Finite Group Databasebeta

← C₁₀₁×#17301 #38799452

Subgroups — C₁₀₁×#17301 #38799452

Order 25856.

926 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#1443	C₂	1	5	yes	maximal
2	C₁₀₁×#1442	C₂	1	5	yes	maximal
3	C₁₀₁×#1441	C₂	1	5	yes	maximal
4	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	5	yes	—
5	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
6	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
7	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
8	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
9	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
10	C₂×#95×C₁₀₁	C₂²	1	5	yes	—
11	C₂³×C₄×C₁₀₁	C₂³	1	5	yes	—
12	C₂³×C₄×C₁₀₁	C₂³	1	5	yes	—
13	C₂³×C₄×C₁₀₁	C₂³	1	5	yes	—
14	C₂×C₄⋊C₄×C₁₀₁	—	2	10	no	—
15	C₂×C₄⋊C₄×C₁₀₁	—	4	5	no	—
16	C₂×C₄⋊C₄×C₁₀₁	—	4	5	no	—
17	#95×C₁₀₁	—	2	10	no	—
18	#95×C₁₀₁	—	2	10	no	—
19	#95×C₁₀₁	—	4	5	no	—
20	#95×C₁₀₁	—	4	5	no	—
21	#95×C₁₀₁	—	4	5	no	—
22	#95×C₁₀₁	—	4	5	no	—
23	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
24	C₂²×C₄×C₁₀₁	—	2	5	no	—
25	C₂²×C₄×C₁₀₁	—	2	5	no	—
26	C₂²×C₄×C₁₀₁	—	2	5	no	—
27	C₂²×C₄×C₁₀₁	—	2	5	no	—
28	C₂²×C₄×C₁₀₁	—	2	5	no	—
29	C₂²×C₄×C₁₀₁	—	2	5	no	—
30	C₂²×C₄×C₁₀₁	—	2	5	no	—
31	C₂²×C₄×C₁₀₁	—	2	5	no	—
32	C₂²×C₄×C₁₀₁	—	2	5	no	—
33	C₂²×C₄×C₁₀₁	—	2	5	no	—
34	C₂²×C₄×C₁₀₁	—	2	5	no	—
35	C₂²×C₄×C₁₀₁	—	2	5	no	—
36	C₂²×C₄×C₁₀₁	—	2	5	no	—
37	C₂²×C₄×C₁₀₁	—	2	5	no	—
38	C₂²×C₄×C₁₀₁	—	2	5	no	—
39	C₂²×C₄×C₁₀₁	—	2	5	no	—
40	C₂²×C₄×C₁₀₁	—	2	5	no	—
41	C₂²×C₄×C₁₀₁	—	2	5	no	—
42	C₂²×C₄×C₁₀₁	—	2	5	no	—
43	C₂²×C₄×C₁₀₁	—	2	5	no	—
44	C₂²×C₄×C₁₀₁	#41	1	10	yes	—
45	C₄⋊C₄×C₁₀₁	—	4	20	no	—
46	C₂³×C₁₀₁	C₂×#41	1	5	yes	—
47	C₂³×C₁₀₁	H(5,𝔽₂)	1	5	yes	—
48	C₂³×C₁₀₁	2₋¹⁺⁴	1	5	yes	—
49	C₂×C₄×C₁₀₁	—	2	10	no	—
50	C₂×C₄×C₁₀₁	—	2	10	no	—
51	C₂×C₄×C₁₀₁	—	2	10	no	—
52	C₂×C₄×C₁₀₁	—	4	5	no	—
53	C₂×C₄×C₁₀₁	—	4	5	no	—
54	C₂×C₄×C₁₀₁	—	4	5	no	—
55	C₂×C₄×C₁₀₁	—	4	5	no	—
56	C₂×C₄×C₁₀₁	—	4	5	no	—
57	C₂×C₄×C₁₀₁	—	4	5	no	—
58	C₂×C₄×C₁₀₁	—	4	5	no	—
59	C₂×C₄×C₁₀₁	—	4	5	no	—
60	C₂×C₄×C₁₀₁	—	4	5	no	—
61	C₂×C₄×C₁₀₁	—	4	5	no	—
62	C₂×C₄×C₁₀₁	—	4	5	no	—
63	C₂×C₄×C₁₀₁	—	4	5	no	—
64	C₂×C₄×C₁₀₁	—	4	5	no	—
65	C₂×C₄×C₁₀₁	—	4	5	no	—
66	C₂×C₄×C₁₀₁	—	4	5	no	—
67	C₂×C₄×C₁₀₁	—	4	5	no	—
68	C₂×C₄×C₁₀₁	—	4	5	no	—
69	C₂×C₄×C₁₀₁	—	4	5	no	—
70	C₂²×C₁₀₁	#538	1	5	yes	—
71	C₂²×C₁₀₁	#541	1	5	yes	—
72	C₂²×C₁₀₁	#542	1	5	yes	—
73	C₂²×C₁₀₁	#552	1	5	yes	—
74	C₂²×C₁₀₁	#553	1	5	yes	—
75	C₂²×C₁₀₁	#562	1	5	yes	—
76	C₂²×C₁₀₁	#563	1	5	yes	—
77	C₄×C₁₀₁	—	4	10	no	—
78	C₄×C₁₀₁	—	8	5	no	—
79	C₄×C₁₀₁	—	8	5	no	—
80	#17301	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂×C₁₀₁	#2766	1	5	yes	—
