₃	—	5	1	no	—
91	C₂²×C₃×C₄	—	5	1	no	—
92	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
93	C₂²×Dic₃	—	5	1	no	—
94	C₂²×Dic₃	—	5	8	no	—
95	C₂²×Dic₃	—	5	4	no	—
96	C₂²×Dic₃	—	5	1	no	—
97	C₂²×Dic₃	C₂×D₅	1	1	yes	characteristic
98	C₂²×Dic₃	C₂×D₅	1	1	yes	characteristic
99	C₃×C₂²⋊C₄	—	5	4	no	—
100	#217	—	5	4	no	—
101	Dic₃⋊C₄	—	5	4	no	—
102	Dic₃⋊C₄	—	5	4	no	—
103	C₄×Dic₃	—	5	4	no	—
104	C₄×Dic₃	C₂×D₅	1	4	yes	complemented
105	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
106	C₂²×D₅	—	2	2	no	—
107	C₂²×D₅	—	2	2	no	—
108	C₂²×D₅	C₄×D₃	1	4	yes	—
109	C₂²×D₅	C₂²×D₃	1	2	yes	—
110	C₂×C₄×C₅	—	2	2	no	—
111	C₂×C₄×C₅	—	3	4	no	—
112	C₂×C₄×C₅	—	3	2	no	—
113	C₂×C₄×C₅	—	3	2	no	—
114	C₂×C₄×C₅	—	6	2	no	—
115	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
116	C₂×Dic₅	—	2	2	no	—
117	C₂×Dic₅	—	3	4	no	—
118	C₂×Dic₅	—	3	2	no	—
119	C₂×Dic₅	—	3	2	no	—
120	C₂×Dic₅	—	6	2	no	—
121	C₂×Dic₅	C₂²×D₃	1	2	yes	—
122	C₄×D₅	—	3	16	no	—
123	C₂³×C₄	—	15	1	no	—
124	#117	—	15	8	no	—
125	C₂×C₄⋊C₄	—	15	1	no	—
126	C₂×C₄⋊C₄	—	15	1	no	—
127	C₂×C₂²⋊C₄	—	5	1	no	—
128	C₂×C₂²⋊C₄	—	15	1	no	—
129	C₂×C₄²	—	3	1	no	—
130	C₂×C₄²	—	15	1	no	—
131	C₂×C₃×C₅	#117	1	4	yes	complemented
132	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
134	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
135	C₃×D₅	—	2	4	no	—
136	C₂³×C₃	—	5	4	no	—
137	C₂³×C₃	—	5	2	no	—
138	C₂³×C₃	—	10	2	no	—
139	C₂³×C₃	—	10	2	no	—
140	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	5	2	no	—
143	C₂×C₃×C₄	—	10	2	no	—
144	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
145	C₂×Dic₃	—	2	2	no	—
146	C₂×Dic₃	—	5	4	no	—
147	C₂×Dic₃	—	5	2	no	—
148	C₂×Dic₃	—	5	16	no	—
149	C₂×Dic₃	—	5	2	no	—
150	C₂×Dic₃	—	10	2	no	—
151	C₂×Dic₃	C₄×D₅	1	4	yes	—
152	C₂×Dic₃	C₂²×D₅	1	2	yes	—
153	C₂×Dic₃	C₂²×D₅	1	2	yes	—
154	C₂²×C₅	C₂×C₄×D₃	1	2	yes	—
155	C₂²×C₅	#237	1	2	yes	—
156	C₂²×C₅	#237	1	2	yes	—
157	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
158	C₂×D₅	—	2	8	no	—
159	C₂×D₅	—	2	2	no	—
160	C₂×D₅	—	2	2	no	—
161	C₂×D₅	C₂×C₄×D₃	1	4	yes	—
162	C₄×C₅	—	2	2	no	—
163	C₄×C₅	—	3	4	no	—
164	C₄×C₅	—	6	2	no	—
165	Dic₅	—	2	2	no	—
166	Dic₅	—	3	4	no	—
167	Dic₅	—	6	2	no	—
168	C₂⁴	—	5	1	no	—
169	C₂²×C₄	—	3	1	no	—
170	C₂²×C₄	—	3	1	no	—
171	C₂²×C₄	—	5	1	no	—
172	C₂²×C₄	—	15	4	no	—
173	C₂²×C₄	—	15	8	no	—
174	C₂²×C₄	—	15	1	no	—
175	C₂²×C₄	—	15	1	no	—
176	C₂²×C₄	D₃×D₅	1	1	yes	characteristic
177	C₄⋊C₄	—	15	4	no	—
178	C₄⋊C₄	—	15	4	no	—
179	C₂²⋊C₄	—	5	4	no	—
180	C₂²⋊C₄	—	15	4	no	—
181	C₄²	—	3	4	no	—
182	C₄²	—	15	4	no	—
183	C₃×C₅	C₂×#117	1	1	yes	characteristic, complemented, Hall
184	C₂²×C₃	—	5	4	no	—
185	C₂²×C₃	—	10	2	no	—
186	C₂²×C₃	—	10	2	no	—
187	C₂²×C₃	—	10	8	no	—
188	C₂²×C₃	C₂×C₄×D₅	1	2	yes	—
189	C₂²×C₃	#709	1	2	yes	—
190	C₂²×C₃	#709	1	2	yes	—
