Subgroups — C₄×#14579123 #23765745

Order 10112.

924 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579123	C₂	1	2	yes	maximal
3	C₂×C₄²×D₇₉	C₂	1	2	yes	maximal, complemented
4	C₄⋊C₄×Dic₇₉	C₂	1	2	yes	maximal, complemented
5	C₄×(C₂×D₇₉)⋊C₄	C₂	1	2	yes	maximal, complemented
6	#19098410	C₂	1	4	yes	maximal, complemented
7	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₇₉	C₂²	1	4	yes	—
11	C₂²×C₄×D₇₉	C₂²	1	2	yes	—
12	C₄×D₃₁₆	C₄	1	8	yes	complemented
13	#14579123	C₄	1	16	yes	direct product factor
14	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
15	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
16	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
18	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
20	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
21	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
22	C₄²×D₇₉	—	2	8	no	—
23	C₇₉⋊#95	C₂²	1	4	yes	—
24	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
25	C₂×C₄²×C₇₉	C₂²	1	2	yes	—
26	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
27	#95×C₇₉	C₂²	1	2	yes	—
28	C₂³×D₇₉	C₂³	1	2	yes	—
29	C₂×D₃₁₆	C₂×C₄	1	8	yes	—
30	C₂×D₃₁₆	C₂×C₄	1	4	yes	—
31	C₂²×Dic₇₉	C₂³	1	2	yes	—
32	C₂²×Dic₇₉	C₂³	1	2	yes	—
33	C₂²×Dic₇₉	C₂³	1	2	yes	—
34	C₂×C₄×D₇₉	—	2	8	no	—
35	C₂×C₄×D₇₉	—	2	8	no	—
36	C₂×C₄×D₇₉	—	2	4	no	—
37	C₂×C₄×D₇₉	—	2	4	no	—
38	C₂×C₄×D₇₉	C₂×C₄	1	16	yes	complemented
39	C₂×C₄×D₇₉	C₂×C₄	1	8	yes	complemented
40	C₄⋊Dic₇₉	C₂×C₄	1	4	yes	complemented
41	(C₂×D₇₉)⋊C₄	C₂×C₄	1	16	yes	complemented
42	(C₂×D₇₉)⋊C₄	C₂×C₄	1	8	yes	complemented
43	C₄×Dic₇₉	—	2	8	no	—
44	C₄×Dic₇₉	—	2	4	no	—
45	C₄×Dic₇₉	—	2	2	no	—
46	C₄×Dic₇₉	C₂×C₄	1	8	yes	complemented
47	C₄×Dic₇₉	D₄	1	4	yes	complemented
48	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
50	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₇₉	C₂×C₄	1	8	yes	complemented
53	C₄²×C₇₉	—	2	4	no	—
54	C₄²×C₇₉	C₂×C₄	1	4	yes	complemented
55	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
56	C₂²×D₇₉	—	2	2	no	—
57	C₂²×D₇₉	—	2	4	no	—
58	C₂²×D₇₉	—	2	2	no	—
59	C₂²×D₇₉	C₂²×C₄	1	8	yes	—
60	C₂²×D₇₉	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₇₉	—	2	4	no	—
62	C₂×C₄×C₇₉	—	2	2	no	—
63	C₂×C₄×C₇₉	—	2	4	no	—
64	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₇₉	C₂²×C₄	1	8	yes	—
66	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
67	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₇₉	#41	1	2	yes	—
71	C₂×Dic₇₉	—	2	2	no	—
72	C₂×Dic₇₉	—	2	2	no	—
73	C₂×Dic₇₉	—	2	2	no	—
74	C₂×Dic₇₉	—	2	2	no	—
75	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
76	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
