Subgroups — Dic₁₃×#368 #15778333

Order 3328.

314 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718098	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#108×Dic₁₃	C₂	1	2	yes	maximal
4	#13112929	C₂	1	2	yes	maximal
5	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	2	yes	—
8	M₁₆×Dic₁₃	—	2	2	no	—
9	C₂×#88059	C₂²	1	2	yes	—
10	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6090	C₂²	1	1	yes	characteristic
12	C₁₃×#368	C₄	1	4	yes	complemented
13	#11718150	—	2	2	no	—
14	#11718098	C₄	1	4	yes	complemented
15	C₁₆×Dic₁₃	C₄	1	4	yes	—
16	C₂×C₁₃×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
19	C₂×#6099	—	2	2	no	—
20	C₂²×#1055	D₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
24	C₁₃×#108	—	2	2	no	—
25	C₁₃×#108	C₂×C₄	1	4	yes	—
26	#88059	—	2	2	no	—
27	#88059	C₂×C₄	1	4	yes	—
28	#88055	—	4	2	no	—
29	C₈×Dic₁₃	—	4	2	no	—
30	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
31	C₈×Dic₁₃	Q₈	1	2	yes	—
32	C₂×#6090	—	2	1	no	—
33	C₂×#6090	—	2	1	no	—
34	C₂×#6090	C₂×C₄	1	2	yes	—
35	C₄×#368	—	13	1	no	maximal, Sylow
36	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×Dic₁₃	Q₁₆	1	2	yes	—
38	C₁₃×M₁₆	—	2	4	no	—
39	C₁₃×M₁₆	—	4	2	no	—
40	C₂×C₈×C₁₃	—	4	2	no	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
46	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
47	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
48	C₄×Dic₁₃	D₈	1	1	yes	characteristic
49	C₄×Dic₁₃	D₈	1	1	yes	characteristic
50	#6099	—	2	4	no	—
51	#6099	—	4	2	no	—
52	C₂×#1055	—	2	1	no	—
53	C₂×#1055	—	2	1	no	—
54	C₂×#1055	—	4	2	no	—
55	C₂×#1055	C₄⋊C₄	1	2	yes	—
56	C₁₃×C₁₆	C₄²	1	4	yes	—
57	#6090	—	2	2	no	—
58	C₂×#368	—	13	1	no	—
59	C₂×#368	D₁₃	1	1	yes	characteristic
60	C₂×C₄×C₁₆	—	13	1	no	—
61	C₄×#108	—	13	2	no	—
62	#1381	—	13	2	no	—
63	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
70	C₂×Dic₁₃	—	2	4	no	—
71	C₂×Dic₁₃	#107	1	2	yes	—
72	C₂×Dic₁₃	#107	1	2	yes	—
73	C₈×C₁₃	—	4	4	no	—
74	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
75	C₈×C₁₃	#117	1	1	yes	characteristic
76	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
77	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
78	#1055	—	2	2	no	—
79	#1055	—	4	4	no	—
80	C₂²×C₁₆	—	13	1	no	—
81	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
82	C₂×#108	—	13	2	no	—
83	C₂×#108	C₂×D₁₃	1	2	yes	—
84	C₄×M₁₆	—	26	2	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	#368	—	13	4	no	—
87	#368	Dic₁₃	1	4	yes	direct product factor
88	C₄×C₁₆	—	13	4	no	—
89	#341	—	26	2	no	—
90	C₂²×C₁₃	—	2	2	no	—
91	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
92	C₂²×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
93	C₂²×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
94	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
95	C₄×C₁₃	#427	1	1	yes	characteristic
96	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
97	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
98	Dic₁₃	—	2	2	no	—
99	Dic₁₃	#368	1	4	yes	direct product factor
100	C₂×M₁₆	—	2	2	no	—
101	C₂×M₁₆	—	26	2	no	—
102	C₂²×C₈	—	13	1	no	—
103	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
104	C₂×C₄²	—	13	1	no	—
105	C₂×C₁₆	—	13	2	no	—
106	C₂×C₁₆	—	26	1	no	—
107	C₂×C₁₆	—	26	1	no	—
108	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
109	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
110	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
111	#108	—	2	2	no	—
112	#108	—	13	4	no	—
113	#108	—	26	2	no	—
114	#108	C₂×Dic₁₃	1	4	yes	—
115	#97	—	52	2	no	—
116	C₄×C₈	—	13	2	no	—
117	C₄×C₈	—	13	2	no	—
118	C₄×C₈	—	52	2	no	—
119	C₂×C₁₃	—	2	1	no	—
120	C₂×C₁₃	—	2	1	no	—
121	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
122	C₂×C₁₃	C₂×#368	1	2	yes	—
123	C₂²×C₄	—	13	2	no	—
124	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
125	M₁₆	—	2	4	no	—
126	M₁₆	—	4	2	no	—
127	M₁₆	—	26	4	no	—
128	M₁₆	—	52	2	no	—
129	C₂×C₈	—	4	2	no	—
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	26	1	no	—
132	C₂×C₈	—	26	1	no	—
133	C₂×C₈	—	52	2	no	—
134	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
136	C₂×C₈	#6129	1	1	yes	characteristic
137	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
138	C₂×C₈	#6131	1	1	yes	characteristic
139	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
140	C₄²	—	13	2	no	—
141	C₄²	—	13	1	no	—
142	C₄²	—	13	1	no	—
143	C₁₆	—	26	2	no	—
144	C₁₆	C₄×Dic₁₃	1	4	yes	—
145	C₁₃	C₄×#368	1	1	yes	characteristic, complemented, Sylow
146	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
147	C₂×C₄	—	13	2	no	—
148	C₂×C₄	—	13	2	no	—
149	C₂×C₄	—	26	4	no	—
150	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
151	C₂×C₄	#88147	1	1	yes	characteristic
152	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
153	C₂×C₄	#88166	1	1	yes	characteristic
154	C₂×C₄	#88173	1	1	yes	characteristic
155	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
156	C₈	—	4	4	no	—
157	C₈	—	26	2	no	—
158	C₈	—	52	4	no	—
159	C₈	#88141	1	1	yes	characteristic
160	C₈	#88146	1	1	yes	characteristic
161	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
162	C₈	Q₈×Dic₁₃	1	1	yes	characteristic
163	C₂²	—	2	2	no	—
164	C₂²	#11718534	1	1	yes	characteristic
165	C₂²	D₁₃×#107	1	1	yes	characteristic
166	C₂²	Q₁₆×Dic₁₃	1	1	yes	characteristic
167	C₄	—	13	4	no	—
168	C₄	—	26	2	no	—
169	C₄	#11718533	1	1	yes	characteristic
170	C₄	#11718541	1	1	yes	characteristic
171	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
172	C₄	D₈×Dic₁₃	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	#107×Dic₁₃	1	1	yes	characteristic
176	C₂	D₁₃×#368	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₃
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#368	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#368	D₁₃
hypocenter	C₁₃	C₄×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
12. C₁₃×#368	C₄	semidirect
14. #11718098	C₄	semidirect
87. #368	Dic₁₃	direct (N × H)
99. Dic₁₃	#368	direct (N × H)
145. C₁₃	C₄×#368	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718098	2
C₂×C₁₆×Dic₁₃	2
#108×Dic₁₃	2
#13112929	2
C₂×C₁₃×#368	2
C₄×#368	13

Subgroups — Dic13×#368 #15778333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#368 #15778333