Subgroups — C₂²×C₇₉⋊#564 #35195165

Order 20224.

6374 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊#564	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#14579153	C₂	1	2	yes	maximal
3	C₂²×#14579152	C₂	1	4	yes	maximal
4	C₂²×#14579151	C₂	1	4	yes	maximal
5	C₂²×#14579151	C₂	1	4	yes	maximal
6	C₂²×#125×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₇₉⋊#564	C₂²	1	256	yes	direct product factor
8	C₂×#14579153	C₂²	1	48	yes	—
9	C₂×#14579152	C₂²	1	96	yes	—
10	C₂×#14579151	C₂²	1	96	yes	—
11	C₂×#14579151	C₂²	1	96	yes	—
12	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊Dic₇₉	C₂²	1	4	yes	—
14	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	—
15	C₂²×Dic₇₉⋊C₄	C₂²	1	4	yes	—
16	C₂²×Dic₇₉⋊C₄	C₂²	1	4	yes	—
17	C₂²×Dic₇₉⋊C₄	C₂²	1	4	yes	—
18	C₂²×Dic₇₉⋊C₄	C₂²	1	4	yes	—
19	C₂²×C₄×Dic₇₉	C₂²	1	4	yes	—
20	C₂×#125×C₇₉	C₂²	1	24	yes	—
21	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
23	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
24	C₂³×Dic₇₉	C₂³	1	4	yes	—
25	C₂³×Dic₇₉	C₂³	1	4	yes	—
26	#14579153	C₂³	1	128	yes	—
27	#14579152	C₂³	1	256	yes	—
28	#14579151	C₂³	1	256	yes	—
29	#14579151	C₂³	1	256	yes	—
30	C₂×C₄⋊Dic₇₉	C₂³	1	24	yes	—
31	C₂×C₄⋊Dic₇₉	C₂³	1	48	yes	—
32	C₂×C₄⋊Dic₇₉	C₂³	1	24	yes	—
33	C₂×Dic₇₉⋊C₄	C₂³	1	48	yes	—
34	C₂×Dic₇₉⋊C₄	C₂³	1	48	yes	—
35	C₂×Dic₇₉⋊C₄	C₂³	1	48	yes	—
36	C₂×Dic₇₉⋊C₄	C₂³	1	48	yes	—
37	C₂×C₄×Dic₇₉	C₂³	1	48	yes	—
38	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
41	#125×C₇₉	C₂³	1	64	yes	—
42	C₂×C₄⋊C₄×C₇₉	C₂³	1	24	yes	—
43	C₂×C₄⋊C₄×C₇₉	C₂³	1	48	yes	—
44	C₂×C₄²×C₇₉	C₂³	1	12	yes	—
45	C₂²×Dic₇₉	—	2	16	no	—
46	C₂²×Dic₇₉	—	2	16	no	—
47	C₂²×Dic₇₉	C₂⁴	1	24	yes	—
48	C₂²×Dic₇₉	C₂⁴	1	24	yes	—
49	C₄⋊Dic₇₉	C₂⁴	1	32	yes	—
50	C₄⋊Dic₇₉	C₂⁴	1	64	yes	—
51	C₄⋊Dic₇₉	C₂⁴	1	32	yes	—
52	Dic₇₉⋊C₄	C₂⁴	1	64	yes	—
53	Dic₇₉⋊C₄	C₂⁴	1	64	yes	—
54	Dic₇₉⋊C₄	C₂⁴	1	64	yes	—
55	Dic₇₉⋊C₄	C₂⁴	1	64	yes	—
56	C₄×Dic₇₉	C₂⁴	1	64	yes	—
57	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	—	2	8	no	—
59	C₂²×C₄×C₇₉	—	2	16	no	—
60	C₂²×C₄×C₇₉	—	2	4	no	—
61	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
62	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
63	C₂²×C₄×C₇₉	C₂⁴	1	24	yes	—
64	C₄⋊C₄×C₇₉	C₂⁴	1	32	yes	—
65	C₄⋊C₄×C₇₉	C₂⁴	1	64	yes	—
66	C₄²×C₇₉	C₂⁴	1	16	yes	—
67	C₂³×C₇₉	2₋¹⁺⁴	1	8	yes	—
68	C₂³×C₇₉	2₋¹⁺⁴	1	4	yes	—
69	C₂³×C₇₉	C₂⁵	1	3	yes	—
70	C₂×C₄×C₇₉	—	2	24	no	—
71	C₂×C₄×C₇₉	—	2	48	no	—
72	C₂×C₄×C₇₉	—	2	12	no	—
73	C₂×C₄×C₇₉	C₂⁵	1	16	yes	—
74	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
75	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
76	C₂×Dic₇₉	—	2	48	no	—
77	C₂×Dic₇₉	—	2	48	no	—
78	C₂×Dic₇₉	C₂⁵	1	16	yes	—
79	C₂×Dic₇₉	C₂⁵	1	16	yes	—
80	C₂²×C₇₉	#564	1	16	yes	complemented
81	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	12	yes	—
82	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	6	yes	—
83	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
84	C₄×C₇₉	—	2	16	no	—
85	C₄×C₇₉	—	2	8	no	—
86	C₄×C₇₉	—	2	4	no	—
87	Dic₇₉	—	2	16	no	—
88	Dic₇₉	—	2	16	no	—
89	C₂²×#564	—	79	1	no	maximal, Sylow
90	C₂×C₇₉	C₂×#564	1	12	yes	complemented
91	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	2	yes	—
92	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
93	C₂×#564	—	79	48	no	—
94	C₂²×#125	—	79	2	no	—
95	C₂²×#125	—	79	4	no	—
96	C₂²×#125	—	79	4	no	—
97	C₂²×#125	—	79	4	no	—
