Subgroups — C₁₃×#17550 #15703889

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1509	C₂	1	3	yes	maximal, complemented
5	C₁₃×#1505	C₂	1	3	yes	maximal, complemented
6	C₁₃×#1502	C₂	1	3	yes	maximal, complemented
7	C₁₃×#1500	C₂	1	3	yes	maximal, complemented
8	C₁₃×#559	C₄	1	3	yes	complemented
9	Q₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
10	C₁₃×#554	C₄	1	3	yes	complemented
11	C₁₃×#550	C₄	1	1	yes	characteristic, complemented
12	C₁₃×#548	—	2	1	no	—
13	C₁₃×#547	—	2	3	no	—
14	C₁₃×#542	—	2	3	no	—
15	C₁₃×#532	C₂²	1	3	yes	—
16	C₁₃×#529	C₂²	1	3	yes	—
17	C₁₃×#520	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#446	—	2	3	no	—
21	C₈×Q₈×C₁₃	—	2	1	no	—
22	C₁₃×#432	C₂²	1	3	yes	—
23	C₁₃×#431	C₂²	1	3	yes	—
24	C₄×C₁₃×C₄⋊C₄	—	2	3	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
26	C₁₃×#376	C₂²	1	3	yes	—
27	C₁₃×#328	C₂²	1	1	yes	characteristic
28	C₁₃×#328	C₂²	1	3	yes	—
29	C₁₃×#327	C₂²	1	3	yes	—
30	C₁₃×#327	C₂²	1	3	yes	—
31	C₁₃×#327	C₂²	1	6	yes	—
32	C₂×C₁₃×#41	—	2	1	no	—
33	C₂×C₁₃×#41	—	2	3	no	—
34	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
35	C₁₃×C₄⋊Q₈	—	2	3	no	—
36	C₁₃×C₄⋊Q₈	C₂×C₄	1	3	yes	—
37	C₁₃×#127	C₂×C₄	1	3	yes	—
38	C₁₃×#126	—	2	3	no	—
39	C₁₃×#125	C₂×C₄	1	3	yes	—
40	C₁₃×#124	—	2	3	no	—
41	C₁₃×#124	—	2	3	no	—
42	C₁₃×#124	C₂×C₄	1	3	yes	—
43	C₁₃×#123	—	2	3	no	—
44	C₁₃×#123	—	2	6	no	—
45	C₁₃×C₂²⋊Q₈	—	2	3	no	—
46	C₁₃×C₂²⋊Q₈	—	2	6	no	—
47	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
48	C₁₃×#121	—	2	3	no	—
49	C₁₃×#121	—	2	3	no	—
50	C₁₃×#121	C₂³	1	3	yes	—
51	C₄×Q₈×C₁₃	—	2	8	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	3	yes	—
54	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	C₂×C₄	1	3	yes	—
56	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₃	D₄	1	3	yes	—
58	C₄×D₄×C₁₃	—	2	3	no	—
59	C₄×D₄×C₁₃	—	2	3	no	—
60	C₄×D₄×C₁₃	—	2	3	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₁₃	C₂×C₄	1	6	yes	—
63	C₁₃×#117	—	2	3	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
66	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
67	C₂×C₄²×C₁₃	—	2	3	no	—
68	C₂×C₄²×C₁₃	—	2	3	no	—
69	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
70	C₁₃×C₄⋊C₈	—	2	3	no	—
71	C₁₃×C₄⋊C₈	—	2	3	no	—
72	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
74	C₁₃×#97	—	2	3	no	—
75	C₄×C₈×C₁₃	—	2	3	no	—
76	C₁₃×#95	—	2	3	no	—
77	C₁₃×#95	C₂³	1	3	yes	—
78	C₁₃×#95	C₂³	1	1	yes	characteristic
79	#17550	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₁₃×#41	—	4	4	no	—
81	C₁₃×#41	—	8	3	no	—
82	C₁₃×#41	—	8	3	no	—
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	2	3	no	—
85	C₂×Q₈×C₁₃	C₂²⋊C₄	1	3	yes	—
86	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×D₄×C₁₃	—	2	3	no	—
89	C₂×D₄×C₁₃	—	2	3	no	—
90	C₂×D₄×C₁₃	—	2	3	no	—
91	C₂×D₄×C₁₃	C₂²×C₄	1	3	yes	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	3	no	—
94	C₂²×C₄×C₁₃	—	2	3	no	—
