Subgroups — C₂×D₁₃×#368 #16015969

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×#108	C₂	1	2	yes	maximal
3	C₂×#11718098	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718085	C₂	1	2	yes	maximal, complemented
5	D₁₃×#368	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×M₁₆×D₁₃	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#108	C₂²	1	2	yes	—
11	C₂×#88062	—	2	2	no	—
12	C₂×#88059	C₂²	1	2	yes	—
13	C₂²×#6090	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×D₁₃	C₄	1	4	yes	—
15	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
16	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
17	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
18	D₁₃×#108	—	2	4	no	—
19	D₁₃×#108	C₂²	1	8	yes	—
20	C₁₃×#368	C₂²	1	4	yes	complemented
21	#11718098	C₂²	1	4	yes	complemented
22	#11718085	C₂²	1	8	yes	complemented
23	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×#6099	—	2	2	no	—
27	C₂²×#1055	D₄	1	1	yes	characteristic
28	M₁₆×D₁₃	—	2	8	no	—
29	M₁₆×D₁₃	—	4	4	no	—
30	C₂×#6094	—	4	2	no	—
31	C₂×C₈×D₁₃	—	4	2	no	—
32	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₈×D₁₃	D₄	1	2	yes	—
36	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
37	C₂×C₈×D₁₃	Q₈	1	2	yes	—
38	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
39	C₂×C₈×D₁₃	C₂³	1	2	yes	—
40	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
43	C₁₃×#108	—	2	2	no	—
44	C₁₃×#108	C₂³	1	4	yes	—
45	#88062	—	2	8	no	—
46	#88059	—	2	2	no	—
47	#88059	C₂³	1	4	yes	—
48	C₂×#6090	C₂×C₄	1	2	yes	—
49	C₂×#6090	C₂×C₄	1	2	yes	—
50	C₂×#6090	C₂³	1	2	yes	—
51	C₁₆×D₁₃	C₂×C₄	1	8	yes	—
52	C₁₆×D₁₃	C₂×C₄	1	8	yes	—
53	C₂²×#368	—	13	1	no	maximal, Sylow
54	C₂³×D₁₃	Q₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	Q₁₆	1	1	yes	characteristic
57	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
58	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
61	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
62	C₂×C₄×D₁₃	D₈	1	2	yes	—
63	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
64	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
65	C₁₃×M₁₆	—	2	4	no	—
66	C₁₃×M₁₆	—	4	2	no	—
67	C₂×C₈×C₁₃	—	4	2	no	—
68	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
73	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
74	#6099	—	2	4	no	—
75	#6099	—	4	2	no	—
76	C₂×#1055	—	4	2	no	—
77	C₂×#1055	C₄⋊C₄	1	2	yes	—
78	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
79	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
80	C₂×#1055	C₂×D₄	1	2	yes	—
81	#6094	—	4	8	no	—
82	C₈×D₁₃	—	4	8	no	—
83	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
84	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
85	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
86	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
87	C₈×D₁₃	C₂²×C₄	1	2	yes	—
88	C₈×D₁₃	C₂²×C₄	1	2	yes	—
89	C₈×D₁₃	C₂×Q₈	1	2	yes	—
90	C₈×D₁₃	C₂×Q₈	1	2	yes	—
91	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
92	#6090	C₂²×C₄	1	4	yes	—
93	C₂³×C₁₆	—	13	1	no	—
94	C₂²×#108	—	13	2	no	—
95	C₂×#368	—	13	1	no	—
96	C₂×#368	—	13	2	no	—
97	C₂×#368	—	13	8	no	—
98	C₂×#368	D₁₃	1	1	yes	characteristic, direct product factor
99	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
100	C₂²×D₁₃	—	2	4	no	—
101	C₂²×D₁₃	#107	1	1	yes	characteristic
102	C₂²×D₁₃	#107	1	2	yes	—
103	C₂²×D₁₃	#107	1	1	yes	characteristic
