Subgroups — C₁₃×#60940 #15747279

Order 3328.

2362 conjugacy classes of subgroups.

The subgroup lattice has 474 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×#3245	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3226	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3205	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3186	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3169	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3100	C₂	1	8	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	2	no	—
10	C₁₃×#532	—	2	2	no	—
11	C₁₃×#532	—	2	2	no	—
12	C₁₃×#532	—	2	2	no	—
13	C₁₃×#532	—	2	2	no	—
14	C₁₃×#532	C₂²	1	4	yes	—
15	C₁₃×#532	C₂²	1	4	yes	—
16	C₁₃×#532	C₂²	1	4	yes	complemented
17	C₁₃×#532	C₂²	1	4	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#124	—	2	2	no	—
21	C₂×C₁₃×#121	—	2	2	no	—
22	C₂×C₁₃×#121	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	—	2	2	no	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	4	yes	complemented
27	C₁₃×#493	C₂²	1	4	yes	complemented
28	C₁₃×#486	C₂²	1	8	yes	complemented
29	C₁₃×#480	C₂²	1	16	yes	complemented
30	C₁₃×#474	C₂²	1	16	yes	complemented
31	C₁₃×#466	C₂²	1	16	yes	complemented
32	C₁₃×#459	C₂²	1	16	yes	complemented
33	C₁₃×#447	C₂²	1	16	yes	complemented
34	C₄×C₁₃×D₈	C₂²	1	16	yes	complemented
35	C₁₃×#431	C₂²	1	4	yes	complemented
36	C₁₃×#431	C₂²	1	4	yes	complemented
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	2	4	no	—
42	C₂×C₁₃×#41	—	2	4	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	4	16	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₃	—	2	4	no	—
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×D₈	C₂³	1	16	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₃×#127	—	2	2	no	—
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#127	C₂³	1	4	yes	—
63	C₁₃×#127	C₂³	1	4	yes	—
64	C₁₃×#124	—	2	4	no	—
65	C₁₃×#124	—	2	4	no	—
66	C₁₃×#124	—	2	4	no	—
67	C₁₃×#124	—	2	4	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#121	—	2	4	no	—
70	C₁₃×#121	—	2	4	no	—
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	C₂³	1	8	yes	—
75	C₁₃×#121	C₂³	1	8	yes	—
76	C₄×D₄×C₁₃	—	2	4	no	—
77	C₄×D₄×C₁₃	—	2	4	no	—
78	C₄×D₄×C₁₃	—	2	4	no	—
79	C₄×D₄×C₁₃	—	2	4	no	—
80	C₄×D₄×C₁₃	—	2	4	no	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	C₂³	1	8	yes	—
83	C₄×D₄×C₁₃	C₂³	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
88	C₂×C₄²×C₁₃	D₄	1	2	yes	—
89	C₂×C₄²×C₁₃	D₄	1	2	yes	—
90	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
96	C₁₃×#107	C₂³	1	16	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
98	C₁₃×#102	C₂³	1	32	yes	—
99	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
100	C₄×C₈×C₁₃	C₂³	1	4	yes	—
101	C₄×C₈×C₁₃	C₂³	1	4	yes	—
102	#60940	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	4	no	—
104	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₁₃×#41	—	4	16	no	—
106	C₁₃×#41	—	4	16	no	—
107	C₁₃×#41	—	4	16	no	—
108	C₁₃×#41	—	4	16	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	4	8	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	4	8	no	—
120	C₂×D₄×C₁₃	—	4	8	no	—
121	C₂×D₄×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	4	8	no	—
123	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	8	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	16	no	—
130	C₂²×C₄×C₁₃	D₈	1	8	yes	complemented
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×D₈	—	4	16	no	—
144	C₂×C₈×C₁₃	—	4	4	no	—
145	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
150	C₁₃×C₂²⋊C₄	—	2	8	no	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₄²×C₁₃	C₂⁴	1	2	yes	—
163	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×#532	C₂×C₁₃	1	2	yes	complemented
165	#3245	C₂×C₁₃	1	4	yes	complemented
166	#3226	C₂×C₁₃	1	4	yes	complemented
167	#3205	C₂×C₁₃	1	4	yes	complemented
168	#3186	C₂×C₁₃	1	4	yes	complemented
169	#3169	C₂×C₁₃	1	4	yes	complemented
