Subgroups — C₁₃×#17692 #15704031

Order 3328.

872 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2971	C₂	1	2	yes	maximal
3	C₁₃×#1537	C₂	1	3	yes	maximal, complemented
4	C₁₃×#1528	C₂	1	6	yes	maximal, complemented
5	C₁₃×#1526	C₂	1	3	yes	maximal, complemented
6	C₁₃×#557	—	2	2	no	—
7	C₁₃×#554	—	2	6	no	—
8	C₁₃×#544	C₄	1	6	yes	—
9	C₁₃×#533	C₂²	1	3	yes	—
10	C₂×C₁₃×#125	C₂²	1	3	yes	—
11	C₁₃×#520	C₄	1	2	yes	—
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₈×Q₈×C₁₃	—	2	2	no	—
14	C₁₃×#436	—	2	6	no	—
15	C₁₃×#432	C₂²	1	6	yes	—
16	C₄×C₁₃×M₁₆	C₂²	1	6	yes	—
17	C₁₃×#330	C₂²	1	1	yes	characteristic
18	C₁₃×#330	C₂²	1	6	yes	—
19	C₁₃×#330	C₂²	1	3	yes	—
20	C₁₃×#330	C₂²	1	6	yes	—
21	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×M₁₆	—	2	6	no	—
23	C₁₃×C₄⋊Q₈	—	2	6	no	—
24	C₁₃×C₄⋊Q₈	C₂×C₄	1	6	yes	—
25	C₁₃×#125	—	2	6	no	—
26	C₁₃×#125	—	2	6	no	—
27	C₁₃×#125	C₂×C₄	1	6	yes	—
28	C₁₃×#125	C₂³	1	3	yes	—
29	C₁₃×#125	C₂³	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	—	2	6	no	—
31	C₁₃×C₂²⋊Q₈	—	2	12	no	—
32	C₄×Q₈×C₁₃	—	2	2	no	—
33	C₄×Q₈×C₁₃	—	2	6	no	—
34	C₄×Q₈×C₁₃	D₄	1	2	yes	—
35	C₄×D₄×C₁₃	—	2	6	no	—
36	C₄×D₄×C₁₃	D₄	1	6	yes	—
37	C₁₃×#117	C₂×C₄	1	6	yes	—
38	C₁₃×#117	C₂×C₄	1	3	yes	—
39	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	6	yes	—
41	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
42	C₁₃×C₄⋊C₈	—	2	6	no	—
43	C₁₃×C₂²⋊C₈	—	2	6	no	—
44	C₁₃×#97	C₂³	1	2	yes	—
45	C₁₃×#97	C₂³	1	6	yes	—
46	C₄×C₈×C₁₃	—	2	6	no	—
47	#17692	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₁₃×#41	—	2	4	no	—
49	C₂×Q₈×C₁₃	—	2	6	no	—
50	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×D₄×C₁₃	C₂²⋊C₄	1	3	yes	—
52	C₂²×C₄×C₁₃	—	2	6	no	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
54	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
55	C₁₃×M₁₆	—	4	12	no	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	6	no	—
58	C₁₃×C₄⋊C₄	—	2	12	no	—
59	C₁₃×C₄⋊C₄	—	2	6	no	—
60	C₁₃×C₄⋊C₄	—	2	6	no	—
61	C₁₃×C₄⋊C₄	—	2	6	no	—
62	C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
64	C₁₃×C₄⋊C₄	C₂²×C₄	1	6	yes	—
65	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
66	C₁₃×C₂²⋊C₄	—	2	6	no	—
67	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	6	yes	—
68	C₄²×C₁₃	—	2	6	no	—
69	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
70	C₄²×C₁₃	C₂×D₄	1	6	yes	—
71	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
72	#3504	C₂×C₁₃	1	1	yes	characteristic
73	#2971	C₂×C₁₃	1	2	yes	—
74	#1537	C₂×C₁₃	1	3	yes	complemented
75	#1528	C₂×C₁₃	1	6	yes	complemented
76	#1526	C₂×C₁₃	1	3	yes	complemented
77	C₂³×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
78	Q₈×C₁₃	—	8	6	no	—
79	Q₈×C₁₃	#101	1	4	yes	—
80	D₄×C₁₃	—	2	6	no	—
81	C₂×C₄×C₁₃	—	2	6	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	6	no	—
84	C₂×C₄×C₁₃	—	4	6	no	—
85	C₂×C₄×C₁₃	—	8	6	no	—
86	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	6	yes	—
87	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
88	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
90	C₈×C₁₃	—	2	4	no	—
91	C₈×C₁₃	—	4	6	no	—
92	#557	—	2	2	no	—
93	#554	—	2	6	no	—
94	#544	C₄×C₁₃	1	6	yes	—
95	#533	C₂²×C₁₃	1	3	yes	—
96	C₂×#125	C₂²×C₁₃	1	3	yes	—
97	#520	C₄×C₁₃	1	2	yes	—
98	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
99	C₈×Q₈	—	2	2	no	—
100	#436	—	2	6	no	—
101	#432	C₂²×C₁₃	1	6	yes	—
102	C₄×M₁₆	C₂²×C₁₃	1	6	yes	—
103	#330	C₂²×C₁₃	1	3	yes	—
