Subgroups — C₁₃×#34257 #15720596

Order 3328.

5050 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2341	C₂	1	8	yes	maximal, complemented
5	Q₈×C₁₃×C₂²⋊C₄	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2311	C₂	1	6	yes	maximal, complemented
7	C₁₃×#2297	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
9	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
10	C₂×C₁₃×2₋¹⁺⁴	C₄	1	16	yes	complemented
11	C₂²×C₁₃×#41	C₂²	1	6	yes	—
12	C₂²×C₁₃×#41	C₂²	1	4	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	4	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#519	—	2	8	no	—
16	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	—
19	C₂×C₁₃×#117	C₂²	1	6	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
22	C₁₃×#391	C₂²	1	12	yes	—
23	C₁₃×#391	C₂²	1	12	yes	—
24	C₁₃×#390	C₂²	1	12	yes	—
25	C₁₃×#390	C₂²	1	12	yes	—
26	C₁₃×#386	C₂²	1	4	yes	—
27	C₁₃×#386	C₂²	1	12	yes	—
28	C₁₃×#380	C₂²	1	24	yes	—
29	C₄×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	—
30	C₁₃×2₋¹⁺⁴	—	2	128	no	—
31	C₂×C₁₃×#41	—	2	16	no	—
32	C₂×C₁₃×#41	—	2	16	no	—
33	C₂×C₁₃×#41	—	2	24	no	—
34	C₂×C₁₃×#41	—	2	24	no	—
35	C₂×C₁₃×#41	C₂×C₄	1	48	yes	—
36	C₂×C₁₃×#41	C₂×C₄	1	32	yes	complemented
37	C₂²×Q₈×C₁₃	—	2	16	no	—
38	C₂²×Q₈×C₁₃	—	2	16	no	—
39	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	32	yes	complemented
41	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
42	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
51	C₄×Q₈×C₁₃	—	2	32	no	—
52	C₄×Q₈×C₁₃	—	2	32	no	—
53	C₁₃×#117	—	2	24	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
57	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
58	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
59	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
60	C₂×C₄²×C₁₃	—	2	12	no	—
61	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
63	C₁₃×#95	C₂³	1	8	yes	—
64	C₁₃×#95	C₂³	1	24	yes	—
65	#34257	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
67	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₁₃×#41	—	2	128	no	—
69	C₁₃×#41	—	2	192	no	—
70	C₂×Q₈×C₁₃	—	2	128	no	—
71	C₂×Q₈×C₁₃	—	2	12	no	—
72	C₂×Q₈×C₁₃	—	2	12	no	—
73	C₂×Q₈×C₁₃	C₂²⋊C₄	1	64	yes	complemented
74	C₂×Q₈×C₁₃	C₂²×C₄	1	24	yes	—
75	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
76	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	—
77	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	—
78	C₂×D₄×C₁₃	—	2	8	no	—
79	C₂×D₄×C₁₃	—	2	8	no	—
80	C₂×D₄×C₁₃	—	2	12	no	—
81	C₂×D₄×C₁₃	—	2	12	no	—
82	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
83	C₂×D₄×C₁₃	C₂²×C₄	1	24	yes	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	24	no	—
86	C₂²×C₄×C₁₃	—	2	24	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	6	no	—
89	C₂²×C₄×C₁₃	—	4	6	no	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	48	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
99	C₁₃×C₄⋊C₄	—	2	24	no	—
100	C₁₃×C₄⋊C₄	—	2	24	no	—
101	C₁₃×C₂²⋊C₄	—	2	8	no	—
102	C₁₃×C₂²⋊C₄	—	2	16	no	—
103	C₁₃×C₂²⋊C₄	—	4	24	no	—
104	C₄²×C₁₃	—	2	24	no	—
105	C₄²×C₁₃	—	2	24	no	—
106	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic
107	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
108	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
109	#2341	C₂×C₁₃	1	8	yes	complemented
110	Q₈×C₂²⋊C₄	C₂×C₁₃	1	8	yes	complemented
111	#2311	C₂×C₁₃	1	6	yes	complemented
112	#2297	C₂×C₁₃	1	6	yes	complemented
113	C₂³×C₁₃	—	2	2	no	—
114	C₂³×C₁₃	—	2	2	no	—
115	C₂³×C₁₃	—	2	4	no	—
116	C₂³×C₁₃	—	2	4	no	—
117	C₂³×C₁₃	—	2	8	no	—
118	C₂³×C₁₃	—	2	8	no	—
119	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
120	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
121	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
122	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
123	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
124	Q₈×C₁₃	—	2	48	no	—
125	Q₈×C₁₃	C₂×C₂²⋊C₄	1	64	yes	—
126	D₄×C₁₃	—	2	32	no	—
127	D₄×C₁₃	—	2	48	no	—