98	C₂²×#125	D₇₉	1	1	yes	characteristic
99	C₇₉	C₂²×#564	1	1	yes	characteristic, complemented, Sylow
100	#564	—	79	256	no	—
101	C₂×#125	—	79	96	no	—
102	C₂×#125	—	79	96	no	—
103	C₂×#125	—	79	96	no	—
104	C₂×#125	—	79	48	no	—
105	C₂×#125	C₂×D₇₉	1	24	yes	—
106	C₂²×C₄⋊C₄	—	79	4	no	—
107	C₂²×C₄⋊C₄	—	79	4	no	—
108	C₂²×C₄⋊C₄	—	79	4	no	—
109	C₂²×C₄⋊C₄	—	79	4	no	—
110	C₂²×C₄⋊C₄	—	79	2	no	—
111	C₂²×C₄⋊C₄	—	79	2	no	—
112	C₂²×C₄⋊C₄	—	79	4	no	—
113	C₂²×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
114	C₂²×C₄⋊C₄	C₂×D₇₉	1	4	yes	—
115	C₂²×C₄²	—	79	4	no	—
116	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
117	C₂³×C₄	—	79	4	no	—
118	C₂³×C₄	—	79	4	no	—
119	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
120	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
121	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
122	#125	—	79	256	no	—
123	#125	—	79	256	no	—
124	#125	—	79	256	no	—
125	#125	—	79	128	no	—
126	#125	C₂²×D₇₉	1	64	yes	—
127	C₂×C₄⋊C₄	—	79	48	no	—
128	C₂×C₄⋊C₄	—	79	48	no	—
129	C₂×C₄⋊C₄	—	79	48	no	—
130	C₂×C₄⋊C₄	—	79	48	no	—
131	C₂×C₄⋊C₄	—	79	48	no	—
132	C₂×C₄⋊C₄	—	79	24	no	—
133	C₂×C₄⋊C₄	—	79	24	no	—
134	C₂×C₄⋊C₄	C₂²×D₇₉	1	24	yes	—
135	C₂×C₄⋊C₄	C₂²×D₇₉	1	48	yes	—
136	C₂×C₄²	—	79	48	no	—
137	C₂×C₄²	C₂²×D₇₉	1	12	yes	—
138	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	—	2	16	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	79	24	no	—
143	C₂²×C₄	—	79	24	no	—
144	C₂²×C₄	—	158	16	no	—
145	C₂²×C₄	—	158	16	no	—
146	C₂²×C₄	C₂³×D₇₉	1	24	yes	—
147	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
148	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
149	C₄⋊C₄	—	79	64	no	—
150	C₄⋊C₄	—	79	64	no	—
151	C₄⋊C₄	—	79	64	no	—
152	C₄⋊C₄	—	79	64	no	—
153	C₄⋊C₄	—	79	64	no	—
154	C₄⋊C₄	—	79	32	no	—
155	C₄⋊C₄	—	79	32	no	—
156	C₄⋊C₄	C₂³×D₇₉	1	32	yes	—
157	C₄⋊C₄	C₂³×D₇₉	1	64	yes	—
158	C₄²	—	79	64	no	—
159	C₄²	C₂³×D₇₉	1	16	yes	—
160	C₂³	#14579208	1	8	yes	—
161	C₂³	#14579209	1	4	yes	—
162	C₂³	C₂⁴×D₇₉	1	3	yes	—
163	C₂×C₄	—	2	48	no	—
164	C₂×C₄	—	2	24	no	—
165	C₂×C₄	—	2	12	no	—
166	C₂×C₄	—	79	16	no	—
167	C₂×C₄	—	79	16	no	—
168	C₂×C₄	—	158	48	no	—
169	C₂×C₄	—	158	48	no	—
170	C₂×C₄	C₂⁴×D₇₉	1	16	yes	—
171	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
172	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
173	C₂²	C₇₉⋊#564	1	16	yes	direct product factor
174	C₂²	C₂×#14579208	1	12	yes	—
175	C₂²	C₂×#14579209	1	6	yes	—
176	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
177	C₄	—	2	16	no	—
178	C₄	—	2	8	no	—
179	C₄	—	2	4	no	—
180	C₄	—	158	16	no	—
181	C₄	—	158	16	no	—
182	C₂	C₂×C₇₉⋊#564	1	12	yes	direct product factor
183	C₂	C₂²×#14579208	1	2	yes	—
184	C₂	C₂²×#14579209	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×#125×C₇₉	C₂
socle, prime radical	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#125	D₇₉
hypocenter	C₇₉	C₂²×#564
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₇₉⋊#564	C₂	direct (N × H)
7. C₇₉⋊#564	C₂²	direct (N × H)
80. C₂²×C₇₉	#564	semidirect
90. C₂×C₇₉	C₂×#564	semidirect
99. C₇₉	C₂²×#564	semidirect
173. C₂²	C₇₉⋊#564	direct (N × H)
182. C₂	C₂×C₇₉⋊#564	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×C₇₉⋊#564	2
C₂²×#14579153	2
C₂²×#14579152	2
C₂²×#14579151	2
C₂²×#125×C₇₉	2
C₂²×#564	79

Subgroups — C22×C79⋊#564 #35195165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇₉⋊#564 #35195165