Subgroups — Dic₁₃×#364 #15778239

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	1	yes	maximal, characteristic
2	M₃₂×Dic₁₃	C₂	1	2	yes	maximal
3	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13112917	C₂	1	2	yes	maximal
5	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	2	yes	—
13	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic
15	C₁₃×#364	C₄	1	4	yes	complemented
16	#11718094	—	2	2	no	—
17	C₁₆×Dic₁₃	—	2	2	no	—
18	#11718055	C₄	1	4	yes	complemented
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₃	—	2	2	no	—
23	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
26	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
27	C₁₃×M₃₂	—	2	2	no	—
28	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
29	C₂×C₁₃×C₁₆	—	2	2	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₈×Dic₁₃	—	2	1	no	—
33	C₈×Dic₁₃	—	2	1	no	—
34	C₈×Dic₁₃	C₈	1	4	yes	—
35	C₈×Dic₁₃	C₈	1	4	yes	—
36	C₈×Dic₁₃	D₄	1	1	yes	characteristic
37	C₈×Dic₁₃	D₄	1	1	yes	characteristic
38	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
39	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
40	#88052	—	2	2	no	—
41	#88052	C₂×C₄	1	4	yes	—
42	C₂×#6090	—	2	2	no	—
43	C₄×#1055	—	2	2	no	—
44	C₄×#364	—	13	1	no	maximal, Sylow
45	C₂²×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×Dic₁₃	—	2	1	no	—
48	C₂²×Dic₁₃	M₁₆	1	2	yes	—
49	C₂×C₈×C₁₃	C₄²	1	2	yes	—
50	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
51	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
52	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
57	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
58	C₄²×C₁₃	—	2	1	no	—
59	C₄²×C₁₃	C₄²	1	2	yes	—
60	C₄×Dic₁₃	—	2	8	no	—
61	C₄×Dic₁₃	—	2	1	no	—
62	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
63	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
64	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
65	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
66	C₂×#1055	—	2	1	no	—
67	C₂×#1055	—	2	1	no	—
68	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
69	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
70	C₂×#1055	C₂×C₈	1	2	yes	—
71	C₂×#1055	C₂×C₈	1	2	yes	—
72	C₂×#1055	M₁₆	1	2	yes	—
73	C₁₃×C₁₆	—	2	4	no	—
74	#6090	—	2	4	no	—
75	C₂×#364	—	13	1	no	—
76	C₂×#364	D₁₃	1	1	yes	characteristic
77	C₄×M₃₂	—	13	2	no	—
78	C₄²×C₈	—	13	1	no	—
79	#1376	—	13	2	no	—
80	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	4	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
89	C₂×Dic₁₃	—	2	4	no	—
90	C₂×Dic₁₃	—	2	2	no	—
91	C₂×Dic₁₃	—	2	4	no	—
92	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
93	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
94	C₈×C₁₃	C₄×C₈	1	4	yes	—
95	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
96	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
97	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
98	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
99	#1055	—	2	2	no	—
100	#1055	C₄⋊C₈	1	2	yes	—
101	#1055	C₄⋊C₈	1	2	yes	—
102	C₂×M₃₂	—	13	2	no	—
103	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
104	C₂×C₄×C₈	—	13	1	no	—
105	C₂×C₄×C₈	—	13	1	no	—
106	C₂×C₄×C₈	—	13	1	no	—
107	C₂×C₄×C₈	—	13	1	no	—
108	C₂×C₄×C₈	—	13	1	no	—
109	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
110	C₄³	—	13	1	no	—
111	#364	—	13	4	no	—
112	#364	Dic₁₃	1	4	yes	direct product factor
113	#346	—	26	2	no	—
114	C₄×C₁₆	—	26	2	no	—
115	C₂²×C₁₃	—	2	2	no	—
116	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
117	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
118	C₂²×C₁₃	#431	1	1	yes	characteristic
119	C₄×C₁₃	—	2	4	no	—
120	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
121	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
