Subgroups — C₁₃×C₄⋊C₄×Q₁₆ #15709023

Order 3328.

926 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	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₁₃×#1942	C₂	1	2	yes	maximal
5	C₁₃×#1863	C₂	1	4	yes	maximal
6	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1803	C₂	1	2	yes	maximal
8	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
11	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₄×C₁₃×Q₁₆	—	2	8	no	—
13	C₄×C₁₃×Q₁₆	C₄	1	8	yes	complemented
14	C₂×C₁₃×#107	C₂²	1	2	yes	—
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	C₂²	1	4	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#389	—	2	4	no	—
23	C₁₃×#389	C₂²	1	4	yes	—
24	C₁₃×#384	—	2	2	no	—
25	C₁₃×#384	C₂²	1	2	yes	—
26	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₃×#340	C₂²	1	4	yes	—
29	C₁₃×#336	C₂²	1	2	yes	—
30	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
31	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
33	C₂×C₁₃×Q₁₆	Q₈	1	4	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₄×Q₈×C₁₃	—	2	4	no	—
38	C₄×Q₈×C₁₃	—	2	8	no	—
39	C₄×Q₈×C₁₃	—	4	4	no	—
40	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
41	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₃	—	2	4	no	—
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#107	—	2	4	no	—
55	C₁₃×#107	—	4	2	no	—
56	C₁₃×#107	C₂×C₄	1	4	yes	—
57	C₁₃×C₄⋊C₈	—	2	2	no	—
58	C₁₃×#103	—	2	8	no	—
59	C₁₃×#103	C₂×C₄	1	8	yes	—
60	C₄×C₈×C₁₃	—	2	4	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
62	C₁₃×#95	—	2	4	no	—
63	C₁₃×#95	D₄	1	2	yes	—
64	C₄⋊C₄×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂×Q₈×C₁₃	—	2	2	no	—
66	C₂×Q₈×C₁₃	—	2	2	no	—
67	C₂×Q₈×C₁₃	—	2	2	no	—
68	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
69	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
70	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	4	no	—
74	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
79	C₁₃×Q₁₆	C₄⋊C₄	1	16	yes	direct product factor
80	C₂×C₈×C₁₃	—	2	1	no	—
81	C₂×C₈×C₁₃	—	2	1	no	—
82	C₂×C₈×C₁₃	—	2	2	no	—
83	C₂×C₈×C₁₃	—	2	2	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
88	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
89	C₁₃×C₄⋊C₄	—	2	8	no	—
90	C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₁₃×C₄⋊C₄	—	4	8	no	—
95	C₁₃×C₄⋊C₄	—	4	4	no	—
96	C₁₃×C₄⋊C₄	—	8	2	no	—
97	C₁₃×C₄⋊C₄	—	8	4	no	—
98	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	direct product factor
99	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
100	C₄²×C₁₃	—	2	8	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	—	4	8	no	—
104	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₃	#41	1	2	yes	—
106	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	—
107	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
108	Q₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
109	#1942	C₂×C₁₃	1	2	yes	—
110	#1863	C₂×C₁₃	1	4	yes	—
111	#1845	C₂×C₁₃	1	1	yes	characteristic
112	#1803	C₂×C₁₃	1	2	yes	—
113	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
114	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
115	Q₈×C₁₃	—	2	4	no	—
116	Q₈×C₁₃	—	2	4	no	—
117	Q₈×C₁₃	—	2	4	no	—
118	Q₈×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
119	C₂×C₄×C₁₃	—	2	4	no	—
120	C₂×C₄×C₁₃	—	2	2	no	—
121	C₂×C₄×C₁₃	—	2	4	no	—
122	C₂×C₄×C₁₃	—	2	4	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	1	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	4	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	4	2	no	—
131	C₂×C₄×C₁₃	—	4	2	no	—
132	C₂×C₄×C₁₃	—	4	4	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	4	no	—
135	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
138	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
139	C₂×C₄×C₁₃	#135	1	2	yes	—
140	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
146	C₈×C₁₃	—	2	2	no	—
147	C₈×C₁₃	—	4	2	no	—
148	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
149	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
150	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
151	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
152	C₄×Q₁₆	—	2	8	no	—
153	C₄×Q₁₆	C₄×C₁₃	1	8	yes	complemented
154	C₂×#107	C₂²×C₁₃	1	2	yes	—
155	C₂×#107	C₂²×C₁₃	1	2	yes	—
156	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×#103	C₂²×C₁₃	1	4	yes	—
159	C₂×#103	C₂²×C₁₃	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
162	#389	—	2	4	no	—
163	#389	C₂²×C₁₃	1	4	yes	—
164	#384	—	2	2	no	—
165	#384	C₂²×C₁₃	1	2	yes	—
166	C₄×C₄⋊C₄	—	2	2	no	—
167	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
168	#340	C₂²×C₁₃	1	4	yes	—
169	#336	C₂²×C₁₃	1	2	yes	—
170	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₁₃	D₄²	1	1	yes	characteristic
172	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
173	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
174	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
175	C₂²×C₁₃	#576	1	1	yes	characteristic
176	C₂²×C₁₃	#578	1	1	yes	characteristic
177	C₄×C₁₃	—	2	8	no	—
178	C₄×C₁₃	—	2	2	no	—
179	C₄×C₁₃	—	2	4	no	—
180	C₄×C₁₃	—	4	4	no	—
181	C₄×C₁₃	—	4	2	no	—
182	C₄×C₁₃	—	8	4	no	—
183	C₄×C₁₃	C₄×Q₁₆	1	4	yes	complemented
