Subgroups — #16015905

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
3	#13116593	C₂	1	8	yes	maximal, complemented
4	#13116592	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116591	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6094	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88126	C₄	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88055	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88052	C₂²	1	2	yes	—
15	C₂×#88043	C₄	1	1	yes	characteristic
16	D₁₃×M₃₂	—	2	8	no	—
17	C₂×#88038	C₂²	1	4	yes	—
18	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
19	#11718350	C₄	1	4	yes	—
20	#11718350	C₂²	1	4	yes	—
21	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
22	#11718093	C₂²	1	8	yes	complemented
23	C₄⋊#6090	C₂²	1	4	yes	complemented
24	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×#6103	C₈	1	2	yes	—
29	C₂×#6101	C₈	1	2	yes	—
30	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
33	C₂×#6094	—	2	4	no	—
34	C₂×#6094	C₂×C₄	1	4	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₈×D₁₃	D₄	1	4	yes	—
37	C₂×C₈×D₁₃	Q₈	1	4	yes	—
38	C₂×C₈×D₁₃	C₂³	1	2	yes	—
39	#88126	C₈	1	4	yes	—
40	#88126	C₂×C₄	1	4	yes	—
41	C₁₃×M₃₂	—	2	4	no	—
42	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
43	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₁₃	C₂³	1	2	yes	—
45	#88055	C₂×C₄	1	4	yes	—
46	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
47	C₈×Dic₁₃	C₂³	1	2	yes	—
48	#88052	—	2	4	no	—
49	C₂×#6090	C₂³	1	4	yes	—
50	#88043	C₂×C₄	1	4	yes	—
51	#88038	—	2	8	no	—
52	C₁₆×D₁₃	—	2	8	no	—
53	#33397	—	13	1	no	maximal, Sylow
54	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
58	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
59	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
60	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
61	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
62	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
68	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
69	C₄²×C₁₃	C₂×C₈	1	2	yes	—
70	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
71	#6103	C₂×C₈	1	8	yes	—
72	#6101	C₂×C₈	1	8	yes	—
73	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
74	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
75	C₂×#1055	—	2	2	no	—
76	C₂×#1055	C₄⋊C₄	1	4	yes	—
77	C₂×#1055	C₂²×C₄	1	2	yes	—
78	C₂×#1055	C₂²×C₄	1	2	yes	—
79	#6094	—	2	8	no	—
80	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
81	C₈×D₁₃	C₂×D₄	1	4	yes	—
82	C₈×D₁₃	C₂×Q₈	1	4	yes	—
83	C₁₃×C₁₆	—	2	4	no	—
84	#6090	—	2	4	no	—
85	C₂²×M₃₂	—	13	2	no	—
86	C₂×#405	—	13	1	no	—
87	#2151	—	13	8	no	—
88	#2150	—	13	2	no	—
89	#2150	—	13	1	no	—
90	#2150	D₁₃	1	1	yes	characteristic, complemented
91	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
92	C₂²×D₁₃	—	4	2	no	—
93	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
94	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
98	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
100	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
101	C₂×Dic₁₃	—	4	2	no	—
102	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
103	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
104	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
105	C₄×D₁₃	C₄⋊C₈	1	8	yes	—
106	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
107	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
108	C₈×C₁₃	—	2	2	no	—
109	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
110	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
111	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
112	#1055	—	2	2	no	—
113	#1055	C₂×C₄⋊C₄	1	4	yes	—
114	C₂²×M₁₆	—	13	1	no	—
115	C₂³×C₈	—	13	1	no	—
116	C₂×#117	—	13	1	no	—
117	C₂×M₃₂	—	13	2	no	—
118	C₂×M₃₂	—	13	4	no	—
119	C₂×M₃₂	—	26	8	no	—
120	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
121	C₂²×C₁₆	—	13	4	no	—
122	#405	—	13	4	no	—
123	#405	—	13	4	no	—
124	C₂×#97	—	13	1	no	—
125	C₂×#97	—	13	1	no	—
126	C₂×C₄×C₈	—	13	1	no	—
127	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
128	C₄⋊C₁₆	—	13	8	no	—
129	C₄⋊C₁₆	—	13	4	no	—
130	C₄⋊C₁₆	C₂×D₁₃	1	4	yes	complemented
131	C₂²×C₁₃	—	2	2	no	—
