Subgroups — #13129263

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719538	C₂	1	2	yes	maximal, complemented
3	#11719535	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719530	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719440	C₂	1	2	yes	maximal, complemented
6	#11719425	C₂	1	2	yes	maximal, complemented
7	#11719384	C₂	1	2	yes	maximal, complemented
8	#11719375	C₂	1	2	yes	maximal, complemented
9	#11719320	C₂	1	4	yes	maximal, complemented
10	#11719318	C₂	1	4	yes	maximal, complemented
11	#11719270	C₂	1	2	yes	maximal, complemented
12	#11719257	C₂	1	2	yes	maximal, complemented
13	#11719255	C₂	1	2	yes	maximal, complemented
14	#11719246	C₂	1	2	yes	maximal, complemented
15	#11719184	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂×#6127	C₂²	1	2	yes	—
19	C₂²×D₅₂	C₂²	1	1	yes	characteristic
20	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#121	C₂²	1	2	yes	—
26	C₁₃×#121	C₂²	1	2	yes	complemented
27	C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	#88201	C₂²	1	2	yes	—
31	#88200	C₂²	1	4	yes	complemented
32	#88198	C₂²	1	2	yes	complemented
33	#88194	C₂²	1	2	yes	—
34	#88193	C₂²	1	4	yes	complemented
35	#88193	C₂²	1	4	yes	complemented
36	#88193	C₂²	1	4	yes	complemented
37	#88193	C₂²	1	4	yes	complemented
38	#88192	C₂²	1	4	yes	complemented
39	#88191	C₂²	1	4	yes	—
40	#88191	C₂²	1	2	yes	—
41	#88191	C₂²	1	2	yes	—
42	#88190	C₂²	1	2	yes	—
43	#88189	C₂²	1	4	yes	—
44	#88189	C₂²	1	2	yes	—
45	#88189	C₂²	1	2	yes	complemented
46	#88184	C₂²	1	2	yes	—
47	#88184	C₂²	1	2	yes	—
48	#88184	C₂²	1	2	yes	—
49	#88183	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
51	#88180	C₂²	1	1	yes	characteristic
52	#88180	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
54	#88178	C₂²	1	2	yes	—
55	#88178	C₂²	1	2	yes	complemented
56	#88178	C₂²	1	2	yes	complemented
57	#88152	C₂²	1	4	yes	complemented
58	#88150	C₂²	1	4	yes	complemented
59	#88148	C₂²	1	4	yes	—
60	#88143	C₂²	1	4	yes	complemented
61	#88139	C₂²	1	4	yes	complemented
62	#88138	C₂²	1	4	yes	—
63	#88137	C₂²	1	4	yes	complemented
64	#88135	C₂²	1	4	yes	complemented
65	#88135	C₂²	1	4	yes	complemented
66	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
67	#88133	C₂²	1	4	yes	—
68	#88131	C₂²	1	4	yes	complemented
69	#88130	C₂²	1	4	yes	complemented
70	#88129	C₂²	1	2	yes	—
71	C₄×D₅₂	C₂²	1	2	yes	—
72	#88126	C₂²	1	4	yes	complemented
73	#88124	C₂²	1	2	yes	complemented
74	C₄×Dic₂₆	C₂²	1	2	yes	complemented
75	C₂³×D₁₃	C₂³	1	2	yes	—
76	C₁₃×#41	—	4	2	no	—
77	C₁₃×#41	—	4	2	no	—
78	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
96	C₂²×Dic₁₃	C₂³	1	4	yes	—
97	C₂²×Dic₁₃	C₂³	1	2	yes	—
98	#6127	—	4	4	no	—
99	C₂×D₅₂	—	4	2	no	—
100	C₂×D₅₂	C₂³	1	2	yes	—
101	C₂×D₅₂	C₂³	1	2	yes	—
102	C₂×C₄×D₁₃	C₂³	1	4	yes	—
103	C₂×C₄×D₁₃	C₂³	1	4	yes	—
104	C₂×Dic₂₆	—	4	2	no	—
105	C₂×Dic₂₆	C₂³	1	2	yes	—
