Subgroups — C₂×#13131053 #16806747

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 304 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×#11718262	C₂	1	2	yes	maximal, complemented
3	#13131053	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718232	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
9	C₂×#88106	C₂²	1	4	yes	—
10	D₁₃⋊M₃₂	C₄	1	8	yes	complemented
11	D₁₃⋊M₃₂	C₂²	1	8	yes	—
12	C₂×#88098	C₄	1	4	yes	complemented
13	C₂×D₁₃⋊C₁₆	C₄	1	4	yes	complemented
14	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
15	C₂×#88055	C₄	1	1	yes	characteristic
16	C₂×#88055	C₂²	1	1	yes	characteristic
17	C₂×#88043	C₂²	1	1	yes	characteristic
18	D₁₃×#97	C₄	1	4	yes	—
19	D₁₃×#97	C₂²	1	4	yes	—
20	#11718262	C₂²	1	8	yes	complemented
21	#11718232	C₂²	1	8	yes	complemented
22	C₂²×C₄×D₁₃	—	2	1	no	—
23	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	—	2	1	no	—
28	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂³	1	1	yes	characteristic
31	C₂×C₈×D₁₃	—	2	1	no	—
32	C₂×C₈×D₁₃	—	2	2	no	—
33	C₂×C₈×D₁₃	—	2	1	no	—
34	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
39	C₂×C₈×D₁₃	C₂³	1	2	yes	—
40	C₄²×D₁₃	—	2	2	no	—
41	C₄²×D₁₃	C₂×C₄	1	4	yes	—
42	#88106	C₂×C₄	1	8	yes	complemented
43	#88106	C₂³	1	8	yes	—
44	C₂×#6092	C₂×C₄	1	8	yes	complemented
45	#88098	C₂×C₄	1	16	yes	complemented
46	D₁₃⋊C₁₆	C₂×C₄	1	16	yes	complemented
47	C₁₃×#97	C₂×C₄	1	4	yes	—
48	#88055	C₂×C₄	1	4	yes	—
49	#88055	C₂×C₄	1	2	yes	—
50	#88055	C₂³	1	2	yes	—
51	#88043	C₂×C₄	1	2	yes	—
52	#88043	C₂³	1	2	yes	—
53	C₂²×#347	—	13	1	no	maximal, Sylow
54	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×Dic₁₃	—	2	1	no	—
58	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
59	C₂×C₄×D₁₃	—	2	4	no	—
60	C₂×C₄×D₁₃	—	4	4	no	—
61	C₂×C₄×D₁₃	C₄²	1	2	yes	—
62	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
63	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
64	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
65	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
66	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
67	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
68	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₁₃	—	2	1	no	—
70	C₂×C₈×C₁₃	—	2	1	no	—
71	C₂×C₈×C₁₃	C₄²	1	2	yes	—
72	C₂×C₈×C₁₃	C₄²	1	2	yes	—
73	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
75	C₄²×C₁₃	—	2	1	no	—
76	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
77	C₄×Dic₁₃	—	2	1	no	—
78	C₄×Dic₁₃	—	2	4	no	—
79	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
80	C₂×#1055	—	2	1	no	—
81	C₂×#1055	—	2	1	no	—
82	C₂×#1055	C₂²×C₄	1	2	yes	—
83	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
84	C₂×#1055	C₂²×C₄	1	2	yes	—
85	C₂×#1055	C₂²×C₄	1	2	yes	—
86	C₂×#1055	C₂⁴	1	1	yes	characteristic
87	C₈×D₁₃	—	2	4	no	—
88	C₈×D₁₃	—	2	4	no	—
89	C₈×D₁₃	C₄²	1	4	yes	—
90	C₈×D₁₃	C₄²	1	4	yes	—
91	C₈×D₁₃	C₂²×C₄	1	4	yes	—
92	C₈×D₁₃	C₂²×C₄	1	4	yes	—
93	#6092	C₂²×C₄	1	16	yes	complemented
94	C₂²×M₃₂	—	13	2	no	—
95	C₂²×#97	—	13	1	no	—
96	C₂×#347	—	13	2	no	—
97	C₂×#347	—	13	8	no	—
98	C₂×#347	—	13	2	no	—
99	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
100	C₂²×D₁₃	—	2	4	no	—
101	C₂²×D₁₃	#97	1	1	yes	characteristic
102	C₂²×D₁₃	#97	1	2	yes	—
103	C₂²×D₁₃	#97	1	1	yes	characteristic