128	C₂×C₄×C₁₃	—	2	8	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	96	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	6	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	12	no	—
139	C₂×C₄×C₁₃	—	4	12	no	—
140	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	48	yes	—
141	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
143	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
145	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	complemented
146	C₂×2₋¹⁺⁴	—	2	8	no	—
147	C₂×2₋¹⁺⁴	—	2	8	no	—
148	C₂×2₋¹⁺⁴	C₄×C₁₃	1	16	yes	complemented
149	C₂²×#41	C₂²×C₁₃	1	6	yes	—
150	C₂²×#41	C₂²×C₁₃	1	4	yes	—
151	C₂³×Q₈	C₂²×C₁₃	1	4	yes	—
152	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
153	#519	—	2	8	no	—
154	C₂×C₄×Q₈	—	2	8	no	—
155	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	—
156	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	—
157	C₂×#117	C₂²×C₁₃	1	6	yes	—
158	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
159	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
160	#391	C₂²×C₁₃	1	12	yes	—
161	#391	C₂²×C₁₃	1	12	yes	—
162	#390	C₂²×C₁₃	1	12	yes	—
163	#390	C₂²×C₁₃	1	12	yes	—
164	#386	C₂²×C₁₃	1	12	yes	—
165	#386	C₂²×C₁₃	1	4	yes	—
166	#380	C₂²×C₁₃	1	24	yes	—
167	C₄×C₂²⋊C₄	C₂²×C₁₃	1	24	yes	—
168	C₂²×C₁₃	—	2	4	no	—
169	C₂²×C₁₃	—	2	2	no	—
170	C₂²×C₁₃	—	2	2	no	—
171	C₂²×C₁₃	—	2	4	no	—
172	C₂²×C₁₃	—	2	8	no	—
173	C₂²×C₁₃	—	2	16	no	—
174	C₂²×C₁₃	—	4	4	no	—
175	C₂²×C₁₃	—	4	4	no	—
176	C₂²×C₁₃	—	4	8	no	—
177	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
178	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
179	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
180	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
181	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₁₃	#585	1	2	yes	—
183	C₄×C₁₃	—	2	8	no	—
184	C₄×C₁₃	—	2	4	no	—
185	C₄×C₁₃	—	4	6	no	—
186	C₄×C₁₃	—	4	8	no	—
187	C₄×C₁₃	C₂²×C₂²⋊C₄	1	24	yes	—
188	2₋¹⁺⁴	—	2	128	no	—
189	C₂×#41	—	2	16	no	—
190	C₂×#41	—	2	16	no	—
191	C₂×#41	—	2	24	no	—
192	C₂×#41	—	2	24	no	—
193	C₂×#41	C₂×C₄×C₁₃	1	48	yes	—
194	C₂×#41	C₂×C₄×C₁₃	1	32	yes	complemented
195	C₂²×Q₈	—	2	16	no	—
196	C₂²×Q₈	—	2	16	no	—
197	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
198	C₂²×Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
199	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
200	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
201	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
202	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
203	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
204	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
209	C₄×Q₈	—	2	32	no	—
210	C₄×Q₈	—	2	32	no	—
211	#117	—	2	24	no	—
212	C₂×C₄⋊C₄	—	2	12	no	—
213	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
216	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
217	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
218	C₂×C₄²	—	2	12	no	—
219	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
220	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
221	#95	C₂³×C₁₃	1	8	yes	—
222	#95	C₂³×C₁₃	1	24	yes	—
223	C₂×C₁₃	—	2	4	no	—
224	C₂×C₁₃	—	4	8	no	—
225	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
227	C₂×C₁₃	#3486	1	1	yes	characteristic
228	C₂×C₁₃	#3487	1	1	yes	characteristic
229	C₂×C₁₃	#3497	1	2	yes	—
230	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
231	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
232	#41	—	2	128	no	—
233	#41	—	2	192	no	—
234	C₂×Q₈	—	2	128	no	—
235	C₂×Q₈	—	2	12	no	—
236	C₂×Q₈	—	2	12	no	—
237	C₂×Q₈	C₁₃×C₂²⋊C₄	1	64	yes	complemented
238	C₂×Q₈	C₂²×C₄×C₁₃	1	24	yes	—
239	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
240	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	—
241	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	—
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	12	no	—
245	C₂×D₄	—	2	12	no	—
246	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
