Subgroups — C₁₃×#34172 #15720511

Order 3328.

5430 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2339	C₂	1	16	yes	maximal, complemented
4	C₁₃×#2310	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2308	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2280	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#381	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#41	—	2	16	no	—
9	C₂²×C₁₃×#41	C₄	1	16	yes	complemented
10	C₂²×C₁₃×#41	C₂²	1	8	yes	—
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#518	—	2	16	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
18	C₂×C₁₃×#117	C₂²	1	4	yes	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
20	C₁₃×#391	C₂²	1	16	yes	complemented
21	C₁₃×#386	C₂²	1	32	yes	complemented
22	C₁₃×#381	C₂²	1	4	yes	—
23	C₁₃×#381	C₂²	1	8	yes	—
24	C₁₃×#381	C₂²	1	16	yes	complemented
25	C₁₃×#380	C₂²	1	8	yes	complemented
26	C₁₃×#379	C₂²	1	4	yes	—
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#95	C₂²	1	16	yes	complemented
29	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
30	C₂⁵×C₁₃	C₂³	1	2	yes	—
31	C₂×C₁₃×#41	—	2	128	no	—
32	C₂×C₁₃×#41	—	2	64	no	—
33	C₂×C₁₃×#41	C₂×C₄	1	64	yes	complemented
34	C₂²×Q₈×C₁₃	—	2	8	no	—
35	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
36	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
37	C₂²×D₄×C₁₃	—	2	16	no	—
38	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
40	C₂²×D₄×C₁₃	D₄	1	16	yes	—
41	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	—	2	16	no	—
44	C₂³×C₄×C₁₃	—	2	8	no	—
45	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
46	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	64	no	—
54	C₁₃×#117	—	2	16	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
57	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
58	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
59	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
61	C₁₃×#95	C₂³	1	16	yes	—
62	C₁₃×#95	C₂³	1	32	yes	—
63	#34172	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁴×C₁₃	—	2	4	no	—
65	C₂⁴×C₁₃	—	4	8	no	—
66	C₂⁴×C₁₃	—	4	4	no	—
67	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
68	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
69	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
70	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
71	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
72	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
73	C₁₃×#41	—	2	256	no	—
74	C₂×Q₈×C₁₃	—	2	32	no	—
75	C₂×Q₈×C₁₃	—	2	16	no	—
76	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
77	C₂×D₄×C₁₃	—	2	64	no	—
78	C₂×D₄×C₁₃	—	2	32	no	—
79	C₂×D₄×C₁₃	C₂²⋊C₄	1	64	yes	complemented
80	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	—
81	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
82	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	—
83	C₂²×C₄×C₁₃	—	2	64	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	2	32	no	—
87	C₂²×C₄×C₁₃	—	2	32	no	—
88	C₂²×C₄×C₁₃	—	2	16	no	—
89	C₂²×C₄×C₁₃	—	2	32	no	—
90	C₂²×C₄×C₁₃	—	4	32	no	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
101	C₁₃×C₄⋊C₄	—	2	16	no	—
102	C₁₃×C₂²⋊C₄	—	2	16	no	—
103	C₁₃×C₂²⋊C₄	—	2	32	no	—
104	C₁₃×C₂²⋊C₄	—	4	16	no	—
105	C₄²×C₁₃	—	2	16	no	—
106	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic
107	C₂×#518	C₂×C₁₃	1	2	yes	complemented
108	#2339	C₂×C₁₃	1	16	yes	complemented
109	#2310	C₂×C₁₃	1	2	yes	complemented
110	#2308	C₂×C₁₃	1	4	yes	complemented
111	#2280	C₂×C₁₃	1	2	yes	complemented
112	C₂×#381	C₂×C₁₃	1	4	yes	complemented
113	C₂³×C₁₃	—	2	16	no	—
114	C₂³×C₁₃	—	2	4	no	—
115	C₂³×C₁₃	—	2	8	no	—
116	C₂³×C₁₃	—	2	4	no	—
117	C₂³×C₁₃	—	2	8	no	—
118	C₂³×C₁₃	—	4	16	no	—
119	C₂³×C₁₃	—	4	8	no	—
120	C₂³×C₁₃	—	4	32	no	—
121	C₂³×C₁₃	—	4	16	no	—
122	C₂³×C₁₃	C₂×C₂²⋊C₄	1	32	yes	—
123	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
124	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
125	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
126	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
127	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
128	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
129	Q₈×C₁₃	—	2	32	no	—
130	D₄×C₁₃	—	2	64	no	—