104	C₂²×D₁₃	C₂×M₁₆	1	2	yes	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	4	2	no	—
107	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
113	C₂×Dic₁₃	—	2	2	no	—
114	C₂×Dic₁₃	—	4	2	no	—
115	C₂×Dic₁₃	#97	1	2	yes	—
116	C₂×Dic₁₃	#97	1	1	yes	characteristic
117	C₂×Dic₁₃	#97	1	1	yes	characteristic
118	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
119	C₄×D₁₃	—	4	8	no	—
120	C₄×D₁₃	#97	1	2	yes	—
121	C₄×D₁₃	#97	1	2	yes	—
122	C₄×D₁₃	#97	1	2	yes	—
123	C₄×D₁₃	#97	1	2	yes	—
124	C₄×D₁₃	C₂×C₄²	1	2	yes	—
125	C₄×D₁₃	C₂×C₄²	1	2	yes	—
126	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
127	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
128	C₈×C₁₃	—	2	2	no	—
129	C₈×C₁₃	C₂×C₄²	1	4	yes	—
130	#1055	—	2	2	no	—
131	#1055	C₂×C₄²	1	2	yes	—
132	#1055	C₂³×C₄	1	2	yes	—
133	C₂³×C₈	—	13	1	no	—
134	C₂³×C₈	—	13	1	no	—
135	C₂²×C₄²	—	13	1	no	—
136	C₂×M₃₂	—	13	8	no	—
137	C₂×M₃₂	—	13	4	no	—
138	C₂×M₃₂	—	13	4	no	—
139	C₂×M₃₂	—	13	8	no	—
140	C₂²×C₁₆	—	13	4	no	—
141	C₂×#97	—	13	1	no	—
142	C₂×#97	—	13	1	no	—
143	C₂×#97	—	13	1	no	—
144	C₂×#97	—	13	4	no	—
145	C₂×#97	—	13	4	no	—
146	C₂×#97	#261	1	1	yes	characteristic
147	#347	—	13	8	no	—
148	#347	—	13	8	no	—
149	C₂²×C₁₃	—	2	2	no	—
150	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
151	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
152	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
153	C₂×D₁₃	—	2	2	no	—
154	C₂×D₁₃	—	2	4	no	—
155	C₂×D₁₃	—	2	4	no	—
156	C₂×D₁₃	#347	1	4	yes	complemented
157	C₂×D₁₃	C₂×#97	1	2	yes	—
158	C₂×D₁₃	C₂×#97	1	2	yes	—
159	C₄×C₁₃	—	4	2	no	—
160	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
161	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
162	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
163	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
164	Dic₁₃	—	4	2	no	—
165	Dic₁₃	C₂×#97	1	2	yes	—
166	Dic₁₃	C₂×#97	1	2	yes	—
167	C₂³×C₄	—	13	1	no	—
168	C₂³×C₄	—	26	1	no	—
169	C₂²×C₈	—	13	1	no	—
170	C₂²×C₈	—	13	2	no	—
171	C₂²×C₈	—	13	4	no	—
172	C₂²×C₈	—	13	2	no	—
173	C₂²×C₈	—	13	2	no	—
174	C₂²×C₈	—	13	2	no	—
175	C₂²×C₈	—	13	1	no	—
176	C₂²×C₈	—	13	4	no	—
177	C₂²×C₈	—	26	1	no	—
178	C₂²×C₈	—	26	1	no	—
179	C₂²×C₈	—	26	2	no	—
180	C₂²×C₈	C₂×#261	1	1	yes	characteristic
181	C₂²×C₈	C₂×#261	1	1	yes	characteristic
182	C₂×C₄²	—	13	1	no	—
183	C₂×C₄²	—	13	4	no	—
184	C₂×C₄²	—	26	2	no	—
185	C₂×C₄²	—	26	1	no	—
186	C₂×C₄²	C₂×#261	1	1	yes	characteristic
187	M₃₂	—	13	16	no	—
188	M₃₂	—	13	8	no	—
189	M₃₂	—	13	8	no	—
190	C₂×C₁₆	—	13	16	no	—
191	C₂×C₁₆	—	13	8	no	—
192	#97	—	13	2	no	—
193	#97	—	13	2	no	—
194	#97	—	13	4	no	—
195	#97	—	13	2	no	—
196	#97	—	13	2	no	—
197	#97	C₂×#261	1	4	yes	—
198	C₂×C₁₃	—	2	1	no	—
199	C₂×C₁₃	—	2	1	no	—
200	C₂×C₁₃	C₂×#347	1	2	yes	complemented
201	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
202	D₁₃	—	2	2	no	—
203	D₁₃	C₂×#347	1	4	yes	complemented
204	C₂⁴	—	13	1	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	—	13	1	no	—
207	C₂²×C₄	—	13	2	no	—
208	C₂²×C₄	—	13	1	no	—
209	C₂²×C₄	—	13	2	no	—
210	C₂²×C₄	—	13	1	no	—
211	C₂²×C₄	—	13	2	no	—
212	C₂²×C₄	—	13	1	no	—
213	C₂²×C₄	—	13	1	no	—
214	C₂²×C₄	—	13	2	no	—
215	C₂²×C₄	—	26	4	no	—
216	C₂²×C₄	—	26	1	no	—
217	C₂²×C₄	—	52	4	no	—
