Subgroups — C₁₃×#22438 #15708777

Order 3328.

1494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1971	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1877	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1788	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	2	yes	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	C₄	1	8	yes	complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
17	C₁₃×#442	—	2	8	no	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	4	yes	—
20	C₂×C₁₃×#102	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#97	C₂²	1	2	yes	—
23	C₁₃×#391	C₂²	1	4	yes	—
24	C₁₃×#386	—	2	4	no	—
25	C₁₃×#381	—	2	2	no	—
26	C₁₃×#380	C₂²	1	2	yes	—
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#95	—	2	2	no	—
29	C₁₃×#340	C₂²	1	2	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	2	8	no	—
33	C₂×C₁₃×#41	—	4	4	no	—
34	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
35	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	—	2	4	no	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₁₃×#135	—	2	32	no	—
42	C₂×C₁₃×Q₁₆	—	2	4	no	—
43	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
44	C₂×C₁₃×SD₁₆	—	2	8	no	—
45	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	complemented
46	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
47	C₂×C₁₃×D₈	D₄	1	8	yes	—
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	8	no	—
54	C₄×D₄×C₁₃	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₁₃×#106	—	2	4	no	—
61	C₁₃×#103	—	4	4	no	—
62	C₁₃×#102	—	2	8	no	—
63	C₁₃×C₂²⋊C₈	—	2	2	no	—
64	C₁₃×#97	—	2	4	no	—
65	C₁₃×#95	—	2	2	no	—
66	C₁₃×#95	—	2	4	no	—
67	C₁₃×#95	—	2	4	no	—
68	C₁₃×#95	D₄	1	2	yes	—
69	#22438	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₃	—	2	2	no	—
71	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₁₃×#41	—	2	16	no	—
73	C₁₃×#41	—	4	8	no	—
74	C₁₃×#41	—	4	16	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
79	C₂×D₄×C₁₃	—	2	8	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	4	8	no	—
83	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	—	4	8	no	—
91	C₂²×C₄×C₁₃	—	4	8	no	—
92	C₂²×C₄×C₁₃	—	4	8	no	—
93	C₂²×C₄×C₁₃	—	8	4	no	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	#41	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₁₃×Q₁₆	—	2	8	no	—
100	C₁₃×SD₁₆	—	2	16	no	—
101	C₁₃×D₈	C₂²⋊C₄	1	16	yes	complemented
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	8	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₁₃×C₂²⋊C₄	—	4	2	no	—
113	C₁₃×C₂²⋊C₄	—	4	8	no	—
114	C₁₃×C₂²⋊C₄	—	8	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic
118	C₂×#442	C₂×C₁₃	1	2	yes	complemented
119	#2339	C₂×C₁₃	1	2	yes	complemented
120	#1971	C₂×C₁₃	1	2	yes	complemented
121	#1877	C₂×C₁₃	1	4	yes	complemented
122	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
123	#1788	C₂×C₁₃	1	2	yes	complemented
124	#1752	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	2	8	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	4	4	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	C₄×D₄	1	2	yes	—
134	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₁₃	—	2	4	no	—
136	Q₈×C₁₃	—	2	4	no	—
137	Q₈×C₁₃	—	4	4	no	—
138	D₄×C₁₃	—	2	4	no	—
139	D₄×C₁₃	—	2	8	no	—
140	D₄×C₁₃	—	4	16	no	—
141	D₄×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	4	16	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	8	16	no	—
156	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
161	C₈×C₁₃	—	2	2	no	—
162	C₈×C₁₃	—	4	2	no	—
163	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂²×#41	C₂²×C₁₃	1	2	yes	—
165	C₂×#135	—	2	8	no	—
166	C₂×#135	C₄×C₁₃	1	8	yes	complemented
167	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
168	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
169	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
172	#442	—	2	8	no	—
173	C₂×#106	C₂²×C₁₃	1	2	yes	—
174	C₂×#103	C₂²×C₁₃	1	4	yes	—
175	C₂×#102	C₂²×C₁₃	1	4	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
177	C₂×#97	C₂²×C₁₃	1	2	yes	—
178	#391	C₂²×C₁₃	1	4	yes	—
179	#386	—	2	4	no	—
180	#381	—	2	2	no	—
181	#380	C₂²×C₁₃	1	2	yes	—
182	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×#95	—	2	2	no	—
184	#340	C₂²×C₁₃	1	2	yes	—
185	#336	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₁₃	—	2	2	no	—
187	C₂²×C₁₃	—	2	8	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	4	4	no	—
191	C₂²×C₁₃	—	4	4	no	—
192	C₂²×C₁₃	—	4	8	no	—
