Subgroups — #15778118

Order 3328.

452 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	#13116521	C₂	1	1	yes	maximal, characteristic
2	#13116501	C₂	1	1	yes	maximal, characteristic
3	#13114636	C₂	1	2	yes	maximal, complemented
4	#13112965	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#131	C₄	1	1	yes	characteristic, complemented
7	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
8	C₁₃×#532	C₂²	1	1	yes	characteristic
9	C₁₃×#435	—	2	2	no	—
10	C₁₃×#435	—	2	2	no	—
11	C₁₃×#423	C₄	1	1	yes	characteristic, complemented
12	C₁₃×#408	C₄	1	1	yes	characteristic, complemented
13	C₁₃×#408	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#97	C₄	1	1	yes	characteristic, complemented
15	#11718901	C₂²	1	2	yes	—
16	#11718898	C₂²	1	2	yes	—
17	#11718762	—	2	2	no	—
18	#11718148	—	2	2	no	—
19	#11718140	C₄	1	2	yes	complemented
20	#11718137	C₄	1	2	yes	—
21	#11718134	C₄	1	2	yes	complemented
22	#11718133	C₄	1	2	yes	—
23	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
25	C₁₃×#131	—	4	2	no	—
26	C₁₃×#131	—	4	2	no	—
27	C₂×C₁₃×M₁₆	—	2	1	no	—
28	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₃	D₄	1	2	yes	—
35	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
37	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
38	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
39	C₁₃×#121	—	2	2	no	—
40	C₄×D₄×C₁₃	—	2	2	no	—
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	#88180	—	2	2	no	—
43	C₂×#6099	—	2	2	no	—
44	C₁₃×C₄⋊C₈	—	2	2	no	—
45	C₁₃×C₂²⋊C₈	—	2	2	no	—
46	C₁₃×C₂²⋊C₈	—	2	2	no	—
47	C₁₃×#97	—	2	1	no	—
48	C₁₃×#97	—	2	1	no	—
49	#88076	C₂×C₄	1	4	yes	—
50	#88074	—	2	2	no	—
51	#88074	C₂×C₄	1	4	yes	—
52	#88073	—	2	2	no	—
53	#88055	—	4	2	no	—
54	C₈×Dic₁₃	—	4	2	no	—
55	#12634	—	13	1	no	maximal, Sylow
56	C₁₃×#41	—	4	1	no	—
57	C₁₃×#41	—	4	1	no	—
58	C₁₃×#41	—	4	1	no	—
59	C₁₃×#41	—	4	1	no	—
60	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
61	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂×D₄×C₁₃	—	2	1	no	—
63	C₂×D₄×C₁₃	—	2	2	no	—
64	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
65	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×D₄×C₁₃	#41	1	2	yes	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
71	C₁₃×M₁₆	—	4	1	no	—
72	C₁₃×M₁₆	—	4	2	no	—
73	C₁₃×M₁₆	—	4	2	no	—
74	C₁₃×M₁₆	—	4	1	no	—
75	C₂×C₈×C₁₃	—	2	2	no	—
76	C₂×C₈×C₁₃	—	2	2	no	—
77	C₂×C₈×C₁₃	—	2	2	no	—
78	C₂×C₈×C₁₃	—	2	1	no	—
79	C₂×C₈×C₁₃	—	2	1	no	—
80	C₂×C₈×C₁₃	—	4	2	no	—
81	C₂×C₈×C₁₃	—	4	1	no	—
82	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
84	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₄²×C₁₃	—	2	1	no	—
89	C₄²×C₁₃	C₄²	1	1	yes	characteristic
90	C₄²×C₁₃	C₄²	1	1	yes	characteristic
91	C₂²⋊Dic₁₃	—	2	4	no	—
92	C₄⋊Dic₁₃	—	4	2	no	—
93	C₄×Dic₁₃	—	4	2	no	—
94	#6099	—	2	4	no	—
95	#6099	—	4	2	no	—
96	C₂×#1055	—	4	2	no	—
97	#2932	D₁₃	1	1	yes	characteristic
98	#2132	—	13	1	no	—
99	#2126	—	13	1	no	—
100	#1757	—	13	2	no	—
101	#1395	—	13	2	no	—
102	C₂³×C₁₃	—	2	1	no	—
103	C₂³×C₁₃	#117	1	1	yes	characteristic
