Subgroups — C₂×C₁₃×#3169 #15747010

Order 3328.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 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×#3169	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#500	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×#466	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×C₁₃×D₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	2	no	—
10	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
11	C₂³×C₈×C₁₃	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×#500	C₂²	1	8	yes	complemented
23	C₁₃×#493	C₂²	1	8	yes	complemented
24	C₁₃×#486	C₂²	1	16	yes	complemented
25	C₁₃×#466	C₂²	1	32	yes	complemented
26	C₄×C₁₃×D₈	C₂²	1	32	yes	complemented
27	C₂×C₁₃×#107	C₂²	1	4	yes	—
28	C₂×C₁₃×#102	C₂²	1	8	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	8	yes	complemented
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	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×D₈	—	2	16	no	—
45	C₂×C₁₃×D₈	C₂³	1	16	yes	—
46	C₂²×C₈×C₁₃	—	2	8	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
52	C₁₃×#127	—	2	4	no	—
53	C₁₃×#127	C₂³	1	8	yes	—
54	C₁₃×#124	—	2	16	no	—
55	C₁₃×#121	—	2	16	no	—
56	C₁₃×#121	—	2	8	no	—
57	C₁₃×#121	C₂³	1	16	yes	—
58	C₄×D₄×C₁₃	—	2	16	no	—
59	C₄×D₄×C₁₃	—	2	8	no	—
60	C₄×D₄×C₁₃	C₂³	1	16	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	4	yes	—
67	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	C₂³	1	16	yes	—
72	C₁₃×#102	C₂³	1	32	yes	—
73	C₄×C₈×C₁₃	C₂³	1	8	yes	—
74	C₄×C₈×C₁₃	C₂³	1	4	yes	—
75	C₄×C₈×C₁₃	C₂³	1	4	yes	—
76	C₂×#3169	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	4	no	—
78	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₁₃×#41	—	4	64	no	—
80	C₂×Q₈×C₁₃	—	2	8	no	—
81	C₂×Q₈×C₁₃	—	4	8	no	—
82	C₂×D₄×C₁₃	—	2	16	no	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	—	2	8	no	—
85	C₂×D₄×C₁₃	—	2	8	no	—
86	C₂×D₄×C₁₃	—	2	16	no	—
87	C₂×D₄×C₁₃	—	4	16	no	—
88	C₂×D₄×C₁₃	—	4	8	no	—
89	C₂×D₄×C₁₃	—	4	8	no	—
90	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	16	no	—
95	C₂²×C₄×C₁₃	—	4	16	no	—
96	C₂²×C₄×C₁₃	D₈	1	8	yes	complemented
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×D₈	—	2	32	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	16	no	—
110	C₂×C₈×C₁₃	#41	1	8	yes	complemented
111	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
112	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
113	C₁₃×C₄⋊C₄	—	2	8	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
116	C₁₃×C₂²⋊C₄	—	2	16	no	—
117	C₁₃×C₂²⋊C₄	—	2	16	no	—
118	C₄²×C₁₃	C₂×D₄	1	4	yes	—
119	C₄²×C₁₃	C₂×D₄	1	2	yes	—
120	C₄²×C₁₃	C₂×D₄	1	4	yes	—
121	C₄²×C₁₃	C₂×D₄	1	2	yes	—
122	C₄²×C₁₃	C₂⁴	1	2	yes	—
123	C₄²×C₁₃	C₂⁴	1	2	yes	—
124	C₂×#532	C₂×C₁₃	1	2	yes	complemented
125	#3169	C₂×C₁₃	1	16	yes	direct product factor
126	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂×#486	C₂×C₁₃	1	2	yes	complemented
129	C₂×#466	C₂×C₁₃	1	4	yes	complemented
130	C₂×C₄×D₈	C₂×C₁₃	1	4	yes	complemented
131	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	—	2	8	no	—
135	C₂³×C₁₃	—	4	8	no	—
136	C₂³×C₁₃	—	4	8	no	—
137	C₂³×C₁₃	—	4	8	no	—
138	C₂³×C₁₃	C₂×D₈	1	4	yes	—
139	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
140	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃	—	4	16	no	—
142	D₄×C₁₃	—	2	16	no	—
143	D₄×C₁₃	—	4	32	no	—
144	D₄×C₁₃	—	4	8	no	—
145	D₄×C₁₃	—	4	16	no	—
