Subgroups — C₄×#19098340 #34203096

Order 20224.

418 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098340	C₂	1	4	yes	maximal
2	C₄×#14579101	C₂	1	1	yes	maximal, characteristic
3	C₄×#14579071	C₂	1	1	yes	maximal, characteristic
4	C₄×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579101	C₂²	1	2	yes	—
6	C₂×#14579071	C₄	1	2	yes	—
7	C₂×#14579071	C₂²	1	2	yes	—
8	C₂×C₄×C₇₉⋊C₈	C₄	1	1	yes	characteristic
9	C₄²×Dic₇₉	C₄	1	1	yes	characteristic
10	#19098340	C₄	1	16	yes	direct product factor
11	#19098339	C₄	1	2	yes	complemented
12	C₄×C₇₉⋊C₁₆	C₄	1	2	yes	complemented
13	C₂×M₃₂×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	#346×C₇₉	C₄	1	2	yes	complemented
16	C₄×C₁₆×C₇₉	C₄	1	2	yes	complemented
17	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
18	C₂×C₄×Dic₇₉	—	2	2	no	—
19	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
20	#14579101	C₂×C₄	1	8	yes	—
21	C₂×C₇₉⋊C₁₆	C₂×C₄	1	4	yes	—
22	#14579071	—	2	4	no	—
23	#14579071	C₂×C₄	1	8	yes	—
24	C₄×C₇₉⋊C₈	—	2	2	no	—
25	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
28	M₃₂×C₇₉	C₂×C₄	1	8	yes	—
29	C₂×C₁₆×C₇₉	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
33	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₇₉	—	2	2	no	—
35	C₂×C₇₉⋊C₈	—	2	2	no	—
36	C₂×C₇₉⋊C₈	—	2	2	no	—
37	C₂×C₇₉⋊C₈	C₄²	1	4	yes	—
38	C₄×Dic₇₉	—	2	2	no	—
39	C₄×Dic₇₉	—	4	4	no	—
40	C₄×Dic₇₉	C₄²	1	4	yes	—
41	C₇₉⋊C₁₆	C₄²	1	8	yes	complemented
42	C₂²×C₄×C₇₉	M₁₆	1	2	yes	—
43	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₇₉	C₄²	1	1	yes	characteristic
45	C₂×C₈×C₇₉	C₄²	1	1	yes	characteristic
46	C₂×C₈×C₇₉	M₁₆	1	4	yes	—
47	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
49	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
50	C₄²×C₇₉	C₄²	1	1	yes	characteristic
51	C₄²×C₇₉	C₄²	1	1	yes	characteristic
52	C₄²×C₇₉	M₁₆	1	2	yes	—
53	C₁₆×C₇₉	C₄²	1	8	yes	complemented
54	C₂³×C₇₉	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₄×C₇₉	—	2	4	no	—
56	C₂×C₄×C₇₉	#97	1	2	yes	—
57	C₂×C₄×C₇₉	#97	1	2	yes	—
58	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
59	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
61	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
62	C₂×Dic₇₉	—	2	4	no	—
63	C₂×Dic₇₉	—	4	4	no	—
64	C₈×C₇₉	#97	1	2	yes	—
65	C₈×C₇₉	#97	1	2	yes	—
66	C₈×C₇₉	C₂×C₄²	1	2	yes	—
67	C₈×C₇₉	C₂×C₄²	1	2	yes	—
68	C₇₉⋊C₈	—	2	4	no	—
69	C₂²×C₇₉	—	2	2	no	—
70	C₂²×C₇₉	C₂×#97	1	1	yes	characteristic
71	C₂²×C₇₉	C₄×M₁₆	1	2	yes	—
72	C₄×C₇₉	—	2	2	no	—
73	C₄×C₇₉	#347	1	4	yes	complemented
74	C₄×C₇₉	C₄³	1	1	yes	characteristic
75	C₄×C₇₉	C₂×#97	1	1	yes	characteristic
76	C₄×C₇₉	C₄×M₁₆	1	2	yes	—
77	Dic₇₉	—	4	4	no	—
78	C₄×#347	—	79	1	no	maximal, Sylow
79	C₂×C₇₉	—	2	2	no	—
80	C₂×C₇₉	C₄×#97	1	1	yes	characteristic
81	C₂×C₇₉	C₂×#347	1	2	yes	—
82	C₂×#347	—	79	4	no	—
83	C₄×M₃₂	—	79	1	no	—
84	C₄×M₃₂	D₇₉	1	1	yes	characteristic
85	C₄×#97	—	79	1	no	—
86	C₇₉	C₄×#347	1	1	yes	characteristic, complemented, Sylow
87	C₂×M₃₂	—	79	2	no	—
88	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
89	C₂×#97	—	79	2	no	—
90	C₂×#97	—	79	2	no	—
91	C₂×C₄×C₈	—	79	1	no	—
92	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
93	C₄³	—	79	1	no	—
94	#347	—	79	16	no	—
95	#346	—	79	2	no	—
96	#346	Dic₇₉	1	2	yes	complemented
97	C₄×C₁₆	—	79	2	no	—
98	C₄×C₁₆	Dic₇₉	1	2	yes	complemented