218	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	2	1	no	—
221	C₂×C₈	—	13	2	no	—
222	C₂×C₈	—	13	2	no	—
223	C₂×C₈	—	13	1	no	—
224	C₂×C₈	—	13	1	no	—
225	C₂×C₈	—	13	4	no	—
226	C₂×C₈	—	13	4	no	—
227	C₂×C₈	—	13	4	no	—
228	C₂×C₈	—	13	4	no	—
229	C₂×C₈	—	13	2	no	—
230	C₂×C₈	—	26	4	no	—
231	C₂×C₈	—	26	4	no	—
232	C₂×C₈	—	26	1	no	—
233	C₂×C₈	—	26	1	no	—
234	C₂×C₈	C₄×#261	1	2	yes	—
235	C₂×C₈	C₄×#261	1	2	yes	—
236	C₂×C₈	C₂²×#261	1	2	yes	—
237	C₂×C₈	C₂²×#261	1	2	yes	—
238	C₄²	—	2	1	no	—
239	C₄²	—	13	2	no	—
240	C₄²	—	26	4	no	—
241	C₄²	—	26	1	no	—
242	C₄²	C₂²×#261	1	2	yes	—
243	C₁₆	—	13	16	no	—
244	C₁₃	C₂²×#347	1	1	yes	characteristic, complemented, Sylow
245	C₂³	—	13	1	no	—
246	C₂³	—	13	2	no	—
247	C₂³	—	13	1	no	—
248	C₂³	—	13	2	no	—
249	C₂³	—	26	4	no	—
250	C₂³	D₁₃⋊M₁₆	1	1	yes	characteristic
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	13	2	no	—
254	C₂×C₄	—	13	1	no	—
255	C₂×C₄	—	13	1	no	—
256	C₂×C₄	—	13	2	no	—
257	C₂×C₄	—	13	2	no	—
258	C₂×C₄	—	13	2	no	—
259	C₂×C₄	—	13	2	no	—
260	C₂×C₄	—	13	2	no	—
261	C₂×C₄	—	13	2	no	—
262	C₂×C₄	—	13	2	no	—
263	C₂×C₄	—	13	2	no	—
264	C₂×C₄	—	13	2	no	—
265	C₂×C₄	—	26	2	no	—
266	C₂×C₄	—	52	8	no	—
267	C₂×C₄	—	52	2	no	—
268	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
269	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
270	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
271	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
272	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
273	C₂×C₄	C₂³×#261	1	1	yes	characteristic
274	C₈	—	2	2	no	—
275	C₈	—	13	2	no	—
276	C₈	—	13	2	no	—
277	C₈	—	26	2	no	—
278	C₈	C₂×C₄×#261	1	4	yes	—
279	C₂²	—	2	2	no	—
280	C₂²	—	13	4	no	—
281	C₂²	—	13	2	no	—
282	C₂²	—	13	2	no	—
283	C₂²	—	26	4	no	—
284	C₂²	—	26	4	no	—
285	C₂²	—	26	2	no	—
286	C₂²	#11719047	1	1	yes	characteristic
287	C₂²	#11719047	1	1	yes	characteristic
288	C₂²	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
289	C₄	—	4	2	no	—
290	C₄	—	13	2	no	—
291	C₄	—	13	2	no	—
292	C₄	—	52	2	no	—
293	C₄	#11719047	1	1	yes	characteristic
294	C₄	#11719047	1	1	yes	characteristic
295	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
296	C₄	C₂²×C₄×#261	1	1	yes	characteristic
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	13	4	no	—
300	C₂	—	26	2	no	—
301	C₂	#13131053	1	2	yes	direct product factor
302	C₂	C₂×#11719047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×#97	#261
hypocenter	C₁₃	C₂²×#347
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. C₂×#11718262	C₂	semidirect
3. #13131053	C₂	direct (N × H)
4. C₂×#11718232	C₂	semidirect
10. D₁₃⋊M₃₂	C₄	semidirect
12. C₂×#88098	C₄	semidirect
13. C₂×D₁₃⋊C₁₆	C₄	semidirect
20. #11718262	C₂²	semidirect
21. #11718232	C₂²	semidirect
42. #88106	C₂×C₄	semidirect
44. C₂×#6092	C₂×C₄	semidirect
45. #88098	C₂×C₄	semidirect
46. D₁₃⋊C₁₆	C₂×C₄	semidirect
93. #6092	C₂²×C₄	semidirect
156. C₂×D₁₃	#347	semidirect
200. C₂×C₁₃	C₂×#347	semidirect
203. D₁₃	C₂×#347	semidirect
244. C₁₃	C₂²×#347	semidirect
301. C₂	#13131053	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×D₁₃⋊M₃₂	2
C₂×#11718262	2
#13131053	2
C₂×#11718232	2
C₂×D₁₃×#97	2
C₂²×#347	13

Subgroups — C2×#13131053 #16806747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13131053 #16806747