Subgroups — C₁₃×#32652 #15718991

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2580	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2092	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1879	C₂	1	2	yes	maximal
9	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#399	—	2	2	no	—
23	C₁₃×#393	—	2	2	no	—
24	C₁₃×#390	C₂²	1	2	yes	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#385	—	2	2	no	—
29	C₁₃×#385	—	2	2	no	—
30	C₁₃×#382	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃	—	2	2	no	—
38	C₂×C₁₃×D₈	—	4	1	no	—
39	C₂×C₁₃×D₈	—	4	1	no	—
40	C₂×C₁₃×D₈	Q₈	1	4	yes	complemented
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₁₃	—	4	1	no	—
45	C₄×Q₈×C₁₃	—	4	1	no	—
46	C₄×D₄×C₁₃	—	4	2	no	—
47	C₄×D₄×C₁₃	—	4	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#107	—	2	2	no	—
63	C₁₃×#107	—	4	1	no	—
64	C₁₃×#107	—	4	1	no	—
65	C₁₃×#106	—	4	2	no	—
66	C₁₃×C₄⋊C₈	—	4	1	no	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₁₃×#102	—	4	2	no	—
70	C₄×C₈×C₁₃	—	4	1	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	#32652	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	1	no	—
79	C₂×Q₈×C₁₃	—	4	1	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	8	2	no	—
91	C₂²×C₄×C₁₃	—	8	2	no	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₁₃×D₈	—	4	4	no	—
98	C₂×C₈×C₁₃	—	2	1	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₁₃	#41	1	2	yes	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₄⋊C₄	—	8	2	no	—
116	C₁₃×C₄⋊C₄	—	8	2	no	—
117	C₁₃×C₂²⋊C₄	—	4	4	no	—
118	C₁₃×C₂²⋊C₄	—	4	4	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	8	2	no	—
121	C₁₃×C₂²⋊C₄	—	8	2	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	2	1	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	#2580	C₂×C₁₃	1	2	yes	complemented
127	#2092	C₂×C₁₃	1	2	yes	complemented
128	#2085	C₂×C₁₃	1	2	yes	complemented
129	#2065	C₂×C₁₃	1	2	yes	complemented
130	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#1970	C₂×C₁₃	1	1	yes	characteristic
132	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#1879	C₂×C₁₃	1	2	yes	—
134	#1862	C₂×C₁₃	1	2	yes	complemented
135	C₂³×C₁₃	—	2	4	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	4	no	—
144	D₄×C₁₃	—	2	4	no	—
145	D₄×C₁₃	—	2	4	no	—
146	D₄×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	8	8	no	—
169	C₂×C₄×C₁₃	#135	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
176	C₈×C₁₃	—	2	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	4	2	no	—
179	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
182	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#106	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#102	C₂²×C₁₃	1	2	yes	—
188	C₂×#102	C₂²×C₁₃	1	2	yes	—
189	C₂×#102	C₂²×C₁₃	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
191	#399	—	2	2	no	—
192	#393	—	2	2	no	—
193	#390	C₂²×C₁₃	1	2	yes	—
194	#390	C₂²×C₁₃	1	2	yes	—
195	#389	C₂²×C₁₃	1	2	yes	—
196	#389	C₂²×C₁₃	1	2	yes	—
197	#385	—	2	2	no	—
198	#385	—	2	2	no	—
199	#382	C₂²×C₁₃	1	2	yes	—
200	#340	C₂²×C₁₃	1	2	yes	—
201	#340	C₂²×C₁₃	1	2	yes	—
202	#336	C₂²×C₁₃	1	2	yes	—
203	#336	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	4	4	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	#534	1	1	yes	characteristic
212	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
213	C₂²×C₁₃	#550	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
215	C₂²×C₁₃	#575	1	1	yes	characteristic
216	C₂²×C₁₃	#576	1	1	yes	characteristic
217	C₂²×C₁₃	#576	1	1	yes	characteristic
