Subgroups — C₄×#19098390 #34203673

Order 20224.

366 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098390	C₂	1	2	yes	maximal
2	C₂×C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×#14579095	C₂	1	1	yes	maximal, characteristic
4	#23761491	C₂	1	2	yes	maximal
5	C₄×#107×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂×#14579095	C₂²	1	2	yes	—
9	C₄×C₄⋊Dic₇₉	—	2	1	no	—
10	#19098390	C₄	1	8	yes	direct product factor
11	C₄×C₇₉⋊C₁₆	C₄	1	4	yes	complemented
12	#19098326	—	2	1	no	—
13	C₂×#107×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
16	#340×C₇₉	—	2	1	no	—
17	C₂×C₄⋊Dic₇₉	—	2	2	no	—
18	C₂×C₄×Dic₇₉	—	4	1	no	—
19	C₂×C₇₉⋊C₁₆	—	2	2	no	—
20	C₂×C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₇₉⋊C₁₆	C₂×C₄	1	4	yes	—
22	C₂×C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
23	#14579095	—	2	2	no	—
24	#14579095	C₂×C₄	1	4	yes	—
25	C₇₉⋊#95	—	4	1	no	—
26	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₂×C₄²×C₇₉	—	4	1	no	—
30	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
31	#107×C₇₉	—	2	2	no	—
32	#107×C₇₉	C₂×C₄	1	4	yes	—
33	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₇₉	Q₈	1	2	yes	—
35	#95×C₇₉	—	4	1	no	—
36	C₂²×Dic₇₉	—	4	2	no	—
37	C₄⋊Dic₇₉	—	2	4	no	—
38	C₄⋊Dic₇₉	—	4	2	no	—
39	C₄×Dic₇₉	—	8	2	no	—
40	C₇₉⋊C₁₆	—	2	2	no	—
41	C₇₉⋊C₁₆	C₄²	1	4	yes	complemented
42	C₂²×C₄×C₇₉	—	4	2	no	—
43	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
44	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₇₉	—	2	2	no	—
47	C₂×C₈×C₇₉	C₄⋊C₄	1	2	yes	—
48	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₇₉	#41	1	2	yes	—
52	C₄⋊C₄×C₇₉	—	2	4	no	—
53	C₄⋊C₄×C₇₉	—	4	2	no	—
54	C₄²×C₇₉	—	8	2	no	—
55	C₄²×C₇₉	C₄⋊C₄	1	2	yes	—
56	C₄²×C₇₉	Q₁₆	1	2	yes	—
57	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₇₉	—	2	2	no	—
59	C₂×C₄×C₇₉	—	4	4	no	—
60	C₂×C₄×C₇₉	—	8	2	no	—
61	C₂×C₄×C₇₉	—	8	2	no	—
62	C₂×C₄×C₇₉	#107	1	2	yes	—
63	C₂×C₄×C₇₉	#107	1	2	yes	—
64	C₂×C₄×C₇₉	SD₃₂	1	2	yes	—
65	C₂×C₄×C₇₉	SD₃₂	1	2	yes	—
66	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
68	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
69	C₂×C₄×C₇₉	#135	1	2	yes	—
70	C₂×Dic₇₉	—	4	4	no	—
71	C₂×Dic₇₉	—	8	2	no	—
72	C₂×Dic₇₉	—	8	2	no	—
73	C₈×C₇₉	—	2	2	no	—
74	C₈×C₇₉	C₂×C₄²	1	1	yes	characteristic
75	C₈×C₇₉	#117	1	1	yes	characteristic
76	C₈×C₇₉	C₄×Q₈	1	2	yes	—
77	C₂²×C₇₉	C₂×#107	1	1	yes	characteristic
78	C₂²×C₇₉	C₄×D₈	1	2	yes	—
79	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
80	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
81	C₂²×C₇₉	#508	1	2	yes	—
82	C₄×C₇₉	—	2	2	no	—
83	C₄×C₇₉	—	8	4	no	—
84	C₄×C₇₉	#367	1	4	yes	complemented
85	C₄×C₇₉	C₄×C₄⋊C₄	1	1	yes	characteristic
86	C₄×C₇₉	#427	1	1	yes	characteristic
87	C₄×C₇₉	C₄×Q₁₆	1	2	yes	—
88	Dic₇₉	—	8	4	no	—
89	C₄×#367	—	79	1	no	maximal, Sylow
90	C₂×C₇₉	C₄×#107	1	1	yes	characteristic
91	C₂×C₇₉	C₂×#367	1	1	yes	characteristic
92	C₂×C₇₉	#2158	1	1	yes	characteristic
93	C₂×C₇₉	C₄×SD₃₂	1	2	yes	—
94	C₂×C₇₉	C₄×SD₃₂	1	2	yes	—
95	C₂×#367	—	79	2	no	—
96	C₂×C₄×C₁₆	—	79	1	no	—
97	C₄×#107	—	79	1	no	—
98	C₄×#107	D₇₉	1	1	yes	characteristic
99	#1380	—	79	2	no	—
100	C₇₉	C₄×#367	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₁₆	—	79	1	no	—
102	C₂²×C₁₆	—	79	1	no	—
103	C₂×#107	—	79	2	no	—
104	C₂×#107	C₂×D₇₉	1	2	yes	—
105	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