132	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
133	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
134	C₂×D₁₃	—	2	4	no	—
135	C₂×D₁₃	—	4	4	no	—
136	C₂×D₁₃	C₂×C₄⋊C₈	1	4	yes	—
137	C₄×C₁₃	—	2	4	no	—
138	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
139	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
140	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
141	Dic₁₃	—	2	4	no	—
142	Dic₁₃	C₂×C₄⋊C₈	1	4	yes	—
143	C₂³×C₄	—	13	1	no	—
144	C₂×M₁₆	—	13	4	no	—
145	C₂×M₁₆	—	26	4	no	—
146	C₂²×C₈	—	13	1	no	—
147	C₂²×C₈	—	13	2	no	—
148	C₂²×C₈	—	13	4	no	—
149	C₂²×C₈	—	13	4	no	—
150	C₂²×C₈	—	13	2	no	—
151	C₂²×C₈	—	13	1	no	—
152	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
153	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
154	#117	—	13	4	no	—
155	#117	—	13	4	no	—
156	C₂×C₄⋊C₄	—	13	2	no	—
157	C₂×C₂²⋊C₄	—	13	2	no	—
158	C₂×C₄²	—	13	1	no	—
159	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
160	M₃₂	—	2	4	no	—
161	M₃₂	—	26	8	no	—
162	M₃₂	—	26	4	no	—
163	C₂×C₁₆	—	13	4	no	—
164	C₂×C₁₆	—	26	8	no	—
165	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
166	#97	—	13	4	no	—
167	#97	—	13	4	no	—
168	C₄×C₈	—	13	2	no	—
169	C₄×C₈	—	13	2	no	—
170	C₄×C₈	C₄×D₁₃	1	2	yes	—
171	C₄×C₈	C₂²×D₁₃	1	2	yes	—
172	C₂×C₁₃	—	2	2	no	—
173	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
174	C₂×C₁₃	#3407	1	2	yes	—
175	D₁₃	—	2	4	no	—
176	C₂⁴	—	13	1	no	—
177	C₂²×C₄	—	13	1	no	—
178	C₂²×C₄	—	13	4	no	—
179	C₂²×C₄	—	13	2	no	—
180	C₂²×C₄	—	13	4	no	—
181	C₂²×C₄	—	13	2	no	—
182	C₂²×C₄	—	13	2	no	—
183	C₂²×C₄	C₈×D₁₃	1	2	yes	—
184	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
185	M₁₆	—	26	8	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	13	4	no	—
188	C₂×C₈	—	13	2	no	—
189	C₂×C₈	—	13	8	no	—
190	C₂×C₈	—	13	4	no	—
191	C₂×C₈	—	13	4	no	—
192	C₂×C₈	—	13	2	no	—
193	C₂×C₈	—	26	2	no	—
194	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
195	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
196	C₂×C₈	D₄×D₁₃	1	2	yes	—
197	C₂×C₈	Q₈×D₁₃	1	2	yes	—
198	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
199	C₄⋊C₄	—	13	8	no	—
200	C₂²⋊C₄	—	13	8	no	—
201	C₄²	—	13	2	no	—
202	C₄²	—	13	2	no	—
203	C₄²	C₈×D₁₃	1	2	yes	—
204	C₄²	C₂×C₄×D₁₃	1	2	yes	—
205	C₁₆	—	2	4	no	—
206	C₁₆	—	26	4	no	—
207	C₁₃	#33397	1	1	yes	characteristic, complemented, Sylow
208	C₂³	—	13	2	no	—
209	C₂³	—	13	4	no	—
210	C₂³	—	52	2	no	—
211	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	13	2	no	—
214	C₂×C₄	—	13	4	no	—
215	C₂×C₄	—	13	4	no	—
216	C₂×C₄	—	13	4	no	—
217	C₂×C₄	—	13	8	no	—
218	C₂×C₄	—	13	4	no	—
219	C₂×C₄	—	52	2	no	—
220	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
221	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
222	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
223	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
224	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
225	C₈	—	2	2	no	—
226	C₈	—	13	4	no	—
227	C₈	—	26	2	no	—
228	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
229	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
230	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	13	4	no	—
233	C₂²	—	26	4	no	—
234	C₂²	—	52	4	no	—
235	C₂²	D₁₃×C₄⋊C₈	1	2	yes	—
236	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
237	C₄	—	2	4	no	—
238	C₄	—	13	4	no	—
239	C₄	—	26	4	no	—
240	C₄	D₁₃×C₄⋊C₈	1	2	yes	—
241	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
242	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
243	C₂	—	2	2	no	—
244	C₂	—	26	4	no	—
245	C₂	C₂×D₁₃×C₄⋊C₈	1	1	yes	characteristic
246	C₂	#13127938	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2150	C₂
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#33397
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
3. #13116593	C₂	semidirect
4. #13116592	C₂	semidirect
5. #13116591	C₂	semidirect
6. C₁₃×#2150	C₂	semidirect
21. C₁₃×C₄⋊C₁₆	C₂²	semidirect
22. #11718093	C₂²	semidirect
23. C₄⋊#6090	C₂²	semidirect
90. #2150	D₁₃	semidirect
130. C₄⋊C₁₆	C₂×D₁₃	semidirect
207. C₁₃	#33397	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×M₃₂	2
C₂×#11718350	2
#13116593	2
#13116592	2
#13116591	2
C₁₃×#2150	2
#33397	13