Subgroups — C₂×C₁₃×#2210 #15719914

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2210	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×SD₁₆	—	2	1	no	—
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	—	2	4	no	—
16	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
17	C₂×C₁₃×D₁₆	—	2	4	no	—
18	C₂×C₁₃×D₁₆	C₂²	1	4	yes	—
19	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₁₃×#495	—	2	2	no	—
22	C₁₃×#495	C₂²	1	4	yes	complemented
23	C₄×C₁₃×D₈	—	2	2	no	—
24	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
29	C₁₃×#358	C₂²	1	4	yes	complemented
30	C₁₃×#357	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂³×C₄×C₁₃	—	4	1	no	—
35	C₂×C₁₃×Q₁₆	—	2	2	no	—
36	C₂×C₁₃×Q₁₆	—	2	1	no	—
37	C₂×C₁₃×Q₁₆	—	2	2	no	—
38	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
39	C₂×C₁₃×SD₁₆	—	2	4	no	—
40	C₂×C₁₃×SD₁₆	—	4	4	no	—
41	C₂×C₁₃×D₈	—	2	1	no	—
42	C₂×C₁₃×D₈	—	2	2	no	—
43	C₂×C₁₃×D₈	—	2	1	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	D₄	1	4	yes	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂×C₁₃×D₈	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#124	—	2	4	no	—
52	C₁₃×#124	—	4	2	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	—	4	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₁₃×SD₃₂	—	2	8	no	—
61	C₁₃×D₁₆	—	2	8	no	—
62	C₂×C₁₃×C₁₆	—	2	2	no	—
63	C₂×C₁₃×C₁₆	—	2	2	no	—
64	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
66	C₁₃×#107	—	2	1	no	—
67	C₁₃×#107	C₂³	1	2	yes	—
68	C₁₃×#102	—	2	4	no	—
69	C₄×C₈×C₁₃	D₄	1	2	yes	—
70	C₄×C₈×C₁₃	C₂³	1	2	yes	—
71	C₂×#2210	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	4	1	no	—
73	C₂⁴×C₁₃	—	4	1	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	4	1	no	—
76	C₂×Q₈×C₁₃	—	4	2	no	—
77	C₂×Q₈×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	—	2	4	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	4	1	no	—
83	C₂×D₄×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	8	4	no	—
90	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₁₃×Q₁₆	—	2	2	no	—
94	C₁₃×Q₁₆	—	2	2	no	—
95	C₁₃×Q₁₆	—	4	2	no	—
96	C₁₃×SD₁₆	—	4	8	no	—
97	C₁₃×D₈	—	2	4	no	—
98	C₁₃×D₈	—	2	2	no	—
99	C₁₃×D₈	—	2	2	no	—
100	C₁₃×D₈	—	2	2	no	—
101	C₁₃×D₈	—	4	2	no	—
102	C₁₃×D₈	C₂×D₄	1	4	yes	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₃	#41	1	2	yes	—
108	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	no	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₄²×C₁₃	D₈	1	2	yes	—
115	C₄²×C₁₃	C₂×D₄	1	2	yes	—
116	C₁₃×C₁₆	—	2	2	no	—
117	C₁₃×C₁₆	—	2	2	no	—
118	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic
120	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
122	#2210	C₂×C₁₃	1	8	yes	direct product factor
123	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
126	C₂³×C₁₃	—	4	2	no	—
127	C₂³×C₁₃	—	4	4	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	—	8	2	no	—
130	C₂³×C₁₃	—	8	2	no	—
131	C₂³×C₁₃	—	8	2	no	—
132	C₂³×C₁₃	—	8	2	no	—
133	C₂³×C₁₃	—	8	2	no	—
134	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
135	Q₈×C₁₃	—	4	2	no	—
136	Q₈×C₁₃	—	4	2	no	—
137	Q₈×C₁₃	—	8	2	no	—
138	D₄×C₁₃	—	2	4	no	—
139	D₄×C₁₃	—	4	2	no	—
140	D₄×C₁₃	—	4	2	no	—
141	D₄×C₁₃	—	4	2	no	—
142	D₄×C₁₃	—	4	4	no	—
143	D₄×C₁₃	—	8	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	8	8	no	—
149	C₂×C₄×C₁₃	—	8	2	no	—
150	C₂×C₄×C₁₃	—	8	2	no	—
151	C₂×C₄×C₁₃	#121	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₃	—	2	2	no	—
