Subgroups — C₂×#13129878 #16789056

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88106	C₂	1	2	yes	maximal
2	#13129878	C₂	1	4	yes	maximal, direct product factor
3	C₂²×#88055	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂³×#1055	C₂²	1	1	yes	characteristic
7	C₂×#88106	—	2	4	no	—
8	C₂×#88106	—	2	4	no	—
9	C₂×#88106	C₄	1	4	yes	complemented
10	C₂×#88106	C₂²	1	4	yes	—
11	C₂²×#6092	C₄	1	4	yes	complemented
12	C₂×#88055	—	2	4	no	—
13	C₂×#88055	C₄	1	2	yes	—
14	C₂×#88055	C₂²	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×Dic₁₃	—	2	1	no	—
17	C₂²×C₈×C₁₃	—	2	2	no	—
18	C₂²×C₈×C₁₃	—	2	1	no	—
19	C₂²×C₈×C₁₃	—	2	1	no	—
20	C₂²×C₈×C₁₃	C₈	1	4	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₃	—	2	2	no	—
23	C₂×C₄×Dic₁₃	—	2	1	no	—
24	C₂×C₄×Dic₁₃	C₈	1	4	yes	—
25	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
26	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
27	C₂²×#1055	C₂×C₄	1	2	yes	—
28	C₂²×#1055	C₂×C₄	1	2	yes	—
29	C₂²×#1055	D₄	1	2	yes	—
30	C₂²×#1055	D₄	1	4	yes	—
31	C₂²×#1055	Q₈	1	2	yes	—
32	C₂²×#1055	C₂³	1	1	yes	characteristic
33	#88106	—	2	8	no	—
34	#88106	—	2	4	no	—
35	#88106	—	2	4	no	—
36	C₂×#6092	—	2	8	no	—
37	C₂×#6092	C₂×C₄	1	8	yes	complemented
38	#88055	—	2	4	no	—
39	#88055	—	2	4	no	—
40	C₂×#1375	—	13	1	no	maximal, Sylow
41	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
48	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	2	4	no	—
53	C₂²×Dic₁₃	—	2	2	no	—
54	C₂²×Dic₁₃	—	4	4	no	—
55	C₂×C₈×C₁₃	—	2	4	no	—
56	C₂×C₈×C₁₃	—	2	4	no	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
60	C₄×Dic₁₃	—	2	4	no	—
61	C₄×Dic₁₃	—	2	2	no	—
62	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
63	C₂×#1055	C₄²	1	2	yes	—
64	C₂×#1055	C₂²⋊C₄	1	2	yes	—
65	C₂×#1055	C₂²⋊C₄	1	4	yes	—
66	C₂×#1055	C₂²⋊C₄	1	4	yes	—
67	C₂×#1055	C₄⋊C₄	1	2	yes	—
68	C₂×#1055	C₄⋊C₄	1	4	yes	—
69	C₂×#1055	C₄⋊C₄	1	4	yes	—
70	C₂×#1055	C₂²×C₄	1	2	yes	—
71	C₂×#1055	C₂×D₄	1	1	yes	characteristic
72	C₂×#1055	C₂×D₄	1	2	yes	—
73	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
74	#6092	—	2	8	no	—
75	C₂²×M₃₂	—	13	2	no	—
76	C₂²×#97	—	13	1	no	—
77	#1375	—	13	4	no	—
78	C₂³×C₁₃	—	2	4	no	—
79	C₂³×C₁₃	#97	1	1	yes	characteristic
80	C₂³×C₁₃	#97	1	1	yes	characteristic
81	C₂³×C₁₃	C₂²⋊C₈	1	2	yes	—
82	C₂³×C₁₃	C₄⋊C₈	1	2	yes	—
83	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#95	1	2	yes	—
85	C₂×C₄×C₁₃	#95	1	2	yes	—
86	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
87	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
88	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
89	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
91	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
94	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
