Subgroups — C₁₃×#9835 #15696174

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1990	C₂	1	2	yes	maximal
3	C₁₃×#1990	C₂	1	2	yes	maximal
4	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	—	2	2	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₁₃×#494	—	2	2	no	—
9	C₁₃×#494	C₄	1	4	yes	complemented
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#384	C₂²	1	2	yes	—
14	C₁₃×#340	—	2	4	no	—
15	C₁₃×#340	—	2	4	no	—
16	C₁₃×#340	—	2	2	no	—
17	C₁₃×#322	—	2	2	no	—
18	C₂²×Q₈×C₁₃	—	2	2	no	—
19	C₂×C₁₃×Q₁₆	—	2	8	no	—
20	C₂×C₁₃×Q₁₆	—	4	8	no	—
21	C₂²×C₈×C₁₃	D₄	1	2	yes	—
22	C₂²×C₈×C₁₃	D₄	1	2	yes	—
23	C₂²×C₈×C₁₃	D₄	1	2	yes	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₄×C₈×C₁₃	—	2	1	no	—
35	C₄×C₈×C₁₃	—	2	1	no	—
36	C₄×C₈×C₁₃	—	2	1	no	—
37	C₄×C₈×C₁₃	—	2	1	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	#9835	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₃	—	2	4	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	8	no	—
44	C₂²×C₄×C₁₃	—	4	2	no	—
45	C₂²×C₄×C₁₃	—	4	2	no	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₁₃×Q₁₆	—	4	16	no	—
50	C₂×C₈×C₁₃	—	2	2	no	—
51	C₂×C₈×C₁₃	—	2	2	no	—
52	C₂×C₈×C₁₃	—	2	4	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	2	4	no	—
55	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
56	C₂×C₈×C₁₃	Q₁₆	1	4	yes	complemented
57	C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	4	4	no	—
62	C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₃	#41	1	1	yes	characteristic
67	C₄²×C₁₃	#41	1	1	yes	characteristic
68	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
69	#1990	C₂×C₁₃	1	2	yes	—
70	#1990	C₂×C₁₃	1	2	yes	—
71	#1834	C₂×C₁₃	1	1	yes	characteristic
72	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
73	C₂³×C₁₃	#127	1	1	yes	characteristic
74	Q₈×C₁₃	—	4	8	no	—
75	Q₈×C₁₃	—	8	4	no	—
76	C₂×C₄×C₁₃	—	4	4	no	—
77	C₂×C₄×C₁₃	—	8	4	no	—
78	C₂×C₄×C₁₃	—	8	2	no	—
79	C₂×C₄×C₁₃	—	8	2	no	—
80	C₂×C₄×C₁₃	—	8	2	no	—
81	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₁₃	#135	1	2	yes	—
89	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
90	C₂×C₄×C₁₃	#137	1	4	yes	—
91	C₈×C₁₃	—	2	4	no	—
92	C₈×C₁₃	—	2	4	no	—
93	C₈×C₁₃	—	4	2	no	—
94	C₂²×Q₁₆	—	2	2	no	—
95	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
96	#494	—	2	2	no	—
97	#494	C₄×C₁₃	1	4	yes	complemented
98	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	#384	C₂²×C₁₃	1	2	yes	—
102	#340	—	2	2	no	—
103	#340	—	2	4	no	—
104	#340	—	2	4	no	—
105	#322	—	2	2	no	—
106	C₂²×C₁₃	#390	1	1	yes	characteristic
107	C₂²×C₁₃	#494	1	1	yes	characteristic
108	C₂²×C₁₃	#495	1	1	yes	characteristic
109	C₂²×C₁₃	#496	1	2	yes	—
110	C₂²×C₁₃	#497	1	2	yes	—
111	C₄×C₁₃	—	8	4	no	—
112	C₄×C₁₃	—	16	2	no	—
113	C₄×C₁₃	#418	1	2	yes	—
114	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
115	C₄×C₁₃	#441	1	2	yes	—
116	C₄×C₁₃	#467	1	2	yes	—
117	C₄×C₁₃	#470	1	2	yes	—
118	C₄×C₁₃	#490	1	2	yes	—
119	C₂²×Q₈	—	2	2	no	—
120	C₂×Q₁₆	—	2	8	no	—
