Subgroups — #15845369

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125422	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124626	C₂	1	2	yes	maximal
3	C₈×#6127	C₂	1	1	yes	maximal, characteristic
4	#13114295	C₂	1	2	yes	maximal, complemented
5	#13114288	C₂	1	2	yes	maximal, complemented
6	#13114241	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114236	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114207	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114202	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113494	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#6127	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718777	—	2	1	no	—
17	#11718777	—	2	1	no	—
18	#11718774	—	2	2	no	—
19	C₈×C₂²⋊D₁₃	—	2	1	no	—
20	C₈×C₂²⋊D₁₃	—	2	1	no	—
21	#11718767	—	2	2	no	—
22	#11718586	C₂²	1	1	yes	characteristic
23	#11718512	C₂²	1	2	yes	—
24	#11718511	C₂²	1	2	yes	—
25	#11718508	—	2	2	no	—
26	#11718507	C₂²	1	2	yes	—
27	#11718503	C₂²	1	2	yes	—
28	#11718490	—	2	2	no	—
29	#11718360	C₂²	1	1	yes	characteristic
30	C₄×Dic₅₂	—	2	1	no	—
31	C₄×Dic₅₂	—	2	1	no	—
32	C₈×D₅₂	C₂²	1	1	yes	characteristic
33	C₈×D₅₂	C₂²	1	1	yes	characteristic
34	#11718346	—	2	1	no	—
35	C₄×C₈×D₁₃	—	2	1	no	—
36	#11718343	C₂²	1	1	yes	characteristic
37	#11718342	C₂²	1	2	yes	—
38	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
39	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
40	C₁₃×#335	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	1	yes	characteristic
42	C₁₃×#335	C₂²	1	2	yes	—
43	#11718078	C₂²	1	2	yes	—
44	#11718078	C₂²	1	2	yes	—
45	#11718073	C₂²	1	2	yes	—
46	#11718073	C₂²	1	2	yes	—
47	C₂×#6127	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	—	2	1	no	—
53	C₄×C₂²⋊D₁₃	—	2	1	no	—
54	#88180	—	2	2	no	—
55	#88180	D₄	1	1	yes	characteristic
56	#88178	—	2	2	no	—
57	#88178	—	2	2	no	—
58	C₂×Dic₅₂	—	2	1	no	—
59	C₂×Dic₅₂	—	2	1	no	—
60	C₂×C₈×D₁₃	—	2	1	no	—
61	C₂×C₈×D₁₃	—	2	1	no	—
62	C₄×D₅₂	D₄	1	1	yes	characteristic
63	C₄×D₅₂	C₂³	1	1	yes	characteristic
64	#88126	—	2	1	no	—
65	C₄²×D₁₃	—	2	1	no	—
66	#88124	—	2	2	no	—
67	#88123	C₂³	1	2	yes	—
68	#88123	C₂³	1	2	yes	—
69	C₄×Dic₂₆	—	2	2	no	—
70	C₄×Dic₂₆	—	2	2	no	—
71	C₄×Dic₂₆	D₄	1	1	yes	characteristic
72	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
76	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²⋊#1055	—	2	1	no	—
81	#88061	—	2	2	no	—
82	#88061	—	2	2	no	—
83	#88060	—	2	1	no	—
84	#88060	—	2	1	no	—
85	#88058	—	2	1	no	—
86	#88058	—	2	1	no	—
87	#88058	—	2	2	no	—
88	#88058	—	2	2	no	—
89	#88057	—	2	2	no	—
90	#88057	—	2	2	no	—
91	#88056	—	2	2	no	—
92	#88056	—	2	2	no	—
93	#88056	—	2	2	no	—
94	#88056	—	2	2	no	—
95	#88054	—	2	1	no	—
96	#88054	—	2	1	no	—
97	C₈×Dic₁₃	—	2	1	no	—
98	C₈×Dic₁₃	—	2	1	no	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	—	2	1	no	—
102	#19126	—	13	1	no	maximal, Sylow
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	—	2	1	no	—
