Subgroups — C₁₃×#9694 #15696033

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 222 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×#1842	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#332	C₂	1	4	yes	maximal
5	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	—	2	1	no	—
12	C₁₃×#384	—	2	2	no	—
13	C₁₃×#384	C₄	1	4	yes	—
14	C₄³×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#336	—	2	1	no	—
16	C₁₃×#332	—	2	8	no	—
17	C₂²×Q₈×C₁₃	—	2	2	no	—
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	4	no	—
23	C₁₃×C₄⋊Q₈	—	4	2	no	—
24	C₁₃×C₄⋊Q₈	—	4	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	D₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×C₄⋊C₈	—	2	4	no	—
35	C₁₃×C₄⋊C₈	—	2	2	no	—
36	C₁₃×C₄⋊C₈	—	4	4	no	—
37	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
38	C₄×C₈×C₁₃	—	4	2	no	—
39	#9694	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×Q₈×C₁₃	—	4	4	no	—
41	C₂×Q₈×C₁₃	—	4	2	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	4	no	—
44	C₂²×C₄×C₁₃	—	2	4	no	—
45	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	—	2	4	no	—
51	C₂×C₈×C₁₃	—	4	2	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₂×C₈×C₁₃	—	4	4	no	—
55	C₁₃×C₄⋊C₄	—	2	8	no	—
56	C₁₃×C₄⋊C₄	—	4	8	no	—
57	C₁₃×C₄⋊C₄	—	4	8	no	—
58	C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₄²×C₁₃	—	2	4	no	—
61	C₄²×C₁₃	—	2	2	no	—
62	C₄²×C₁₃	D₈	1	2	yes	—
63	C₄²×C₁₃	SD₁₆	1	2	yes	—
64	C₄²×C₁₃	SD₁₆	1	4	yes	—
65	C₄²×C₁₃	Q₁₆	1	4	yes	—
66	C₄²×C₁₃	C₂×D₄	1	2	yes	—
67	C₄²×C₁₃	#41	1	2	yes	—
68	#2868	C₂×C₁₃	1	1	yes	characteristic
69	#1842	C₂×C₁₃	1	1	yes	characteristic
70	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
71	C₂×#332	C₂×C₁₃	1	4	yes	—
72	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	Q₈×C₁₃	—	8	4	no	—
74	Q₈×C₁₃	—	8	4	no	—
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	4	4	no	—
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	#101	1	4	yes	—
82	C₂×C₄×C₁₃	#102	1	4	yes	—
83	C₂×C₄×C₁₃	#103	1	4	yes	—
84	C₂×C₄×C₁₃	#103	1	4	yes	—
85	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₃	#121	1	2	yes	—
87	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
93	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
94	C₈×C₁₃	—	4	4	no	—
95	C₈×C₁₃	—	8	2	no	—
96	C₂×C₄⋊Q₈	—	2	1	no	—
97	C₂×C₄⋊Q₈	—	2	1	no	—
98	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
99	C₂×C₄⋊C₈	—	2	2	no	—
100	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
101	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
102	C₂×C₄×C₈	—	2	1	no	—
103	#384	—	2	2	no	—
104	#384	C₄×C₁₃	1	4	yes	—
105	C₄³	C₂²×C₁₃	1	1	yes	characteristic
106	#336	—	2	1	no	—
107	#332	—	2	8	no	—
108	C₂²×C₁₃	#390	1	1	yes	characteristic
109	C₂²×C₁₃	C₂×#101	1	2	yes	—
110	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×#103	1	2	yes	—
112	C₂²×C₁₃	#418	1	1	yes	characteristic
113	C₄×C₁₃	—	2	4	no	—
114	C₄×C₁₃	—	2	2	no	—
115	C₄×C₁₃	—	8	4	no	—
116	C₄×C₁₃	#332	1	8	yes	complemented
117	C₄×C₁₃	#459	1	2	yes	—
118	C₄×C₁₃	#460	1	2	yes	—
119	C₄×C₁₃	#487	1	2	yes	—
120	C₄×C₁₃	#492	1	1	yes	characteristic
121	C₄×C₁₃	#494	1	1	yes	characteristic
122	C₂²×Q₈	—	2	2	no	—
123	C₂²×C₈	—	2	2	no	—
124	C₂²×C₈	—	2	2	no	—
125	C₄⋊Q₈	—	2	4	no	—
126	C₄⋊Q₈	—	2	4	no	—
127	C₄⋊Q₈	—	4	4	no	—