106	C₂×Dic₂₆	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₄²×C₁₃	C₂³	1	2	yes	—
114	C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
121	#6103	C₂³	1	4	yes	—
122	#6103	C₂³	1	4	yes	—
123	#6103	C₂³	1	4	yes	—
124	#6103	C₂³	1	4	yes	—
125	#6103	C₂³	1	4	yes	—
126	#6103	C₂³	1	4	yes	—
127	C₄⋊Dic₁₃	C₂³	1	2	yes	—
128	C₄⋊Dic₁₃	C₂³	1	2	yes	—
129	C₄⋊Dic₁₃	C₂³	1	4	yes	—
130	#6101	C₂³	1	4	yes	—
131	#6101	C₂³	1	4	yes	—
132	#6101	C₂³	1	4	yes	—
133	#6101	C₂³	1	4	yes	—
134	#6101	C₂³	1	4	yes	—
135	#6101	C₂³	1	4	yes	—
136	C₄×Dic₁₃	C₂³	1	4	yes	—
137	C₄×Dic₁₃	C₂³	1	2	yes	—
138	C₄×Dic₁₃	C₂³	1	2	yes	—
139	#3551	—	13	1	no	maximal, Sylow
140	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂³×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×D₁₃	—	4	2	no	—
145	C₂²×D₁₃	—	4	4	no	—
146	C₂²×D₁₃	C₂⁴	1	4	yes	—
147	Q₈×C₁₃	—	4	1	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	1	no	—
154	D₄×C₁₃	—	4	1	no	—
155	D₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₁₃	—	4	4	no	—
169	C₂²⋊D₁₃	—	4	4	no	—
170	C₂²⋊D₁₃	—	4	4	no	—
171	C₂²⋊D₁₃	—	4	4	no	—
172	C₂×Dic₁₃	—	4	2	no	—
173	C₂×Dic₁₃	—	4	4	no	—
174	C₂×Dic₁₃	C₂⁴	1	4	yes	—
175	C₂×Dic₁₃	C₂⁴	1	4	yes	—
176	C₂×Dic₁₃	C₂⁴	1	4	yes	—
177	D₅₂	—	2	4	no	—
178	D₅₂	—	4	2	no	—
179	C₄×D₁₃	—	4	4	no	—
180	C₄×D₁₃	—	4	4	no	—
181	Dic₂₆	—	2	4	no	—
182	Dic₂₆	—	4	2	no	—
183	#563	—	13	2	no	—
184	#560	—	13	2	no	—
185	#555	—	13	2	no	—
186	#553	—	13	2	no	—
187	#552	—	13	2	no	—
188	#551	—	13	2	no	—
189	#548	—	13	2	no	—
190	#546	—	13	2	no	—
191	#540	—	13	4	no	—
192	#538	—	13	4	no	—
193	#537	—	13	2	no	—
194	#536	—	13	1	no	—
195	#535	—	13	1	no	—
196	#532	D₁₃	1	1	yes	characteristic, complemented
197	#529	—	13	2	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
208	C₂×D₁₃	—	2	4	no	—
209	C₂×D₁₃	—	2	4	no	—
210	C₂×D₁₃	—	2	4	no	—
211	C₂×D₁₃	—	8	4	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
219	Dic₁₃	—	2	4	no	—
220	Dic₁₃	—	2	4	no	—
221	Dic₁₃	—	2	4	no	—
222	C₂×#41	—	13	2	no	—
223	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
224	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
225	C₂²×Q₈	—	13	1	no	—
226	C₂²×D₄	—	13	1	no	—
227	C₄⋊Q₈	—	13	2	no	—
228	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
229	#127	—	13	2	no	—
230	#127	C₂×D₁₃	1	1	yes	characteristic
231	#126	—	13	4	no	—
232	#126	—	13	4	no	—
233	#126	—	13	4	no	—
234	#125	—	13	4	no	—
235	#125	—	13	2	no	—
236	#124	—	13	2	no	—
237	#124	—	13	2	no	—
238	#124	—	13	4	no	—
239	#124	—	13	2	no	—
240	#124	C₂×D₁₃	1	1	yes	characteristic
241	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
242	#123	—	13	2	no	—
243	#123	—	13	2	no	—
244	#123	—	13	4	no	—
245	#123	—	13	4	no	—
246	#123	—	13	4	no	—
247	#123	—	13	4	no	—
248	C₂²⋊Q₈	—	13	4	no	—
249	C₂²⋊Q₈	—	13	2	no	—
250	C₂²⋊Q₈	—	13	2	no	—
251	C₂²⋊Q₈	—	13	2	no	—
252	C₂²⋊Q₈	—	13	4	no	—
253	#121	—	13	4	no	—
254	#121	—	13	4	no	—
255	#121	—	13	4	no	—
