Subgroups — C₁₃×#32813 #15719152

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2640	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2056	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2055	C₂	1	2	yes	maximal
5	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2015	C₂	1	2	yes	maximal
10	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₁₃×#400	—	2	2	no	—
24	C₁₃×#400	—	2	2	no	—
25	C₁₃×#397	—	2	2	no	—
26	C₁₃×#393	—	2	2	no	—
27	C₁₃×#391	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#376	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	—	4	2	no	—
44	C₂×C₁₃×Q₁₆	—	4	2	no	—
45	C₂×C₁₃×Q₁₆	—	4	2	no	—
46	C₂×C₁₃×SD₁₆	—	4	2	no	—
47	C₂×C₁₃×SD₁₆	—	4	2	no	—
48	C₂×C₁₃×SD₁₆	—	4	2	no	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	4	2	no	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×#125	—	4	2	no	—
54	C₁₃×#124	—	4	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊C₈	—	4	2	no	—
69	C₁₃×#103	—	4	2	no	—
70	C₁₃×#103	—	4	2	no	—
71	C₁₃×#103	—	4	2	no	—
72	C₁₃×#102	—	4	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	4	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	D₄	1	2	yes	—
79	C₁₃×#95	D₄	1	2	yes	—
80	#32813	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×Q₁₆	—	4	8	no	—
109	C₁₃×SD₁₆	—	4	8	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	4	4	no	—
121	C₁₃×C₄⋊C₄	—	4	2	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	2	no	—
125	C₁₃×C₂²⋊C₄	—	8	2	no	—
126	C₁₃×C₂²⋊C₄	—	8	2	no	—
127	C₄²×C₁₃	—	2	1	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	1	no	—
131	#2642	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2640	C₂×C₁₃	1	1	yes	characteristic
133	#2056	C₂×C₁₃	1	2	yes	complemented
134	#2055	C₂×C₁₃	1	2	yes	—
135	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2025	C₂×C₁₃	1	1	yes	characteristic
137	#2024	C₂×C₁₃	1	2	yes	complemented
138	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2015	C₂×C₁₃	1	2	yes	—
140	#2013	C₂×C₁₃	1	1	yes	characteristic
141	#1832	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	4	2	no	—
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	2	no	—
154	Q₈×C₁₃	—	8	4	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
187	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
193	C₂×#103	C₂²×C₁₃	1	2	yes	—
194	C₂×#103	C₂²×C₁₃	1	2	yes	—
195	C₂×#103	C₂²×C₁₃	1	2	yes	—
196	C₂×#102	C₂²×C₁₃	1	2	yes	—
197	#400	—	2	2	no	—
198	#400	—	2	2	no	—
199	#397	—	2	2	no	—
200	#393	—	2	2	no	—
201	#391	C₂²×C₁₃	1	2	yes	—
202	#391	C₂²×C₁₃	1	1	yes	characteristic
203	#391	C₂²×C₁₃	1	1	yes	characteristic
204	#391	C₂²×C₁₃	1	2	yes	—
205	#390	C₂²×C₁₃	1	1	yes	characteristic
206	#390	C₂²×C₁₃	1	1	yes	characteristic
207	#376	C₂²×C₁₃	1	1	yes	characteristic
208	#340	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	1	yes	characteristic
211	#336	C₂²×C₁₃	1	2	yes	—
212	#336	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₁₃	—	8	1	no	—
214	C₂²×C₁₃	—	8	1	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	#535	1	1	yes	characteristic
219	C₂²×C₁₃	#535	1	1	yes	characteristic
220	C₂²×C₁₃	#537	1	1	yes	characteristic
221	C₂²×C₁₃	#577	1	2	yes	—
222	C₂²×C₁₃	#578	1	2	yes	—
223	C₄×C₁₃	—	4	1	no	—
224	C₄×C₁₃	—	4	1	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	8	1	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	1	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	H(3,𝔽₄)	1	2	yes	—
233	C₄×C₁₃	#562	1	2	yes	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂×Q₁₆	—	4	2	no	—
239	C₂×Q₁₆	—	4	2	no	—
240	C₂×Q₁₆	—	4	2	no	—
241	C₂×SD₁₆	—	4	2	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
245	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
246	C₄⋊Q₈	—	4	2	no	—
247	C₄⋊Q₈	—	4	2	no	—
248	#125	—	4	2	no	—
249	#124	—	4	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	C₄⋊C₈	—	4	2	no	—
264	#103	—	4	2	no	—
265	#103	—	4	2	no	—
266	#103	—	4	2	no	—
267	#102	—	4	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	4	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	D₄×C₁₃	1	2	yes	—
274	#95	D₄×C₁₃	1	2	yes	—
275	C₂×C₁₃	—	16	1	no	—
276	C₂×C₁₃	#2819	1	1	yes	characteristic
277	C₂×C₁₃	#3222	1	1	yes	characteristic
278	C₂×C₁₃	#3223	1	1	yes	characteristic
279	C₂×C₁₃	#3225	1	2	yes	—
280	C₂×C₁₃	#3258	1	2	yes	—
281	C₂⁴	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	8	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	Q₁₆	—	4	8	no	—
309	SD₁₆	—	4	8	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	8	2	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₁₃	#32813	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
372	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
373	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₁₃×#535	1	1	yes	characteristic
382	C₂²	C₁₃×#535	1	1	yes	characteristic
383	C₂²	C₁₃×#537	1	1	yes	characteristic
384	C₂²	C₁₃×#577	1	2	yes	—
385	C₂²	C₁₃×#578	1	2	yes	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	8	1	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₁₃×H(3,𝔽₄)	1	2	yes	—
396	C₄	C₁₃×#562	1	2	yes	—
397	C₂	—	16	1	no	—
398	C₂	C₁₃×#2819	1	1	yes	characteristic
399	C₂	C₁₃×#3222	1	1	yes	characteristic
400	C₂	C₁₃×#3223	1	1	yes	characteristic
401	C₂	C₁₃×#3225	1	2	yes	—
402	C₂	C₁₃×#3258	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2642	C₂	semidirect
3. C₁₃×#2056	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
8. C₁₃×#2016	C₂	semidirect
11. C₁₃×#1832	C₂	semidirect
80. #32813	C₁₃	direct (N × H)
131. #2642	C₂×C₁₃	semidirect
133. #2056	C₂×C₁₃	semidirect
135. #2026	C₂×C₁₃	semidirect
137. #2024	C₂×C₁₃	semidirect
138. #2016	C₂×C₁₃	semidirect
141. #1832	C₂×C₁₃	semidirect
331. C₁₃	#32813	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×#2642	2
C₁₃×#2640	2
C₁₃×#2056	2
C₁₃×#2055	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#2024	2
C₁₃×#2016	2
C₁₃×#2015	2
C₁₃×#2013	2
C₁₃×#1832	2
#32813	13

Subgroups — C13×#32813 #15719152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32813 #15719152