107	#6127	—	2	2	no	—
108	#6127	Q₁₆	1	4	yes	complemented
109	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	—	2	1	no	—
111	C₂×C₄×D₁₃	—	2	1	no	—
112	C₂×C₄×D₁₃	—	2	1	no	—
113	C₂×Dic₂₆	—	2	2	no	—
114	C₂×Dic₂₆	—	2	2	no	—
115	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	—	4	4	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	#41	1	1	yes	characteristic
128	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²⋊Dic₁₃	—	2	1	no	—
130	C₂²⋊Dic₁₃	—	4	2	no	—
131	#6103	—	2	1	no	—
132	#6103	—	2	1	no	—
133	C₄⋊Dic₁₃	—	2	2	no	—
134	C₄⋊Dic₁₃	—	2	2	no	—
135	C₄⋊Dic₁₃	—	2	2	no	—
136	C₄⋊Dic₁₃	—	2	2	no	—
137	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
139	#6101	—	2	1	no	—
140	#6101	—	2	1	no	—
141	#6101	—	4	2	no	—
142	#6101	—	4	2	no	—
143	C₄×Dic₁₃	—	2	1	no	—
144	C₄×Dic₁₃	—	2	1	no	—
145	C₄×Dic₁₃	—	2	1	no	—
146	C₄×Dic₁₃	—	4	2	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	1	no	—
149	Dic₅₂	—	4	2	no	—
150	Dic₅₂	—	4	2	no	—
151	C₈×D₁₃	—	4	2	no	—
152	C₈×D₁₃	—	4	2	no	—
153	#3170	—	13	1	no	—
154	#3076	—	13	2	no	—
155	C₈×#41	—	13	1	no	—
156	#1684	—	13	2	no	—
157	#1683	—	13	2	no	—
158	#1676	—	13	1	no	—
159	#1675	—	13	1	no	—
160	#1670	—	13	1	no	—
161	#1669	—	13	1	no	—
162	C₂×#335	D₁₃	1	1	yes	characteristic, complemented
163	#1542	—	13	2	no	—
164	C₂³×C₁₃	#121	1	1	yes	characteristic
165	C₂²×D₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
173	C₂×C₄×C₁₃	#135	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₁₃	—	2	4	no	—
178	C₂×Dic₁₃	—	2	1	no	—
179	C₂×Dic₁₃	—	2	1	no	—
180	C₂×Dic₁₃	—	2	1	no	—
181	C₂×Dic₁₃	—	4	2	no	—
182	C₂×Dic₁₃	—	4	2	no	—
183	D₅₂	—	2	1	no	—
184	D₅₂	C₂×Q₁₆	1	2	yes	—
185	C₄×D₁₃	—	2	4	no	—
186	C₄×D₁₃	—	4	2	no	—
187	C₄×D₁₃	—	4	1	no	—
188	C₄×D₁₃	—	4	1	no	—
189	Dic₂₆	—	2	1	no	—
190	Dic₂₆	—	4	2	no	—
191	Dic₂₆	—	4	2	no	—
192	Dic₂₆	—	8	2	no	—
193	Dic₂₆	C₂×Q₁₆	1	2	yes	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	—	2	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	4	2	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₈×C₁₃	#135	1	2	yes	—
200	#1055	—	4	1	no	—
201	#1055	—	4	1	no	—
202	#533	—	13	2	no	—
203	C₄×#41	—	13	1	no	—
204	#500	—	13	1	no	—
205	#494	—	13	1	no	—
206	#487	—	13	2	no	—
207	#479	—	26	2	no	—
208	#478	—	26	2	no	—
209	#477	—	13	2	no	—
210	#476	—	13	2	no	—
211	#475	—	13	2	no	—
212	#474	—	13	2	no	—
213	#467	—	26	1	no	—
214	#467	—	26	1	no	—
215	C₈×Q₈	—	13	1	no	—
216	C₈×Q₈	—	13	1	no	—
217	C₄×Q₁₆	—	26	1	no	—
218	C₄×Q₁₆	—	26	1	no	—
219	C₈×D₄	—	13	1	no	—
220	C₈×D₄	—	13	1	no	—
221	C₈×D₄	—	26	1	no	—
222	C₈×D₄	—	26	1	no	—
223	#431	—	13	1	no	—
224	#431	—	26	1	no	—
225	#427	—	26	2	no	—
226	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
227	#416	—	26	2	no	—
228	C₂×C₄×C₈	—	26	1	no	—
229	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
230	#335	C₂×D₁₃	1	1	yes	characteristic
231	#335	C₂×D₁₃	1	1	yes	characteristic
232	#335	C₂×D₁₃	1	2	yes	—
