Subgroups — C₁₃×#10836 #15697175

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×H(3,ℤ/4)	C₂	1	4	yes	maximal
5	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂×C₁₃×#117	C₂²	1	2	yes	—
7	C₂×C₁₃×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#423	—	2	2	no	—
10	C₁₃×#423	—	2	1	no	—
11	C₁₃×#423	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₁₃×#384	—	2	1	no	—
14	C₁₃×#382	—	2	1	no	—
15	C₁₃×#380	—	2	2	no	—
16	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
17	C₄×C₁₃×C₄⋊C₄	C₄	1	4	yes	complemented
18	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
19	C₁₃×#376	C₄	1	2	yes	complemented
20	C₄³×C₁₃	C₄	1	2	yes	complemented
21	C₁₃×H(3,ℤ/4)	—	2	8	no	—
22	C₂³×C₄×C₁₃	D₄	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₁₃×M₁₆	—	2	4	no	—
25	C₂×C₁₃×M₁₆	—	2	2	no	—
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	4	no	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
29	C₁₃×#117	—	2	2	no	—
30	C₁₃×#117	—	2	2	no	—
31	C₁₃×#117	—	2	4	no	—
32	C₁₃×#117	—	2	4	no	—
33	C₁₃×#117	D₄	1	4	yes	—
34	C₁₃×#117	Q₈	1	4	yes	—
35	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
40	C₂×C₄²×C₁₃	—	2	4	no	—
41	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	D₄	1	2	yes	—
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
52	C₁₃×C₄⋊C₈	—	2	4	no	—
53	C₁₃×C₄⋊C₈	—	2	4	no	—
54	C₁₃×#95	—	2	4	no	—
55	C₁₃×#95	—	2	4	no	—
56	#10836	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	4	4	no	—
61	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₁₃	#41	1	2	yes	—
76	C₂²×C₄×C₁₃	#41	1	2	yes	—
77	C₁₃×M₁₆	—	4	4	no	—
78	C₁₃×M₁₆	—	4	2	no	—
79	C₁₃×M₁₆	—	4	2	no	—
80	C₂×C₈×C₁₃	—	2	4	no	—
81	C₂×C₈×C₁₃	—	2	8	no	—
82	C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₁₃×C₄⋊C₄	—	2	4	no	—
84	C₁₃×C₄⋊C₄	—	4	8	no	—
85	C₁₃×C₄⋊C₄	—	4	2	no	—
86	C₁₃×C₄⋊C₄	—	4	2	no	—
87	C₁₃×C₂²⋊C₄	—	2	4	no	—
88	C₁₃×C₂²⋊C₄	—	2	4	no	—
89	C₁₃×C₂²⋊C₄	—	4	4	no	—
90	C₄²×C₁₃	—	2	4	no	—
91	C₄²×C₁₃	—	2	8	no	—
92	C₄²×C₁₃	—	4	8	no	—
93	C₄²×C₁₃	C₄²	1	2	yes	—
94	C₄²×C₁₃	C₄²	1	2	yes	—
95	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
101	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₄⋊C₄	1	8	yes	complemented
104	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
105	#2285	C₂×C₁₃	1	1	yes	characteristic
106	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
107	C₂×H(3,ℤ/4)	C₂×C₁₃	1	4	yes	—
108	C₂³×C₁₃	—	4	2	no	—
109	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂³×C₁₃	#121	1	2	yes	—
113	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
114	C₂×C₄×C₁₃	—	2	4	no	—
115	C₂×C₄×C₁₃	—	2	4	no	—
116	C₂×C₄×C₁₃	—	2	4	no	—
117	C₂×C₄×C₁₃	—	2	8	no	—
118	C₂×C₄×C₁₃	—	4	2	no	—
119	C₂×C₄×C₁₃	—	4	2	no	—
120	C₂×C₄×C₁₃	—	4	2	no	—
121	C₂×C₄×C₁₃	—	4	8	no	—
122	C₂×C₄×C₁₃	—	4	8	no	—
123	C₂×C₄×C₁₃	—	4	4	no	—
124	C₂×C₄×C₁₃	#95	1	2	yes	—
125	C₂×C₄×C₁₃	#95	1	2	yes	—
126	C₂×C₄×C₁₃	#95	1	2	yes	—
127	C₂×C₄×C₁₃	#95	1	2	yes	—
128	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	#117	1	2	yes	—
134	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
137	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₁₃	#121	1	2	yes	—
139	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
141	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#125	1	2	yes	—
143	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
146	C₈×C₁₃	—	4	4	no	—
147	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
148	C₂×#117	C₂²×C₁₃	1	2	yes	—
149	C₂×#117	C₂²×C₁₃	1	2	yes	—
150	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
151	#423	—	2	2	no	—
152	#423	—	2	1	no	—
153	#423	—	2	1	no	—
154	C₂×C₄⋊C₈	C₄×C₁₃	1	4	yes	complemented
155	#384	—	2	1	no	—
156	#382	—	2	1	no	—
157	#380	—	2	2	no	—
158	C₄×C₄⋊C₄	—	2	2	no	—
159	C₄×C₄⋊C₄	C₄×C₁₃	1	4	yes	complemented
160	C₄×C₂²⋊C₄	—	2	2	no	—
161	#376	C₄×C₁₃	1	2	yes	complemented
162	C₄³	C₄×C₁₃	1	2	yes	complemented
163	H(3,ℤ/4)	—	2	8	no	—
164	C₂²×C₁₃	—	2	2	no	—
165	C₂²×C₁₃	—	2	2	no	—
166	C₂²×C₁₃	—	2	2	no	—
167	C₂²×C₁₃	—	4	2	no	—
168	C₂²×C₁₃	—	4	2	no	—
169	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
170	C₂²×C₁₃	#380	1	2	yes	—
171	C₂²×C₁₃	#389	1	2	yes	—
172	C₂²×C₁₃	#390	1	1	yes	characteristic
173	C₂²×C₁₃	#391	1	1	yes	characteristic
174	C₄×C₁₃	—	2	2	no	—
175	C₄×C₁₃	—	2	2	no	—
176	C₄×C₁₃	—	2	2	no	—
177	C₄×C₁₃	—	4	8	no	—
178	C₄×C₁₃	—	8	4	no	—
179	C₄×C₁₃	H(3,ℤ/4)	1	4	yes	complemented
180	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
181	C₄×C₁₃	#382	1	1	yes	characteristic
182	C₄×C₁₃	#384	1	1	yes	characteristic
183	C₄×C₁₃	#389	1	2	yes	—
184	C₄×C₁₃	#390	1	1	yes	characteristic
185	C₄×C₁₃	#391	1	1	yes	characteristic
186	C₂³×C₄	D₄×C₁₃	1	2	yes	—
187	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
188	C₂×M₁₆	—	2	4	no	—
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	4	no	—
192	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
193	#117	—	2	2	no	—
194	#117	—	2	2	no	—
195	#117	—	2	4	no	—
196	#117	—	2	4	no	—
197	#117	D₄×C₁₃	1	4	yes	—
198	#117	Q₈×C₁₃	1	4	yes	—