184	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₁₃	#520	1	1	yes	characteristic
186	C₄×C₁₃	#547	1	1	yes	characteristic
187	C₄×C₁₃	#554	1	1	yes	characteristic
188	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
189	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
190	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
191	C₂×Q₁₆	Q₈×C₁₃	1	4	yes	—
192	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
193	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
194	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
195	C₄×Q₈	—	2	4	no	—
196	C₄×Q₈	—	2	8	no	—
197	C₄×Q₈	—	4	4	no	—
198	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
199	C₂×C₄⋊C₄	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
205	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
207	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	—	2	4	no	—
210	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
211	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
212	#107	—	2	4	no	—
213	#107	—	4	2	no	—
214	#107	C₂×C₄×C₁₃	1	4	yes	—
215	C₄⋊C₈	—	2	2	no	—
216	#103	—	2	8	no	—
217	#103	C₂×C₄×C₁₃	1	8	yes	—
218	C₄×C₈	—	2	4	no	—
219	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
220	#95	—	2	4	no	—
221	#95	D₄×C₁₃	1	2	yes	—
222	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₁₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
224	C₂×C₁₃	#2951	1	1	yes	characteristic
225	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
226	C₂×C₁₃	#3287	1	1	yes	characteristic
227	C₂×C₁₃	Q₈×Q₁₆	1	1	yes	characteristic
228	C₂×C₁₃	#3383	1	1	yes	characteristic
229	C₂×Q₈	—	2	2	no	—
230	C₂×Q₈	—	2	2	no	—
231	C₂×Q₈	—	2	2	no	—
232	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
233	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
234	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
239	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
241	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
243	Q₁₆	C₁₃×C₄⋊C₄	1	16	yes	direct product factor
244	C₂×C₈	—	2	1	no	—
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
250	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
251	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
252	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
253	C₄⋊C₄	—	2	8	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	4	8	no	—
259	C₄⋊C₄	—	4	4	no	—
260	C₄⋊C₄	—	8	2	no	—
261	C₄⋊C₄	—	8	4	no	—
262	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	direct product factor
263	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
264	C₄²	—	2	8	no	—
265	C₄²	—	2	2	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	4	8	no	—
268	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
269	C₄²	C₁₃×#41	1	2	yes	—
270	C₁₃	C₄⋊C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
271	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
272	Q₈	—	2	4	no	—
273	Q₈	—	2	4	no	—
274	Q₈	—	2	4	no	—
275	Q₈	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
293	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
294	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
295	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
296	C₂×C₄	C₁₃×#135	1	2	yes	—
297	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
300	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
301	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
303	C₈	—	2	2	no	—
304	C₈	—	4	2	no	—
305	C₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
306	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
307	C₂²	D₄²×C₁₃	1	1	yes	characteristic
308	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
309	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
310	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
311	C₂²	C₁₃×#576	1	1	yes	characteristic
312	C₂²	C₁₃×#578	1	1	yes	characteristic
313	C₄	—	2	4	no	—
314	C₄	—	2	8	no	—
315	C₄	—	2	2	no	—
316	C₄	—	4	2	no	—
317	C₄	—	4	4	no	—
318	C₄	—	8	4	no	—
319	C₄	C₄×C₁₃×Q₁₆	1	4	yes	complemented
320	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
321	C₄	C₁₃×#520	1	1	yes	characteristic
322	C₄	C₁₃×#547	1	1	yes	characteristic
323	C₄	C₁₃×#554	1	1	yes	characteristic
324	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
325	C₂	C₂×C₄×C₁₃×Q₁₆	1	1	yes	characteristic
326	C₂	C₁₃×#2951	1	1	yes	characteristic
327	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
328	C₂	C₁₃×#3287	1	1	yes	characteristic
329	C₂	Q₈×C₁₃×Q₁₆	1	1	yes	characteristic
330	C₂	C₁₃×#3383	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₄×C₁₃×Q₁₆	C₄	semidirect
64. C₄⋊C₄×Q₁₆	C₁₃	direct (N × H)
79. C₁₃×Q₁₆	C₄⋊C₄	direct (N × H)
98. C₁₃×C₄⋊C₄	Q₁₆	direct (N × H)
153. C₄×Q₁₆	C₄×C₁₃	semidirect
183. C₄×C₁₃	C₄×Q₁₆	semidirect
243. Q₁₆	C₁₃×C₄⋊C₄	direct (N × H)
262. C₄⋊C₄	C₁₃×Q₁₆	direct (N × H)
270. C₁₃	C₄⋊C₄×Q₁₆	direct (N × H)
319. C₄	C₄×C₁₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×Q₁₆	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#1942	2
C₁₃×#1863	2
C₁₃×#1845	2
C₁₃×#1803	2
C₈×C₁₃×C₄⋊C₄	2
C₄⋊C₄×Q₁₆	13

Subgroups — C13×C4⋊C4×Q16 #15709023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₄⋊C₄×Q₁₆ #15709023