95	C₂²×C₄×C₁₃	—	2	6	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	3	no	—
101	C₁₃×C₄⋊C₄	—	2	12	no	—
102	C₁₃×C₄⋊C₄	—	2	3	no	—
103	C₁₃×C₄⋊C₄	—	2	3	no	—
104	C₁₃×C₄⋊C₄	—	2	3	no	—
105	C₁₃×C₄⋊C₄	—	2	3	no	—
106	C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
108	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
109	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
110	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₄	C₂²×C₄	1	3	yes	—
112	C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₁₃×C₂²⋊C₄	—	2	3	no	—
114	C₁₃×C₂²⋊C₄	—	2	3	no	—
115	C₁₃×C₂²⋊C₄	—	2	3	no	—
116	C₁₃×C₂²⋊C₄	—	2	6	no	—
117	C₁₃×C₂²⋊C₄	—	2	3	no	—
118	C₄²×C₁₃	—	2	12	no	—
119	C₄²×C₁₃	—	2	3	no	—
120	C₄²×C₁₃	—	8	3	no	—
121	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
122	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
123	C₄²×C₁₃	C₂×D₄	1	3	yes	—
124	C₄²×C₁₃	C₂×D₄	1	3	yes	—
125	#3522	C₂×C₁₃	1	1	yes	characteristic
126	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#2276	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#1509	C₂×C₁₃	1	3	yes	complemented
129	#1505	C₂×C₁₃	1	3	yes	complemented
130	#1502	C₂×C₁₃	1	3	yes	complemented
131	#1500	C₂×C₁₃	1	3	yes	complemented
132	C₂³×C₁₃	—	2	3	no	—
133	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₃	—	2	6	no	—
135	Q₈×C₁₃	—	4	1	no	—
136	Q₈×C₁₃	—	8	3	no	—
137	Q₈×C₁₃	#104	1	4	yes	—
138	D₄×C₁₃	—	4	3	no	—
139	D₄×C₁₃	—	4	3	no	—
140	D₄×C₁₃	—	4	3	no	—
141	D₄×C₁₃	—	4	6	no	—
142	D₄×C₁₃	—	8	3	no	—
143	C₂×C₄×C₁₃	—	2	3	no	—
144	C₂×C₄×C₁₃	—	2	3	no	—
145	C₂×C₄×C₁₃	—	2	6	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	6	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	3	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	3	no	—
154	C₂×C₄×C₁₃	—	4	3	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	6	no	—
157	C₂×C₄×C₁₃	—	8	6	no	—
158	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
159	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
160	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
161	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₁₃	—	4	1	no	—
165	C₈×C₁₃	—	4	3	no	—
166	#559	C₄×C₁₃	1	3	yes	complemented
167	Q₈²	C₄×C₁₃	1	1	yes	characteristic, complemented
168	#554	C₄×C₁₃	1	3	yes	complemented
169	#550	C₄×C₁₃	1	1	yes	characteristic, complemented
170	#548	—	2	1	no	—
171	#547	—	2	3	no	—
172	#542	—	2	3	no	—
173	#532	C₂²×C₁₃	1	3	yes	—
174	#529	C₂²×C₁₃	1	3	yes	—
175	#520	—	2	1	no	—
176	C₂×C₄×Q₈	—	2	1	no	—
177	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
178	#446	—	2	3	no	—
179	C₈×Q₈	—	2	1	no	—
180	#432	C₂²×C₁₃	1	3	yes	—
181	#431	C₂²×C₁₃	1	3	yes	—
182	C₄×C₄⋊C₄	—	2	3	no	—
183	C₄×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
184	#376	C₂²×C₁₃	1	3	yes	—
185	#328	C₂²×C₁₃	1	1	yes	characteristic
186	#328	C₂²×C₁₃	1	3	yes	—
187	#327	C₂²×C₁₃	1	3	yes	—
188	#327	C₂²×C₁₃	1	3	yes	—