99	C₂²×C₈	—	79	2	no	—
100	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
101	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
102	C₂×C₄²	—	79	2	no	—
103	C₂×C₄²	—	158	2	no	—
104	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
105	M₃₂	—	79	8	no	—
106	M₃₂	C₄×D₇₉	1	8	yes	—
107	C₂×C₁₆	—	79	4	no	—
108	C₂×C₁₆	C₂×Dic₇₉	1	4	yes	—
109	#97	—	79	8	no	—
110	#97	—	158	4	no	—
111	C₄×C₈	—	158	2	no	—
112	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
113	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
114	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
115	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
116	C₂²×C₄	—	158	2	no	—
117	C₂²×C₄	#11929607	1	2	yes	—
118	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
119	C₂×C₈	—	79	4	no	—
120	C₂×C₈	—	158	2	no	—
121	C₂×C₈	—	158	2	no	—
122	C₂×C₈	C₄×Dic₇₉	1	1	yes	characteristic
123	C₂×C₈	C₄×Dic₇₉	1	1	yes	characteristic
124	C₂×C₈	#11929607	1	4	yes	—
125	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
126	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
127	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
128	C₄²	—	316	4	no	—
129	C₄²	—	79	4	no	—
130	C₄²	—	158	2	no	—
131	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
132	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
133	C₄²	#11929607	1	2	yes	—
134	C₁₆	—	79	8	no	—
135	C₁₆	C₄×Dic₇₉	1	8	yes	complemented
136	C₂³	C₂×#11929607	1	1	yes	characteristic
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	316	4	no	—
139	C₂×C₄	—	158	4	no	—
140	C₂×C₄	#14579071	1	2	yes	—
141	C₂×C₄	#14579071	1	2	yes	—
142	C₂×C₄	C₄²×D₇₉	1	2	yes	—
143	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
144	C₂×C₄	C₂×#11929607	1	2	yes	—
145	C₂×C₄	C₂×#11929607	1	1	yes	characteristic
146	C₈	—	158	4	no	—
147	C₈	#14579071	1	2	yes	—
148	C₈	#14579071	1	2	yes	—
149	C₈	C₄²×D₇₉	1	2	yes	—
150	C₈	C₂×C₄×Dic₇₉	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	C₂×#14579071	1	1	yes	characteristic
153	C₂²	C₄×#11929607	1	2	yes	—
154	C₄	—	2	2	no	—
155	C₄	—	316	4	no	—
156	C₄	#19098340	1	4	yes	direct product factor
157	C₄	C₄²×Dic₇₉	1	1	yes	characteristic
158	C₄	C₂×#14579071	1	1	yes	characteristic
159	C₄	C₄×#11929607	1	2	yes	—
160	C₂	—	2	2	no	—
161	C₂	C₄×#14579071	1	1	yes	characteristic
162	C₂	C₂×#19098340	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₇₉
commutator	C₄×C₇₉	C₄³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₄×M₃₂×C₇₉	C₂
socle	C₂²×C₇₉	C₂×#97
prime radical	C₂³×C₇₉	C₂×M₁₆
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₄×M₃₂	D₇₉
hypocenter	C₇₉	C₄×#347
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄² ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
10. #19098340	C₄	direct (N × H)
11. #19098339	C₄	semidirect
12. C₄×C₇₉⋊C₁₆	C₄	semidirect
15. #346×C₇₉	C₄	semidirect
16. C₄×C₁₆×C₇₉	C₄	semidirect
41. C₇₉⋊C₁₆	C₄²	semidirect
53. C₁₆×C₇₉	C₄²	semidirect
73. C₄×C₇₉	#347	semidirect
86. C₇₉	C₄×#347	semidirect
96. #346	Dic₇₉	semidirect
98. C₄×C₁₆	Dic₇₉	semidirect
135. C₁₆	C₄×Dic₇₉	semidirect
156. C₄	#19098340	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×#19098340	2
C₄×#14579101	2
C₄×#14579071	2
C₄×M₃₂×C₇₉	2
C₄×#347	79

Subgroups — C4×#19098340 #34203096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19098340 #34203096