256	#121	—	13	4	no	—
257	#121	—	13	4	no	—
258	#121	—	13	2	no	—
259	#121	—	13	2	no	—
260	#121	—	13	2	no	—
261	#121	—	13	4	no	—
262	#121	C₂×D₁₃	1	2	yes	—
263	#121	C₂×D₁₃	1	2	yes	complemented
264	#120	—	13	2	no	—
265	#120	—	13	2	no	—
266	#120	—	13	4	no	—
267	C₄×Q₈	—	13	2	no	—
268	C₄×D₄	—	13	4	no	—
269	C₄×D₄	—	13	4	no	—
270	C₄×D₄	—	13	4	no	—
271	C₄×D₄	—	13	2	no	—
272	C₄×D₄	C₂×D₁₃	1	2	yes	—
273	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
274	#117	—	13	1	no	—
275	#117	—	13	1	no	—
276	#117	—	13	4	no	—
277	#117	—	13	4	no	—
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₂²⋊C₄	—	13	4	no	—
280	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
281	C₂×C₁₃	—	4	1	no	—
282	C₂×C₁₃	—	4	1	no	—
283	C₂×C₁₃	—	4	2	no	—
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×C₁₃	#585	1	2	yes	—
287	D₁₃	—	4	4	no	—
288	C₂⁴	—	13	2	no	—
289	#41	—	4	2	no	—
290	#41	—	4	2	no	—
291	#41	—	52	4	no	—
292	C₂×Q₈	—	13	2	no	—
293	C₂×Q₈	—	13	2	no	—
294	C₂×Q₈	—	52	2	no	—
295	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×D₄	—	13	4	no	—
298	C₂×D₄	—	13	4	no	—
299	C₂×D₄	—	13	4	no	—
300	C₂×D₄	—	13	4	no	—
301	C₂×D₄	—	13	2	no	—
302	C₂×D₄	—	13	2	no	—
303	C₂×D₄	—	52	2	no	—
304	C₂×D₄	C₂²×D₁₃	1	2	yes	—
305	C₂×D₄	C₂²×D₁₃	1	2	yes	—
306	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
307	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₁₃	1	2	yes	—
309	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	—	13	4	no	—
312	C₂²×C₄	—	13	2	no	—
313	C₂²×C₄	—	13	4	no	—
314	C₂²×C₄	—	13	4	no	—
315	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
317	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
320	C₄⋊C₄	—	13	2	no	—
321	C₄⋊C₄	—	13	2	no	—
322	C₄⋊C₄	—	13	4	no	—
323	C₄⋊C₄	—	13	4	no	—
324	C₄⋊C₄	—	13	4	no	—
325	C₄⋊C₄	—	13	4	no	—
326	C₄⋊C₄	—	13	4	no	—
327	C₄⋊C₄	—	13	4	no	—
328	C₄⋊C₄	—	13	4	no	—
329	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
330	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
331	C₂²⋊C₄	—	13	4	no	—
332	C₂²⋊C₄	—	13	2	no	—
333	C₂²⋊C₄	—	13	4	no	—
334	C₂²⋊C₄	—	13	2	no	—
335	C₂²⋊C₄	—	13	4	no	—
336	C₂²⋊C₄	—	13	4	no	—
337	C₂²⋊C₄	—	13	4	no	—
338	C₂²⋊C₄	—	13	4	no	—
339	C₂²⋊C₄	—	13	4	no	—
340	C₂²⋊C₄	—	13	4	no	—
341	C₂²⋊C₄	—	13	4	no	—
342	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
346	C₄²	—	13	2	no	—
347	C₄²	—	13	4	no	—
348	C₄²	—	13	2	no	—
349	C₄²	C₂²×D₁₃	1	1	yes	characteristic
350	C₄²	C₂²×D₁₃	1	2	yes	—
351	C₄²	C₂²×D₁₃	1	1	yes	characteristic
352	C₁₃	#3551	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	4	no	—
354	C₂³	—	52	2	no	—
355	C₂³	—	52	4	no	—
356	C₂³	C₂³×D₁₃	1	1	yes	characteristic
357	C₂³	C₂³×D₁₃	1	1	yes	characteristic
358	C₂³	C₂³×D₁₃	1	1	yes	characteristic
359	C₂³	C₂³×D₁₃	1	2	yes	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	26	4	no	—
363	Q₈	—	52	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	26	4	no	—
