Subgroups — C₁₃×#3308 #13112366

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#440	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	C₂×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#41	—	2	1	no	—
17	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#124	—	2	1	no	—
26	C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₁₃×#123	—	2	1	no	—
28	C₁₃×#123	—	2	1	no	—
29	C₁₃×C₂²⋊Q₈	—	2	1	no	—
30	C₁₃×C₂²⋊Q₈	—	2	1	no	—
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₃×#121	—	2	1	no	—
33	C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	—	2	1	no	—
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#107	C₂²	1	1	yes	characteristic
43	C₁₃×#107	C₂²	1	1	yes	characteristic
44	C₁₃×#107	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	—	4	1	no	—
61	C₁₃×#41	—	4	4	no	—
62	C₂×Q₈×C₁₃	—	2	1	no	—
63	C₂×Q₈×C₁₃	—	2	1	no	—
64	C₂×Q₈×C₁₃	—	2	2	no	—
65	C₂×Q₈×C₁₃	—	4	1	no	—
66	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₃	—	2	1	no	—
69	C₂×D₄×C₁₃	—	2	1	no	—
70	C₂×D₄×C₁₃	—	2	1	no	—
71	C₂×D₄×C₁₃	—	2	1	no	—
72	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×SD₁₆	—	2	2	no	—
83	C₁₃×SD₁₆	—	4	1	no	—
84	C₁₃×D₈	—	4	1	no	—
85	C₁₃×M₁₆	—	4	1	no	—
86	C₂×C₈×C₁₃	—	4	1	no	—
87	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
96	C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
108	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	#3308	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
117	Q₈×C₁₃	—	2	1	no	—
118	Q₈×C₁₃	—	2	1	no	—
119	Q₈×C₁₃	—	2	1	no	—
120	Q₈×C₁₃	—	4	2	no	—
121	Q₈×C₁₃	—	4	2	no	—
122	Q₈×C₁₃	#41	1	2	yes	complemented
123	D₄×C₁₃	—	2	2	no	—
124	D₄×C₁₃	—	2	1	no	—
125	D₄×C₁₃	—	2	1	no	—
126	D₄×C₁₃	—	2	1	no	—
127	D₄×C₁₃	—	2	1	no	—
128	D₄×C₁₃	—	4	2	no	—
129	D₄×C₁₃	—	4	2	no	—
130	D₄×C₁₃	—	4	2	no	—
131	D₄×C₁₃	—	4	2	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	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	4	2	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₈×C₁₃	—	2	1	no	—
153	C₈×C₁₃	—	2	1	no	—
154	C₈×C₁₃	—	2	1	no	—
155	C₈×C₁₃	—	2	1	no	—
156	#548	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#489	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#484	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#480	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#477	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#468	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#466	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#463	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#449	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#448	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#440	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#435	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#417	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	2	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	—	4	1	no	—
181	C₂²×C₁₃	—	4	1	no	—
182	C₂²×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₁₃	—	2	1	no	—
185	C₄×C₁₃	—	2	1	no	—
186	C₄×C₁₃	—	2	2	no	—
187	C₄×C₁₃	—	2	1	no	—
188	C₄×C₁₃	—	2	1	no	—
189	C₄×C₁₃	—	4	1	no	—
190	C₄×C₁₃	—	4	1	no	—
191	C₄×C₁₃	—	4	1	no	—
192	C₄×C₁₃	—	4	1	no	—
193	C₄×C₁₃	—	4	1	no	—
194	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×#41	—	2	1	no	—
197	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
198	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	#124	—	2	1	no	—
206	#124	C₂²×C₁₃	1	1	yes	characteristic
207	#123	—	2	1	no	—
208	#123	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	no	—