104	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
111	C₂×Dic₁₃	#107	1	2	yes	—
112	C₂×Dic₁₃	#107	1	1	yes	characteristic
113	C₂×Dic₁₃	#107	1	1	yes	characteristic
114	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
115	C₄×D₁₃	#107	1	2	yes	—
116	C₄×D₁₃	#107	1	2	yes	—
117	C₄×D₁₃	#107	1	2	yes	—
118	C₄×D₁₃	#107	1	2	yes	—
119	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₄×D₁₃	C₂×D₈	1	2	yes	—
122	C₄×D₁₃	C₂×D₈	1	2	yes	—
123	C₈×C₁₃	—	4	4	no	—
124	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
127	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
128	#1055	—	4	4	no	—
129	#1055	C₂×C₄⋊C₄	1	2	yes	—
130	#1055	C₂×C₄⋊C₄	1	2	yes	—
131	C₂²×M₁₆	—	26	2	no	—
132	C₂³×C₈	—	13	1	no	—
133	C₂²×C₁₆	—	13	1	no	—
134	C₂²×C₁₆	—	13	2	no	—
135	C₂²×C₁₆	—	13	2	no	—
136	C₂²×C₁₆	—	13	4	no	—
137	C₂²×C₁₆	—	13	4	no	—
138	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
139	C₂×#108	—	13	2	no	—
140	C₂×#108	—	13	8	no	—
141	C₂×#108	—	26	4	no	—
142	C₂×#108	—	26	2	no	—
143	C₂×#108	C₂×D₁₃	1	2	yes	—
144	#368	—	13	4	no	—
145	#368	—	13	8	no	—
146	#368	C₂×D₁₃	1	4	yes	direct product factor
147	C₂²×C₁₃	—	2	2	no	—
148	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
149	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
150	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
151	C₂×D₁₃	—	2	2	no	—
152	C₂×D₁₃	—	2	4	no	—
153	C₂×D₁₃	—	2	4	no	—
154	C₂×D₁₃	#368	1	4	yes	direct product factor
155	C₂×D₁₃	C₂×#107	1	2	yes	—
156	C₂×D₁₃	C₂×#107	1	2	yes	—
157	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
158	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
159	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
161	Dic₁₃	C₂×#107	1	2	yes	—
162	Dic₁₃	C₂×#107	1	2	yes	—
163	C₂³×C₄	—	13	1	no	—
164	C₂×M₁₆	—	2	2	no	—
165	C₂×M₁₆	—	26	8	no	—
166	C₂×M₁₆	—	26	2	no	—
167	C₂×M₁₆	—	52	2	no	—
168	C₂×M₁₆	—	52	4	no	—
169	C₂²×C₈	—	13	1	no	—
170	C₂²×C₈	—	13	1	no	—
171	C₂²×C₈	—	13	1	no	—
172	C₂²×C₈	—	13	2	no	—
173	C₂²×C₈	—	13	2	no	—
174	C₂²×C₈	—	13	1	no	—
175	C₂²×C₈	—	13	1	no	—
176	C₂²×C₈	—	13	2	no	—
177	C₂²×C₈	—	13	2	no	—
178	C₂²×C₈	—	52	2	no	—
179	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
180	C₂×C₁₆	—	13	2	no	—
181	C₂×C₁₆	—	13	2	no	—
182	C₂×C₁₆	—	13	2	no	—
183	C₂×C₁₆	—	13	8	no	—
184	C₂×C₁₆	—	13	8	no	—
185	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
186	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
187	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
188	#108	—	2	2	no	—
189	#108	—	13	4	no	—
190	#108	—	26	8	no	—
191	#108	—	26	2	no	—
192	#108	C₂²×D₁₃	1	4	yes	—
193	C₂×C₁₃	—	2	1	no	—
194	C₂×C₁₃	—	2	1	no	—
195	C₂×C₁₃	C₂×#368	1	2	yes	complemented
196	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
197	D₁₃	—	2	2	no	—
198	D₁₃	C₂×#368	1	4	yes	direct product factor
199	C₂⁴	—	13	1	no	—
200	C₂²×C₄	—	13	1	no	—
201	C₂²×C₄	—	13	1	no	—
202	C₂²×C₄	—	13	2	no	—
203	C₂²×C₄	—	13	1	no	—
204	C₂²×C₄	—	13	2	no	—
205	C₂²×C₄	—	13	1	no	—
206	C₂²×C₄	—	13	1	no	—
207	C₂²×C₄	—	13	2	no	—
208	C₂²×C₄	—	13	2	no	—
209	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
210	M₁₆	—	2	4	no	—
211	M₁₆	—	4	2	no	—
212	M₁₆	—	26	4	no	—
213	M₁₆	—	52	8	no	—
214	M₁₆	—	52	2	no	—
215	C₂×C₈	—	4	2	no	—
216	C₂×C₈	—	13	1	no	—
217	C₂×C₈	—	13	1	no	—
218	C₂×C₈	—	13	2	no	—
219	C₂×C₈	—	13	2	no	—
220	C₂×C₈	—	13	2	no	—
221	C₂×C₈	—	13	2	no	—
222	C₂×C₈	—	13	2	no	—
