Subgroups — C₂×#11751183 #14437955

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#91759	C₂	1	1	yes	maximal, characteristic
3	C₂×#91119	C₂	1	4	yes	maximal
4	#11751183	C₂	1	8	yes	maximal, direct product factor
5	C₂×#91087	C₂	1	1	yes	maximal, characteristic
6	C₂×#65371	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
9	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
13	C₂×#6712	—	2	2	no	—
14	C₂²×C₃⋊#168	C₂²	1	2	yes	—
15	#91759	—	2	2	no	—
16	#91759	C₂²	1	4	yes	—
17	#91119	C₂²	1	16	yes	—
18	#91087	C₂²	1	4	yes	—
19	C₂×#5082	—	5	1	no	maximal, Hall
20	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic
21	C₂×#4016	—	3	1	no	—
22	C₂×#3967	—	3	4	no	—
23	#65371	—	3	8	no	—
24	C₂×#3935	—	3	1	no	—
25	C₂×C₃×C₅×Q₈	—	2	2	no	—
26	C₂×C₃×C₅×Q₈	—	2	8	no	—
27	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₅	—	2	2	no	—
32	C₃×C₅×C₄⋊C₄	—	2	8	no	—
33	C₃×C₄²×C₅	D₄	1	2	yes	—
34	C₃×C₄²×C₅	C₂³	1	2	yes	—
35	C₄⋊Dic₁₅	—	2	2	no	—
36	C₄⋊Dic₁₅	C₂³	1	4	yes	—
37	#6712	—	2	8	no	—
38	C₂×C₃⋊#168	—	2	4	no	—
39	C₂×C₃⋊#168	C₂³	1	4	yes	—
40	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic
41	C₂×#870	—	5	1	no	—
42	C₂×#835	—	5	4	no	—
43	#5082	—	5	8	no	—
44	C₂×#803	—	5	1	no	—
45	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
46	C₅×C₄⋊Q₈	—	2	2	no	—
47	C₅×C₄⋊Q₈	C₂×D₃	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	—	2	2	no	—
49	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
50	C₂×C₄⋊Dic₅	—	3	2	no	—
51	C₂×#683	—	6	2	no	—
52	C₂²×#168	—	3	2	no	—
53	#4016	—	3	4	no	—
54	#4016	—	6	2	no	—
55	#3967	—	3	16	no	—
56	#3935	—	3	4	no	—
57	C₂×#491	—	15	1	no	Sylow
58	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
59	C₃×C₅×Q₈	—	2	8	no	—
60	C₃×C₅×Q₈	—	4	4	no	—
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	4	4	no	—
64	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
65	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	#41	1	4	yes	—
67	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
68	C₂×Dic₁₅	—	2	4	no	—
69	C₂×Dic₁₅	—	4	4	no	—
70	C₃⋊#168	—	2	4	no	—
71	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
72	C₃×C₄⋊Q₈	—	2	2	no	—
73	C₃×C₄⋊Q₈	C₂×D₅	1	4	yes	—
74	C₂×C₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
76	C₂×C₄⋊Dic₃	—	5	2	no	—
77	C₂×Dic₃⋊C₄	—	10	2	no	—
78	C₂²×C₃⋊C₈	—	5	2	no	—
79	#870	—	5	4	no	—
80	#870	—	10	2	no	—
81	#835	—	5	16	no	—
82	#803	—	5	4	no	—
83	C₂×C₅×Q₈	—	2	2	no	—
84	C₂×C₅×Q₈	—	2	8	no	—
85	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	#67	1	2	yes	—
88	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
89	C₂²×Dic₅	—	6	2	no	—
90	C₅×C₄⋊C₄	—	2	8	no	—
91	C₄²×C₅	#67	1	2	yes	—
92	C₄²×C₅	C₂²×D₃	1	2	yes	—
93	C₄⋊Dic₅	—	3	4	no	—
94	C₄⋊Dic₅	—	6	2	no	—
95	#683	—	6	8	no	—
96	C₂×#168	—	3	4	no	—
97	C₂×#168	—	6	4	no	—
98	C₂×C₄⋊Q₈	D₁₅	1	1	yes	characteristic
99	C₂×#125	—	15	1	no	—
100	#491	—	15	8	no	—
101	C₂×#103	—	15	4	no	—
102	C₂×#97	—	15	1	no	—
103	C₂²×C₃×C₅	#124	1	2	yes	—
104	C₂²×C₃×C₅	#137	1	4	yes	—
105	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
106	C₃×C₄×C₅	—	2	4	no	—
107	C₃×C₄×C₅	—	4	4	no	—
108	C₃×C₄×C₅	#124	1	2	yes	—
109	C₃×C₄×C₅	C₂×#41	1	2	yes	—
110	Dic₁₅	—	4	4	no	—
111	C₂×C₃×Q₈	—	2	2	no	—
112	C₂×C₃×Q₈	—	2	8	no	—
113	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
114	C₂²×C₃×C₄	—	2	2	no	—
115	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
116	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
117	C₂²×Dic₃	—	10	2	no	—
118	C₃×C₄⋊C₄	—	2	8	no	—
119	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
120	C₃×C₄²	C₂²×D₅	1	2	yes	—
121	C₄⋊Dic₃	—	5	4	no	—
122	C₄⋊Dic₃	—	10	2	no	—
123	Dic₃⋊C₄	—	10	8	no	—
124	C₂×C₃⋊C₈	—	5	4	no	—
125	C₂×C₃⋊C₈	—	10	4	no	—
126	C₂³×C₅	C₂×#67	1	1	yes	characteristic
127	C₅×Q₈	—	2	8	no	—
128	C₅×Q₈	—	4	4	no	—