95	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
96	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
102	C₂×Dic₁₃	—	2	4	no	—
103	C₂×Dic₁₃	—	4	4	no	—
104	C₂×Dic₁₃	—	4	8	no	—
105	C₈×C₁₃	—	2	4	no	—
106	#1055	#95	1	4	yes	—
107	#1055	C₂×C₂²⋊C₄	1	2	yes	—
108	#1055	C₂×C₄⋊C₄	1	2	yes	—
109	C₂³×C₈	—	13	1	no	—
110	C₂³×C₈	#261	1	1	yes	characteristic
111	C₂²×C₄²	—	13	1	no	—
112	C₂×M₃₂	—	13	4	no	—
113	C₂×M₃₂	—	13	4	no	—
114	C₂×M₃₂	—	26	4	no	—
115	C₂×M₃₂	—	26	4	no	—
116	C₂²×C₁₆	—	13	4	no	—
117	C₂×#97	—	13	2	no	—
118	C₂×#97	—	13	2	no	—
119	C₂×#97	—	26	4	no	—
120	C₂²×C₁₃	—	2	2	no	—
121	C₂²×C₁₃	—	2	2	no	—
122	C₂²×C₁₃	—	2	4	no	—
123	C₂²×C₁₃	—	2	4	no	—
124	C₂²×C₁₃	#336	1	2	yes	—
125	C₂²×C₁₃	#336	1	2	yes	—
126	C₂²×C₁₃	#347	1	4	yes	—
127	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
128	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
129	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
130	C₄×C₁₃	#336	1	2	yes	—
131	C₄×C₁₃	#336	1	2	yes	—
132	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
133	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
134	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
135	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
136	Dic₁₃	—	4	4	no	—
137	C₂³×C₄	—	26	1	no	—
138	C₂³×C₄	C₂×#261	1	1	yes	characteristic
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	13	2	no	—
143	C₂²×C₈	—	13	2	no	—
144	C₂²×C₈	—	13	2	no	—
145	C₂²×C₈	—	13	2	no	—
146	C₂²×C₈	—	13	4	no	—
147	C₂²×C₈	—	13	1	no	—
148	C₂²×C₈	—	13	1	no	—
149	C₂²×C₈	#1057	1	4	yes	—
150	C₂²×C₈	C₂×#261	1	2	yes	—
151	C₂×C₄²	—	13	4	no	—
152	C₂×C₄²	—	13	2	no	—
153	C₂×C₄²	—	26	1	no	—
154	C₂×C₄²	—	26	2	no	—
155	M₃₂	—	26	8	no	—
156	M₃₂	—	26	4	no	—
157	M₃₂	—	26	4	no	—
158	C₂×C₁₆	—	13	8	no	—
159	C₂×C₁₆	—	26	8	no	—
160	#97	—	26	4	no	—
161	#97	—	26	4	no	—
162	C₂×C₁₃	—	2	1	no	—
163	C₂×C₁₃	—	2	2	no	—
164	C₂×C₁₃	—	2	1	no	—
165	C₂×C₁₃	#1375	1	4	yes	complemented
166	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
167	C₂×C₁₃	C₂×#347	1	2	yes	—
168	C₂⁴	#6118	1	1	yes	characteristic
169	C₂²×C₄	—	26	4	no	—
170	C₂²×C₄	—	26	2	no	—
171	C₂²×C₄	—	52	4	no	—
172	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
173	C₂²×C₄	#6118	1	1	yes	characteristic
174	C₂²×C₄	C₄×#261	1	1	yes	characteristic
175	C₂²×C₄	C₄×#261	1	1	yes	characteristic
176	C₂²×C₄	C₄⋊#261	1	2	yes	—
177	C₂²×C₄	C₂×#1057	1	2	yes	—
178	C₂²×C₄	#6122	1	1	yes	characteristic
179	C₂²×C₄	#6122	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊#261	1	2	yes	—
181	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	13	4	no	—
187	C₂×C₈	—	13	4	no	—
188	C₂×C₈	—	13	4	no	—
189	C₂×C₈	—	13	4	no	—
190	C₂×C₈	—	13	2	no	—
191	C₂×C₈	—	13	2	no	—
192	C₂×C₈	—	13	1	no	—
