Subgroups — C₁₃×#3307 #13112365

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#126	—	2	1	no	—
25	C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₁₃×#123	—	2	1	no	—
27	C₁₃×#123	—	2	1	no	—
28	C₁₃×#123	—	2	1	no	—
29	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×#121	—	2	1	no	—
32	C₁₃×#121	—	2	1	no	—
33	C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₃	—	2	1	no	—
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#107	C₂²	1	1	yes	characteristic
43	C₁₃×#106	C₂²	1	1	yes	characteristic
44	C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₁₃×#103	C₂²	1	1	yes	characteristic
48	C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₁₃×#102	C₂²	1	1	yes	characteristic
56	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×#97	C₂²	1	1	yes	characteristic
59	C₁₃×#41	—	2	2	no	—
60	C₁₃×#41	—	2	2	no	—
61	C₁₃×#41	—	4	1	no	—
62	C₁₃×#41	—	4	1	no	—
63	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₁₃	—	2	1	no	—
66	C₂×D₄×C₁₃	—	2	1	no	—
67	C₂×D₄×C₁₃	—	2	1	no	—
68	C₂×D₄×C₁₃	—	2	1	no	—
69	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×SD₁₆	—	4	1	no	—
80	C₁₃×SD₁₆	—	4	1	no	—
81	C₁₃×D₈	—	2	2	no	—
82	C₁₃×M₁₆	—	4	1	no	—
83	C₂×C₈×C₁₃	—	4	1	no	—
84	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₄²×C₁₃	—	2	1	no	—
110	C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	#3307	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₃	—	2	1	no	—
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
116	Q₈×C₁₃	—	2	1	no	—
117	Q₈×C₁₃	—	2	1	no	—
118	Q₈×C₁₃	—	2	1	no	—
119	Q₈×C₁₃	—	2	1	no	—
120	D₄×C₁₃	—	2	1	no	—
121	D₄×C₁₃	—	2	1	no	—
122	D₄×C₁₃	—	2	1	no	—
123	D₄×C₁₃	—	4	1	no	—
124	D₄×C₁₃	—	4	2	no	—
125	D₄×C₁₃	—	4	2	no	—
126	D₄×C₁₃	—	4	2	no	—
127	D₄×C₁₃	—	8	1	no	—
128	D₄×C₁₃	#41	1	2	yes	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	4	2	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	8	1	no	—
143	C₂×C₄×C₁₃	—	8	1	no	—
144	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₈×C₁₃	—	2	1	no	—
150	C₈×C₁₃	—	2	1	no	—
151	C₈×C₁₃	—	2	1	no	—
152	C₈×C₁₃	—	2	1	no	—
153	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#491	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#485	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#483	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#478	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#468	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#465	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#461	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#449	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#449	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#442	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#435	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#417	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#416	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂²×C₁₃	—	2	1	no	—
169	C₂²×C₁₃	—	2	1	no	—
170	C₂²×C₁₃	—	2	2	no	—
171	C₂²×C₁₃	—	2	1	no	—
172	C₂²×C₁₃	—	2	1	no	—
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	2	1	no	—
175	C₂²×C₁₃	—	4	1	no	—
176	C₂²×C₁₃	—	4	1	no	—
177	C₂²×C₁₃	—	4	1	no	—
178	C₂²×C₁₃	—	4	1	no	—
179	C₂²×C₁₃	—	4	1	no	—
180	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₄×C₁₃	—	2	1	no	—
182	C₄×C₁₃	—	2	1	no	—
183	C₄×C₁₃	—	2	1	no	—
184	C₄×C₁₃	—	2	1	no	—
185	C₄×C₁₃	—	4	1	no	—
186	C₄×C₁₃	—	4	1	no	—
187	C₄×C₁₃	—	4	1	no	—
188	C₄×C₁₃	—	4	1	no	—
189	C₄×C₁₃	—	4	1	no	—
190	C₄×C₁₃	—	4	1	no	—
191	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	#126	—	2	1	no	—
202	#125	C₂²×C₁₃	1	1	yes	characteristic
203	#123	—	2	1	no	—
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	C₂²×C₁₃	1	1	yes	characteristic
