Subgroups — C₂×C₁₃×#2658 #15720969

Order 3328.

3590 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
2	C₂²×C₁₃×#124	C₂	1	3	yes	maximal
3	C₁₃×#2658	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#399	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×Q₈×C₁₃	C₂²	1	3	yes	—
7	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊Q₈	—	2	24	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
10	C₂×C₁₃×#124	—	2	24	no	—
11	C₂×C₁₃×#124	C₂²	1	24	yes	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
13	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	—
14	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
15	C₁₃×#399	C₂²	1	64	yes	complemented
16	C₁₃×#376	C₂²	1	8	yes	complemented
17	C₂×C₁₃×#95	C₂²	1	4	yes	—
18	C₂⁵×C₁₃	C₂³	1	2	yes	—
19	C₂²×Q₈×C₁₃	—	2	12	no	—
20	C₂²×Q₈×C₁₃	—	2	24	no	—
21	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
22	C₂²×D₄×C₁₃	—	2	12	no	—
23	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
25	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	—	2	96	no	—
28	C₁₃×#124	—	2	96	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	48	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
31	C₂×C₁₃×C₂²⋊C₄	—	2	48	no	—
32	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
33	C₂×C₄²×C₁₃	D₄	1	24	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
35	C₁₃×#95	C₂³	1	16	yes	—
36	C₂×#2658	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁴×C₁₃	—	2	12	no	—
38	C₂⁴×C₁₃	—	2	16	no	—
39	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
40	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
41	C₂×Q₈×C₁₃	—	2	24	no	—
42	C₂×Q₈×C₁₃	—	2	48	no	—
43	C₂×Q₈×C₁₃	—	4	48	no	—
44	C₂×D₄×C₁₃	—	2	24	no	—
45	C₂×D₄×C₁₃	—	4	16	no	—
46	C₂²×C₄×C₁₃	—	2	24	no	—
47	C₂²×C₄×C₁₃	—	2	12	no	—
48	C₂²×C₄×C₁₃	—	2	24	no	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
53	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	96	no	—
55	C₁₃×C₂²⋊C₄	—	2	96	no	—
56	C₄²×C₁₃	C₂×D₄	1	48	yes	—
57	C₂²×C₄⋊Q₈	C₂×C₁₃	1	3	yes	complemented
58	C₂²×#124	C₂×C₁₃	1	3	yes	—
59	#2658	C₂×C₁₃	1	16	yes	direct product factor
60	C₂×#399	C₂×C₁₃	1	8	yes	complemented
61	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
62	C₂³×C₁₃	—	2	12	no	—
63	C₂³×C₁₃	—	2	16	no	—
64	C₂³×C₁₃	—	4	8	no	—
65	C₂³×C₁₃	—	4	48	no	—
66	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
67	C₂³×C₁₃	2₋¹⁺⁴	1	8	yes	—
68	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
69	Q₈×C₁₃	—	4	48	no	—
70	D₄×C₁₃	—	4	16	no	—
71	C₂×C₄×C₁₃	—	2	48	no	—
72	C₂×C₄×C₁₃	—	2	24	no	—
73	C₂×C₄×C₁₃	—	2	12	no	—
74	C₂×C₄×C₁₃	—	2	24	no	—
75	C₂×C₄×C₁₃	—	4	24	no	—
76	C₂×C₄×C₁₃	#127	1	16	yes	—
77	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
78	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
79	C₂³×Q₈	C₂²×C₁₃	1	3	yes	—
80	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
81	C₂×C₄⋊Q₈	—	2	24	no	—
82	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
83	C₂×#124	—	2	24	no	—
84	C₂×#124	C₂²×C₁₃	1	24	yes	—
85	C₂²×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
86	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	—
87	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
88	#399	C₂²×C₁₃	1	64	yes	complemented
89	#376	C₂²×C₁₃	1	8	yes	complemented
90	C₂×#95	C₂²×C₁₃	1	4	yes	—
91	C₂²×C₁₃	—	4	4	no	—
92	C₂²×C₁₃	—	4	24	no	—
93	C₂²×C₁₃	—	8	16	no	—
94	C₂²×C₁₃	C₂×#127	1	4	yes	—
95	C₂²×C₁₃	#536	1	24	yes	—
96	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
97	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
98	C₄×C₁₃	—	2	24	no	—
99	C₄×C₁₃	—	4	12	no	—