158	C₈×C₁₃	#121	1	2	yes	—
159	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
161	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
162	C₂²×SD₁₆	—	2	1	no	—
163	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
164	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
165	C₂×#124	—	2	1	no	—
166	C₂×C₄×D₄	—	2	1	no	—
167	C₂×SD₃₂	—	2	4	no	—
168	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
169	C₂×D₁₆	—	2	4	no	—
170	C₂×D₁₆	C₂²×C₁₃	1	4	yes	—
171	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
172	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
173	#495	—	2	2	no	—
174	#495	C₂²×C₁₃	1	4	yes	complemented
175	C₄×D₈	—	2	2	no	—
176	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
177	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×#102	—	2	1	no	—
179	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
181	#358	C₂²×C₁₃	1	4	yes	complemented
182	#357	C₂²×C₁₃	1	4	yes	complemented
183	C₂²×C₁₃	—	4	4	no	—
184	C₂²×C₁₃	—	8	2	no	—
185	C₂²×C₁₃	—	8	2	no	—
186	C₂²×C₁₃	—	8	8	no	—
187	C₂²×C₁₃	—	8	2	no	—
188	C₂²×C₁₃	—	8	2	no	—
189	C₂²×C₁₃	—	8	2	no	—
190	C₂²×C₁₃	—	16	4	no	—
191	C₂²×C₁₃	#459	1	2	yes	—
192	C₂²×C₁₃	#508	1	2	yes	—
193	C₂²×C₁₃	#509	1	2	yes	—
194	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	8	2	no	—
198	C₄×C₁₃	—	8	2	no	—
199	C₄×C₁₃	#459	1	2	yes	—
200	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
201	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×Q₈	—	2	1	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂²×D₄	—	2	1	no	—
205	C₂³×C₄	—	4	1	no	—
206	C₂×Q₁₆	—	2	2	no	—
207	C₂×Q₁₆	—	2	1	no	—
208	C₂×Q₁₆	—	2	2	no	—
209	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
210	C₂×SD₁₆	—	2	4	no	—
211	C₂×SD₁₆	—	4	4	no	—
212	C₂×D₈	—	2	1	no	—
213	C₂×D₈	—	2	2	no	—
214	C₂×D₈	—	2	1	no	—
215	C₂×D₈	—	2	2	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	D₄×C₁₃	1	4	yes	—
218	C₂×D₈	C₂³×C₁₃	1	2	yes	—
219	C₂×D₈	C₂³×C₁₃	1	2	yes	—
220	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
222	#124	—	2	4	no	—
223	#124	—	4	2	no	—
224	C₄×D₄	—	2	4	no	—
225	C₄×D₄	—	4	2	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₂²⋊C₄	—	4	1	no	—
228	C₂×C₂²⋊C₄	—	4	1	no	—
229	C₂×C₂²⋊C₄	—	4	1	no	—
230	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
231	SD₃₂	—	2	8	no	—
232	D₁₆	—	2	8	no	—
233	C₂×C₁₆	—	2	2	no	—
234	C₂×C₁₆	—	2	2	no	—
235	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
236	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
237	#107	—	2	1	no	—
238	#107	C₂³×C₁₃	1	2	yes	—
239	#102	—	2	4	no	—
240	C₄×C₈	D₄×C₁₃	1	2	yes	—
241	C₄×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂×C₁₃	—	8	4	no	—
243	C₂×C₁₃	—	16	2	no	—
244	C₂×C₁₃	#2210	1	4	yes	direct product factor
245	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
246	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
247	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
248	C₂⁴	—	4	1	no	—
249	C₂⁴	—	4	1	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	—	4	1	no	—
252	C₂×Q₈	—	4	2	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	4	2	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	—	4	1	no	—
260	C₂×D₄	—	4	2	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	8	4	no	—
266	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
267	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
269	Q₁₆	—	2	2	no	—
270	Q₁₆	—	2	2	no	—