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	—	4	1	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	#539	1	1	yes	characteristic
226	C₄×C₁₃	#543	1	1	yes	characteristic
227	C₄×C₁₃	#554	1	1	yes	characteristic
228	C₄×C₁₃	#562	1	1	yes	characteristic
229	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
230	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
231	C₂³×C₄	—	2	2	no	—
232	C₂×D₈	—	4	1	no	—
233	C₂×D₈	—	4	1	no	—
234	C₂×D₈	Q₈×C₁₃	1	4	yes	complemented
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₄×Q₈	—	4	1	no	—
239	C₄×Q₈	—	4	1	no	—
240	C₄×D₄	—	4	2	no	—
241	C₄×D₄	—	4	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	#107	—	2	2	no	—
257	#107	—	4	1	no	—
258	#107	—	4	1	no	—
259	#106	—	4	2	no	—
260	C₄⋊C₈	—	4	1	no	—
261	#102	—	2	4	no	—
262	#102	—	4	2	no	—
263	#102	—	4	2	no	—
264	C₄×C₈	—	4	1	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	C₂×C₁₃	—	8	4	no	—
270	C₂×C₁₃	#2732	1	1	yes	characteristic
271	C₂×C₁₃	#3191	1	1	yes	characteristic
272	C₂×C₁₃	#3199	1	1	yes	characteristic
273	C₂×C₁₃	#3380	1	1	yes	characteristic
274	C₂×C₁₃	#3389	1	1	yes	characteristic
275	C₂×C₁₃	#3396	1	1	yes	characteristic
276	C₂×C₁₃	#3403	1	1	yes	characteristic
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	8	2	no	—
292	C₂²×C₄	—	8	2	no	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
298	D₈	—	4	4	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
307	C₂×C₈	C₁₃×#41	1	2	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₄⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₁₃	#32652	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	2	4	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	Q₈	—	4	4	no	—
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	8	no	—
362	C₂×C₄	C₁₃×#135	1	2	yes	—
363	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
365	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	2	2	no	—
371	C₈	—	4	2	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	C₁₃×#534	1	1	yes	characteristic
380	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
381	C₂²	C₁₃×#550	1	1	yes	characteristic
382	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
383	C₂²	C₁₃×#575	1	1	yes	characteristic
384	C₂²	C₁₃×#576	1	1	yes	characteristic
385	C₂²	C₁₃×#576	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₁₃×#539	1	1	yes	characteristic
394	C₄	C₁₃×#543	1	1	yes	characteristic
395	C₄	C₁₃×#554	1	1	yes	characteristic
396	C₄	C₁₃×#562	1	1	yes	characteristic
397	C₂	—	8	4	no	—
398	C₂	C₁₃×#2732	1	1	yes	characteristic
399	C₂	C₁₃×#3191	1	1	yes	characteristic
400	C₂	C₁₃×#3199	1	1	yes	characteristic
401	C₂	C₁₃×#3380	1	1	yes	characteristic
402	C₂	C₁₃×#3389	1	1	yes	characteristic
403	C₂	C₁₃×#3396	1	1	yes	characteristic
404	C₂	C₁₃×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2580	C₂	semidirect
2. C₁₃×#2092	C₂	semidirect
3. C₁₃×#2085	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
5. C₁₃×#1984	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1862	C₂	semidirect
40. C₂×C₁₃×D₈	Q₈	semidirect
75. #32652	C₁₃	direct (N × H)
126. #2580	C₂×C₁₃	semidirect
127. #2092	C₂×C₁₃	semidirect
128. #2085	C₂×C₁₃	semidirect
129. #2065	C₂×C₁₃	semidirect
130. #1984	C₂×C₁₃	semidirect
132. #1942	C₂×C₁₃	semidirect
134. #1862	C₂×C₁₃	semidirect
234. C₂×D₈	Q₈×C₁₃	semidirect
327. C₁₃	#32652	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2580	2
C₁₃×#2092	2
C₁₃×#2085	2
C₁₃×#2065	2
C₁₃×#1984	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1879	2
C₁₃×#1862	2
#32652	13

Subgroups — C13×#32652 #15718991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32652 #15718991