100	C₄×C₁₃	C₂×#127	1	8	yes	—
101	C₂⁵	C₂³×C₁₃	1	2	yes	—
102	C₂²×Q₈	—	2	12	no	—
103	C₂²×Q₈	—	2	24	no	—
104	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
105	C₂²×D₄	—	2	12	no	—
106	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
107	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
108	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
109	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
110	C₄⋊Q₈	—	2	96	no	—
111	#124	—	2	96	no	—
112	C₂×C₄⋊C₄	—	2	48	no	—
113	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
114	C₂×C₂²⋊C₄	—	2	48	no	—
115	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
116	C₂×C₄²	D₄×C₁₃	1	24	yes	—
117	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
118	#95	C₂³×C₁₃	1	16	yes	—
119	C₂×C₁₃	—	8	4	no	—
120	C₂×C₁₃	#2658	1	8	yes	direct product factor
121	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
122	C₂×C₁₃	C₂×#536	1	6	yes	—
123	C₂⁴	—	2	12	no	—
124	C₂⁴	—	2	16	no	—
125	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
126	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
127	C₂×Q₈	—	2	24	no	—
128	C₂×Q₈	—	2	48	no	—
129	C₂×Q₈	—	4	48	no	—
130	C₂×D₄	—	2	24	no	—
131	C₂×D₄	—	4	16	no	—
132	C₂²×C₄	—	2	24	no	—
133	C₂²×C₄	—	2	12	no	—
134	C₂²×C₄	—	2	24	no	—
135	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
136	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
137	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
138	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
139	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
140	C₄⋊C₄	—	2	96	no	—
141	C₂²⋊C₄	—	2	96	no	—
142	C₄²	C₂×D₄×C₁₃	1	48	yes	—
143	C₁₃	C₂×#2658	1	1	yes	characteristic, direct product factor, Sylow
144	C₂³	—	2	12	no	—
145	C₂³	—	2	16	no	—
146	C₂³	—	4	8	no	—
147	C₂³	—	4	48	no	—
148	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
149	C₂³	C₁₃×2₋¹⁺⁴	1	8	yes	—
150	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
151	Q₈	—	4	48	no	—
152	D₄	—	4	16	no	—
153	C₂×C₄	—	2	48	no	—
154	C₂×C₄	—	2	24	no	—
155	C₂×C₄	—	2	12	no	—
156	C₂×C₄	—	2	24	no	—
157	C₂×C₄	—	4	24	no	—
158	C₂×C₄	C₁₃×#127	1	16	yes	—
159	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
160	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
161	C₂²	—	4	4	no	—
162	C₂²	—	4	24	no	—
163	C₂²	—	8	16	no	—
164	C₂²	C₂×C₁₃×#127	1	4	yes	—
165	C₂²	C₁₃×#536	1	24	yes	—
166	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
167	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
168	C₄	—	2	24	no	—
169	C₄	—	4	12	no	—
170	C₄	C₂×C₁₃×#127	1	8	yes	—
171	C₂	—	8	4	no	—
172	C₂	C₁₃×#2658	1	8	yes	direct product factor
173	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
174	C₂	C₂×C₁₃×#536	1	6	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2658	C₂	direct (N × H)
4. C₂×C₁₃×#399	C₂	semidirect
5. C₂×C₁₃×#376	C₂	semidirect
9. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
15. C₁₃×#399	C₂²	semidirect
16. C₁₃×#376	C₂²	semidirect
36. C₂×#2658	C₁₃	direct (N × H)
57. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
59. #2658	C₂×C₁₃	direct (N × H)
60. C₂×#399	C₂×C₁₃	semidirect
61. C₂×#376	C₂×C₁₃	semidirect
82. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
88. #399	C₂²×C₁₃	semidirect
89. #376	C₂²×C₁₃	semidirect
120. C₂×C₁₃	#2658	direct (N × H)
143. C₁₃	C₂×#2658	direct (N × H)
172. C₂	C₁₃×#2658	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#124	2
C₁₃×#2658	2
C₂×C₁₃×#399	2
C₂×C₁₃×#376	2
C₂×#2658	13

Subgroups — C2×C13×#2658 #15720969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2658 #15720969