106	C₄×C₄⋊C₄	—	2	1	no	—
107	C₄×C₄⋊C₄	—	158	1	no	—
108	#367	—	79	8	no	—
109	C₄×C₁₆	—	79	4	no	—
110	#340	—	2	1	no	—
111	#340	—	158	1	no	—
112	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
113	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	158	2	no	—
116	C₂×C₄²	—	4	1	no	—
117	C₂×C₄²	—	316	1	no	—
118	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
119	C₂×C₁₆	—	79	2	no	—
120	C₂×C₁₆	—	79	4	no	—
121	C₂×C₁₆	—	79	2	no	—
122	C₂×C₁₆	—	158	2	no	—
123	#107	—	2	2	no	—
124	#107	—	79	4	no	—
125	#107	—	158	2	no	—
126	#107	C₄×D₇₉	1	4	yes	—
127	C₄×C₈	Dic₁₅₈	1	2	yes	—
128	C₄×C₈	C₄×D₇₉	1	2	yes	—
129	#95	—	4	1	no	—
130	#95	—	316	1	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	—	316	2	no	—
133	C₂²×C₄	#11929609	1	1	yes	characteristic
134	C₂²×C₄	#11929609	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	Dic₇₉⋊C₄	1	2	yes	—
138	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
139	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
140	C₂×C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
141	C₂×C₈	#11929624	1	2	yes	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	4	2	no	—
144	C₄⋊C₄	—	316	2	no	—
145	C₄⋊C₄	—	158	4	no	—
146	C₄²	—	8	2	no	—
147	C₄²	—	632	2	no	—
148	C₄²	Dic₇₉⋊C₄	1	2	yes	—
149	C₄²	#11929614	1	2	yes	—
150	C₁₆	—	79	4	no	—
151	C₁₆	—	158	2	no	—
152	C₂³	C₂×#11929609	1	1	yes	characteristic
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	—	8	2	no	—
156	C₂×C₄	—	8	2	no	—
157	C₂×C₄	—	316	4	no	—
158	C₂×C₄	—	632	2	no	—
159	C₂×C₄	—	632	2	no	—
160	C₂×C₄	#14579094	1	2	yes	—
161	C₂×C₄	#14579094	1	2	yes	—
162	C₂×C₄	#14579104	1	2	yes	—
163	C₂×C₄	#14579105	1	2	yes	—
164	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
165	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
166	C₂×C₄	C₂×#11929614	1	1	yes	characteristic
167	C₂×C₄	#14579181	1	2	yes	—
168	C₈	—	2	2	no	—
169	C₈	C₄²×D₇₉	1	1	yes	characteristic
170	C₈	#14579118	1	1	yes	characteristic
171	C₈	C₄×Dic₁₅₈	1	2	yes	—
172	C₂²	C₂×#14579094	1	1	yes	characteristic
173	C₂²	C₄×#11929609	1	2	yes	—
174	C₂²	C₂×#14579104	1	1	yes	characteristic
175	C₂²	C₂×#14579105	1	1	yes	characteristic
176	C₂²	#19098993	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	8	4	no	—
179	C₄	—	632	4	no	—
180	C₄	#19098390	1	4	yes	direct product factor
181	C₄	C₄×Dic₇₉⋊C₄	1	1	yes	characteristic
182	C₄	#19098599	1	1	yes	characteristic
183	C₄	C₄×#11929614	1	2	yes	—
184	C₂	C₄×#14579094	1	1	yes	characteristic
185	C₂	C₂×#19098390	1	1	yes	characteristic
186	C₂	#23765182	1	1	yes	characteristic
187	C₂	C₄×#14579105	1	2	yes	—
188	C₂	C₄×#14579104	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#11929609
commutator	C₈×C₇₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₄×#107×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₈
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₄×#107	D₇₉
hypocenter	C₇₉	C₄×#367
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
10. #19098390	C₄	direct (N × H)
11. C₄×C₇₉⋊C₁₆	C₄	semidirect
41. C₇₉⋊C₁₆	C₄²	semidirect
84. C₄×C₇₉	#367	semidirect
100. C₇₉	C₄×#367	semidirect
180. C₄	#19098390	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×#19098390	2
C₂×C₄×C₇₉⋊C₁₆	2
C₄×#14579095	2
#23761491	2
C₄×#107×C₇₉	2
C₄×#367	79

Subgroups — C4×#19098390 #34203673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19098390 #34203673