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	—	4	8	no	—
195	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₁₃	D₄²	1	2	yes	—
197	C₂²×C₁₃	#575	1	2	yes	—
198	C₂²×C₁₃	#577	1	2	yes	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	4	4	no	—
202	C₄×C₁₃	—	8	4	no	—
203	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₄×C₁₃	#518	1	1	yes	characteristic
205	C₄×C₁₃	#546	1	2	yes	—
206	C₂×#41	—	2	4	no	—
207	C₂×#41	—	2	8	no	—
208	C₂×#41	—	4	4	no	—
209	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
210	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
216	#135	—	2	32	no	—
217	C₂×Q₁₆	—	2	4	no	—
218	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
219	C₂×SD₁₆	—	2	8	no	—
220	C₂×SD₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
221	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
222	C₂×D₈	D₄×C₁₃	1	8	yes	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
225	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₄×D₄	—	2	8	no	—
229	C₄×D₄	—	4	4	no	—
230	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
234	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
235	#106	—	2	4	no	—
236	#103	—	4	4	no	—
237	#102	—	2	8	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	#97	—	2	4	no	—
240	#95	—	2	2	no	—
241	#95	—	2	4	no	—
242	#95	—	2	4	no	—
243	#95	D₄×C₁₃	1	2	yes	—
244	C₂×C₁₃	—	4	2	no	—
245	C₂×C₁₃	—	4	8	no	—
246	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₁₃	#2943	1	1	yes	characteristic
248	C₂×C₁₃	#2952	1	1	yes	characteristic
249	C₂×C₁₃	#3267	1	4	yes	—
250	C₂⁴	—	2	2	no	—
251	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
252	#41	—	2	16	no	—
253	#41	—	4	8	no	—
254	#41	—	4	16	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	4	8	no	—
263	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
264	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	8	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	8	4	no	—
274	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₁₃×#41	1	2	yes	—
278	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
279	Q₁₆	—	2	8	no	—
280	SD₁₆	—	2	16	no	—
281	D₈	C₁₃×C₂²⋊C₄	1	16	yes	complemented
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
289	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	4	8	no	—
294	C₂²⋊C₄	—	8	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₁₃	#22438	1	1	yes	characteristic, direct product factor, Sylow
298	C₂³	—	2	4	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₄×D₄×C₁₃	1	2	yes	—
307	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	2	8	no	—
313	D₄	—	4	16	no	—
314	D₄	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
332	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
333	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
347	C₂²	D₄²×C₁₃	1	2	yes	—
348	C₂²	C₁₃×#575	1	2	yes	—
349	C₂²	C₁₃×#577	1	2	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	4	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
355	C₄	C₁₃×#518	1	1	yes	characteristic
356	C₄	C₁₃×#546	1	2	yes	—
357	C₂	—	4	2	no	—
358	C₂	—	4	8	no	—
359	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
360	C₂	C₁₃×#2943	1	1	yes	characteristic
361	C₂	C₁₃×#2952	1	1	yes	characteristic
362	C₂	C₁₃×#3267	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#442	C₂	semidirect
3. C₁₃×#2339	C₂	semidirect
4. C₁₃×#1971	C₂	semidirect
5. C₁₃×#1877	C₂	semidirect
6. C₁₃×#1807	C₂	semidirect
7. C₁₃×#1788	C₂	semidirect
8. C₁₃×#1752	C₂	semidirect
11. C₂×C₁₃×#135	C₄	semidirect
34. C₂×C₁₃×#41	C₂×C₄	semidirect
43. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
45. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
49. C₂²×C₈×C₁₃	C₂×C₄	semidirect
69. #22438	C₁₃	direct (N × H)
101. C₁₃×D₈	C₂²⋊C₄	semidirect
118. C₂×#442	C₂×C₁₃	semidirect
119. #2339	C₂×C₁₃	semidirect
120. #1971	C₂×C₁₃	semidirect
121. #1877	C₂×C₁₃	semidirect
122. #1807	C₂×C₁₃	semidirect
123. #1788	C₂×C₁₃	semidirect
124. #1752	C₂×C₁₃	semidirect
166. C₂×#135	C₄×C₁₃	semidirect
209. C₂×#41	C₂×C₄×C₁₃	semidirect
218. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
220. C₂×SD₁₆	C₂×C₄×C₁₃	semidirect
224. C₂²×C₈	C₂×C₄×C₁₃	semidirect
281. D₈	C₁₃×C₂²⋊C₄	semidirect
297. C₁₃	#22438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#442	2
C₁₃×#2339	2
C₁₃×#1971	2
C₁₃×#1877	2
C₁₃×#1807	2
C₁₃×#1788	2
C₁₃×#1752	2
#22438	13

Subgroups — C13×#22438 #15708777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22438 #15708777