Subgroups — C₄×C₁₃×#383 #15700113

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#383	C₂	1	2	yes	maximal
2	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1434	C₂	1	6	yes	maximal
4	C₄×C₁₃×#95	C₂	1	6	yes	maximal
5	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#383	C₄	1	16	yes	direct product factor
10	C₂×C₁₃×#95	C₂²	1	12	yes	—
11	C₂×C₁₃×#95	C₂²	1	12	yes	—
12	C₄³×C₁₃	C₄	1	8	yes	complemented
13	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
14	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
16	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	—	2	12	no	—
18	C₂×C₄²×C₁₃	—	2	12	no	—
19	C₂×C₄²×C₁₃	—	2	24	no	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
24	C₁₃×#95	—	2	24	no	—
25	C₁₃×#95	C₂×C₄	1	48	yes	—
26	C₄×#383	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	—	2	6	no	—
29	C₂²×C₄×C₁₃	—	2	6	no	—
30	C₂²×C₄×C₁₃	—	2	6	no	—
31	C₂²×C₄×C₁₃	—	2	6	no	—
32	C₂²×C₄×C₁₃	—	2	24	no	—
33	C₂²×C₄×C₁₃	—	2	24	no	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
39	C₂²×C₄×C₁₃	#41	1	12	yes	—
40	C₂²×C₄×C₁₃	#41	1	12	yes	—
41	C₄²×C₁₃	—	2	24	no	—
42	C₄²×C₁₃	—	2	24	no	—
43	C₄²×C₁₃	—	4	16	no	—
44	C₄²×C₁₃	C₄²	1	16	yes	complemented
45	C₂×#383	C₂×C₁₃	1	2	yes	—
46	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
47	#1434	C₂×C₁₃	1	6	yes	—
48	C₄×#95	C₂×C₁₃	1	6	yes	—
49	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
50	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
51	C₂³×C₁₃	C₂×#41	1	6	yes	—
52	C₂³×C₁₃	C₂×#41	1	6	yes	—
53	C₂×C₄×C₁₃	—	2	6	no	—
54	C₂×C₄×C₁₃	—	2	6	no	—
55	C₂×C₄×C₁₃	—	2	6	no	—
56	C₂×C₄×C₁₃	—	2	6	no	—
57	C₂×C₄×C₁₃	—	2	24	no	—
58	C₂×C₄×C₁₃	—	2	24	no	—
59	C₂×C₄×C₁₃	—	2	48	no	—
60	C₂×C₄×C₁₃	—	4	8	no	—
61	C₂×C₄×C₁₃	—	4	24	no	—
62	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
63	C₂×C₄×C₁₃	#117	1	12	yes	—
64	C₂×C₄×C₁₃	#117	1	12	yes	—
65	C₂×C₄×C₁₃	#126	1	16	yes	—
66	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
67	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
68	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
69	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
70	#383	C₄×C₁₃	1	16	yes	direct product factor
71	C₂×#95	C₂²×C₁₃	1	12	yes	—
72	C₂×#95	C₂²×C₁₃	1	12	yes	—
73	C₄³	C₄×C₁₃	1	8	yes	complemented
74	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
75	C₂²×C₁₃	C₂×#117	1	3	yes	—
76	C₂²×C₁₃	C₂×#117	1	3	yes	—
77	C₂²×C₁₃	C₄×#41	1	12	yes	—
78	C₂²×C₁₃	C₂×#126	1	4	yes	—
79	C₂²×C₁₃	#529	1	12	yes	—
80	C₄×C₁₃	—	2	12	no	—
81	C₄×C₁₃	—	2	12	no	—
82	C₄×C₁₃	—	4	16	no	—
83	C₄×C₁₃	#383	1	8	yes	direct product factor
84	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
85	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
86	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