199	C₂×C₄⋊C₄	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₄²	—	2	4	no	—
205	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
206	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
207	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
208	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
211	C₂×C₄²	D₄×C₁₃	1	2	yes	—
212	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
213	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄²	Q₈×C₁₃	1	1	yes	characteristic
215	C₂×C₄²	Q₈×C₁₃	1	1	yes	characteristic
216	C₄⋊C₈	—	2	4	no	—
217	C₄⋊C₈	—	2	4	no	—
218	#95	—	2	4	no	—
219	#95	—	2	4	no	—
220	C₂×C₁₃	—	2	2	no	—
221	C₂×C₁₃	—	2	1	no	—
222	C₂×C₁₃	—	2	2	no	—
223	C₂×C₁₃	—	2	1	no	—
224	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
225	C₂×C₁₃	C₂×H(3,ℤ/4)	1	2	yes	—
226	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	4	4	no	—
230	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
231	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
232	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
233	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
234	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
235	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
239	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
242	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
244	C₂²×C₄	C₁₃×#41	1	2	yes	—
245	C₂²×C₄	C₁₃×#41	1	2	yes	—
246	M₁₆	—	4	4	no	—
247	M₁₆	—	4	2	no	—
248	M₁₆	—	4	2	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	8	no	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	4	8	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₂²⋊C₄	—	2	4	no	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	4	4	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	8	no	—
261	C₄²	—	4	8	no	—
262	C₄²	C₄²×C₁₃	1	2	yes	—
263	C₄²	C₄²×C₁₃	1	2	yes	—
264	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
265	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
266	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
267	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
268	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
269	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
270	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
271	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
272	C₄²	C₁₃×C₄⋊C₄	1	8	yes	complemented
273	C₁₃	#10836	1	1	yes	characteristic, direct product factor, Sylow
274	C₂³	—	4	2	no	—
275	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
276	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
278	C₂³	C₁₃×#121	1	2	yes	—
279	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	8	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	C₁₃×#95	1	2	yes	—
291	C₂×C₄	C₁₃×#95	1	2	yes	—
292	C₂×C₄	C₁₃×#95	1	2	yes	—
293	C₂×C₄	C₁₃×#95	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
295	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
297	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄	C₁₃×#117	1	2	yes	—
300	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
301	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
302	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
304	C₂×C₄	C₁₃×#121	1	2	yes	—
305	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
306	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
307	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
308	C₂×C₄	C₁₃×#125	1	2	yes	—
309	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
310	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
311	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
312	C₈	—	4	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
319	C₂²	C₁₃×#380	1	2	yes	—
320	C₂²	C₁₃×#389	1	2	yes	—
321	C₂²	C₁₃×#390	1	1	yes	characteristic
322	C₂²	C₁₃×#391	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	8	no	—
327	C₄	—	8	4	no	—
328	C₄	C₁₃×H(3,ℤ/4)	1	4	yes	complemented
329	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
330	C₄	C₁₃×#382	1	1	yes	characteristic
331	C₄	C₁₃×#384	1	1	yes	characteristic
332	C₄	C₁₃×#389	1	2	yes	—
333	C₄	C₁₃×#390	1	1	yes	characteristic
334	C₄	C₁₃×#391	1	1	yes	characteristic
335	C₂	—	2	2	no	—
336	C₂	—	2	1	no	—
337	C₂	—	2	2	no	—
338	C₂	—	2	1	no	—
339	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
340	C₂	C₂×C₁₃×H(3,ℤ/4)	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
17. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
19. C₁₃×#376	C₄	semidirect
20. C₄³×C₁₃	C₄	semidirect
56. #10836	C₁₃	direct (N × H)
103. C₄²×C₁₃	C₄⋊C₄	semidirect
154. C₂×C₄⋊C₈	C₄×C₁₃	semidirect
159. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
161. #376	C₄×C₁₃	semidirect
162. C₄³	C₄×C₁₃	semidirect
179. C₄×C₁₃	H(3,ℤ/4)	semidirect
272. C₄²	C₁₃×C₄⋊C₄	semidirect
273. C₁₃	#10836	direct (N × H)
328. C₄	C₁₃×H(3,ℤ/4)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#423	2
C₁₃×#2285	2
C₄×C₁₃×#117	2
C₂×C₁₃×H(3,ℤ/4)	2
#10836	13

Subgroups — C13×#10836 #15697175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10836 #15697175