104	C₂³×C₁₃	C₄×D₄	1	2	yes	—
105	Q₈×C₁₃	—	4	1	no	—
106	Q₈×C₁₃	—	4	1	no	—
107	D₄×C₁₃	—	4	1	no	—
108	D₄×C₁₃	—	4	2	no	—
109	D₄×C₁₃	—	4	1	no	—
110	D₄×C₁₃	—	4	2	no	—
111	D₄×C₁₃	—	8	2	no	—
112	C₂×C₄×C₁₃	—	2	2	no	—
113	C₂×C₄×C₁₃	—	2	1	no	—
114	C₂×C₄×C₁₃	—	2	2	no	—
115	C₂×C₄×C₁₃	—	2	1	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	1	no	—
119	C₂×C₄×C₁₃	—	4	1	no	—
120	C₂×C₄×C₁₃	—	4	1	no	—
121	C₂×C₄×C₁₃	—	8	1	no	—
122	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
125	C₂×Dic₁₃	—	4	4	no	—
126	C₈×C₁₃	—	2	1	no	—
127	C₈×C₁₃	—	2	2	no	—
128	C₈×C₁₃	—	4	1	no	—
129	C₈×C₁₃	—	4	1	no	—
130	C₈×C₁₃	#99	1	2	yes	—
131	#1055	—	4	4	no	—
132	C₂×#131	Dic₁₃	1	1	yes	characteristic, complemented
133	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
134	#532	C₂×D₁₃	1	1	yes	characteristic
135	#435	—	2	2	no	—
136	#435	—	2	2	no	—
137	#423	Dic₁₃	1	1	yes	characteristic, complemented
138	#413	—	13	2	no	—
139	#410	—	13	2	no	—
140	#408	Dic₁₃	1	1	yes	characteristic, complemented
141	#408	C₂×D₁₃	1	1	yes	characteristic
142	#405	—	26	2	no	—
143	C₂×#97	Dic₁₃	1	1	yes	characteristic, complemented
144	#356	—	13	2	no	—
145	#355	—	13	2	no	—
146	#354	—	13	2	no	—
147	#353	—	13	2	no	—
148	#344	—	26	2	no	—
149	C₂²×C₁₃	—	2	2	no	—
150	C₂²×C₁₃	—	2	1	no	—
151	C₂²×C₁₃	—	4	1	no	—
152	C₂²×C₁₃	—	4	2	no	—
153	C₂²×C₁₃	—	4	2	no	—
154	C₂²×C₁₃	—	4	1	no	—
155	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
156	C₄×C₁₃	—	2	2	no	—
157	C₄×C₁₃	—	2	1	no	—
158	C₄×C₁₃	—	4	1	no	—
159	C₄×C₁₃	—	4	1	no	—
160	C₄×C₁₃	—	4	1	no	—
161	C₄×C₁₃	C₂×#99	1	1	yes	characteristic
162	C₄×C₁₃	#410	1	1	yes	characteristic
163	Dic₁₃	—	8	4	no	—
164	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
165	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
166	#131	—	4	2	no	—
167	#131	—	4	2	no	—
168	C₂×M₁₆	—	2	1	no	—
169	C₂×M₁₆	—	26	2	no	—
170	C₂×M₁₆	C₂×Dic₁₃	1	1	yes	characteristic
171	C₂×M₁₆	C₂×Dic₁₃	1	1	yes	characteristic
172	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
175	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
176	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
177	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
178	#127	C₄×D₁₃	1	1	yes	characteristic
179	#124	C₄×D₁₃	1	1	yes	characteristic
180	#124	C₄×D₁₃	1	1	yes	characteristic
181	#121	—	2	2	no	—
182	C₄×D₄	—	2	2	no	—
183	#117	—	26	2	no	—
184	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
185	C₄⋊C₈	—	2	2	no	—
186	#101	—	13	4	no	—
187	#100	—	26	2	no	—
188	#99	—	13	4	no	—
189	#99	—	26	2	no	—
190	C₂²⋊C₈	—	2	2	no	—
191	C₂²⋊C₈	—	2	2	no	—
192	#97	—	2	1	no	—
193	#97	—	2	1	no	—
194	#97	—	52	2	no	—
195	C₄×C₈	—	52	2	no	—
196	C₂×C₁₃	—	2	1	no	—
197	C₂×C₁₃	—	4	2	no	—
198	C₂×C₁₃	—	4	1	no	—
199	C₂×C₁₃	—	8	1	no	—
200	C₂×C₁₃	C₄×#99	1	1	yes	characteristic
201	#41	—	4	1	no	—
202	#41	—	4	1	no	—
203	#41	—	4	1	no	—
204	#41	—	4	1	no	—
205	C₂×Q₈	C₄×Dic₁₃	1	1	yes	characteristic
206	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
207	C₂×D₄	—	2	1	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	C₄×Dic₁₃	1	1	yes	characteristic
