Subgroups — C₁₃×#17993 #15704332

Order 3328.

576 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2993	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1495	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#529	C₂²	1	2	yes	—
11	C₁₃×#499	C₄	1	1	yes	characteristic
12	C₁₃×#495	C₄	1	1	yes	characteristic
13	C₁₃×#488	C₄	1	2	yes	—
14	C₁₃×#467	C₄	1	1	yes	characteristic
15	C₁₃×#466	C₄	1	1	yes	characteristic
16	C₁₃×#465	C₄	1	2	yes	—
17	C₁₃×#446	C₂²	1	2	yes	—
18	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₁₃×#436	—	2	2	no	—
23	C₁₃×#436	C₂²	1	2	yes	—
24	C₁₃×#435	—	2	2	no	—
25	C₈×D₄×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#433	—	2	2	no	—
27	C₁₃×#431	C₂²	1	1	yes	characteristic
28	C₁₃×#431	C₂²	1	1	yes	characteristic
29	C₁₃×#424	—	2	2	no	—
30	C₁₃×#423	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#334	C₂²	1	1	yes	characteristic
33	C₁₃×#334	C₂²	1	1	yes	characteristic
34	C₁₃×#334	C₂²	1	2	yes	—
35	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	2	yes	—
40	C₁₃×#322	C₂²	1	2	yes	—
41	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₁₃×#126	—	2	2	no	—
50	C₁₃×#125	C₂×C₄	1	2	yes	—
51	C₁₃×#124	C₂×C₄	1	2	yes	—
52	C₁₃×#123	—	2	2	no	—
53	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
54	C₁₃×#121	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#117	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#106	C₂×C₄	1	2	yes	—
63	C₁₃×C₄⋊C₈	—	2	2	no	—
64	C₁₃×C₄⋊C₈	—	2	2	no	—
65	C₁₃×C₄⋊C₈	—	2	2	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
69	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₃×#103	C₂×C₄	1	2	yes	—
71	C₁₃×#103	C₂×C₄	1	2	yes	—
72	C₁₃×#102	C₂×C₄	1	2	yes	—
73	C₁₃×#102	C₂×C₄	1	2	yes	—
74	C₁₃×C₂²⋊C₈	—	2	1	no	—
75	C₁₃×C₂²⋊C₈	—	2	2	no	—
76	C₁₃×C₂²⋊C₈	—	2	2	no	—
77	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	2	yes	—
87	#17993	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
95	C₁₃×Q₁₆	—	4	1	no	—
96	C₁₃×SD₁₆	—	4	2	no	—
97	C₁₃×D₈	—	4	1	no	—
98	C₁₃×M₁₆	—	8	2	no	—
99	C₁₃×M₁₆	—	8	2	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	4	1	no	—
104	C₂×C₈×C₁₃	—	4	1	no	—
105	C₂×C₈×C₁₃	—	8	2	no	—
106	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
118	C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	#41	1	1	yes	characteristic
127	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
128	#3168	C₂×C₁₃	1	1	yes	characteristic
129	#2993	C₂×C₁₃	1	2	yes	complemented
130	#1587	C₂×C₁₃	1	2	yes	complemented
131	#1586	C₂×C₁₃	1	2	yes	complemented
132	#1583	C₂×C₁₃	1	2	yes	complemented
133	#1582	C₂×C₁₃	1	2	yes	complemented
134	#1566	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1495	C₂×C₁₃	1	2	yes	complemented
136	#1452	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
139	Q₈×C₁₃	—	2	2	no	—
140	Q₈×C₁₃	—	2	2	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	—	2	2	no	—
143	D₄×C₁₃	—	8	2	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
159	C₈×C₁₃	—	2	1	no	—
160	C₈×C₁₃	—	2	1	no	—
161	C₈×C₁₃	—	2	1	no	—
162	C₈×C₁₃	—	2	1	no	—
163	C₈×C₁₃	—	2	2	no	—
164	C₈×C₁₃	—	2	2	no	—
165	C₈×C₁₃	—	4	2	no	—
166	C₈×C₁₃	—	4	2	no	—
167	C₈×C₁₃	—	4	2	no	—
168	#529	C₂²×C₁₃	1	2	yes	—
169	#499	C₄×C₁₃	1	1	yes	characteristic
170	#495	C₄×C₁₃	1	1	yes	characteristic
171	#488	C₄×C₁₃	1	2	yes	—
172	#467	C₄×C₁₃	1	1	yes	characteristic
173	#466	C₄×C₁₃	1	1	yes	characteristic
174	#465	C₄×C₁₃	1	2	yes	—
175	#446	C₂²×C₁₃	1	2	yes	—
176	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
177	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
178	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
179	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
180	#436	—	2	2	no	—
181	#436	C₂²×C₁₃	1	2	yes	—
182	#435	—	2	2	no	—
183	C₈×D₄	C₂²×C₁₃	1	2	yes	—
184	#433	—	2	2	no	—
185	#431	C₂²×C₁₃	1	1	yes	characteristic
186	#431	C₂²×C₁₃	1	1	yes	characteristic
187	#424	—	2	2	no	—
188	#423	C₂²×C₁₃	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
