Subgroups — C₁₃×#9702 #15696041

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#333	C₂	1	4	yes	maximal
5	C₂×C₁₃×C₄⋊Q₈	C₄	1	4	yes	—
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₃×#97	—	2	1	no	—
10	C₁₃×#384	—	2	1	no	—
11	C₁₃×#384	—	2	2	no	—
12	C₁₃×#384	—	2	1	no	—
13	C₄³×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#336	—	2	1	no	—
15	C₁₃×#336	—	2	2	no	—
16	C₁₃×#333	—	2	8	no	—
17	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
18	C₂²×C₈×C₁₃	—	2	2	no	—
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₁₃×C₄⋊Q₈	—	2	4	no	—
21	C₁₃×C₄⋊Q₈	—	2	4	no	—
22	C₁₃×C₄⋊Q₈	—	4	8	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×C₄⋊C₈	—	2	4	no	—
33	C₁₃×C₄⋊C₈	—	2	2	no	—
34	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
35	C₁₃×#97	—	4	2	no	—
36	#9702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×Q₈×C₁₃	—	2	8	no	—
38	C₂×Q₈×C₁₃	—	4	8	no	—
39	C₂²×C₄×C₁₃	—	2	4	no	—
40	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	—	2	4	no	—
46	C₂×C₈×C₁₃	—	4	2	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	—	4	2	no	—
49	C₂×C₈×C₁₃	—	4	4	no	—
50	C₁₃×C₄⋊C₄	—	4	8	no	—
51	C₁₃×C₄⋊C₄	—	4	8	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	4	2	no	—
55	C₄²×C₁₃	—	2	4	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	4	no	—
58	C₄²×C₁₃	SD₁₆	1	2	yes	—
59	C₄²×C₁₃	Q₁₆	1	2	yes	—
60	C₄²×C₁₃	C₂×D₄	1	2	yes	—
61	C₄²×C₁₃	#41	1	2	yes	—
62	#2868	C₂×C₁₃	1	1	yes	characteristic
63	#1831	C₂×C₁₃	1	1	yes	characteristic
64	#1767	C₂×C₁₃	1	1	yes	characteristic
65	C₂×#333	C₂×C₁₃	1	4	yes	—
66	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	Q₈×C₁₃	—	8	8	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	4	4	no	—
74	C₂×C₄×C₁₃	—	4	8	no	—
75	C₂×C₄×C₁₃	#100	1	4	yes	—
76	C₂×C₄×C₁₃	#103	1	4	yes	—
77	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
78	C₂×C₄×C₁₃	#121	1	2	yes	—
79	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#137	1	2	yes	—
84	C₂×C₄×C₁₃	#137	1	4	yes	—
85	C₈×C₁₃	—	4	4	no	—
86	C₈×C₁₃	—	8	2	no	—
87	C₂×C₄⋊Q₈	C₄×C₁₃	1	4	yes	—
88	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
89	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
90	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
91	C₂×#97	—	2	1	no	—
92	#384	—	2	1	no	—
93	#384	—	2	2	no	—
94	#384	—	2	1	no	—
95	C₄³	C₂²×C₁₃	1	1	yes	characteristic
96	#336	—	2	2	no	—
97	#336	—	2	1	no	—
98	#333	—	2	8	no	—
99	C₂²×C₁₃	#390	1	1	yes	characteristic
100	C₂²×C₁₃	C₂×#100	1	2	yes	—
101	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
102	C₂²×C₁₃	#419	1	2	yes	—
103	C₂²×C₁₃	#419	1	1	yes	characteristic
104	C₄×C₁₃	—	2	4	no	—
105	C₄×C₁₃	—	2	4	no	—
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	—	8	4	no	—
108	C₄×C₁₃	#461	1	2	yes	—
109	C₄×C₁₃	#462	1	2	yes	—
110	C₄×C₁₃	#491	1	2	yes	—
111	C₄×C₁₃	#497	1	2	yes	—
112	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
113	C₂²×C₈	—	2	2	no	—
114	C₂²×C₈	—	2	2	no	—
115	C₄⋊Q₈	—	2	4	no	—
116	C₄⋊Q₈	—	2	4	no	—
117	C₄⋊Q₈	—	4	8	no	—
118	C₂×C₄⋊C₄	—	2	4	no	—
119	C₂×C₄⋊C₄	—	2	4	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
123	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
124	C₂×C₄²	D₄×C₁₃	1	2	yes	—
125	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
126	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
127	C₄⋊C₈	—	2	4	no	—
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
130	#97	—	4	2	no	—
131	C₂×C₁₃	#1548	1	2	yes	—
132	C₂×C₁₃	#1558	1	2	yes	—
133	C₂×C₁₃	#1960	1	1	yes	characteristic
134	C₂×C₁₃	#1965	1	1	yes	characteristic
135	C₂×C₁₃	#1981	1	1	yes	characteristic
136	C₂×Q₈	—	2	8	no	—
137	C₂×Q₈	—	4	8	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
140	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
141	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
142	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
143	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	4	2	no	—
148	C₂×C₈	—	4	4	no	—
149	C₄⋊C₄	—	4	8	no	—
150	C₄⋊C₄	—	4	8	no	—
151	C₄⋊C₄	—	4	4	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄²	—	2	4	no	—
155	C₄²	—	2	2	no	—
156	C₄²	—	2	4	no	—
157	C₄²	C₁₃×SD₁₆	1	2	yes	—
158	C₄²	C₁₃×Q₁₆	1	2	yes	—
159	C₄²	C₂×D₄×C₁₃	1	2	yes	—
160	C₄²	C₁₃×#41	1	2	yes	—
161	C₁₃	#9702	1	1	yes	characteristic, direct product factor, Sylow
162	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
163	Q₈	—	8	8	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	4	8	no	—
171	C₂×C₄	C₁₃×#100	1	4	yes	—
172	C₂×C₄	C₁₃×#103	1	4	yes	—
173	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
174	C₂×C₄	C₁₃×#121	1	2	yes	—
175	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
176	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
177	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
178	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
179	C₂×C₄	C₁₃×#137	1	2	yes	—
180	C₂×C₄	C₁₃×#137	1	4	yes	—
181	C₈	—	4	4	no	—
182	C₈	—	8	2	no	—
183	C₂²	C₁₃×#390	1	1	yes	characteristic
184	C₂²	C₂×C₁₃×#100	1	2	yes	—
185	C₂²	C₂×C₁₃×#103	1	1	yes	characteristic
186	C₂²	C₁₃×#419	1	2	yes	—
187	C₂²	C₁₃×#419	1	1	yes	characteristic
188	C₄	—	2	4	no	—
189	C₄	—	2	4	no	—
190	C₄	—	2	2	no	—
191	C₄	—	8	4	no	—
192	C₄	C₁₃×#461	1	2	yes	—
193	C₄	C₁₃×#462	1	2	yes	—
194	C₄	C₁₃×#491	1	2	yes	—
195	C₄	C₁₃×#497	1	2	yes	—
196	C₂	C₁₃×#1548	1	2	yes	—
197	C₂	C₁₃×#1558	1	2	yes	—
198	C₂	C₁₃×#1960	1	1	yes	characteristic
199	C₂	C₁₃×#1965	1	1	yes	characteristic
200	C₂	C₁₃×#1981	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
36. #9702	C₁₃	direct (N × H)
161. C₁₃	#9702	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×#2868	2
C₁₃×#1831	2
C₁₃×#1767	2
C₂×C₁₃×#333	2
#9702	13

Subgroups — C13×#9702 #15696041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9702 #15696041