77	C₂×Dic₇₉	C₂²×C₄	1	4	yes	—
78	C₂×Dic₇₉	C₂×D₄	1	4	yes	—
79	C₂×Dic₇₉	#41	1	4	yes	—
80	D₃₁₆	C₄²	1	16	yes	complemented
81	C₄×D₇₉	—	2	16	no	—
82	C₄×D₇₉	—	2	32	no	—
83	C₂²×C₇₉	C₂³×C₄	1	2	yes	—
84	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
85	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
86	C₂²×C₇₉	C₂×#41	1	2	yes	—
87	C₂²×C₇₉	C₂×#41	1	1	yes	characteristic
88	C₂×D₇₉	—	2	8	no	—
89	C₂×D₇₉	—	2	4	no	—
90	C₂×D₇₉	—	2	4	no	—
91	C₂×D₇₉	—	2	8	no	—
92	C₂×D₇₉	C₂×C₄²	1	8	yes	complemented
93	C₄×C₇₉	—	2	8	no	—
94	C₄×C₇₉	—	2	2	no	—
95	C₄×C₇₉	C₂×C₄²	1	4	yes	complemented
96	C₄×C₇₉	C₄×D₄	1	4	yes	complemented
97	Dic₇₉	—	2	4	no	—
98	Dic₇₉	—	2	4	no	—
99	Dic₇₉	C₄×D₄	1	8	yes	complemented
100	C₂×C₇₉	C₂²×C₄²	1	1	yes	characteristic
101	C₂×C₇₉	C₂×C₄×D₄	1	2	yes	—
102	C₂×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
103	C₂×C₇₉	C₄×#41	1	1	yes	characteristic
104	C₂×C₇₉	C₄×#41	1	2	yes	—
105	D₇₉	—	2	8	no	—
106	C₄²×D₄	—	79	1	no	maximal, Sylow
107	C₇₉	C₄²×D₄	1	1	yes	characteristic, complemented, Sylow
108	C₂×C₄×D₄	—	79	2	no	—
109	C₂×C₄×D₄	—	79	1	no	—
110	C₂²×C₄²	—	79	2	no	—
111	C₄×C₄⋊C₄	—	79	2	no	—
112	C₄×C₄⋊C₄	D₇₉	1	1	yes	characteristic, complemented
113	C₄×C₂²⋊C₄	—	79	2	no	—
114	C₄×C₂²⋊C₄	—	79	4	no	—
115	C₄³	—	79	1	no	—
116	C₂²×D₄	—	79	1	no	—
117	C₂³×C₄	—	79	4	no	—
118	C₂³×C₄	—	79	2	no	—
119	C₄×D₄	—	79	16	no	—
120	C₄×D₄	—	79	8	no	—
121	C₂×C₄⋊C₄	—	79	1	no	—
122	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
123	C₂×C₂²⋊C₄	—	79	4	no	—
124	C₂×C₂²⋊C₄	—	79	2	no	—
125	C₂×C₄²	—	79	2	no	—
126	C₂×C₄²	—	79	1	no	—
127	C₂×C₄²	—	79	2	no	—
128	C₂×C₄²	—	79	4	no	—
129	C₂×C₄²	—	79	1	no	—
130	C₂×C₄²	—	158	8	no	—
131	C₂×C₄²	C₂×D₇₉	1	2	yes	—
132	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
133	#95	—	79	4	no	—
134	#95	C₂×D₇₉	1	2	yes	—
135	C₂⁴	—	79	2	no	—
136	C₂×D₄	—	79	8	no	—
137	C₂×D₄	—	79	4	no	—
138	C₂²×C₄	—	79	2	no	—
139	C₂²×C₄	—	79	2	no	—
140	C₂²×C₄	—	79	2	no	—
141	C₂²×C₄	—	79	16	no	—
142	C₂²×C₄	—	79	8	no	—
143	C₂²×C₄	—	158	8	no	—
144	C₂²×C₄	—	158	8	no	—
145	C₂²×C₄	—	158	4	no	—
146	C₂²×C₄	—	158	4	no	—
147	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
148	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
149	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
150	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
151	C₄⋊C₄	—	79	4	no	—
152	C₄⋊C₄	C₄×D₇₉	1	8	yes	complemented
153	C₂²⋊C₄	—	79	16	no	—
154	C₂²⋊C₄	—	79	8	no	—
155	C₄²	—	2	4	no	—
156	C₄²	—	79	8	no	—
157	C₄²	—	79	4	no	—
158	C₄²	—	158	4	no	—
159	C₄²	—	158	8	no	—
160	C₄²	—	158	2	no	—
161	C₄²	C₄×D₇₉	1	4	yes	complemented
162	C₂³	—	79	8	no	—
163	C₂³	—	79	4	no	—
164	C₂³	—	158	4	no	—