190	#334	C₂²×C₁₃	1	1	yes	characteristic
191	#334	C₂²×C₁₃	1	1	yes	characteristic
192	#334	C₂²×C₁₃	1	2	yes	—
193	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
194	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
195	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
196	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
197	#322	C₂²×C₁₃	1	2	yes	—
198	#322	C₂²×C₁₃	1	2	yes	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	4	2	no	—
211	C₄×C₁₃	—	4	2	no	—
212	C₄×C₁₃	—	4	2	no	—
213	C₄×C₁₃	#568	1	1	yes	characteristic
214	C₄×C₁₃	#568	1	1	yes	characteristic
215	C₄×C₁₃	#577	1	2	yes	—
216	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
217	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
218	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
224	#126	—	2	2	no	—
225	#125	C₂×C₄×C₁₃	1	2	yes	—
226	#124	C₂×C₄×C₁₃	1	2	yes	—
227	#123	—	2	2	no	—
228	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
229	#121	C₂×C₄×C₁₃	1	2	yes	—
230	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	C₂³×C₁₃	1	2	yes	—
233	#117	—	2	2	no	—
234	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
235	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
236	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
237	#106	C₂×C₄×C₁₃	1	2	yes	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
243	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
244	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
245	#103	C₂×C₄×C₁₃	1	2	yes	—
246	#103	C₂×C₄×C₁₃	1	2	yes	—
247	#102	C₂×C₄×C₁₃	1	2	yes	—
248	#102	C₂×C₄×C₁₃	1	2	yes	—
249	C₂²⋊C₈	—	2	1	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
253	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
254	#97	—	2	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₁₃	1	2	yes	—
259	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₁₃	1	2	yes	—
262	C₂×C₁₃	—	4	1	no	—
263	C₂×C₁₃	—	8	2	no	—
264	C₂×C₁₃	#2932	1	1	yes	characteristic
265	C₂×C₁₃	#2952	1	1	yes	characteristic
266	C₂×C₁₃	#2957	1	1	yes	characteristic
267	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
274	Q₁₆	—	4	1	no	—
275	SD₁₆	—	4	2	no	—
276	D₈	—	4	1	no	—
277	M₁₆	—	8	2	no	—
278	M₁₆	—	8	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	8	2	no	—
285	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
296	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₄²	C₁₃×#41	1	1	yes	characteristic
306	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₁₃	#17993	1	1	yes	characteristic, direct product factor, Sylow
308	C₂³	—	2	2	no	—
309	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	—	8	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
330	C₈	—	2	1	no	—
331	C₈	—	2	1	no	—
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	2	no	—
335	C₈	—	2	2	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	C₁₃×#568	1	1	yes	characteristic
354	C₄	C₁₃×#568	1	1	yes	characteristic
355	C₄	C₁₃×#577	1	2	yes	—
356	C₂	—	4	1	no	—
357	C₂	—	8	2	no	—
358	C₂	C₁₃×#2932	1	1	yes	characteristic
359	C₂	C₁₃×#2952	1	1	yes	characteristic
360	C₂	C₁₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2993	C₂	semidirect
3. C₁₃×#1587	C₂	semidirect
4. C₁₃×#1586	C₂	semidirect
5. C₁₃×#1583	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₁₃×#1566	C₂	semidirect
8. C₁₃×#1495	C₂	semidirect
9. C₁₃×#1452	C₂	semidirect
87. #17993	C₁₃	direct (N × H)
129. #2993	C₂×C₁₃	semidirect
130. #1587	C₂×C₁₃	semidirect
131. #1586	C₂×C₁₃	semidirect
132. #1583	C₂×C₁₃	semidirect
133. #1582	C₂×C₁₃	semidirect
134. #1566	C₂×C₁₃	semidirect
135. #1495	C₂×C₁₃	semidirect
136. #1452	C₂×C₁₃	semidirect
307. C₁₃	#17993	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×#3168	2
C₁₃×#2993	2
C₁₃×#1587	2
C₁₃×#1586	2
C₁₃×#1583	2
C₁₃×#1582	2
C₁₃×#1566	2
C₁₃×#1495	2
C₁₃×#1452	2
#17993	13

Subgroups — C13×#17993 #15704332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17993 #15704332