Subgroups — #15755788

Order 3328.

368 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113584	C₂	1	2	yes	maximal, complemented
2	#13113150	C₂	1	2	yes	maximal
3	#13112667	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
6	C₁₃×#433	—	2	2	no	—
7	C₁₃×#433	—	2	2	no	—
8	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#11718586	C₂²	1	4	yes	—
15	#11718120	—	2	2	no	—
16	#11718117	—	2	2	no	—
17	#11718050	—	2	2	no	—
18	#11718049	—	2	2	no	—
19	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₁₃×#117	—	2	2	no	—
25	C₁₃×#117	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₄	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×C₄⋊C₈	—	2	1	no	—
33	C₁₃×C₄⋊C₈	—	2	2	no	—
34	C₁₃×C₄⋊C₈	—	2	1	no	—
35	C₁₃×C₂²⋊C₈	—	2	1	no	—
36	C₁₃×C₂²⋊C₈	—	2	2	no	—
37	C₁₃×C₂²⋊C₈	—	2	1	no	—
38	C₁₃×#97	—	2	2	no	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	C₄×C₈×C₁₃	D₄	1	2	yes	—
41	C₂²⋊#1055	—	2	4	no	—
42	C₄⋊#1055	—	2	4	no	—
43	C₄×#1055	—	2	4	no	—
44	#8603	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	1	no	—
59	C₂×C₈×C₁₃	—	2	1	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₄²×C₁₃	—	2	1	no	—
70	C₄²×C₁₃	—	2	1	no	—
71	C₄²×C₁₃	C₂×D₄	1	2	yes	—
72	C₄²×C₁₃	#41	1	2	yes	—
73	C₂×#1055	—	4	4	no	—
74	C₂×#433	D₁₃	1	1	yes	characteristic
75	#1564	—	13	2	no	—
76	#1458	—	13	2	no	—
77	#1275	—	13	2	no	—
78	C₂³×C₁₃	—	2	1	no	—
79	C₂³×C₁₃	—	2	2	no	—
80	C₂³×C₁₃	—	4	1	no	—
81	C₂³×C₁₃	—	4	1	no	—
82	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	4	1	no	—
88	C₂×C₄×C₁₃	—	4	1	no	—
89	C₂×C₄×C₁₃	—	4	1	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	1	no	—
94	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#121	1	2	yes	—
97	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₁₃	#131	1	2	yes	—
99	C₂×C₄×C₁₃	#131	1	2	yes	—
100	C₈×C₁₃	—	2	1	no	—
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	—	2	1	no	—
103	C₈×C₁₃	—	4	1	no	—
104	C₈×C₁₃	—	4	1	no	—
105	#1055	—	8	4	no	—
106	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
107	#433	—	2	2	no	—
108	#433	—	2	2	no	—
109	#431	—	13	4	no	—
110	C₂×C₄⋊C₈	Dic₁₃	1	1	yes	characteristic
111	C₂×C₄⋊C₈	Dic₁₃	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	Dic₁₃	1	1	yes	characteristic
113	C₂×C₂²⋊C₈	Dic₁₃	1	1	yes	characteristic
114	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
116	#335	—	26	2	no	—
117	#334	—	26	2	no	—
118	#324	—	26	2	no	—
119	#323	—	26	2	no	—
120	C₂²×C₁₃	—	2	1	no	—
121	C₂²×C₁₃	—	2	1	no	—
122	C₂²×C₁₃	—	4	1	no	—
123	C₂²×C₁₃	—	4	1	no	—
124	C₂²×C₁₃	—	4	1	no	—
125	C₂²×C₁₃	—	8	2	no	—
126	C₂²×C₁₃	#380	1	1	yes	characteristic
127	C₂²×C₁₃	#424	1	2	yes	—
128	C₄×C₁₃	—	2	2	no	—
129	C₄×C₁₃	—	2	2	no	—
130	C₄×C₁₃	—	4	1	no	—
131	C₄×C₁₃	—	4	1	no	—
132	C₄×C₁₃	—	4	1	no	—
133	C₄×C₁₃	#408	1	1	yes	characteristic
134	C₄×C₁₃	#408	1	1	yes	characteristic
135	C₄×C₁₃	#433	1	2	yes	—
136	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
137	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
138	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
139	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
140	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
141	#117	—	2	2	no	—
142	#117	—	2	2	no	—
143	C₂×C₄⋊C₄	Dic₂₆	1	1	yes	characteristic
144	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	Dic₂₆	1	1	yes	characteristic
146	C₂×C₂²⋊C₄	D₅₂	1	1	yes	characteristic
147	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
148	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
149	C₄⋊C₈	—	2	1	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	26	4	no	—
153	C₂²⋊C₈	—	2	1	no	—
154	C₂²⋊C₈	—	2	2	no	—
155	C₂²⋊C₈	—	2	1	no	—
156	C₂²⋊C₈	—	26	4	no	—
157	#97	—	2	2	no	—
158	C₄×C₈	—	26	4	no	—
159	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
160	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
161	C₂×C₁₃	—	2	2	no	—
162	C₂×C₁₃	—	8	1	no	—
163	C₂×C₁₃	#1798	1	1	yes	characteristic
164	C₂×C₁₃	#1812	1	1	yes	characteristic
165	C₂×C₁₃	#1813	1	1	yes	characteristic
166	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
172	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
175	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
176	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	—	52	4	no	—
184	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
185	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
186	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	2	no	—
191	C₄²	—	2	1	no	—
192	C₄²	—	2	1	no	—
193	C₄²	#6127	1	2	yes	—
194	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
195	C₁₃	#8603	1	1	yes	characteristic, complemented, Sylow
196	C₂³	—	2	1	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	4	1	no	—
199	C₂³	—	4	1	no	—
200	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#88178	1	2	yes	—
213	C₂×C₄	#88180	1	1	yes	characteristic
214	C₂×C₄	#88184	1	2	yes	—
215	C₂×C₄	#88202	1	2	yes	—
216	C₂×C₄	#88202	1	2	yes	—
217	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	2	2	no	—
220	C₈	—	2	1	no	—
221	C₈	—	4	1	no	—
222	C₈	—	4	1	no	—
223	C₈	—	104	4	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	8	2	no	—
230	C₂²	#11718660	1	2	yes	—
231	C₂²	#11718873	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	4	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	1	no	—
237	C₄	#11718661	1	2	yes	—
238	C₄	#11718895	1	1	yes	characteristic
239	C₄	#11718895	1	1	yes	characteristic
240	C₂	—	2	2	no	—
241	C₂	—	8	1	no	—
242	C₂	#13114820	1	1	yes	characteristic
243	C₂	#13114882	1	1	yes	characteristic
244	C₂	#13114886	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88180
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#433	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#433	D₁₃
hypocenter	C₁₃	#8603
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
1. #13113584	C₂	semidirect
3. #13112667	C₂	semidirect
195. C₁₃	#8603	semidirect

Maximal subgroups

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

subgroup	index
#13113584	2
#13113150	2
#13112667	2
C₂×C₁₃×#433	2
#8603	13