233	#333	—	13	2	no	—
234	#333	—	13	2	no	—
235	#332	—	13	2	no	—
236	#332	—	13	2	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	#467	1	2	yes	—
240	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
241	C₂×D₁₃	—	2	2	no	—
242	C₂×D₁₃	—	4	1	no	—
243	C₂×D₁₃	—	4	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	#467	1	2	yes	—
248	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
249	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
250	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
251	C₄×C₁₃	#575	1	1	yes	characteristic
252	Dic₁₃	—	2	2	no	—
253	Dic₁₃	—	4	1	no	—
254	Dic₁₃	—	4	1	no	—
255	Dic₁₃	—	8	2	no	—
256	Dic₁₃	—	8	2	no	—
257	C₂×#41	—	13	1	no	—
258	C₂×Q₁₆	—	26	1	no	—
259	C₂×Q₁₆	—	26	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	26	1	no	—
262	C₂²×C₈	—	26	1	no	—
263	C₂²×C₈	D₅₂	1	1	yes	characteristic
264	C₂²×C₈	D₅₂	1	1	yes	characteristic
265	C₄⋊Q₈	—	13	2	no	—
266	C₄⋊Q₈	—	13	2	no	—
267	#125	—	26	2	no	—
268	C₂²⋊Q₈	—	26	2	no	—
269	C₂²⋊Q₈	—	26	2	no	—
270	C₄×Q₈	—	13	1	no	—
271	C₄×Q₈	—	13	1	no	—
272	C₄×Q₈	—	26	2	no	—
273	C₄×Q₈	—	26	2	no	—
274	C₄×D₄	—	13	1	no	—
275	C₄×D₄	—	13	1	no	—
276	C₄×D₄	—	26	1	no	—
277	C₄×D₄	—	26	1	no	—
278	#117	—	13	1	no	—
279	#117	—	26	1	no	—
280	#117	—	26	2	no	—
281	C₂×C₄²	—	26	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	#107	—	26	2	no	—
284	#107	—	26	2	no	—
285	#107	—	26	1	no	—
286	#107	—	26	1	no	—
287	#106	—	26	2	no	—
288	#106	—	26	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	13	1	no	—
291	C₄⋊C₈	—	13	1	no	—
292	C₄⋊C₈	—	26	1	no	—
293	C₄⋊C₈	—	26	1	no	—
294	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
295	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
296	#103	—	26	2	no	—
297	#103	—	26	2	no	—
298	#103	—	26	2	no	—
299	#103	—	26	2	no	—
300	#102	—	26	2	no	—
301	#102	—	26	2	no	—
302	C₂²⋊C₈	—	26	1	no	—
303	C₂²⋊C₈	—	26	1	no	—
304	C₂²⋊C₈	—	26	1	no	—
305	C₄×C₈	—	26	1	no	—
306	C₄×C₈	—	26	1	no	—
307	C₄×C₈	—	26	1	no	—
308	C₄×C₈	D₅₂	1	1	yes	characteristic
309	C₄×C₈	D₅₂	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	#3035	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
315	C₂×C₁₃	#3067	1	1	yes	characteristic
316	D₁₃	—	4	2	no	—
317	#41	—	13	4	no	—
318	#41	—	26	2	no	—
319	C₂×Q₈	—	13	1	no	—
320	C₂×Q₈	—	26	2	no	—
321	C₂×Q₈	—	26	2	no	—
322	C₂×D₄	—	13	1	no	—
323	C₂×D₄	—	26	1	no	—
324	C₂²×C₄	—	26	1	no	—
325	C₂²×C₄	—	26	1	no	—
326	C₂²×C₄	—	26	1	no	—
327	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
329	C₂²×C₄	#6131	1	1	yes	characteristic
330	Q₁₆	—	52	2	no	—
331	Q₁₆	—	52	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	52	2	no	—
340	C₂×C₈	—	52	2	no	—
341	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
342	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
343	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
344	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
345	C₄⋊C₄	—	13	1	no	—