131	D₄×C₁₃	C₂×C₂²⋊C₄	1	64	yes	—
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	16	no	—
134	C₂×C₄×C₁₃	—	2	64	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	32	no	—
138	C₂×C₄×C₁₃	—	2	16	no	—
139	C₂×C₄×C₁₃	—	2	32	no	—
140	C₂×C₄×C₁₃	—	8	32	no	—
141	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
144	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
145	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
146	C₂²×#41	—	2	16	no	—
147	C₂²×#41	C₄×C₁₃	1	16	yes	complemented
148	C₂²×#41	C₂²×C₁₃	1	8	yes	—
149	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
150	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
151	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
152	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
153	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
154	#518	—	2	16	no	—
155	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
156	C₂×#117	C₂²×C₁₃	1	4	yes	—
157	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
158	#391	C₂²×C₁₃	1	16	yes	complemented
159	#386	C₂²×C₁₃	1	32	yes	complemented
160	#381	C₂²×C₁₃	1	8	yes	—
161	#381	C₂²×C₁₃	1	4	yes	—
162	#381	C₂²×C₁₃	1	16	yes	complemented
163	#380	C₂²×C₁₃	1	8	yes	complemented
164	#379	C₂²×C₁₃	1	4	yes	—
165	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
166	C₂×#95	C₂²×C₁₃	1	16	yes	complemented
167	C₂²×C₁₃	—	2	4	no	—
168	C₂²×C₁₃	—	2	16	no	—
169	C₂²×C₁₃	—	2	32	no	—
170	C₂²×C₁₃	—	2	8	no	—
171	C₂²×C₁₃	—	2	4	no	—
172	C₂²×C₁₃	—	2	8	no	—
173	C₂²×C₁₃	—	4	32	no	—
174	C₂²×C₁₃	—	4	16	no	—
175	C₂²×C₁₃	—	4	8	no	—
176	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
177	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	16	yes	—
178	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
179	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
180	C₂²×C₁₃	#585	1	4	yes	—
181	C₄×C₁₃	—	2	4	no	—
182	C₄×C₁₃	—	2	8	no	—
183	C₄×C₁₃	—	4	16	no	—
184	C₄×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
185	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
186	C₂⁵	C₂³×C₁₃	1	2	yes	—
187	C₂×#41	—	2	128	no	—
188	C₂×#41	—	2	64	no	—
189	C₂×#41	C₂×C₄×C₁₃	1	64	yes	complemented
190	C₂²×Q₈	—	2	8	no	—
191	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
192	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
193	C₂²×D₄	—	2	16	no	—
194	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
195	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
196	C₂²×D₄	D₄×C₁₃	1	16	yes	—
197	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
198	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
199	C₂³×C₄	—	2	16	no	—
200	C₂³×C₄	—	2	8	no	—
201	C₂³×C₄	C₂×C₄×C₁₃	1	16	yes	complemented
202	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
203	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
204	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
206	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
209	C₄×D₄	—	2	64	no	—
210	#117	—	2	16	no	—
211	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
212	C₂×C₂²⋊C₄	—	2	32	no	—
213	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
216	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
217	#95	C₂³×C₁₃	1	16	yes	—
218	#95	C₂³×C₁₃	1	32	yes	—
219	C₂×C₁₃	—	2	4	no	—
220	C₂×C₁₃	—	2	16	no	—
221	C₂×C₁₃	—	4	4	no	—
222	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₁₃	#3428	1	2	yes	—
224	C₂×C₁₃	#3485	1	4	yes	—
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	4	8	no	—
227	C₂⁴	—	4	4	no	—
228	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
229	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
230	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
231	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
232	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
233	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
234	#41	—	2	256	no	—
235	C₂×Q₈	—	2	32	no	—
236	C₂×Q₈	—	2	16	no	—
237	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
238	C₂×D₄	—	2	64	no	—
239	C₂×D₄	—	2	32	no	—
240	C₂×D₄	C₁₃×C₂²⋊C₄	1	64	yes	complemented
241	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	—
242	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