271	Q₁₆	—	4	2	no	—
272	SD₁₆	—	4	8	no	—
273	D₈	—	2	4	no	—
274	D₈	—	2	2	no	—
275	D₈	—	2	2	no	—
276	D₈	—	2	2	no	—
277	D₈	—	4	2	no	—
278	D₈	C₂×D₄×C₁₃	1	4	yes	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
281	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
283	C₂×C₈	C₁₃×#41	1	2	yes	—
284	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	4	4	no	—
290	C₄²	C₁₃×D₈	1	2	yes	—
291	C₄²	C₂×D₄×C₁₃	1	2	yes	—
292	C₁₆	—	2	2	no	—
293	C₁₆	—	2	2	no	—
294	C₁₃	C₂×#2210	1	1	yes	characteristic, direct product factor, Sylow
295	C₂³	—	4	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	8	2	no	—
299	C₂³	—	8	2	no	—
300	C₂³	—	8	2	no	—
301	C₂³	—	8	2	no	—
302	C₂³	—	8	2	no	—
303	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	8	2	no	—
307	D₄	—	2	4	no	—
308	D₄	—	4	4	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	2	no	—
312	D₄	—	8	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	8	8	no	—
318	C₂×C₄	—	8	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	C₁₃×#121	1	2	yes	—
321	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
322	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
323	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
324	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
326	C₈	—	2	2	no	—
327	C₈	C₁₃×#121	1	2	yes	—
328	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
330	C₂²	—	4	4	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	8	2	no	—
333	C₂²	—	8	8	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	8	2	no	—
337	C₂²	—	16	4	no	—
338	C₂²	C₁₃×#459	1	2	yes	—
339	C₂²	C₁₃×#508	1	2	yes	—
340	C₂²	C₁₃×#509	1	2	yes	—
341	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	8	2	no	—
345	C₄	—	8	2	no	—
346	C₄	C₁₃×#459	1	2	yes	—
347	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
348	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂	—	8	4	no	—
350	C₂	—	16	2	no	—
351	C₂	C₁₃×#2210	1	4	yes	direct product factor
352	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
353	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
354	C₂	C₂×C₁₃×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×SD₃₂	C₂	semidirect
3. C₂×C₁₃×#495	C₂	semidirect
4. C₂×C₄×C₁₃×D₈	C₂	semidirect
5. C₁₃×#2210	C₂	direct (N × H)
6. C₂×C₁₃×C₄⋊C₁₆	C₂	semidirect
7. C₂×C₁₃×#358	C₂	semidirect
8. C₂×C₁₃×#357	C₂	semidirect
16. C₂×C₁₃×SD₃₂	C₂²	semidirect
22. C₁₃×#495	C₂²	semidirect
24. C₄×C₁₃×D₈	C₂²	semidirect
28. C₁₃×C₄⋊C₁₆	C₂²	semidirect
29. C₁₃×#358	C₂²	semidirect
30. C₁₃×#357	C₂²	semidirect
71. C₂×#2210	C₁₃	direct (N × H)
118. C₂²×SD₃₂	C₂×C₁₃	semidirect
120. C₂×#495	C₂×C₁₃	semidirect
121. C₂×C₄×D₈	C₂×C₁₃	semidirect
122. #2210	C₂×C₁₃	direct (N × H)
123. C₂×C₄⋊C₁₆	C₂×C₁₃	semidirect
124. C₂×#358	C₂×C₁₃	semidirect
125. C₂×#357	C₂×C₁₃	semidirect
168. C₂×SD₃₂	C₂²×C₁₃	semidirect
174. #495	C₂²×C₁₃	semidirect
176. C₄×D₈	C₂²×C₁₃	semidirect
180. C₄⋊C₁₆	C₂²×C₁₃	semidirect
181. #358	C₂²×C₁₃	semidirect
182. #357	C₂²×C₁₃	semidirect
244. C₂×C₁₃	#2210	direct (N × H)
294. C₁₃	C₂×#2210	direct (N × H)
351. C₂	C₁₃×#2210	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×SD₃₂	2
C₂²×C₁₃×D₁₆	2
C₂×C₁₃×#495	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2210	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₁₃×#358	2
C₂×C₁₃×#357	2
C₂×#2210	13

Subgroups — C2×C13×#2210 #15719914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2210 #15719914