122	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
123	C₄×C₁₃	#431	1	1	yes	characteristic
124	Dic₁₃	—	2	4	no	—
125	Dic₁₃	—	2	2	no	—
126	Dic₁₃	#364	1	4	yes	direct product factor
127	C₂²×C₈	—	13	1	no	—
128	C₂²×C₈	—	13	1	no	—
129	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
130	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
131	C₂×C₄²	—	13	1	no	—
132	C₂×C₄²	—	13	1	no	—
133	C₂×C₄²	—	26	2	no	—
134	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
135	M₃₂	—	2	2	no	—
136	M₃₂	—	13	4	no	—
137	M₃₂	—	26	2	no	—
138	M₃₂	C₂×Dic₁₃	1	4	yes	—
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	26	2	no	—
141	C₄×C₈	—	13	4	no	—
142	C₄×C₈	—	13	4	no	—
143	C₄×C₈	—	13	1	no	—
144	C₄×C₈	—	13	1	no	—
145	C₄×C₈	—	13	1	no	—
146	C₄×C₈	—	13	1	no	—
147	C₄×C₈	—	26	2	no	—
148	C₄×C₈	—	26	1	no	—
149	C₄×C₈	—	26	1	no	—
150	C₄×C₈	C₄×D₁₃	1	2	yes	—
151	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
152	C₂×C₁₃	—	2	1	no	—
153	C₂×C₁₃	—	2	1	no	—
154	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
155	C₂×C₁₃	C₂×#364	1	2	yes	—
156	C₂²×C₄	—	2	1	no	—
157	C₂²×C₄	—	13	2	no	—
158	C₂²×C₄	—	26	1	no	—
159	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
160	C₂×C₈	—	13	1	no	—
161	C₂×C₈	—	13	1	no	—
162	C₂×C₈	—	13	2	no	—
163	C₂×C₈	—	13	2	no	—
164	C₂×C₈	—	13	2	no	—
165	C₂×C₈	—	26	1	no	—
166	C₂×C₈	—	26	1	no	—
167	C₂×C₈	C₈×D₁₃	1	2	yes	—
168	C₂×C₈	C₈×D₁₃	1	2	yes	—
169	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
170	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
171	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
172	C₂×C₈	#6129	1	1	yes	characteristic
173	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
174	C₂×C₈	#6131	1	1	yes	characteristic
175	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
176	C₄²	—	2	1	no	—
177	C₄²	—	13	1	no	—
178	C₄²	—	13	1	no	—
179	C₄²	—	13	2	no	—
180	C₄²	—	13	2	no	—
181	C₄²	—	26	8	no	—
182	C₄²	—	26	1	no	—
183	C₄²	C₄×Dic₁₃	1	2	yes	—
184	C₁₆	—	2	4	no	—
185	C₁₆	—	26	4	no	—
186	C₁₃	C₄×#364	1	1	yes	characteristic, complemented, Sylow
187	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	13	2	no	—
191	C₂×C₄	—	13	2	no	—
192	C₂×C₄	—	26	4	no	—
193	C₂×C₄	—	26	4	no	—
194	C₂×C₄	—	26	2	no	—
195	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
196	C₂×C₄	#88146	1	1	yes	characteristic
197	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
198	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
199	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
200	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
201	C₈	—	13	2	no	—
202	C₈	—	13	2	no	—
203	C₈	—	26	2	no	—
204	C₈	C₈×Dic₁₃	1	4	yes	—
205	C₈	#88141	1	1	yes	characteristic
206	C₈	#88147	1	1	yes	characteristic
207	C₈	D₄×Dic₁₃	1	1	yes	characteristic
208	C₈	Q₈×Dic₁₃	1	1	yes	characteristic
209	C₂²	—	2	2	no	—
210	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
211	C₂²	#11718494	1	1	yes	characteristic
212	C₂²	M₁₆×Dic₁₃	1	1	yes	characteristic
213	C₄	—	2	4	no	—
214	C₄	—	13	4	no	—
215	C₄	—	26	4	no	—
216	C₄	—	26	2	no	—
217	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
218	C₄	#11718494	1	1	yes	characteristic
219	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
220	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	C₄⋊C₈×Dic₁₃	1	1	yes	characteristic
224	C₂	D₁₃×#364	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	C₄×#364
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
15. C₁₃×#364	C₄	semidirect
18. #11718055	C₄	semidirect
112. #364	Dic₁₃	direct (N × H)
126. Dic₁₃	#364	direct (N × H)
186. C₁₃	C₄×#364	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
M₃₂×Dic₁₃	2
C₄×C₈×Dic₁₃	2
#13112917	2
C₂×C₁₃×#364	2
C₄×#364	13

Subgroups — Dic13×#364 #15778239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#364 #15778239