104	#330	C₂²×C₁₃	1	6	yes	—
105	#330	C₂²×C₁₃	1	1	yes	characteristic
106	#330	C₂²×C₁₃	1	6	yes	—
107	C₂²×C₁₃	—	2	3	no	—
108	C₂²×C₁₃	—	2	6	no	—
109	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
110	C₄×C₁₃	—	2	1	no	—
111	C₄×C₁₃	—	2	2	no	—
112	C₄×C₁₃	—	2	6	no	—
113	C₄×C₁₃	—	4	6	no	—
114	C₄×C₁₃	—	4	2	no	—
115	C₄×C₁₃	C₂×#101	1	6	yes	—
116	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
117	C₂×M₁₆	—	2	6	no	—
118	C₄⋊Q₈	—	2	6	no	—
119	C₄⋊Q₈	C₂×C₄×C₁₃	1	6	yes	—
120	#125	—	2	6	no	—
121	#125	—	2	6	no	—
122	#125	C₂×C₄×C₁₃	1	6	yes	—
123	#125	C₂³×C₁₃	1	3	yes	—
124	#125	C₂³×C₁₃	1	1	yes	characteristic
125	C₂²⋊Q₈	—	2	6	no	—
126	C₂²⋊Q₈	—	2	12	no	—
127	C₄×Q₈	—	2	2	no	—
128	C₄×Q₈	—	2	6	no	—
129	C₄×Q₈	D₄×C₁₃	1	2	yes	—
130	C₄×D₄	—	2	6	no	—
131	C₄×D₄	D₄×C₁₃	1	6	yes	—
132	#117	C₂×C₄×C₁₃	1	6	yes	—
133	#117	C₂×C₄×C₁₃	1	3	yes	—
134	C₂×C₄⋊C₄	—	2	6	no	—
135	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	6	yes	—
136	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
137	C₄⋊C₈	—	2	6	no	—
138	C₂²⋊C₈	—	2	6	no	—
139	#97	C₂³×C₁₃	1	2	yes	—
140	#97	C₂³×C₁₃	1	6	yes	—
141	C₄×C₈	—	2	6	no	—
142	C₂×C₁₃	—	4	3	no	—
143	C₂×C₁₃	C₂²×#101	1	1	yes	characteristic
144	C₂×C₁₃	#2901	1	2	yes	—
145	#41	—	2	4	no	—
146	C₂×Q₈	—	2	6	no	—
147	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×D₄	C₁₃×C₂²⋊C₄	1	3	yes	—
149	C₂²×C₄	—	2	6	no	—
150	C₂²×C₄	C₂²×C₄×C₁₃	1	3	yes	—
151	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
152	M₁₆	—	4	12	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	6	no	—
155	C₄⋊C₄	—	2	12	no	—
156	C₄⋊C₄	—	2	6	no	—
157	C₄⋊C₄	—	2	6	no	—
158	C₄⋊C₄	—	2	6	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	6	yes	—
161	C₄⋊C₄	C₂²×C₄×C₁₃	1	6	yes	—
162	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
163	C₂²⋊C₄	—	2	6	no	—
164	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	6	yes	—
165	C₄²	—	2	6	no	—
166	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
167	C₄²	C₂×D₄×C₁₃	1	6	yes	—
168	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
169	C₁₃	#17692	1	1	yes	characteristic, direct product factor, Sylow
170	C₂³	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
171	Q₈	—	8	6	no	—
172	Q₈	C₁₃×#101	1	4	yes	—
173	D₄	—	2	6	no	—
174	C₂×C₄	—	2	6	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	6	no	—
177	C₂×C₄	—	4	6	no	—
178	C₂×C₄	—	8	6	no	—
179	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	6	yes	—
180	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
181	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
182	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
183	C₈	—	2	4	no	—
184	C₈	—	4	6	no	—
185	C₂²	—	2	3	no	—
186	C₂²	—	2	6	no	—
187	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₄	—	2	1	no	—
189	C₄	—	2	2	no	—
190	C₄	—	2	6	no	—
191	C₄	—	4	6	no	—
192	C₄	—	4	2	no	—
193	C₄	C₂×C₁₃×#101	1	6	yes	—
194	C₂	—	4	3	no	—
195	C₂	C₂²×C₁₃×#101	1	1	yes	characteristic
196	C₂	C₁₃×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1537	C₂	semidirect
4. C₁₃×#1528	C₂	semidirect
5. C₁₃×#1526	C₂	semidirect
47. #17692	C₁₃	direct (N × H)
74. #1537	C₂×C₁₃	semidirect
75. #1528	C₂×C₁₃	semidirect
76. #1526	C₂×C₁₃	semidirect
169. C₁₃	#17692	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3504	2
C₁₃×#2971	2
C₁₃×#1537	2
C₁₃×#1528	2
C₁₃×#1526	2
#17692	13

Subgroups — C13×#17692 #15704031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17692 #15704031