Subgroups — C₂×C₁₃×#3184 #15747030

Order 3328.

2514 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3184	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#469	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#442	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	2	no	—
10	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#532	—	2	8	no	—
13	C₁₃×#532	C₂²	1	16	yes	complemented
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#124	—	2	2	no	—
17	C₂×C₁₃×#121	—	2	2	no	—
18	C₂×C₁₃×#121	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	—	2	2	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#498	C₂²	1	8	yes	complemented
23	C₁₃×#493	C₂²	1	8	yes	complemented
24	C₁₃×#486	C₂²	1	16	yes	complemented
25	C₁₃×#469	C₂²	1	32	yes	complemented
26	C₁₃×#442	C₂²	1	32	yes	complemented
27	C₂×C₁₃×#106	C₂²	1	4	yes	—
28	C₂×C₁₃×#102	C₂²	1	8	yes	—
29	C₄×C₁₃×M₁₆	C₂²	1	8	yes	complemented
30	C₂×C₁₃×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#41	—	2	16	no	—
34	C₂×C₁₃×#41	—	4	16	no	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₃	—	2	4	no	—
41	C₂³×C₄×C₁₃	D₄	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×D₈	—	2	16	no	—
44	C₂×C₁₃×D₈	C₂³	1	16	yes	—
45	C₂×C₁₃×M₁₆	—	2	8	no	—
46	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
51	C₁₃×#127	—	2	4	no	—
52	C₁₃×#127	C₂³	1	8	yes	—
53	C₁₃×#124	—	2	16	no	—
54	C₁₃×#121	—	2	16	no	—
55	C₁₃×#121	—	2	8	no	—
56	C₁₃×#121	C₂³	1	16	yes	—
57	C₄×D₄×C₁₃	—	2	16	no	—
58	C₄×D₄×C₁₃	—	2	8	no	—
59	C₄×D₄×C₁₃	C₂³	1	16	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₄²×C₁₃	D₄	1	2	yes	—
65	C₂×C₄²×C₁₃	D₄	1	4	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
69	C₁₃×#106	C₂³	1	16	yes	—
70	C₁₃×#102	C₂³	1	32	yes	—
71	C₁₃×#97	C₂³	1	8	yes	—
72	C₄×C₈×C₁₃	C₂³	1	4	yes	—
73	C₄×C₈×C₁₃	C₂³	1	4	yes	—
74	C₂×#3184	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	2	4	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₁₃×#41	—	4	64	no	—
78	C₂×Q₈×C₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₃	—	4	8	no	—
80	C₂×D₄×C₁₃	—	2	16	no	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	2	8	no	—
83	C₂×D₄×C₁₃	—	2	8	no	—
84	C₂×D₄×C₁₃	—	2	16	no	—
85	C₂×D₄×C₁₃	—	4	16	no	—
86	C₂×D₄×C₁₃	—	4	8	no	—
87	C₂×D₄×C₁₃	—	4	8	no	—
88	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	16	no	—
93	C₂²×C₄×C₁₃	—	4	16	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×D₈	—	2	32	no	—
102	C₁₃×M₁₆	—	2	16	no	—
103	C₂×C₈×C₁₃	—	2	4	no	—
104	C₂×C₈×C₁₃	#41	1	8	yes	complemented
105	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
106	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
107	C₁₃×C₄⋊C₄	—	2	8	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
110	C₁₃×C₂²⋊C₄	—	2	16	no	—
111	C₁₃×C₂²⋊C₄	—	2	16	no	—
112	C₄²×C₁₃	C₂×D₄	1	2	yes	—
113	C₄²×C₁₃	C₂×D₄	1	8	yes	—
114	C₄²×C₁₃	C₂×D₄	1	2	yes	—
115	C₄²×C₁₃	C₂⁴	1	2	yes	—
116	C₄²×C₁₃	C₂⁴	1	2	yes	—
117	C₂×#532	C₂×C₁₃	1	2	yes	complemented
118	#3184	C₂×C₁₃	1	16	yes	direct product factor
119	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
120	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂×#486	C₂×C₁₃	1	2	yes	complemented
122	C₂×#469	C₂×C₁₃	1	4	yes	complemented
123	C₂×#442	C₂×C₁₃	1	4	yes	complemented
124	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	—	2	8	no	—
128	C₂³×C₁₃	—	4	8	no	—
129	C₂³×C₁₃	—	4	8	no	—
130	C₂³×C₁₃	—	4	8	no	—
131	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
132	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₃	—	4	16	no	—
134	D₄×C₁₃	—	2	16	no	—
135	D₄×C₁₃	—	4	32	no	—