223	C₂×C₈	—	13	2	no	—
224	C₂×C₈	—	13	2	no	—
225	C₂×C₈	—	13	2	no	—
226	C₂×C₈	—	13	2	no	—
227	C₂×C₈	—	13	2	no	—
228	C₂×C₈	—	52	8	no	—
229	C₂×C₈	—	52	2	no	—
230	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
231	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
232	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
233	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
234	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
235	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
236	C₁₆	—	13	4	no	—
237	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
238	C₁₃	C₂²×#368	1	1	yes	characteristic, complemented, Sylow
239	C₂³	—	13	1	no	—
240	C₂³	—	13	2	no	—
241	C₂³	—	13	2	no	—
242	C₂³	—	13	1	no	—
243	C₂³	—	26	4	no	—
244	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
245	C₂×C₄	—	13	2	no	—
246	C₂×C₄	—	13	2	no	—
247	C₂×C₄	—	13	1	no	—
248	C₂×C₄	—	13	1	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	2	no	—
251	C₂×C₄	—	13	2	no	—
252	C₂×C₄	—	13	2	no	—
253	C₂×C₄	—	13	2	no	—
254	C₂×C₄	—	13	2	no	—
255	C₂×C₄	—	13	2	no	—
256	C₂×C₄	—	13	2	no	—
257	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
258	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
259	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
260	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
261	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
262	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
263	C₈	—	4	4	no	—
264	C₈	—	13	2	no	—
265	C₈	—	13	2	no	—
266	C₈	—	52	4	no	—
267	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
268	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
269	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
270	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
271	C₂²	—	2	2	no	—
272	C₂²	—	13	2	no	—
273	C₂²	—	13	4	no	—
274	C₂²	—	13	2	no	—
275	C₂²	—	26	4	no	—
276	C₂²	—	26	4	no	—
277	C₂²	—	26	2	no	—
278	C₂²	D₁₃×#107	1	1	yes	characteristic
279	C₂²	D₁₃×#107	1	1	yes	characteristic
280	C₂²	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
281	C₄	—	13	2	no	—
282	C₄	—	13	2	no	—
283	C₄	D₁₃×#107	1	1	yes	characteristic
284	C₄	D₁₃×#107	1	1	yes	characteristic
285	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
286	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
287	C₂	—	2	1	no	—
288	C₂	—	2	1	no	—
289	C₂	—	13	4	no	—
290	C₂	—	26	2	no	—
291	C₂	D₁₃×#368	1	2	yes	direct product factor
292	C₂	C₂×D₁₃×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#368	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×D₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#368	D₁₃
hypocenter	C₁₃	C₂²×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
3. C₂×#11718098	C₂	semidirect
4. C₂×#11718085	C₂	semidirect
5. D₁₃×#368	C₂	direct (N × H)
6. C₂×C₁₃×#368	C₂	semidirect
20. C₁₃×#368	C₂²	semidirect
21. #11718098	C₂²	semidirect
22. #11718085	C₂²	semidirect
98. C₂×#368	D₁₃	direct (N × H)
146. #368	C₂×D₁₃	direct (N × H)
154. C₂×D₁₃	#368	direct (N × H)
195. C₂×C₁₃	C₂×#368	semidirect
198. D₁₃	C₂×#368	direct (N × H)
238. C₁₃	C₂²×#368	semidirect
291. C₂	D₁₃×#368	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×C₁₆×D₁₃	2
C₂×D₁₃×#108	2
C₂×#11718098	2
C₂×#11718085	2
D₁₃×#368	2
C₂×C₁₃×#368	2
C₂²×#368	13

Subgroups — C2×D13×#368 #16015969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#368 #16015969