191	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
192	C₃×C₄	—	2	2	no	—
193	C₃×C₄	—	10	2	no	—
194	Dic₃	—	2	2	no	—
195	Dic₃	—	5	4	no	—
196	Dic₃	—	10	2	no	—
197	Dic₃	C₂×C₄×D₅	1	4	yes	—
198	C₂×C₅	#877	1	4	yes	complemented
199	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
200	C₂×C₅	C₂×#237	1	1	yes	characteristic
201	C₂×C₅	C₂×#237	1	1	yes	characteristic
202	D₅	—	2	4	no	—
203	C₂³	—	5	4	no	—
204	C₂³	—	5	2	no	—
205	C₂³	—	10	2	no	—
206	C₂³	—	10	2	no	—
207	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	3	4	no	—
210	C₂×C₄	—	3	2	no	—
211	C₂×C₄	—	3	2	no	—
212	C₂×C₄	—	5	2	no	—
213	C₂×C₄	—	6	2	no	—
214	C₂×C₄	—	10	2	no	—
215	C₂×C₄	—	15	16	no	—
216	C₂×C₄	—	15	4	no	—
217	C₂×C₄	—	15	2	no	—
218	C₂×C₄	—	15	2	no	—
219	C₂×C₄	—	30	2	no	—
220	C₂×C₄	C₂×D₃×D₅	1	2	yes	—
221	C₂×C₃	—	10	4	no	—
222	C₂×C₃	#4018	1	4	yes	complemented
223	C₂×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
224	C₂×C₃	C₂×#709	1	1	yes	characteristic
225	C₂×C₃	C₂×#709	1	1	yes	characteristic
226	C₅	C₂×#877	1	1	yes	characteristic, complemented, Sylow
227	C₂²	—	5	4	no	—
228	C₂²	—	10	8	no	—
229	C₂²	—	10	2	no	—
230	C₂²	—	10	2	no	—
231	C₂²	#6765	1	2	yes	—
232	C₂²	C₄×D₃×D₅	1	2	yes	—
233	C₂²	#6779	1	2	yes	—
234	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	3	4	no	—
237	C₄	—	6	2	no	—
238	C₄	—	10	2	no	—
239	C₄	—	15	4	no	—
240	C₄	—	30	2	no	—
241	C₃	C₂×#4018	1	1	yes	characteristic, complemented, Sylow
242	C₂	—	10	4	no	—
243	C₂	#91393	1	4	yes	direct product factor
244	C₂	C₂×#6765	1	1	yes	characteristic
245	C₂	C₂×C₄×D₃×D₅	1	1	yes	characteristic
246	C₂	C₂×#6779	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₄
Frattini	C₂²	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂³
prime radical	C₂³×C₃×D₅	C₂²
cosocle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₂²×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#117
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#6712	C₂	semidirect
3. C₂×C₄×C₅×Dic₃	C₂	semidirect
5. C₂×#6669	C₂	semidirect
7. C₂×Dic₃×Dic₅	C₂	semidirect
8. #91393	C₂	direct (N × H)
17. C₂×D₅×Dic₃	C₄	semidirect
19. #6712	C₂²	semidirect
20. C₄×C₅×Dic₃	C₂²	semidirect
22. #6669	C₂²	semidirect
24. Dic₃×Dic₅	C₂²	semidirect
51. D₅×Dic₃	C₂×C₄	semidirect
58. C₂×C₄×Dic₃	D₅	semidirect
104. C₄×Dic₃	C₂×D₅	semidirect
131. C₂×C₃×C₅	#117	semidirect
183. C₃×C₅	C₂×#117	semidirect
198. C₂×C₅	#877	semidirect
222. C₂×C₃	#4018	semidirect
226. C₅	C₂×#877	semidirect
241. C₃	C₂×#4018	semidirect
243. C₂	#91393	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₅×Dic₃	2
C₂×#6712	2
C₂×C₄×C₅×Dic₃	2
C₂×C₃×#685	2
C₂×#6669	2
C₂×#6665	2
C₂×Dic₃×Dic₅	2
#91393	2
C₂×#4018	3
C₂×#877	5

Subgroups — C2×#91393 #11754281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#91393 #11754281