243	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	—
244	C₂²×C₄	—	2	64	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	32	no	—
248	C₂²×C₄	—	2	32	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	32	no	—
251	C₂²×C₄	—	4	32	no	—
252	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	32	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
257	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
261	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
262	C₄⋊C₄	—	2	16	no	—
263	C₂²⋊C₄	—	2	16	no	—
264	C₂²⋊C₄	—	2	32	no	—
265	C₂²⋊C₄	—	4	16	no	—
266	C₄²	—	2	16	no	—
267	C₁₃	#34172	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³	—	2	16	no	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	8	no	—
273	C₂³	—	4	16	no	—
274	C₂³	—	4	8	no	—
275	C₂³	—	4	32	no	—
276	C₂³	—	4	16	no	—
277	C₂³	C₂×C₁₃×C₂²⋊C₄	1	32	yes	—
278	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
279	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
280	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
281	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
282	C₂³	C₂²×D₄×C₁₃	1	16	yes	—
283	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
284	Q₈	—	2	32	no	—
285	D₄	—	2	64	no	—
286	D₄	C₂×C₁₃×C₂²⋊C₄	1	64	yes	—
287	C₂×C₄	—	2	8	no	—
288	C₂×C₄	—	2	16	no	—
289	C₂×C₄	—	2	64	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	32	no	—
293	C₂×C₄	—	2	16	no	—
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	8	32	no	—
296	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	16	yes	—
297	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
298	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
299	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
300	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	16	no	—
303	C₂²	—	2	32	no	—
304	C₂²	—	2	8	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	8	no	—
307	C₂²	—	4	32	no	—
308	C₂²	—	4	16	no	—
309	C₂²	—	4	8	no	—
310	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
311	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	16	yes	—
312	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
313	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
314	C₂²	C₁₃×#585	1	4	yes	—
315	C₄	—	2	4	no	—
316	C₄	—	2	8	no	—
317	C₄	—	4	16	no	—
318	C₄	C₂²×C₁₃×C₂²⋊C₄	1	8	yes	—
319	C₂	—	2	4	no	—
320	C₂	—	2	16	no	—
321	C₂	—	4	4	no	—
322	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂	C₁₃×#3428	1	2	yes	—
324	C₂	C₁₃×#3485	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×C₁₃×#41	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×#518	C₂	semidirect
3. C₁₃×#2339	C₂	semidirect
4. C₁₃×#2310	C₂	semidirect
5. C₁₃×#2308	C₂	semidirect
6. C₁₃×#2280	C₂	semidirect
7. C₂×C₁₃×#381	C₂	semidirect
9. C₂²×C₁₃×#41	C₄	semidirect
17. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₁₃×#391	C₂²	semidirect
21. C₁₃×#386	C₂²	semidirect
24. C₁₃×#381	C₂²	semidirect
25. C₁₃×#380	C₂²	semidirect
27. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₁₃×#95	C₂²	semidirect
33. C₂×C₁₃×#41	C₂×C₄	semidirect
35. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
39. C₂²×D₄×C₁₃	C₂×C₄	semidirect
45. C₂³×C₄×C₁₃	C₂×C₄	semidirect
46. C₂³×C₄×C₁₃	C₂×C₄	semidirect
63. #34172	C₁₃	direct (N × H)
79. C₂×D₄×C₁₃	C₂²⋊C₄	semidirect
107. C₂×#518	C₂×C₁₃	semidirect
108. #2339	C₂×C₁₃	semidirect
109. #2310	C₂×C₁₃	semidirect
110. #2308	C₂×C₁₃	semidirect
111. #2280	C₂×C₁₃	semidirect
112. C₂×#381	C₂×C₁₃	semidirect
147. C₂²×#41	C₄×C₁₃	semidirect
155. C₂×C₄×D₄	C₂²×C₁₃	semidirect
158. #391	C₂²×C₁₃	semidirect
159. #386	C₂²×C₁₃	semidirect
162. #381	C₂²×C₁₃	semidirect
163. #380	C₂²×C₁₃	semidirect
165. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
166. C₂×#95	C₂²×C₁₃	semidirect
189. C₂×#41	C₂×C₄×C₁₃	semidirect
191. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
195. C₂²×D₄	C₂×C₄×C₁₃	semidirect
201. C₂³×C₄	C₂×C₄×C₁₃	semidirect
202. C₂³×C₄	C₂×C₄×C₁₃	semidirect
240. C₂×D₄	C₁₃×C₂²⋊C₄	semidirect
267. C₁₃	#34172	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂×C₁₃×#518	2
C₁₃×#2339	2
C₁₃×#2310	2
C₁₃×#2308	2
C₁₃×#2280	2
C₂×C₁₃×#381	2
#34172	13

Subgroups — C13×#34172 #15720511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34172 #15720511