189	#327	C₂²×C₁₃	1	6	yes	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	4	3	no	—
193	C₂²×C₁₃	—	4	3	no	—
194	C₂²×C₁₃	—	4	3	no	—
195	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₁₃	#576	1	1	yes	characteristic
197	C₂²×C₁₃	#577	1	1	yes	characteristic
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	1	no	—
200	C₄×C₁₃	—	2	3	no	—
201	C₄×C₁₃	—	2	3	no	—
202	C₄×C₁₃	—	2	3	no	—
203	C₄×C₁₃	—	4	6	no	—
204	C₄×C₁₃	—	4	2	no	—
205	C₄×C₁₃	—	4	1	no	—
206	C₄×C₁₃	—	4	3	no	—
207	C₄×C₁₃	—	4	1	no	—
208	C₄×C₁₃	C₂×#104	1	6	yes	—
209	C₂×#41	—	2	1	no	—
210	C₂×#41	—	2	3	no	—
211	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	3	no	—
213	C₄⋊Q₈	C₂×C₄×C₁₃	1	3	yes	—
214	#127	C₂×C₄×C₁₃	1	3	yes	—
215	#126	—	2	3	no	—
216	#125	C₂×C₄×C₁₃	1	3	yes	—
217	#124	—	2	3	no	—
218	#124	—	2	3	no	—
219	#124	C₂×C₄×C₁₃	1	3	yes	—
220	#123	—	2	3	no	—
221	#123	—	2	6	no	—
222	C₂²⋊Q₈	—	2	3	no	—
223	C₂²⋊Q₈	—	2	6	no	—
224	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
225	#121	—	2	3	no	—
226	#121	—	2	3	no	—
227	#121	C₂³×C₁₃	1	3	yes	—
228	C₄×Q₈	—	2	8	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	C₂×C₄×C₁₃	1	3	yes	—
231	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₄×Q₈	C₂×C₄×C₁₃	1	3	yes	—
233	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
234	C₄×Q₈	D₄×C₁₃	1	3	yes	—
235	C₄×D₄	—	2	3	no	—
236	C₄×D₄	—	2	3	no	—
237	C₄×D₄	—	2	3	no	—
238	C₄×D₄	C₂×C₄×C₁₃	1	3	yes	—
239	C₄×D₄	C₂×C₄×C₁₃	1	6	yes	—
240	#117	—	2	3	no	—
241	C₂×C₄⋊C₄	—	2	3	no	—
242	C₂×C₄⋊C₄	—	2	3	no	—
243	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
244	C₂×C₄²	—	2	3	no	—
245	C₂×C₄²	—	2	3	no	—
246	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
247	C₄⋊C₈	—	2	3	no	—
248	C₄⋊C₈	—	2	3	no	—
249	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
251	#97	—	2	3	no	—
252	C₄×C₈	—	2	3	no	—
253	#95	—	2	3	no	—
254	#95	C₂³×C₁₃	1	1	yes	characteristic
255	#95	C₂³×C₁₃	1	3	yes	—
256	C₂×C₁₃	—	2	1	no	—
257	C₂×C₁₃	—	2	1	no	—
258	C₂×C₁₃	—	8	3	no	—
259	C₂×C₁₃	#2884	1	1	yes	characteristic
260	C₂×C₁₃	#2897	1	1	yes	characteristic
261	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
262	#41	—	4	4	no	—
263	#41	—	8	3	no	—
264	#41	—	8	3	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	3	no	—
267	C₂×Q₈	C₁₃×C₂²⋊C₄	1	3	yes	—
268	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
270	C₂×D₄	—	2	3	no	—
271	C₂×D₄	—	2	3	no	—
272	C₂×D₄	—	2	3	no	—
273	C₂×D₄	C₂²×C₄×C₁₃	1	3	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	3	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
280	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	3	no	—
283	C₄⋊C₄	—	2	12	no	—
284	C₄⋊C₄	—	2	3	no	—
285	C₄⋊C₄	—	2	3	no	—
286	C₄⋊C₄	—	2	3	no	—
287	C₄⋊C₄	—	2	3	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	3	yes	—
290	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	3	yes	—
291	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	6	yes	—