170	#3100	C₂×C₁₃	1	8	yes	complemented
171	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	—	4	8	no	—
177	C₂³×C₁₃	—	4	8	no	—
178	C₂³×C₁₃	C₂×D₈	1	4	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	8	no	—
182	Q₈×C₁₃	—	4	8	no	—
183	D₄×C₁₃	—	2	16	no	—
184	D₄×C₁₃	—	4	8	no	—
185	D₄×C₁₃	—	4	8	no	—
186	D₄×C₁₃	—	4	16	no	—
187	D₄×C₁₃	—	4	16	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	8	no	—
190	D₄×C₁₃	—	4	8	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	16	no	—
202	C₂×C₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	C₂×D₈	1	8	yes	—
204	C₂×C₄×C₁₃	C₂×D₈	1	8	yes	—
205	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
206	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₃	—	2	8	no	—
217	C₂²×#41	—	2	2	no	—
218	#532	—	2	2	no	—
219	#532	—	2	2	no	—
220	#532	—	2	2	no	—
221	#532	—	2	2	no	—
222	#532	C₂²×C₁₃	1	4	yes	—
223	#532	C₂²×C₁₃	1	4	yes	—
224	#532	C₂²×C₁₃	1	4	yes	complemented
225	#532	C₂²×C₁₃	1	4	yes	complemented
226	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
227	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
228	C₂×#124	—	2	2	no	—
229	C₂×#121	—	2	2	no	—
230	C₂×#121	C₂²×C₁₃	1	4	yes	—
231	C₂×C₄×D₄	—	2	2	no	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
233	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
234	#500	C₂²×C₁₃	1	4	yes	complemented
235	#493	C₂²×C₁₃	1	4	yes	complemented
236	#486	C₂²×C₁₃	1	8	yes	complemented
237	#480	C₂²×C₁₃	1	16	yes	complemented
238	#474	C₂²×C₁₃	1	16	yes	complemented
239	#466	C₂²×C₁₃	1	16	yes	complemented
240	#459	C₂²×C₁₃	1	16	yes	complemented
241	#447	C₂²×C₁₃	1	16	yes	complemented
242	C₄×D₈	C₂²×C₁₃	1	16	yes	complemented
243	#431	C₂²×C₁₃	1	4	yes	complemented
244	#431	C₂²×C₁₃	1	4	yes	complemented
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
246	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
248	C₂²×C₁₃	—	2	2	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	8	no	—
254	C₂²×C₁₃	—	4	8	no	—
255	C₂²×C₁₃	—	4	8	no	—
256	C₂²×C₁₃	—	8	16	no	—
257	C₂²×C₁₃	C₂²×D₈	1	4	yes	—
258	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
259	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	4	8	no	—
265	C₄×C₁₃	C₂²×D₈	1	2	yes	—
266	C₄×C₁₃	C₂²×D₈	1	4	yes	—
267	C₄×C₁₃	C₂²×D₈	1	2	yes	—
268	C₄×C₁₃	#575	1	2	yes	—
269	C₄×C₁₃	#585	1	2	yes	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	4	16	no	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×D₈	C₂³×C₁₃	1	16	yes	—
285	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
289	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
290	#127	—	2	2	no	—
291	#127	—	2	2	no	—
292	#127	C₂³×C₁₃	1	4	yes	—
293	#127	C₂³×C₁₃	1	4	yes	—
294	#124	—	2	4	no	—
295	#124	—	2	4	no	—
296	#124	—	2	4	no	—
297	#124	—	2	4	no	—
298	#121	—	2	4	no	—
299	#121	—	2	4	no	—
300	#121	—	2	4	no	—
301	#121	—	2	4	no	—
302	#121	—	2	4	no	—
303	#121	—	2	4	no	—
304	#121	C₂³×C₁₃	1	8	yes	—
305	#121	C₂³×C₁₃	1	8	yes	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	C₂³×C₁₃	1	8	yes	—
313	C₄×D₄	C₂³×C₁₃	1	8	yes	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
316	C₂×C₂²⋊C₄	—	2	4	no	—
317	C₂×C₂²⋊C₄	—	2	4	no	—
318	C₂×C₄²	D₄×C₁₃	1	2	yes	—
319	C₂×C₄²	D₄×C₁₃	1	2	yes	—
320	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	#107	C₂³×C₁₃	1	16	yes	—
327	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
328	#102	C₂³×C₁₃	1	32	yes	—
329	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
330	C₄×C₈	C₂³×C₁₃	1	4	yes	—
331	C₄×C₈	C₂³×C₁₃	1	4	yes	—
332	C₂×C₁₃	—	2	4	no	—
333	C₂×C₁₃	—	2	2	no	—
334	C₂×C₁₃	—	8	8	no	—
335	C₂×C₁₃	#3449	1	1	yes	characteristic
336	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
337	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
338	C₂⁴	—	2	4	no	—
339	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
340	#41	—	4	16	no	—
341	#41	—	4	16	no	—
342	#41	—	4	16	no	—