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	4	4	no	—
132	C₂×C₄×C₅	#237	1	4	yes	—
133	C₂×C₄×C₅	C₂×#67	1	4	yes	—
134	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
135	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
136	C₂×Dic₅	—	6	4	no	—
137	C₂×Dic₅	—	12	4	no	—
138	#168	—	6	4	no	—
139	C₂²×Q₈	C₂×D₁₅	1	2	yes	—
140	C₂²×C₈	—	15	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	C₂×D₁₅	1	4	yes	—
143	#125	—	15	4	no	—
144	#125	—	30	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	15	2	no	—
147	C₂×C₄⋊C₄	—	30	2	no	—
148	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
149	#103	—	15	16	no	—
150	#97	—	15	4	no	—
151	C₂×C₃×C₅	#491	1	4	yes	complemented
152	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
153	C₂×C₃×C₅	C₂×#137	1	2	yes	—
154	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
155	C₃×Q₈	—	2	8	no	—
156	C₃×Q₈	—	4	4	no	—
157	C₂×C₃×C₄	—	2	4	no	—
158	C₂×C₃×C₄	—	2	4	no	—
159	C₂×C₃×C₄	—	4	4	no	—
160	C₂×C₃×C₄	#711	1	4	yes	—
161	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
162	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
164	C₂×Dic₃	—	10	4	no	—
165	C₂×Dic₃	—	20	4	no	—
166	C₃⋊C₈	—	10	4	no	—
167	C₂²×C₅	#936	1	2	yes	—
168	C₂²×C₅	#942	1	4	yes	—
169	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
170	C₄×C₅	—	2	4	no	—
171	C₄×C₅	—	4	4	no	—
172	C₄×C₅	#936	1	2	yes	—
173	C₄×C₅	C₂×#237	1	2	yes	—
174	Dic₅	—	12	4	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	8	no	—
177	C₂×Q₈	C₂²×D₁₅	1	4	yes	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	30	2	no	—
180	C₂²×C₄	#1220	1	2	yes	—
181	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
182	C₂×C₈	—	15	4	no	—
183	C₂×C₈	—	30	4	no	—
184	C₄⋊C₄	—	2	8	no	—
185	C₄⋊C₄	—	15	4	no	—
186	C₄⋊C₄	—	30	2	no	—
187	C₄⋊C₄	—	30	8	no	—
188	C₄²	#1220	1	2	yes	—
189	C₄²	C₂²×D₁₅	1	2	yes	—
190	C₃×C₅	C₂×#491	1	1	yes	characteristic, complemented, Hall
191	C₂²×C₃	#4082	1	2	yes	—
192	C₂²×C₃	#4088	1	4	yes	—
193	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
194	C₃×C₄	—	2	4	no	—
195	C₃×C₄	—	4	4	no	—
196	C₃×C₄	#4082	1	2	yes	—
197	C₃×C₄	C₂×#711	1	2	yes	—
198	Dic₃	—	20	4	no	—
199	C₂×C₅	#5082	1	4	yes	complemented
200	C₂×C₅	C₂×#936	1	1	yes	characteristic
201	C₂×C₅	C₂×#942	1	2	yes	—
202	C₂³	C₂×#1220	1	1	yes	characteristic
203	Q₈	—	2	8	no	—
204	Q₈	—	4	4	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	30	4	no	—
209	C₂×C₄	—	60	4	no	—
210	C₂×C₄	#6819	1	4	yes	—
211	C₂×C₄	C₂×#1220	1	4	yes	—
212	C₂×C₄	C₂×#1220	1	1	yes	characteristic
213	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
214	C₈	—	30	4	no	—
215	C₂×C₃	#65371	1	4	yes	complemented
216	C₂×C₃	C₂×#4082	1	1	yes	characteristic
217	C₂×C₃	C₂×#4088	1	2	yes	—
218	C₅	C₂×#5082	1	1	yes	characteristic, complemented, Sylow
219	C₂²	#91825	1	2	yes	—
220	C₂²	#91831	1	4	yes	—
221	C₂²	C₂²×#1220	1	1	yes	characteristic
222	C₄	—	2	4	no	—
223	C₄	—	4	4	no	—
224	C₄	—	60	4	no	—
225	C₄	#91825	1	2	yes	—
226	C₄	C₂×#6819	1	2	yes	—
227	C₃	C₂×#65371	1	1	yes	characteristic, complemented, Sylow
228	C₂	#11751183	1	4	yes	direct product factor
229	C₂	C₂×#91825	1	1	yes	characteristic
230	C₂	C₂×#91831	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#1220
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₁₅
hypocenter	C₃×C₅	C₂×#491
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
4. #11751183	C₂	direct (N × H)
151. C₂×C₃×C₅	#491	semidirect
190. C₃×C₅	C₂×#491	semidirect
199. C₂×C₅	#5082	semidirect
215. C₂×C₃	#65371	semidirect
218. C₅	C₂×#5082	semidirect
227. C₃	C₂×#65371	semidirect
228. C₂	#11751183	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×C₄⋊Q₈	2
C₂×#91759	2
C₂×#91119	2
#11751183	2
C₂×#91087	2
C₂×#65371	3
C₂×#5082	5

Subgroups — C2×#11751183 #14437955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751183 #14437955