211	#121	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
216	#117	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	#107	C₂²×C₁₃	1	1	yes	characteristic
220	#106	C₂²×C₁₃	1	1	yes	characteristic
221	#106	C₂²×C₁₃	1	1	yes	characteristic
222	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
223	#103	C₂²×C₁₃	1	1	yes	characteristic
224	#103	C₂²×C₁₃	1	1	yes	characteristic
225	#103	C₂²×C₁₃	1	1	yes	characteristic
226	#103	C₂²×C₁₃	1	1	yes	characteristic
227	#103	C₂²×C₁₃	1	1	yes	characteristic
228	#103	C₂²×C₁₃	1	1	yes	characteristic
229	#102	C₂²×C₁₃	1	1	yes	characteristic
230	#102	C₂²×C₁₃	1	1	yes	characteristic
231	#102	C₂²×C₁₃	1	1	yes	characteristic
232	#102	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	#97	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₁₃	—	4	1	no	—
237	C₂×C₁₃	—	4	1	no	—
238	C₂×C₁₃	—	4	2	no	—
239	C₂×C₁₃	—	8	1	no	—
240	C₂×C₁₃	#546	1	1	yes	characteristic
241	C₂×C₁₃	#575	1	1	yes	characteristic
242	C₂×C₁₃	#577	1	1	yes	characteristic
243	#41	—	2	2	no	—
244	#41	—	2	2	no	—
245	#41	—	4	1	no	—
246	#41	—	4	1	no	—
247	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
254	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
263	SD₁₆	—	4	1	no	—
264	SD₁₆	—	4	1	no	—
265	D₈	—	2	2	no	—
266	M₁₆	—	4	1	no	—
267	C₂×C₈	—	4	1	no	—
268	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
280	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²⋊C₄	—	2	1	no	—
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	1	no	—
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
292	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
293	C₄²	—	2	1	no	—
294	C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₁₃	#3307	1	1	yes	characteristic, direct product factor, Sylow
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
300	Q₈	—	2	1	no	—
301	Q₈	—	2	1	no	—
302	Q₈	—	2	1	no	—
303	Q₈	—	2	1	no	—
304	D₄	—	2	1	no	—
305	D₄	—	2	1	no	—
306	D₄	—	2	1	no	—
307	D₄	—	4	1	no	—
308	D₄	—	4	2	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	8	1	no	—
312	D₄	C₁₃×#41	1	2	yes	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	8	1	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	4	1	no	—
355	C₄	—	4	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
361	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂	—	4	1	no	—
363	C₂	—	4	1	no	—
364	C₂	—	4	2	no	—
365	C₂	—	8	1	no	—
366	C₂	C₁₃×#546	1	1	yes	characteristic
367	C₂	C₁₃×#575	1	1	yes	characteristic
368	C₂	C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. C₁₃×#547	C₂	semidirect
3. C₁₃×#491	C₂	semidirect
4. C₁₃×#485	C₂	semidirect
5. C₁₃×#483	C₂	semidirect
6. C₁₃×#478	C₂	semidirect
7. C₁₃×#468	C₂	semidirect
8. C₁₃×#465	C₂	semidirect
9. C₁₃×#461	C₂	semidirect
10. C₁₃×#449	C₂	semidirect
11. C₁₃×#449	C₂	semidirect
12. C₁₃×#442	C₂	semidirect
13. C₁₃×#435	C₂	semidirect
14. C₁₃×#417	C₂	semidirect
15. C₁₃×#416	C₂	semidirect
111. #3307	C₁₃	direct (N × H)
153. #553	C₂×C₁₃	semidirect
154. #547	C₂×C₁₃	semidirect
155. #491	C₂×C₁₃	semidirect
156. #485	C₂×C₁₃	semidirect
157. #483	C₂×C₁₃	semidirect
158. #478	C₂×C₁₃	semidirect
159. #468	C₂×C₁₃	semidirect
160. #465	C₂×C₁₃	semidirect
161. #461	C₂×C₁₃	semidirect
162. #449	C₂×C₁₃	semidirect
163. #449	C₂×C₁₃	semidirect
164. #442	C₂×C₁₃	semidirect
165. #435	C₂×C₁₃	semidirect
166. #417	C₂×C₁₃	semidirect
167. #416	C₂×C₁₃	semidirect
295. C₁₃	#3307	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
C₁₃×#547	2
C₁₃×#491	2
C₁₃×#485	2
C₁₃×#483	2
C₁₃×#478	2
C₁₃×#468	2
C₁₃×#465	2
C₁₃×#461	2
C₁₃×#449	2
C₁₃×#442	2
C₁₃×#435	2
C₁₃×#417	2
C₁₃×#416	2
#3307	13

Subgroups — C13×#3307 #13112365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3307 #13112365