343	#41	—	4	16	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	4	8	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	4	16	no	—
357	C₂×D₄	—	4	8	no	—
358	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	16	no	—
365	C₂²×C₄	C₁₃×D₈	1	8	yes	complemented
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
378	D₈	—	4	16	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₁₃	1	2	yes	—
391	C₄²	C₂×D₄×C₁₃	1	2	yes	—
392	C₄²	C₂×D₄×C₁₃	1	2	yes	—
393	C₄²	C₂×D₄×C₁₃	1	2	yes	—
394	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₁₃	1	2	yes	—
396	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₄²	C₂⁴×C₁₃	1	2	yes	—
399	C₁₃	#60940	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	8	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	8	no	—
404	C₂³	—	4	8	no	—
405	C₂³	—	4	8	no	—
406	C₂³	C₂×C₁₃×D₈	1	4	yes	—
407	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
408	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	Q₈	—	4	8	no	—
410	Q₈	—	4	8	no	—
411	D₄	—	2	16	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	16	no	—
415	D₄	—	4	16	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	16	no	—
430	C₂×C₄	—	4	16	no	—
431	C₂×C₄	C₂×C₁₃×D₈	1	8	yes	—
432	C₂×C₄	C₂×C₁₃×D₈	1	8	yes	—
433	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
434	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
444	C₈	—	2	8	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	8	16	no	—
454	C₂²	C₂²×C₁₃×D₈	1	4	yes	—
455	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
456	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	8	no	—
462	C₄	C₂²×C₁₃×D₈	1	2	yes	—
463	C₄	C₂²×C₁₃×D₈	1	4	yes	—
464	C₄	C₂²×C₁₃×D₈	1	2	yes	—
465	C₄	C₁₃×#575	1	2	yes	—
466	C₄	C₁₃×#585	1	2	yes	—
467	C₂	—	2	4	no	—
468	C₂	—	2	2	no	—
469	C₂	—	8	8	no	—
470	C₂	C₁₃×#3449	1	1	yes	characteristic
471	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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×#3245	C₂	semidirect
3. C₁₃×#3226	C₂	semidirect
4. C₁₃×#3205	C₂	semidirect
5. C₁₃×#3186	C₂	semidirect
6. C₁₃×#3169	C₂	semidirect
7. C₁₃×#3100	C₂	semidirect
8. C₂×C₁₃×#431	C₂	semidirect
16. C₁₃×#532	C₂²	semidirect
17. C₁₃×#532	C₂²	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#127	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#500	C₂²	semidirect
27. C₁₃×#493	C₂²	semidirect
28. C₁₃×#486	C₂²	semidirect
29. C₁₃×#480	C₂²	semidirect
30. C₁₃×#474	C₂²	semidirect
31. C₁₃×#466	C₂²	semidirect
32. C₁₃×#459	C₂²	semidirect
33. C₁₃×#447	C₂²	semidirect
34. C₄×C₁₃×D₈	C₂²	semidirect
35. C₁₃×#431	C₂²	semidirect
36. C₁₃×#431	C₂²	semidirect
37. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
39. C₂×C₄×C₈×C₁₃	C₂²	semidirect
102. #60940	C₁₃	direct (N × H)
130. C₂²×C₄×C₁₃	D₈	semidirect
164. C₂×#532	C₂×C₁₃	semidirect
165. #3245	C₂×C₁₃	semidirect
166. #3226	C₂×C₁₃	semidirect
167. #3205	C₂×C₁₃	semidirect
168. #3186	C₂×C₁₃	semidirect
169. #3169	C₂×C₁₃	semidirect
170. #3100	C₂×C₁₃	semidirect
171. C₂×#431	C₂×C₁₃	semidirect
224. #532	C₂²×C₁₃	semidirect
225. #532	C₂²×C₁₃	semidirect
226. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
227. C₂×#127	C₂²×C₁₃	semidirect
232. C₂×C₄×D₄	C₂²×C₁₃	semidirect
234. #500	C₂²×C₁₃	semidirect
235. #493	C₂²×C₁₃	semidirect
236. #486	C₂²×C₁₃	semidirect
237. #480	C₂²×C₁₃	semidirect
238. #474	C₂²×C₁₃	semidirect
239. #466	C₂²×C₁₃	semidirect
240. #459	C₂²×C₁₃	semidirect
241. #447	C₂²×C₁₃	semidirect
242. C₄×D₈	C₂²×C₁₃	semidirect
243. #431	C₂²×C₁₃	semidirect
244. #431	C₂²×C₁₃	semidirect
245. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
247. C₂×C₄×C₈	C₂²×C₁₃	semidirect
365. C₂²×C₄	C₁₃×D₈	semidirect
399. C₁₃	#60940	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×#3245	2
C₁₃×#3226	2
C₁₃×#3205	2
C₁₃×#3186	2
C₁₃×#3169	2
C₁₃×#3100	2
C₂×C₁₃×#431	2
#60940	13

Subgroups — C13×#60940 #15747279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60940 #15747279