146	D₄×C₁₃	—	4	16	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	8	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	4	8	no	—
154	C₂×C₄×C₁₃	—	4	32	no	—
155	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
156	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
157	C₂×C₄×C₁₃	C₂×D₈	1	16	yes	complemented
158	C₂×C₄×C₁₃	#135	1	4	yes	—
159	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
166	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
167	C₈×C₁₃	—	2	4	no	—
168	C₈×C₁₃	C₂×#41	1	8	yes	complemented
169	C₂²×#41	—	2	2	no	—
170	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
171	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
172	#532	—	2	8	no	—
173	#532	C₂²×C₁₃	1	16	yes	complemented
174	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
175	C₂×#127	C₂²×C₁₃	1	2	yes	—
176	C₂×#124	—	2	2	no	—
177	C₂×#121	—	2	2	no	—
178	C₂×#121	C₂²×C₁₃	1	4	yes	—
179	C₂×C₄×D₄	—	2	2	no	—
180	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
181	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
182	#500	C₂²×C₁₃	1	8	yes	complemented
183	#493	C₂²×C₁₃	1	8	yes	complemented
184	#486	C₂²×C₁₃	1	16	yes	complemented
185	#466	C₂²×C₁₃	1	32	yes	complemented
186	C₄×D₈	C₂²×C₁₃	1	32	yes	complemented
187	C₂×#107	C₂²×C₁₃	1	4	yes	—
188	C₂×#102	C₂²×C₁₃	1	8	yes	—
189	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₁₃	1	8	yes	complemented
193	C₂²×C₁₃	—	2	8	no	—
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	—	4	8	no	—
197	C₂²×C₁₃	—	4	8	no	—
198	C₂²×C₁₃	—	4	8	no	—
199	C₂²×C₁₃	—	8	16	no	—
200	C₂²×C₁₃	#532	1	2	yes	—
201	C₂²×C₁₃	C₂²×D₈	1	4	yes	—
202	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
203	C₂²×C₁₃	C₂×#135	1	2	yes	—
204	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	2	no	—
207	C₄×C₁₃	—	4	8	no	—
208	C₄×C₁₃	#532	1	2	yes	—
209	C₄×C₁₃	C₂²×D₈	1	4	yes	—
210	C₄×C₁₃	C₂²×D₈	1	4	yes	—
211	C₄×C₁₃	C₂×#135	1	4	yes	—
212	C₄×C₁₃	C₂²×#41	1	2	yes	—
213	C₂×#41	—	2	16	no	—
214	C₂×#41	—	4	16	no	—
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×D₈	—	2	16	no	—
225	C₂×D₈	C₂³×C₁₃	1	16	yes	—
226	C₂²×C₈	—	2	8	no	—
227	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
229	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
232	#127	—	2	4	no	—
233	#127	C₂³×C₁₃	1	8	yes	—
234	#124	—	2	16	no	—
235	#121	—	2	16	no	—
236	#121	—	2	8	no	—
237	#121	C₂³×C₁₃	1	16	yes	—
238	C₄×D₄	—	2	16	no	—
239	C₄×D₄	—	2	8	no	—
240	C₄×D₄	C₂³×C₁₃	1	16	yes	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₁₃	1	4	yes	—
248	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
251	#107	C₂³×C₁₃	1	16	yes	—
252	#102	C₂³×C₁₃	1	32	yes	—
253	C₄×C₈	C₂³×C₁₃	1	8	yes	—
254	C₄×C₈	C₂³×C₁₃	1	4	yes	—
255	C₄×C₈	C₂³×C₁₃	1	4	yes	—
256	C₂×C₁₃	—	2	4	no	—
257	C₂×C₁₃	—	8	8	no	—
258	C₂×C₁₃	#3169	1	4	yes	direct product factor
259	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
260	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
261	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
262	C₂⁴	—	2	4	no	—
263	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
264	#41	—	4	64	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	4	8	no	—
267	C₂×D₄	—	2	16	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	16	no	—
272	C₂×D₄	—	4	16	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	16	no	—
280	C₂²×C₄	—	4	16	no	—
281	C₂²×C₄	C₁₃×D₈	1	8	yes	complemented
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
292	D₈	—	2	32	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	16	no	—