292	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
293	C₄⋊C₄	C₂²×C₄×C₁₃	1	3	yes	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	3	no	—
296	C₂²⋊C₄	—	2	3	no	—
297	C₂²⋊C₄	—	2	3	no	—
298	C₂²⋊C₄	—	2	6	no	—
299	C₂²⋊C₄	—	2	3	no	—
300	C₄²	—	2	12	no	—
301	C₄²	—	2	3	no	—
302	C₄²	—	8	3	no	—
303	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
304	C₄²	C₂²×C₄×C₁₃	1	3	yes	—
305	C₄²	C₂×D₄×C₁₃	1	3	yes	—
306	C₄²	C₂×D₄×C₁₃	1	3	yes	—
307	C₁₃	#17550	1	1	yes	characteristic, direct product factor, Sylow
308	C₂³	—	2	3	no	—
309	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
310	Q₈	—	2	6	no	—
311	Q₈	—	4	1	no	—
312	Q₈	—	8	3	no	—
313	Q₈	C₁₃×#104	1	4	yes	—
314	D₄	—	4	3	no	—
315	D₄	—	4	3	no	—
316	D₄	—	4	3	no	—
317	D₄	—	4	6	no	—
318	D₄	—	8	3	no	—
319	C₂×C₄	—	2	3	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	6	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	3	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	3	no	—
330	C₂×C₄	—	4	3	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	8	6	no	—
334	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
335	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
336	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
337	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
338	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₈	—	4	1	no	—
341	C₈	—	4	3	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	3	no	—
345	C₂²	—	4	3	no	—
346	C₂²	—	4	3	no	—
347	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²	C₁₃×#576	1	1	yes	characteristic
349	C₂²	C₁₃×#577	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	3	no	—
353	C₄	—	2	3	no	—
354	C₄	—	2	3	no	—
355	C₄	—	4	6	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	3	no	—
359	C₄	—	4	1	no	—
360	C₄	C₂×C₁₃×#104	1	6	yes	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	8	3	no	—
364	C₂	C₁₃×#2884	1	1	yes	characteristic
365	C₂	C₁₃×#2897	1	1	yes	characteristic
366	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2984	C₂	semidirect
3. C₁₃×#2276	C₂	semidirect
4. C₁₃×#1509	C₂	semidirect
5. C₁₃×#1505	C₂	semidirect
6. C₁₃×#1502	C₂	semidirect
7. C₁₃×#1500	C₂	semidirect
8. C₁₃×#559	C₄	semidirect
9. Q₈²×C₁₃	C₄	semidirect
10. C₁₃×#554	C₄	semidirect
11. C₁₃×#550	C₄	semidirect
79. #17550	C₁₃	direct (N × H)
126. #2984	C₂×C₁₃	semidirect
127. #2276	C₂×C₁₃	semidirect
128. #1509	C₂×C₁₃	semidirect
129. #1505	C₂×C₁₃	semidirect
130. #1502	C₂×C₁₃	semidirect
131. #1500	C₂×C₁₃	semidirect
166. #559	C₄×C₁₃	semidirect
167. Q₈²	C₄×C₁₃	semidirect
168. #554	C₄×C₁₃	semidirect
169. #550	C₄×C₁₃	semidirect
307. C₁₃	#17550	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×#3522	2
C₁₃×#2984	2
C₁₃×#2276	2
C₁₃×#1509	2
C₁₃×#1505	2
C₁₃×#1502	2
C₁₃×#1500	2
#17550	13

Subgroups — C13×#17550 #15703889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17550 #15703889