128	C₄⋊Q₈	—	4	2	no	—
129	C₄⋊Q₈	—	4	2	no	—
130	C₂×C₄⋊C₄	—	2	4	no	—
131	C₂×C₄⋊C₄	—	2	4	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
134	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
135	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
136	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
137	C₂×C₄²	D₄×C₁₃	1	2	yes	—
138	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
139	C₄⋊C₈	—	2	4	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	4	4	no	—
142	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
143	C₄×C₈	—	4	2	no	—
144	C₂×C₁₃	C₂×#332	1	2	yes	—
145	C₂×C₁₃	#1549	1	2	yes	—
146	C₂×C₁₃	#1956	1	1	yes	characteristic
147	C₂×C₁₃	#1966	1	1	yes	characteristic
148	C₂×C₁₃	#1982	1	1	yes	characteristic
149	C₂×Q₈	—	4	4	no	—
150	C₂×Q₈	—	4	2	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	4	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
155	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
156	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
158	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	—	4	2	no	—
163	C₂×C₈	—	4	4	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄⋊C₄	—	4	8	no	—
166	C₄⋊C₄	—	4	8	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄²	—	2	4	no	—
170	C₄²	—	2	2	no	—
171	C₄²	C₁₃×D₈	1	2	yes	—
172	C₄²	C₁₃×SD₁₆	1	2	yes	—
173	C₄²	C₁₃×SD₁₆	1	4	yes	—
174	C₄²	C₁₃×Q₁₆	1	4	yes	—
175	C₄²	C₂×D₄×C₁₃	1	2	yes	—
176	C₄²	C₁₃×#41	1	2	yes	—
177	C₁₃	#9694	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
179	Q₈	—	8	4	no	—
180	Q₈	—	8	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	C₁₃×#101	1	4	yes	—
188	C₂×C₄	C₁₃×#102	1	4	yes	—
189	C₂×C₄	C₁₃×#103	1	4	yes	—
190	C₂×C₄	C₁₃×#103	1	4	yes	—
191	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
192	C₂×C₄	C₁₃×#121	1	2	yes	—
193	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
194	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
195	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
196	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
197	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
198	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
199	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
200	C₈	—	4	4	no	—
201	C₈	—	8	2	no	—
202	C₂²	C₁₃×#390	1	1	yes	characteristic
203	C₂²	C₂×C₁₃×#101	1	2	yes	—
204	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
205	C₂²	C₂×C₁₃×#103	1	2	yes	—
206	C₂²	C₁₃×#418	1	1	yes	characteristic
207	C₄	—	2	4	no	—
208	C₄	—	2	2	no	—
209	C₄	—	8	4	no	—
210	C₄	C₁₃×#332	1	8	yes	complemented
211	C₄	C₁₃×#459	1	2	yes	—
212	C₄	C₁₃×#460	1	2	yes	—
213	C₄	C₁₃×#487	1	2	yes	—
214	C₄	C₁₃×#492	1	1	yes	characteristic
215	C₄	C₁₃×#494	1	1	yes	characteristic
216	C₂	C₂×C₁₃×#332	1	2	yes	—
217	C₂	C₁₃×#1549	1	2	yes	—
218	C₂	C₁₃×#1956	1	1	yes	characteristic
219	C₂	C₁₃×#1966	1	1	yes	characteristic
220	C₂	C₁₃×#1982	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
39. #9694	C₁₃	direct (N × H)
116. C₄×C₁₃	#332	semidirect
177. C₁₃	#9694	direct (N × H)
210. C₄	C₁₃×#332	semidirect

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×#1842	2
C₄×C₁₃×C₄⋊C₈	2
C₂×C₁₃×#332	2
#9694	13

Subgroups — C13×#9694 #15696033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9694 #15696033