295	C₂×C₈	C₁₃×#41	1	8	yes	complemented
296	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
297	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	2	16	no	—
303	C₄²	C₂×D₄×C₁₃	1	4	yes	—
304	C₄²	C₂×D₄×C₁₃	1	2	yes	—
305	C₄²	C₂×D₄×C₁₃	1	4	yes	—
306	C₄²	C₂×D₄×C₁₃	1	2	yes	—
307	C₄²	C₂⁴×C₁₃	1	2	yes	—
308	C₄²	C₂⁴×C₁₃	1	2	yes	—
309	C₁₃	C₂×#3169	1	1	yes	characteristic, direct product factor, Sylow
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	4	8	no	—
316	C₂³	C₂×C₁₃×D₈	1	4	yes	—
317	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
318	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
319	Q₈	—	4	16	no	—
320	D₄	—	2	16	no	—
321	D₄	—	4	32	no	—
322	D₄	—	4	8	no	—
323	D₄	—	4	16	no	—
324	D₄	—	4	16	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	—	4	32	no	—
333	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
334	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
335	C₂×C₄	C₂×C₁₃×D₈	1	16	yes	complemented
336	C₂×C₄	C₁₃×#135	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
343	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
344	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
345	C₈	—	2	4	no	—
346	C₈	C₂×C₁₃×#41	1	8	yes	complemented
347	C₂²	—	2	2	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₃×#532	1	2	yes	—
355	C₂²	C₂²×C₁₃×D₈	1	4	yes	—
356	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
357	C₂²	C₂×C₁₃×#135	1	2	yes	—
358	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	8	no	—
362	C₄	C₁₃×#532	1	2	yes	—
363	C₄	C₂²×C₁₃×D₈	1	4	yes	—
364	C₄	C₂²×C₁₃×D₈	1	4	yes	—
365	C₄	C₂×C₁₃×#135	1	4	yes	—
366	C₄	C₂²×C₁₃×#41	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₁₃×#3169	1	4	yes	direct product factor
370	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
371	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
372	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×#3169	C₂	direct (N × H)
3. C₂×C₁₃×#500	C₂	semidirect
4. C₂×C₁₃×#493	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#466	C₂	semidirect
7. C₂×C₄×C₁₃×D₈	C₂	semidirect
8. C₂²×C₄×C₈×C₁₃	C₂	semidirect
13. C₁₃×#532	C₂²	semidirect
22. C₁₃×#500	C₂²	semidirect
23. C₁₃×#493	C₂²	semidirect
24. C₁₃×#486	C₂²	semidirect
25. C₁₃×#466	C₂²	semidirect
26. C₄×C₁₃×D₈	C₂²	semidirect
32. C₂×C₄×C₈×C₁₃	C₂²	semidirect
76. C₂×#3169	C₁₃	direct (N × H)
96. C₂²×C₄×C₁₃	D₈	semidirect
110. C₂×C₈×C₁₃	#41	semidirect
124. C₂×#532	C₂×C₁₃	semidirect
125. #3169	C₂×C₁₃	direct (N × H)
126. C₂×#500	C₂×C₁₃	semidirect
127. C₂×#493	C₂×C₁₃	semidirect
128. C₂×#486	C₂×C₁₃	semidirect
129. C₂×#466	C₂×C₁₃	semidirect
130. C₂×C₄×D₈	C₂×C₁₃	semidirect
131. C₂²×C₄×C₈	C₂×C₁₃	semidirect
157. C₂×C₄×C₁₃	C₂×D₈	semidirect
168. C₈×C₁₃	C₂×#41	semidirect
173. #532	C₂²×C₁₃	semidirect
182. #500	C₂²×C₁₃	semidirect
183. #493	C₂²×C₁₃	semidirect
184. #486	C₂²×C₁₃	semidirect
185. #466	C₂²×C₁₃	semidirect
186. C₄×D₈	C₂²×C₁₃	semidirect
192. C₂×C₄×C₈	C₂²×C₁₃	semidirect
258. C₂×C₁₃	#3169	direct (N × H)
281. C₂²×C₄	C₁₃×D₈	semidirect
295. C₂×C₈	C₁₃×#41	semidirect
309. C₁₃	C₂×#3169	direct (N × H)
335. C₂×C₄	C₂×C₁₃×D₈	semidirect
346. C₈	C₂×C₁₃×#41	semidirect
369. C₂	C₁₃×#3169	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×#3169	2
C₂×C₁₃×#500	2
C₂×C₁₃×#493	2
C₂×C₁₃×#486	2
C₂×C₁₃×#466	2
C₂×C₄×C₁₃×D₈	2
C₂²×C₄×C₈×C₁₃	2
C₂×#3169	13

Subgroups — C2×C13×#3169 #15747010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3169 #15747010