87	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
88	C₂×C₄²	—	2	12	no	—
89	C₂×C₄²	—	2	12	no	—
90	C₂×C₄²	—	2	24	no	—
91	C₂×C₄²	C₂×C₄×C₁₃	1	12	yes	—
92	C₂×C₄²	C₂×C₄×C₁₃	1	12	yes	—
93	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
94	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
95	#95	—	2	24	no	—
96	#95	C₂×C₄×C₁₃	1	48	yes	—
97	C₂×C₁₃	C₄×#117	1	3	yes	—
98	C₂×C₁₃	C₂×#383	1	1	yes	characteristic
99	C₂×C₁₃	#2283	1	3	yes	—
100	C₂×C₁₃	C₄×#126	1	8	yes	—
101	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
102	C₂²×C₄	—	2	6	no	—
103	C₂²×C₄	—	2	6	no	—
104	C₂²×C₄	—	2	6	no	—
105	C₂²×C₄	—	2	6	no	—
106	C₂²×C₄	—	2	24	no	—
107	C₂²×C₄	—	2	24	no	—
108	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
109	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
110	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
111	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
112	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
113	C₂²×C₄	C₁₃×#41	1	12	yes	—
114	C₂²×C₄	C₁₃×#41	1	12	yes	—
115	C₄²	—	2	24	no	—
116	C₄²	—	2	24	no	—
117	C₄²	—	4	16	no	—
118	C₄²	C₄²×C₁₃	1	16	yes	complemented
119	C₁₃	C₄×#383	1	1	yes	characteristic, direct product factor, Sylow
120	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
121	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
122	C₂³	C₂×C₁₃×#41	1	6	yes	—
123	C₂³	C₂×C₁₃×#41	1	6	yes	—
124	C₂×C₄	—	2	6	no	—
125	C₂×C₄	—	2	6	no	—
126	C₂×C₄	—	2	6	no	—
127	C₂×C₄	—	2	6	no	—
128	C₂×C₄	—	2	24	no	—
129	C₂×C₄	—	2	24	no	—
130	C₂×C₄	—	2	48	no	—
131	C₂×C₄	—	4	8	no	—
132	C₂×C₄	—	4	24	no	—
133	C₂×C₄	C₂×C₄²×C₁₃	1	12	yes	—
134	C₂×C₄	C₁₃×#117	1	12	yes	—
135	C₂×C₄	C₁₃×#117	1	12	yes	—
136	C₂×C₄	C₁₃×#126	1	16	yes	—
137	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
138	C₂²	C₂×C₁₃×#117	1	3	yes	—
139	C₂²	C₂×C₁₃×#117	1	3	yes	—
140	C₂²	C₄×C₁₃×#41	1	12	yes	—
141	C₂²	C₂×C₁₃×#126	1	4	yes	—
142	C₂²	C₁₃×#529	1	12	yes	—
143	C₄	—	2	12	no	—
144	C₄	—	2	12	no	—
145	C₄	—	4	16	no	—
146	C₄	C₁₃×#383	1	8	yes	direct product factor
147	C₂	C₄×C₁₃×#117	1	3	yes	—
148	C₂	C₂×C₁₃×#383	1	1	yes	characteristic
149	C₂	C₁₃×#2283	1	3	yes	—
150	C₂	C₄×C₁₃×#126	1	8	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
socle, prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₃×#383	C₄	direct (N × H)
12. C₄³×C₁₃	C₄	semidirect
26. C₄×#383	C₁₃	direct (N × H)
44. C₄²×C₁₃	C₄²	semidirect
70. #383	C₄×C₁₃	direct (N × H)
73. C₄³	C₄×C₁₃	semidirect
83. C₄×C₁₃	#383	direct (N × H)
118. C₄²	C₄²×C₁₃	semidirect
119. C₁₃	C₄×#383	direct (N × H)
146. C₄	C₁₃×#383	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×C₁₃×#383	2
C₂×C₄³×C₁₃	2
C₁₃×#1434	2
C₄×C₁₃×#95	2
C₄×#383	13

Subgroups — C4×C13×#383 #15700113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#383 #15700113