372	D₄	—	52	2	no	—
373	D₄	—	52	4	no	—
374	D₄	—	52	4	no	—
375	D₄	—	52	4	no	—
376	D₄	—	52	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	13	4	no	—
383	C₂×C₄	—	13	4	no	—
384	C₂×C₄	—	13	4	no	—
385	C₂×C₄	—	52	4	no	—
386	C₂×C₄	—	52	4	no	—
387	C₂×C₄	—	52	4	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	C₂³×D₁₃	1	2	yes	—
390	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₃	1	2	yes	—
393	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₃	1	2	yes	—
395	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	26	4	no	—
406	C₂²	—	26	4	no	—
407	C₂²	—	26	4	no	—
408	C₂²	—	104	4	no	—
409	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	26	4	no	—
417	C₄	—	26	4	no	—
418	C₄	—	26	4	no	—
419	C₄	#88251	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	52	4	no	—
425	C₂	C₂×#88251	1	1	yes	characteristic
426	C₂	#11719648	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#532	C₂
hypercenter	#532	D₁₃
hypocenter	C₁₃	#3551
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₁₃×#532	C₂	semidirect
2. #11719538	C₂	semidirect
3. #11719535	C₂	semidirect
4. #11719530	C₂	semidirect
5. #11719440	C₂	semidirect
6. #11719425	C₂	semidirect
7. #11719384	C₂	semidirect
8. #11719375	C₂	semidirect
9. #11719320	C₂	semidirect
10. #11719318	C₂	semidirect
11. #11719270	C₂	semidirect
12. #11719257	C₂	semidirect
13. #11719255	C₂	semidirect
14. #11719246	C₂	semidirect
15. #11719184	C₂	semidirect
17. C₂×C₁₃×#41	C₂²	semidirect
20. C₂²×Dic₂₆	C₂²	semidirect
21. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×#124	C₂²	semidirect
26. C₁₃×#121	C₂²	semidirect
28. C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×C₄²×C₁₃	C₂²	semidirect
31. #88200	C₂²	semidirect
32. #88198	C₂²	semidirect
34. #88193	C₂²	semidirect
35. #88193	C₂²	semidirect
36. #88193	C₂²	semidirect
37. #88193	C₂²	semidirect
38. #88192	C₂²	semidirect
45. #88189	C₂²	semidirect
49. #88183	C₂²	semidirect
50. C₄×C₂²⋊D₁₃	C₂²	semidirect
52. #88180	C₂²	semidirect
53. C₂×C₄⋊Dic₁₃	C₂²	semidirect
55. #88178	C₂²	semidirect
56. #88178	C₂²	semidirect
57. #88152	C₂²	semidirect
58. #88150	C₂²	semidirect
60. #88143	C₂²	semidirect
61. #88139	C₂²	semidirect
63. #88137	C₂²	semidirect
64. #88135	C₂²	semidirect
65. #88135	C₂²	semidirect
68. #88131	C₂²	semidirect
69. #88130	C₂²	semidirect
72. #88126	C₂²	semidirect
73. #88124	C₂²	semidirect
74. C₄×Dic₂₆	C₂²	semidirect
196. #532	D₁₃	semidirect
224. C₂×#41	C₂×D₁₃	semidirect
228. C₄⋊Q₈	C₂×D₁₃	semidirect
241. #124	C₂×D₁₃	semidirect
263. #121	C₂×D₁₃	semidirect
273. C₄×D₄	C₂×D₁₃	semidirect
280. C₂×C₄²	C₂×D₁₃	semidirect
352. C₁₃	#3551	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#532	2
#11719538	2
#11719535	2
#11719530	2
#11719440	2
#11719425	2
#11719384	2
#11719375	2
#11719320	2
#11719318	2
#11719270	2
#11719257	2
#11719255	2
#11719246	2
#11719184	2
#3551	13