247	C₂×D₄	C₂²×C₄×C₁₃	1	24	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	24	no	—
250	C₂²×C₄	—	2	24	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	6	no	—
253	C₂²×C₄	—	4	6	no	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	48	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
256	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
257	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
260	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
261	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
262	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
263	C₄⋊C₄	—	2	24	no	—
264	C₄⋊C₄	—	2	24	no	—
265	C₂²⋊C₄	—	2	8	no	—
266	C₂²⋊C₄	—	2	16	no	—
267	C₂²⋊C₄	—	4	24	no	—
268	C₄²	—	2	24	no	—
269	C₄²	—	2	24	no	—
270	C₁₃	#34257	1	1	yes	characteristic, direct product factor, Sylow
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	8	no	—
276	C₂³	—	2	8	no	—
277	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
278	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
279	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
280	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
281	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
282	Q₈	—	2	48	no	—
283	Q₈	C₂×C₁₃×C₂²⋊C₄	1	64	yes	—
284	D₄	—	2	32	no	—
285	D₄	—	2	48	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	96	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	6	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	12	no	—
297	C₂×C₄	—	4	12	no	—
298	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	48	yes	—
299	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
300	C₂×C₄	C₂³×C₄×C₁₃	1	12	yes	—
301	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
302	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
303	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	complemented
304	C₂²	—	2	4	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	8	no	—
309	C₂²	—	2	16	no	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	4	no	—
312	C₂²	—	4	8	no	—
313	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
314	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
315	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
316	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
317	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
318	C₂²	C₁₃×#585	1	2	yes	—
319	C₄	—	2	8	no	—
320	C₄	—	2	4	no	—
321	C₄	—	4	6	no	—
322	C₄	—	4	8	no	—
323	C₄	C₂²×C₁₃×C₂²⋊C₄	1	24	yes	—
324	C₂	—	2	4	no	—
325	C₂	—	4	8	no	—
326	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
327	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
328	C₂	C₁₃×#3486	1	1	yes	characteristic
329	C₂	C₁₃×#3487	1	1	yes	characteristic
330	C₂	C₁₃×#3497	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#519	C₂	semidirect
3. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#2341	C₂	semidirect
5. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
6. C₁₃×#2311	C₂	semidirect
7. C₁₃×#2297	C₂	semidirect
10. C₂×C₁₃×2₋¹⁺⁴	C₄	semidirect
36. C₂×C₁₃×#41	C₂×C₄	semidirect
40. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
65. #34257	C₁₃	direct (N × H)
73. C₂×Q₈×C₁₃	C₂²⋊C₄	semidirect
107. C₂×#519	C₂×C₁₃	semidirect
108. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
109. #2341	C₂×C₁₃	semidirect
110. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
111. #2311	C₂×C₁₃	semidirect
112. #2297	C₂×C₁₃	semidirect
145. C₂×C₄×C₁₃	2₋¹⁺⁴	semidirect
148. C₂×2₋¹⁺⁴	C₄×C₁₃	semidirect
194. C₂×#41	C₂×C₄×C₁₃	semidirect
198. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
237. C₂×Q₈	C₁₃×C₂²⋊C₄	semidirect
270. C₁₃	#34257	direct (N × H)
303. C₂×C₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×2₋¹⁺⁴	2
C₂×C₁₃×#519	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2341	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2311	2
C₁₃×#2297	2
#34257	13

Subgroups — C13×#34257 #15720596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34257 #15720596