Subgroups — #15761474

Order 3328.

378 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	#13115552	C₂	1	2	yes	maximal
2	C₄×#88057	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718046	C₂	1	1	yes	maximal, characteristic
4	#13112675	C₂	1	2	yes	maximal
5	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88057	C₄	1	2	yes	—
9	C₂×#88054	—	2	2	no	—
10	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₁₃×#334	—	2	2	no	—
14	#11718143	C₄	1	1	yes	characteristic
15	#11718143	C₄	1	1	yes	characteristic
16	#11718142	—	2	2	no	—
17	#11718046	—	2	2	no	—
18	C₂²×C₈×C₁₃	—	2	2	no	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₁₃	—	2	2	no	—
25	C₂²×#1055	—	2	1	no	—
26	C₂²×#1055	D₄	1	2	yes	—
27	C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₁₃×C₄⋊C₈	—	2	2	no	—
29	C₄×C₈×C₁₃	D₄	1	2	yes	—
30	C₄×C₈×C₁₃	Q₈	1	2	yes	—
31	#88071	—	2	2	no	—
32	#88057	—	2	4	no	—
33	#88054	—	4	4	no	—
34	C₄×#1055	—	2	1	no	—
35	C₄×#1055	—	2	1	no	—
36	C₄×#1055	—	2	1	no	—
37	C₄×#1055	Q₈	1	2	yes	—
38	#9597	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂²×Dic₁₃	—	2	2	no	—
43	C₂²×Dic₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	—	4	2	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	—	4	2	no	—
49	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
51	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₄²×C₁₃	#41	1	1	yes	characteristic
55	C₄⋊Dic₁₃	—	2	2	no	—
56	C₄⋊Dic₁₃	—	2	2	no	—
57	C₄⋊Dic₁₃	—	2	2	no	—
58	C₄⋊Dic₁₃	M₁₆	1	4	yes	—
59	C₄×Dic₁₃	—	4	2	no	—
60	C₄×Dic₁₃	—	4	2	no	—
61	C₂×#1055	—	2	2	no	—
62	C₂×#1055	—	2	2	no	—
63	C₂×#1055	—	2	2	no	—
64	C₂×#1055	—	4	1	no	—
65	C₂×#1055	—	4	1	no	—
66	C₂×#1055	SD₁₆	1	4	yes	—
67	#1939	—	13	2	no	—
68	C₄×#106	—	13	1	no	—
69	C₂×#334	D₁₃	1	1	yes	characteristic
70	C₂×#322	—	13	1	no	—
71	#1279	—	13	2	no	—
72	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	—	2	1	no	—
74	C₂×C₄×C₁₃	—	2	1	no	—
75	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
82	C₂×C₄×C₁₃	#131	1	2	yes	—
83	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
84	C₂×C₄×C₁₃	#135	1	2	yes	—
85	C₂×Dic₁₃	—	2	4	no	—
86	C₂×Dic₁₃	—	4	2	no	—
87	C₂×Dic₁₃	—	4	2	no	—
88	C₂×Dic₁₃	—	4	2	no	—
89	C₂×Dic₁₃	—	4	2	no	—
90	C₂×Dic₁₃	—	4	2	no	—
91	C₈×C₁₃	—	2	2	no	—
92	C₈×C₁₃	—	2	2	no	—
93	C₈×C₁₃	—	8	2	no	—
94	#1055	—	2	4	no	—
95	#1055	—	4	2	no	—
96	C₂×#106	—	13	2	no	—
97	C₂×C₄⋊C₈	—	26	2	no	—
98	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
102	C₄×C₄⋊C₄	—	13	2	no	—
103	#340	—	13	1	no	—
104	#340	—	13	1	no	—
105	#336	—	26	2	no	—
106	#334	—	2	2	no	—
107	#322	—	26	2	no	—
108	C₂²×C₁₃	#389	1	1	yes	characteristic
109	C₂²×C₁₃	#435	1	2	yes	—
110	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
111	C₂²×C₁₃	#444	1	1	yes	characteristic
112	C₂²×C₁₃	#444	1	1	yes	characteristic
113	C₄×C₁₃	—	2	1	no	—
114	C₄×C₁₃	—	2	1	no	—
115	C₄×C₁₃	#423	1	1	yes	characteristic
116	C₄×C₁₃	#424	1	1	yes	characteristic
117	C₄×C₁₃	#446	1	2	yes	—
118	C₄×C₁₃	#465	1	2	yes	—
119	C₄×C₁₃	#498	1	1	yes	characteristic
120	C₄×C₁₃	#499	1	1	yes	characteristic
121	Dic₁₃	—	4	4	no	—
122	Dic₁₃	—	8	2	no	—
123	C₂²×C₈	—	2	2	no	—
124	C₂²×C₈	—	13	2	no	—
125	C₂²×C₈	—	26	1	no	—
126	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
127	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
128	C₂×C₄⋊C₄	—	13	2	no	—
