Subgroups — C₄×C₁₃×#364 #15698994

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₄×C₈×C₁₃	D₄
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#364	C₄	direct (N × H)
36. C₄×#364	C₁₃	direct (N × H)
96. #364	C₄×C₁₃	direct (N × H)
106. C₄×C₁₃	#364	direct (N × H)
162. C₁₃	C₄×#364	direct (N × H)
190. C₄	C₁₃×#364	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×#364	2
C₄×C₁₃×M₃₂	2
C₄²×C₈×C₁₃	2
C₁₃×#1376	2
C₄×#364	13

Subgroups — C4×C13×#364 #15698994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#364 #15698994