211	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	#121	—	2	1	no	—
213	#121	C₂²×C₁₃	1	1	yes	characteristic
214	#121	C₂²×C₁₃	1	1	yes	characteristic
215	#121	C₂²×C₁₃	1	1	yes	characteristic
216	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	#107	C₂²×C₁₃	1	1	yes	characteristic
223	#107	C₂²×C₁₃	1	1	yes	characteristic
224	#107	C₂²×C₁₃	1	1	yes	characteristic
225	C₄⋊C₈	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	#103	C₂²×C₁₃	1	1	yes	characteristic
230	#103	C₂²×C₁₃	1	1	yes	characteristic
231	#103	C₂²×C₁₃	1	1	yes	characteristic
232	#102	C₂²×C₁₃	1	1	yes	characteristic
233	#102	C₂²×C₁₃	1	1	yes	characteristic
234	#102	C₂²×C₁₃	1	1	yes	characteristic
235	#102	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
238	#97	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₁₃	—	2	2	no	—
240	C₂×C₁₃	—	4	1	no	—
241	C₂×C₁₃	—	8	1	no	—
242	C₂×C₁₃	—	8	1	no	—
243	C₂×C₁₃	#546	1	1	yes	characteristic
244	C₂×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₁₃	#578	1	1	yes	characteristic
246	#41	—	2	2	no	—
247	#41	—	4	1	no	—
248	#41	—	4	4	no	—
249	C₂×Q₈	—	2	1	no	—
250	C₂×Q₈	—	2	1	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	4	1	no	—
253	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
260	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
269	SD₁₆	—	2	2	no	—
270	SD₁₆	—	4	1	no	—
271	D₈	—	4	1	no	—
272	M₁₆	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₄²	—	2	1	no	—
298	C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₁₃	#3308	1	1	yes	characteristic, direct product factor, Sylow
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
304	Q₈	—	2	1	no	—
305	Q₈	—	2	1	no	—
306	Q₈	—	2	1	no	—
307	Q₈	—	4	2	no	—
308	Q₈	—	4	2	no	—
309	Q₈	C₁₃×#41	1	2	yes	complemented
310	D₄	—	2	2	no	—
311	D₄	—	2	1	no	—
312	D₄	—	2	1	no	—
313	D₄	—	2	1	no	—
314	D₄	—	2	1	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	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	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
355	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
367	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	—	8	1	no	—
371	C₂	—	8	1	no	—
372	C₂	C₁₃×#546	1	1	yes	characteristic
373	C₂	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂	C₁₃×#578	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×#548	C₂	semidirect
2. C₁₃×#547	C₂	semidirect
3. C₁₃×#489	C₂	semidirect
4. C₁₃×#484	C₂	semidirect
5. C₁₃×#480	C₂	semidirect
6. C₁₃×#477	C₂	semidirect
7. C₁₃×#468	C₂	semidirect
8. C₁₃×#466	C₂	semidirect
9. C₁₃×#463	C₂	semidirect
10. C₁₃×#449	C₂	semidirect
11. C₁₃×#448	C₂	semidirect
12. C₁₃×#440	C₂	semidirect
13. C₁₃×#435	C₂	semidirect
14. C₁₃×#417	C₂	semidirect
15. C₂×C₁₃×#103	C₂	semidirect
112. #3308	C₁₃	direct (N × H)
122. Q₈×C₁₃	#41	semidirect
156. #548	C₂×C₁₃	semidirect
157. #547	C₂×C₁₃	semidirect
158. #489	C₂×C₁₃	semidirect
159. #484	C₂×C₁₃	semidirect
160. #480	C₂×C₁₃	semidirect
161. #477	C₂×C₁₃	semidirect
162. #468	C₂×C₁₃	semidirect
163. #466	C₂×C₁₃	semidirect
164. #463	C₂×C₁₃	semidirect
165. #449	C₂×C₁₃	semidirect
166. #448	C₂×C₁₃	semidirect
167. #440	C₂×C₁₃	semidirect
168. #435	C₂×C₁₃	semidirect
169. #417	C₂×C₁₃	semidirect
170. C₂×#103	C₂×C₁₃	semidirect
299. C₁₃	#3308	direct (N × H)
309. Q₈	C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#548	2
C₁₃×#547	2
C₁₃×#489	2
C₁₃×#484	2
C₁₃×#480	2
C₁₃×#477	2
C₁₃×#468	2
C₁₃×#466	2
C₁₃×#463	2
C₁₃×#449	2
C₁₃×#448	2
C₁₃×#440	2
C₁₃×#435	2
C₁₃×#417	2
C₂×C₁₃×#103	2
#3308	13

Subgroups — C13×#3308 #13112366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3308 #13112366