129	C₂×C₄⋊C₄	—	13	2	no	—
130	C₂×C₄²	—	26	2	no	—
131	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
132	#106	—	26	4	no	—
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	52	4	no	—
136	C₄×C₈	—	13	2	no	—
137	C₄×C₈	—	26	1	no	—
138	C₄×C₈	—	26	1	no	—
139	C₄×C₈	—	26	1	no	—
140	C₄×C₈	Dic₂₆	1	2	yes	—
141	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
142	#95	—	26	2	no	—
143	C₂×C₁₃	#1582	1	2	yes	—
144	C₂×C₁₃	#1583	1	2	yes	—
145	C₂×C₁₃	#1940	1	1	yes	characteristic
146	C₂×C₁₃	#1941	1	1	yes	characteristic
147	C₂×C₁₃	#1946	1	1	yes	characteristic
148	C₂²×C₄	—	26	2	no	—
149	C₂²×C₄	—	26	2	no	—
150	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
151	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
152	C₂²×C₄	#6131	1	1	yes	characteristic
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	4	2	no	—
156	C₂×C₈	—	4	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	13	4	no	—
159	C₂×C₈	—	26	2	no	—
160	C₂×C₈	—	26	2	no	—
161	C₂×C₈	—	26	2	no	—
162	C₂×C₈	—	52	1	no	—
163	C₂×C₈	—	52	1	no	—
164	C₂×C₈	#6101	1	2	yes	—
165	C₂×C₈	#6101	1	2	yes	—
166	C₄⋊C₄	—	13	4	no	—
167	C₄⋊C₄	—	26	2	no	—
168	C₄⋊C₄	—	26	2	no	—
169	C₄⋊C₄	—	26	2	no	—
170	C₄²	—	52	2	no	—
171	C₄²	—	52	2	no	—
172	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
173	C₄²	#6129	1	1	yes	characteristic
174	C₄²	Q₈×D₁₃	1	1	yes	characteristic
175	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
176	C₁₃	#9597	1	1	yes	characteristic, complemented, Sylow
177	C₂³	#88147	1	1	yes	characteristic
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	26	4	no	—
181	C₂×C₄	—	52	2	no	—
182	C₂×C₄	—	52	2	no	—
183	C₂×C₄	—	52	2	no	—
184	C₂×C₄	—	52	2	no	—
185	C₂×C₄	—	52	2	no	—
186	C₂×C₄	#88141	1	1	yes	characteristic
187	C₂×C₄	#88142	1	1	yes	characteristic
188	C₂×C₄	#88144	1	1	yes	characteristic
189	C₂×C₄	#88155	1	2	yes	—
190	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
191	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
192	C₂×C₄	#88170	1	2	yes	—
193	C₂×C₄	C₂×#6101	1	1	yes	characteristic
194	C₂×C₄	#88192	1	1	yes	characteristic
195	C₂×C₄	#88200	1	1	yes	characteristic
196	C₈	—	2	2	no	—
197	C₈	—	2	2	no	—
198	C₈	—	8	2	no	—
199	C₈	—	26	4	no	—
200	C₈	—	52	2	no	—
201	C₂²	#11718497	1	2	yes	—
202	C₂²	#11718513	1	2	yes	—
203	C₂²	#11718555	1	1	yes	characteristic
204	C₂²	#11718555	1	1	yes	characteristic
205	C₂²	#11718634	1	1	yes	characteristic
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	52	4	no	—
209	C₄	—	104	2	no	—
210	C₄	#11718489	1	2	yes	—
211	C₄	#11718516	1	1	yes	characteristic
212	C₄	#11718519	1	1	yes	characteristic
213	C₄	#11718763	1	1	yes	characteristic
214	C₄	#11718779	1	1	yes	characteristic
215	C₄	#11718832	1	2	yes	—
216	C₂	#13113671	1	2	yes	—
217	C₂	#13113678	1	2	yes	—
218	C₂	#13115557	1	1	yes	characteristic
219	C₂	#13115562	1	1	yes	characteristic
220	C₂	#13115587	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#334	C₂
socle, prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#334	D₁₃
hypocenter	C₁₃	#9597
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
176. C₁₃	#9597	semidirect

Maximal subgroups

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

subgroup	index
#13115552	2
C₄×#88057	2
C₂×#11718046	2
#13112675	2
C₂×C₁₃×#334	2
#9597	13