136	D₄×C₁₃	—	4	8	no	—
137	D₄×C₁₃	—	4	16	no	—
138	D₄×C₁₃	—	4	16	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	16	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	4	32	no	—
146	C₂×C₄×C₁₃	—	4	8	no	—
147	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	8	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
153	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
154	C₈×C₁₃	—	2	4	no	—
155	C₈×C₁₃	C₂×#41	1	8	yes	complemented
156	C₂²×#41	—	2	2	no	—
157	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
158	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
159	#532	—	2	8	no	—
160	#532	C₂²×C₁₃	1	16	yes	complemented
161	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
162	C₂×#127	C₂²×C₁₃	1	2	yes	—
163	C₂×#124	—	2	2	no	—
164	C₂×#121	—	2	2	no	—
165	C₂×#121	C₂²×C₁₃	1	4	yes	—
166	C₂×C₄×D₄	—	2	2	no	—
167	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
168	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
169	#498	C₂²×C₁₃	1	8	yes	complemented
170	#493	C₂²×C₁₃	1	8	yes	complemented
171	#486	C₂²×C₁₃	1	16	yes	complemented
172	#469	C₂²×C₁₃	1	32	yes	complemented
173	#442	C₂²×C₁₃	1	32	yes	complemented
174	C₂×#106	C₂²×C₁₃	1	4	yes	—
175	C₂×#102	C₂²×C₁₃	1	8	yes	—
176	C₄×M₁₆	C₂²×C₁₃	1	8	yes	complemented
177	C₂×#97	C₂²×C₁₃	1	2	yes	—
178	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₁₃	—	2	2	no	—
181	C₂²×C₁₃	—	2	4	no	—
182	C₂²×C₁₃	—	4	4	no	—
183	C₂²×C₁₃	—	4	8	no	—
184	C₂²×C₁₃	—	4	8	no	—
185	C₂²×C₁₃	—	4	8	no	—
186	C₂²×C₁₃	—	8	16	no	—
187	C₂²×C₁₃	#532	1	2	yes	—
188	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
189	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₁₃	—	2	2	no	—
191	C₄×C₁₃	—	2	4	no	—
192	C₄×C₁₃	—	4	8	no	—
193	C₄×C₁₃	#532	1	2	yes	—
194	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	8	yes	—
195	C₄×C₁₃	C₂²×#41	1	2	yes	—
196	C₂×#41	—	2	16	no	—
197	C₂×#41	—	4	16	no	—
198	C₂²×Q₈	—	2	2	no	—
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	2	2	no	—
201	C₂²×D₄	—	2	2	no	—
202	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
203	C₂³×C₄	—	2	4	no	—
204	C₂³×C₄	D₄×C₁₃	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
206	C₂×D₈	—	2	16	no	—
207	C₂×D₈	C₂³×C₁₃	1	16	yes	—
208	C₂×M₁₆	—	2	8	no	—
209	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
210	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
211	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
212	C₄⋊Q₈	—	2	4	no	—
213	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
214	#127	—	2	4	no	—
215	#127	C₂³×C₁₃	1	8	yes	—
216	#124	—	2	16	no	—
217	#121	—	2	16	no	—
218	#121	—	2	8	no	—
219	#121	C₂³×C₁₃	1	16	yes	—
220	C₄×D₄	—	2	16	no	—
221	C₄×D₄	—	2	8	no	—
222	C₄×D₄	C₂³×C₁₃	1	16	yes	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
225	C₂×C₂²⋊C₄	—	2	4	no	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₄²	D₄×C₁₃	1	2	yes	—
228	C₂×C₄²	D₄×C₁₃	1	4	yes	—
229	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
232	#106	C₂³×C₁₃	1	16	yes	—
233	#102	C₂³×C₁₃	1	32	yes	—
234	#97	C₂³×C₁₃	1	8	yes	—
235	C₄×C₈	C₂³×C₁₃	1	4	yes	—
236	C₄×C₈	C₂³×C₁₃	1	4	yes	—
237	C₂×C₁₃	—	4	2	no	—
238	C₂×C₁₃	—	8	8	no	—
239	C₂×C₁₃	#3184	1	4	yes	direct product factor
240	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
241	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	2	yes	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
244	#41	—	4	64	no	—
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	4	8	no	—
247	C₂×D₄	—	2	16	no	—
248	C₂×D₄	—	2	4	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	8	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	4	16	no	—