82	C₂×C₁₀₁	#2779	1	5	yes	—
83	C₂×C₁₀₁	#2831	1	5	yes	—
84	#1443	C₂×C₁₀₁	1	5	yes	—
85	#1442	C₂×C₁₀₁	1	5	yes	—
86	#1441	C₂×C₁₀₁	1	5	yes	—
87	C₁₀₁	#17301	1	1	yes	characteristic, direct product factor, Sylow
88	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	5	yes	—
89	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
90	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
91	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
92	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
93	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
94	C₂×#95	C₂²×C₁₀₁	1	5	yes	—
95	C₂³×C₄	C₂³×C₁₀₁	1	5	yes	—
96	C₂³×C₄	C₂³×C₁₀₁	1	5	yes	—
97	C₂³×C₄	C₂³×C₁₀₁	1	5	yes	—
98	C₂×C₄⋊C₄	—	2	10	no	—
99	C₂×C₄⋊C₄	—	4	5	no	—
100	C₂×C₄⋊C₄	—	4	5	no	—
101	#95	—	2	10	no	—
102	#95	—	2	10	no	—
103	#95	—	4	5	no	—
104	#95	—	4	5	no	—
105	#95	—	4	5	no	—
106	#95	—	4	5	no	—
107	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
108	C₂²×C₄	—	2	5	no	—
109	C₂²×C₄	—	2	5	no	—
110	C₂²×C₄	—	2	5	no	—
111	C₂²×C₄	—	2	5	no	—
112	C₂²×C₄	—	2	5	no	—
113	C₂²×C₄	—	2	5	no	—
114	C₂²×C₄	—	2	5	no	—
115	C₂²×C₄	—	2	5	no	—
116	C₂²×C₄	—	2	5	no	—
117	C₂²×C₄	—	2	5	no	—
118	C₂²×C₄	—	2	5	no	—
119	C₂²×C₄	—	2	5	no	—
120	C₂²×C₄	—	2	5	no	—
121	C₂²×C₄	—	2	5	no	—
122	C₂²×C₄	—	2	5	no	—
123	C₂²×C₄	—	2	5	no	—
124	C₂²×C₄	—	2	5	no	—
125	C₂²×C₄	—	2	5	no	—
126	C₂²×C₄	—	2	5	no	—
127	C₂²×C₄	—	2	5	no	—
128	C₂²×C₄	#41×C₁₀₁	1	10	yes	—
129	C₄⋊C₄	—	4	20	no	—
130	C₂³	C₂×#41×C₁₀₁	1	5	yes	—
131	C₂³	H(5,𝔽₂)×C₁₀₁	1	5	yes	—
132	C₂³	2₋¹⁺⁴×C₁₀₁	1	5	yes	—
133	C₂×C₄	—	2	10	no	—
134	C₂×C₄	—	2	10	no	—
135	C₂×C₄	—	2	10	no	—
136	C₂×C₄	—	4	5	no	—
137	C₂×C₄	—	4	5	no	—
138	C₂×C₄	—	4	5	no	—
139	C₂×C₄	—	4	5	no	—
140	C₂×C₄	—	4	5	no	—
141	C₂×C₄	—	4	5	no	—
142	C₂×C₄	—	4	5	no	—
143	C₂×C₄	—	4	5	no	—
144	C₂×C₄	—	4	5	no	—
145	C₂×C₄	—	4	5	no	—
146	C₂×C₄	—	4	5	no	—
147	C₂×C₄	—	4	5	no	—
148	C₂×C₄	—	4	5	no	—
149	C₂×C₄	—	4	5	no	—
150	C₂×C₄	—	4	5	no	—
151	C₂×C₄	—	4	5	no	—
152	C₂×C₄	—	4	5	no	—
153	C₂×C₄	—	4	5	no	—
154	C₂²	#538×C₁₀₁	1	5	yes	—
155	C₂²	#541×C₁₀₁	1	5	yes	—
156	C₂²	#542×C₁₀₁	1	5	yes	—
157	C₂²	#552×C₁₀₁	1	5	yes	—
158	C₂²	#553×C₁₀₁	1	5	yes	—
159	C₂²	#562×C₁₀₁	1	5	yes	—
160	C₂²	#563×C₁₀₁	1	5	yes	—
161	C₄	—	4	10	no	—
162	C₄	—	8	5	no	—
163	C₄	—	8	5	no	—
164	C₂	C₁₀₁×#2766	1	5	yes	—
165	C₂	C₁₀₁×#2779	1	5	yes	—
166	C₂	C₁₀₁×#2831	1	5	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
80. #17301	C₁₀₁	direct (N × H)
87. C₁₀₁	#17301	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₀₁×#1443	2
C₁₀₁×#1442	2
C₁₀₁×#1441	2
#17301	101