165	C₂³	—	158	2	no	—
166	C₂³	—	158	2	no	—
167	C₂³	C₂³×D₇₉	1	1	yes	characteristic
168	D₄	—	79	16	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	79	4	no	—
173	C₂×C₄	—	79	4	no	—
174	C₂×C₄	—	79	4	no	—
175	C₂×C₄	—	79	4	no	—
176	C₂×C₄	—	79	4	no	—
177	C₂×C₄	—	158	32	no	—
178	C₂×C₄	—	158	2	no	—
179	C₂×C₄	—	158	2	no	—
180	C₂×C₄	—	158	2	no	—
181	C₂×C₄	—	158	2	no	—
182	C₂×C₄	—	158	16	no	—
183	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
184	C₂×C₄	C₂×C₄×D₇₉	1	8	yes	—
185	C₂×C₄	C₂×C₄×D₇₉	1	4	yes	—
186	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
187	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
188	C₂×C₄	D₄×D₇₉	1	2	yes	—
189	C₂×C₄	#11929625	1	2	yes	—
190	C₂²	—	79	8	no	—
191	C₂²	—	158	8	no	—
192	C₂²	—	158	4	no	—
193	C₂²	—	158	4	no	—
194	C₂²	—	158	8	no	—
195	C₂²	C₂²×C₄×D₇₉	1	2	yes	—
196	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
197	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
198	C₂²	#41×D₇₉	1	2	yes	—
199	C₂²	C₂×#11929625	1	1	yes	characteristic
200	C₄	—	2	8	no	—
201	C₄	—	2	2	no	—
202	C₄	—	79	8	no	—
203	C₄	—	158	4	no	—
204	C₄	—	158	4	no	—
205	C₄	C₄²×D₇₉	1	4	yes	complemented
206	C₄	#14579123	1	4	yes	direct product factor
207	C₂	—	158	8	no	—
208	C₂	C₂×C₄²×D₇₉	1	1	yes	characteristic
209	C₂	C₄×D₄×D₇₉	1	2	yes	—
210	C₂	C₂×#14579123	1	1	yes	characteristic
211	C₂	#19099031	1	1	yes	characteristic
212	C₂	C₄×#11929625	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator	C₂×C₇₉	C₂²×C₄²
Frattini	C₂³	C₂³×D₇₉
Fitting	C₄×C₄⋊C₄×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂²×D₃₁₆	C₂²
hypercenter	C₄×C₄⋊C₄	D₇₉
hypocenter	C₇₉	C₄²×D₄
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×D₇₉	C₂	semidirect
4. C₄⋊C₄×Dic₇₉	C₂	semidirect
5. C₄×(C₂×D₇₉)⋊C₄	C₂	semidirect
6. #19098410	C₂	semidirect
7. C₄²×Dic₇₉	C₂	semidirect
8. C₄×C₄⋊C₄×C₇₉	C₂	semidirect
12. C₄×D₃₁₆	C₄	semidirect
13. #14579123	C₄	direct (N × H)
38. C₂×C₄×D₇₉	C₂×C₄	semidirect
39. C₂×C₄×D₇₉	C₂×C₄	semidirect
40. C₄⋊Dic₇₉	C₂×C₄	semidirect
41. (C₂×D₇₉)⋊C₄	C₂×C₄	semidirect
42. (C₂×D₇₉)⋊C₄	C₂×C₄	semidirect
46. C₄×Dic₇₉	C₂×C₄	semidirect
47. C₄×Dic₇₉	D₄	semidirect
52. C₄⋊C₄×C₇₉	C₂×C₄	semidirect
54. C₄²×C₇₉	C₂×C₄	semidirect
80. D₃₁₆	C₄²	semidirect
92. C₂×D₇₉	C₂×C₄²	semidirect
95. C₄×C₇₉	C₂×C₄²	semidirect
96. C₄×C₇₉	C₄×D₄	semidirect
99. Dic₇₉	C₄×D₄	semidirect
107. C₇₉	C₄²×D₄	semidirect
112. C₄×C₄⋊C₄	D₇₉	semidirect
152. C₄⋊C₄	C₄×D₇₉	semidirect
161. C₄²	C₄×D₇₉	semidirect
205. C₄	C₄²×D₇₉	semidirect
206. C₄	#14579123	direct (N × H)

Subgroups — C4×#14579123 #23765745

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14579123 #23765745