193	C₂×C₈	—	13	2	no	—
194	C₂×C₈	—	13	1	no	—
195	C₂×C₈	—	13	2	no	—
196	C₂×C₈	—	13	2	no	—
197	C₂×C₈	C₂×#1057	1	4	yes	—
198	C₄²	—	13	4	no	—
199	C₄²	—	26	4	no	—
200	C₄²	—	26	2	no	—
201	C₁₆	—	26	8	no	—
202	C₁₃	C₂×#1375	1	1	yes	characteristic, complemented, Sylow
203	C₂³	—	2	4	no	—
204	C₂³	C₄⋊#1057	1	2	yes	—
205	C₂³	#88110	1	1	yes	characteristic
206	C₂³	#88110	1	1	yes	characteristic
207	C₂³	#88111	1	2	yes	—
208	C₂³	C₂×#6118	1	1	yes	characteristic
209	C₂×C₄	—	26	4	no	—
210	C₂×C₄	—	52	4	no	—
211	C₂×C₄	—	52	8	no	—
212	C₂×C₄	C₄×#1057	1	2	yes	—
213	C₂×C₄	C₄×#1057	1	2	yes	—
214	C₂×C₄	C₄⋊#1057	1	2	yes	—
215	C₂×C₄	#88110	1	1	yes	characteristic
216	C₂×C₄	#88110	1	1	yes	characteristic
217	C₂×C₄	#88111	1	2	yes	—
218	C₂×C₄	#88112	1	2	yes	—
219	C₂×C₄	#88112	1	2	yes	—
220	C₂×C₄	(C₂×#261)⋊C₄	1	2	yes	—
221	C₂×C₄	(C₂×#261)⋊C₄	1	2	yes	—
222	C₂×C₄	C₂²⋊#1057	1	2	yes	—
223	C₂×C₄	C₂²⋊#1057	1	2	yes	—
224	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
225	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
226	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
227	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
228	C₂×C₄	C₂×#6122	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
230	C₈	—	2	4	no	—
231	C₈	—	13	2	no	—
232	C₈	—	13	4	no	—
233	C₈	—	13	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	2	no	—
236	C₂²	—	2	4	no	—
237	C₂²	—	2	4	no	—
238	C₂²	#11718262	1	4	yes	—
239	C₂²	#11718290	1	2	yes	—
240	C₂²	#11718290	1	2	yes	—
241	C₂²	C₂×C₄⋊#1057	1	1	yes	characteristic
242	C₂²	C₂×#88110	1	1	yes	characteristic
243	C₂²	C₂×#88111	1	1	yes	characteristic
244	C₄	—	52	4	no	—
245	C₄	#11718290	1	2	yes	—
246	C₄	#11718290	1	2	yes	—
247	C₄	C₂×C₄×#1057	1	1	yes	characteristic
248	C₄	C₂×#88112	1	1	yes	characteristic
249	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
250	C₄	C₂×C₂²⋊#1057	1	1	yes	characteristic
251	C₂	—	2	1	no	—
252	C₂	—	2	2	no	—
253	C₂	—	2	1	no	—
254	C₂	#13129878	1	4	yes	direct product factor
255	C₂	C₂×#11718290	1	1	yes	characteristic
256	C₂	C₂×#11718262	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₄×#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	#97
prime radical	C₂⁴×C₁₃	M₁₆
cosocle	C₂²×#1055	C₂³
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂×#1375
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13129878	C₂	direct (N × H)
9. C₂×#88106	C₄	semidirect
11. C₂²×#6092	C₄	semidirect
37. C₂×#6092	C₂×C₄	semidirect
165. C₂×C₁₃	#1375	semidirect
202. C₁₃	C₂×#1375	semidirect
254. C₂	#13129878	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88106	2
#13129878	2
C₂²×#88055	2
C₂×#1375	13

Subgroups — C2×#13129878 #16789056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129878 #16789056