121	C₂×Q₁₆	—	4	8	no	—
122	C₂²×C₈	D₄×C₁₃	1	2	yes	—
123	C₂²×C₈	D₄×C₁₃	1	2	yes	—
124	C₂²×C₈	D₄×C₁₃	1	2	yes	—
125	C₄⋊Q₈	—	2	2	no	—
126	C₄⋊Q₈	—	2	2	no	—
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
135	C₄×C₈	—	2	1	no	—
136	C₄×C₈	—	2	1	no	—
137	C₄×C₈	—	2	1	no	—
138	C₄×C₈	—	2	1	no	—
139	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
140	C₄×C₈	D₄×C₁₃	1	2	yes	—
141	C₂×C₁₃	#1720	1	2	yes	—
142	C₂×C₁₃	#1723	1	2	yes	—
143	C₂×C₁₃	#1961	1	1	yes	characteristic
144	C₂×C₁₃	#1969	1	1	yes	characteristic
145	C₂×C₁₃	#1971	1	1	yes	characteristic
146	C₂×Q₈	—	2	4	no	—
147	C₂×Q₈	—	4	2	no	—
148	C₂×Q₈	—	4	8	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
152	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
153	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
154	Q₁₆	—	4	16	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	C₁₃×C₂²⋊C₄	1	4	yes	—
161	C₂×C₈	C₁₃×Q₁₆	1	4	yes	complemented
162	C₄⋊C₄	—	2	4	no	—
163	C₄⋊C₄	—	2	4	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	4	4	no	—
167	C₄⋊C₄	—	4	4	no	—
168	C₄⋊C₄	—	4	4	no	—
169	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
170	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
171	C₄²	C₁₃×#41	1	1	yes	characteristic
172	C₄²	C₁₃×#41	1	1	yes	characteristic
173	C₁₃	#9835	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	C₁₃×#127	1	1	yes	characteristic
175	Q₈	—	4	8	no	—
176	Q₈	—	8	4	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	8	4	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
184	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
185	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
186	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
187	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
188	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
189	C₂×C₄	C₁₃×#135	1	2	yes	—
190	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
191	C₂×C₄	C₁₃×#137	1	4	yes	—
192	C₈	—	2	4	no	—
193	C₈	—	2	4	no	—
194	C₈	—	4	2	no	—
195	C₂²	C₁₃×#390	1	1	yes	characteristic
196	C₂²	C₁₃×#494	1	1	yes	characteristic
197	C₂²	C₁₃×#495	1	1	yes	characteristic
198	C₂²	C₁₃×#496	1	2	yes	—
199	C₂²	C₁₃×#497	1	2	yes	—
200	C₄	—	8	4	no	—
201	C₄	—	16	2	no	—
202	C₄	C₁₃×#418	1	2	yes	—
203	C₄	C₄×C₁₃×Q₁₆	1	2	yes	—
204	C₄	C₁₃×#441	1	2	yes	—
205	C₄	C₁₃×#467	1	2	yes	—
206	C₄	C₁₃×#470	1	2	yes	—
207	C₄	C₁₃×#490	1	2	yes	—
208	C₂	C₁₃×#1720	1	2	yes	—
209	C₂	C₁₃×#1723	1	2	yes	—
210	C₂	C₁₃×#1961	1	1	yes	characteristic
211	C₂	C₁₃×#1969	1	1	yes	characteristic
212	C₂	C₁₃×#1971	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₃×#494	C₄	semidirect
40. #9835	C₁₃	direct (N × H)
56. C₂×C₈×C₁₃	Q₁₆	semidirect
97. #494	C₄×C₁₃	semidirect
161. C₂×C₈	C₁₃×Q₁₆	semidirect
173. C₁₃	#9835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#494	2
C₁₃×#1990	2
C₁₃×#1834	2
C₂×C₁₃×#322	2
#9835	13

Subgroups — C13×#9835 #15696174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9835 #15696174