253	C₂×D₄	—	4	8	no	—
254	C₂×D₄	—	4	8	no	—
255	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	4	16	no	—
261	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
268	D₈	—	2	32	no	—
269	M₁₆	—	2	16	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	C₁₃×#41	1	8	yes	complemented
272	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
273	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
277	C₂²⋊C₄	—	2	16	no	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₄²	C₂×D₄×C₁₃	1	2	yes	—
280	C₄²	C₂×D₄×C₁₃	1	8	yes	—
281	C₄²	C₂×D₄×C₁₃	1	2	yes	—
282	C₄²	C₂⁴×C₁₃	1	2	yes	—
283	C₄²	C₂⁴×C₁₃	1	2	yes	—
284	C₁₃	C₂×#3184	1	1	yes	characteristic, direct product factor, Sylow
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	8	no	—
290	C₂³	—	4	8	no	—
291	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
292	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
293	Q₈	—	4	16	no	—
294	D₄	—	2	16	no	—
295	D₄	—	4	32	no	—
296	D₄	—	4	8	no	—
297	D₄	—	4	16	no	—
298	D₄	—	4	16	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	4	32	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
309	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
310	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
312	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
313	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
314	C₈	—	2	4	no	—
315	C₈	C₂×C₁₃×#41	1	8	yes	complemented
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	8	no	—
320	C₂²	—	4	8	no	—
321	C₂²	—	4	8	no	—
322	C₂²	—	8	16	no	—
323	C₂²	C₁₃×#532	1	2	yes	—
324	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
325	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	8	no	—
329	C₄	C₁₃×#532	1	2	yes	—
330	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	8	yes	—
331	C₄	C₂²×C₁₃×#41	1	2	yes	—
332	C₂	—	4	2	no	—
333	C₂	—	8	8	no	—
334	C₂	C₁₃×#3184	1	4	yes	direct product factor
335	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
336	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₁₃×#3184	C₂	direct (N × H)
3. C₂×C₁₃×#498	C₂	semidirect
4. C₂×C₁₃×#493	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#469	C₂	semidirect
7. C₂×C₁₃×#442	C₂	semidirect
8. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
13. C₁₃×#532	C₂²	semidirect
22. C₁₃×#498	C₂²	semidirect
23. C₁₃×#493	C₂²	semidirect
24. C₁₃×#486	C₂²	semidirect
25. C₁₃×#469	C₂²	semidirect
26. C₁₃×#442	C₂²	semidirect
29. C₄×C₁₃×M₁₆	C₂²	semidirect
74. C₂×#3184	C₁₃	direct (N × H)
104. C₂×C₈×C₁₃	#41	semidirect
117. C₂×#532	C₂×C₁₃	semidirect
118. #3184	C₂×C₁₃	direct (N × H)
119. C₂×#498	C₂×C₁₃	semidirect
120. C₂×#493	C₂×C₁₃	semidirect
121. C₂×#486	C₂×C₁₃	semidirect
122. C₂×#469	C₂×C₁₃	semidirect
123. C₂×#442	C₂×C₁₃	semidirect
124. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
155. C₈×C₁₃	C₂×#41	semidirect
160. #532	C₂²×C₁₃	semidirect
169. #498	C₂²×C₁₃	semidirect
170. #493	C₂²×C₁₃	semidirect
171. #486	C₂²×C₁₃	semidirect
172. #469	C₂²×C₁₃	semidirect
173. #442	C₂²×C₁₃	semidirect
176. C₄×M₁₆	C₂²×C₁₃	semidirect
239. C₂×C₁₃	#3184	direct (N × H)
271. C₂×C₈	C₁₃×#41	semidirect
284. C₁₃	C₂×#3184	direct (N × H)
315. C₈	C₂×C₁₃×#41	semidirect
334. C₂	C₁₃×#3184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₁₃×#3184	2
C₂×C₁₃×#498	2
C₂×C₁₃×#493	2
C₂×C₁₃×#486	2
C₂×C₁₃×#469	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3184	13

Subgroups — C2×C13×#3184 #15747030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3184 #15747030