210	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
211	C₂×D₄	#6127	1	2	yes	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
215	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
216	M₁₆	—	4	1	no	—
217	M₁₆	—	4	2	no	—
218	M₁₆	—	4	2	no	—
219	M₁₆	—	4	1	no	—
220	M₁₆	—	26	4	no	—
221	M₁₆	—	52	2	no	—
222	C₂×C₈	—	2	2	no	—
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	4	2	no	—
228	C₂×C₈	—	4	1	no	—
229	C₂×C₈	—	52	2	no	—
230	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
231	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
232	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	52	2	no	—
235	C₂²⋊C₄	—	2	2	no	—
236	C₂²⋊C₄	—	2	2	no	—
237	C₂²⋊C₄	—	26	4	no	—
238	C₄²	—	2	1	no	—
239	C₄²	—	52	2	no	—
240	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
241	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
242	C₁₃	#12634	1	1	yes	characteristic, complemented, Sylow
243	C₂³	—	2	1	no	—
244	C₂³	#88180	1	1	yes	characteristic
245	C₂³	C₄×C₂²⋊D₁₃	1	2	yes	—
246	Q₈	—	4	1	no	—
247	Q₈	—	4	1	no	—
248	D₄	—	4	1	no	—
249	D₄	—	4	2	no	—
250	D₄	—	4	1	no	—
251	D₄	—	4	2	no	—
252	D₄	—	8	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	8	1	no	—
263	C₂×C₄	—	52	4	no	—
264	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
265	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
266	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
267	C₈	—	2	1	no	—
268	C₈	—	2	2	no	—
269	C₈	—	4	1	no	—
270	C₈	—	4	1	no	—
271	C₈	—	52	4	no	—
272	C₈	#88074	1	2	yes	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	1	no	—
275	C₂²	—	4	1	no	—
276	C₂²	—	4	2	no	—
277	C₂²	—	4	2	no	—
278	C₂²	—	4	1	no	—
279	C₂²	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
280	C₄	—	2	2	no	—
281	C₄	—	2	1	no	—
282	C₄	—	4	1	no	—
283	C₄	—	4	1	no	—
284	C₄	—	4	1	no	—
285	C₄	—	104	4	no	—
286	C₄	C₂×#88074	1	1	yes	characteristic
287	C₄	#11718901	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	4	2	no	—
290	C₂	—	4	1	no	—
291	C₂	—	8	1	no	—
292	C₂	C₄×#88074	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#88074
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×#41	C₂²×D₁₃
Fitting	C₁₃×#2932	C₂
socle	C₂×C₁₃	C₄×#99
prime radical	C₁₃×#532	C₂²
cosocle	C₂×C₁₃×#41	C₂³
hypercenter	#2932	D₁₃
hypocenter	C₁₃	#12634
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×#131 ◁ #2932

Complements

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

N	H ≅ G/N	type
3. #13114636	C₂	semidirect
4. #13112965	C₂	semidirect
6. C₂×C₁₃×#131	C₄	semidirect
11. C₁₃×#423	C₄	semidirect
12. C₁₃×#408	C₄	semidirect
14. C₂×C₁₃×#97	C₄	semidirect
19. #11718140	C₄	semidirect
21. #11718134	C₄	semidirect
132. C₂×#131	Dic₁₃	semidirect
137. #423	Dic₁₃	semidirect
140. #408	Dic₁₃	semidirect
143. C₂×#97	Dic₁₃	semidirect
242. C₁₃	#12634	semidirect

Maximal subgroups

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

subgroup	index
#13116521	2
#13116501	2
#13114636	2
#13112965	2
C₁₃×#2932	2
#12634	13