Subgroups — C₁₃×#33475 #15719814

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2183	C₂	1	8	yes	maximal, complemented
3	C₁₃×#2151	C₂	1	2	yes	maximal
4	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2108	C₂	1	2	yes	maximal
6	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	C₄	1	1	yes	characteristic
8	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
9	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₃×#446	C₄	1	4	yes	—
12	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
13	C₁₃×#424	C₄	1	2	yes	—
14	C₁₃×#423	C₄	1	1	yes	characteristic
15	C₁₃×#405	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	—
18	C₁₃×C₄⋊C₁₆	C₂²	1	8	yes	—
19	C₁₃×#346	C₂²	1	4	yes	—
20	C₁₃×#346	C₂²	1	4	yes	—
21	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₈	1	2	yes	—
26	C₁₃×#125	C₈	1	2	yes	—
27	C₁₃×C₂²⋊Q₈	C₈	1	4	yes	—
28	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
29	C₁₃×#117	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₁₃×M₃₂	—	2	4	no	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
34	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
35	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
36	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
37	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
38	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
39	C₁₃×#97	C₂×C₄	1	4	yes	—
40	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₃	C₂³	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	4	yes	—
43	#33475	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₁₃×M₁₆	—	2	4	no	—
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
53	C₂×C₈×C₁₃	#41	1	2	yes	—
54	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
55	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
56	C₁₃×C₄⋊C₄	C₂×C₈	1	8	yes	—
57	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
58	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
59	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
60	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
61	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
62	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
63	C₁₃×C₁₆	—	2	2	no	—
64	C₁₃×C₁₆	—	2	4	no	—
65	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
66	#2960	C₂×C₁₃	1	1	yes	characteristic
67	#2183	C₂×C₁₃	1	8	yes	complemented
68	#2151	C₂×C₁₃	1	2	yes	—
69	#2150	C₂×C₁₃	1	1	yes	characteristic
70	#2108	C₂×C₁₃	1	2	yes	—
71	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
72	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
73	Q₈×C₁₃	—	4	4	no	—
74	C₂×C₄×C₁₃	—	4	2	no	—
75	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
76	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
77	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂²×C₈	1	8	yes	—
79	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#131	1	2	yes	—
81	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
82	C₈×C₁₃	—	2	2	no	—
83	C₈×C₁₃	—	2	4	no	—
84	C₈×C₁₃	C₄×Q₈	1	2	yes	—
85	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
87	#533	C₄×C₁₃	1	1	yes	characteristic
88	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
89	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
90	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
91	#446	C₄×C₁₃	1	4	yes	—
92	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
93	#424	C₄×C₁₃	1	2	yes	—
94	#423	C₄×C₁₃	1	1	yes	characteristic
95	#405	C₂²×C₁₃	1	2	yes	—
96	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
97	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	—
98	C₄⋊C₁₆	C₂²×C₁₃	1	8	yes	—
99	#346	C₂²×C₁₃	1	4	yes	—
100	#346	C₂²×C₁₃	1	4	yes	—
101	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
102	C₂²×C₁₃	—	2	2	no	—
103	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
104	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	—	2	8	no	—
108	C₄×C₁₃	C₈×Q₈	1	2	yes	—
109	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
110	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
111	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
112	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
114	C₄⋊Q₈	C₈×C₁₃	1	2	yes	—
115	#125	C₈×C₁₃	1	2	yes	—
116	C₂²⋊Q₈	C₈×C₁₃	1	4	yes	—
117	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
118	#117	C₂×C₄×C₁₃	1	2	yes	—
119	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
120	M₃₂	—	2	4	no	—
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
123	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
124	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
125	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
126	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
127	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
128	#97	C₂×C₄×C₁₃	1	4	yes	—
129	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
130	C₄×C₈	C₂³×C₁₃	1	4	yes	—
131	C₄×C₈	C₂³×C₁₃	1	2	yes	—
132	C₂×C₁₃	—	2	2	no	—
133	C₂×C₁₃	C₂×C₈×Q₈	1	1	yes	characteristic
134	C₂×C₁₃	#3407	1	2	yes	—
135	C₂×Q₈	C₂×C₈×C₁₃	1	4	yes	—
136	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
137	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
138	M₁₆	—	2	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
141	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
142	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
143	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
144	C₂×C₈	C₁₃×#41	1	2	yes	—
145	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
146	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
147	C₄⋊C₄	C₂×C₈×C₁₃	1	8	yes	—
148	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
149	C₂²⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
150	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
151	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
152	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
153	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
154	C₁₆	—	2	2	no	—
155	C₁₆	—	2	4	no	—
156	C₁₆	C₂×Q₈×C₁₃	1	4	yes	—
157	C₁₃	#33475	1	1	yes	characteristic, direct product factor, Sylow
158	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
159	Q₈	—	4	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
162	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
163	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
164	C₂×C₄	C₂²×C₈×C₁₃	1	8	yes	—
165	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
166	C₂×C₄	C₁₃×#131	1	2	yes	—
167	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	2	4	no	—
170	C₈	C₄×Q₈×C₁₃	1	2	yes	—
171	C₈	C₂²×Q₈×C₁₃	1	1	yes	characteristic
172	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
173	C₂²	—	2	2	no	—
174	C₂²	C₈×Q₈×C₁₃	1	2	yes	—
175	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	2	8	no	—
179	C₄	C₈×Q₈×C₁₃	1	2	yes	—
180	C₄	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
181	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
182	C₂	—	2	2	no	—
183	C₂	C₂×C₈×Q₈×C₁₃	1	1	yes	characteristic
184	C₂	C₁₃×#3407	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2183	C₂	semidirect
33. C₂×C₁₃×C₁₆	Q₈	semidirect
43. #33475	C₁₃	direct (N × H)
67. #2183	C₂×C₁₃	semidirect
122. C₂×C₁₆	Q₈×C₁₃	semidirect
157. C₁₃	#33475	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×#2960	2
C₁₃×#2183	2
C₁₃×#2151	2
C₁₃×#2150	2
C₁₃×#2108	2
C₂×C₁₃×#346	2
#33475	13

Subgroups — C13×#33475 #15719814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33475 #15719814