346	C₄⋊C₄	—	13	1	no	—
347	C₄⋊C₄	—	26	1	no	—
348	C₄⋊C₄	—	26	1	no	—
349	C₄⋊C₄	—	26	2	no	—
350	C₄⋊C₄	—	26	2	no	—
351	C₄⋊C₄	—	26	2	no	—
352	C₄⋊C₄	—	26	2	no	—
353	C₄⋊C₄	—	52	2	no	—
354	C₄⋊C₄	—	52	2	no	—
355	C₂²⋊C₄	—	26	1	no	—
356	C₂²⋊C₄	—	26	1	no	—
357	C₂²⋊C₄	—	26	1	no	—
358	C₂²⋊C₄	—	52	2	no	—
359	C₄²	—	26	1	no	—
360	C₄²	—	26	1	no	—
361	C₄²	—	26	1	no	—
362	C₄²	—	52	2	no	—
363	C₄²	C₂×D₅₂	1	1	yes	characteristic
364	C₄²	D₄×D₁₃	1	1	yes	characteristic
365	C₄²	#6131	1	1	yes	characteristic
366	C₄²	C₂³×D₁₃	1	1	yes	characteristic
367	C₁₃	#19126	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	26	1	no	—
369	C₂³	#88149	1	1	yes	characteristic
370	Q₈	—	13	2	no	—
371	Q₈	—	26	1	no	—
372	Q₈	—	52	2	no	—
373	Q₈	—	52	2	no	—
374	Q₈	—	104	2	no	—
375	D₄	—	13	2	no	—
376	D₄	—	26	4	no	—
377	D₄	—	26	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	26	1	no	—
382	C₂×C₄	—	26	4	no	—
383	C₂×C₄	—	26	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	52	2	no	—
386	C₂×C₄	—	52	1	no	—
387	C₂×C₄	—	52	1	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	#88149	1	1	yes	characteristic
391	C₂×C₄	#88149	1	1	yes	characteristic
392	C₂×C₄	#88149	1	1	yes	characteristic
393	C₂×C₄	#88166	1	2	yes	—
394	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
395	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂×#6131	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	52	1	no	—
404	C₈	—	52	1	no	—
405	C₈	#88158	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	26	2	no	—
409	C₂²	—	52	1	no	—
410	C₂²	—	52	1	no	—
411	C₂²	#11718548	1	2	yes	—
412	C₂²	C₂×#88149	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	26	2	no	—
417	C₄	—	52	1	no	—
418	C₄	—	52	1	no	—
419	C₄	—	104	2	no	—
420	C₄	—	104	2	no	—
421	C₄	#11718548	1	2	yes	—
422	C₄	C₂×#88158	1	1	yes	characteristic
423	C₄	#11719453	1	1	yes	characteristic
424	C₄	C₂×#88166	1	1	yes	characteristic
425	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	52	2	no	—
428	C₂	#13124293	1	1	yes	characteristic
429	C₂	C₂×#11718548	1	1	yes	characteristic
430	C₂	#13124557	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88149
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#335	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×#6127	D₄
hypercenter	C₂×#335	D₁₃
hypocenter	C₁₃	#19126
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
1. #13125422	C₂	semidirect
4. #13114295	C₂	semidirect
5. #13114288	C₂	semidirect
6. #13114241	C₂	semidirect
7. #13114236	C₂	semidirect
8. #13114207	C₂	semidirect
9. #13114202	C₂	semidirect
10. #13113494	C₂	semidirect
11. C₂×C₁₃×#335	C₂	semidirect
108. #6127	Q₁₆	semidirect
162. C₂×#335	D₁₃	semidirect
367. C₁₃	#19126	semidirect

Maximal subgroups

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

subgroup	index
#13125422	2
#13124626	2
C₈×#6127	2
#13114295	2
#13114288	2
#13114241	2
#13114236	2
#13114207	2
#13114202	2
#13113494	2
C₂×C₁₃×#335	2
#19126	13