Subgroups — C₁₃×#29152 #15715491

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1804	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1802	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
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×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#398	—	2	2	no	—
24	C₁₃×#395	—	2	2	no	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#386	—	2	2	no	—
27	C₁₃×#386	—	2	2	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#382	C₂²	1	1	yes	characteristic
31	C₁₃×#382	C₂²	1	1	yes	characteristic
32	C₁₃×#382	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×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×C₄⋊Q₈	—	4	2	no	—
46	C₁₃×#127	—	2	2	no	—
47	C₁₃×#127	Q₈	1	4	yes	complemented
48	C₁₃×#125	—	4	2	no	—
49	C₄×D₄×C₁₃	—	2	4	no	—
50	C₄×D₄×C₁₃	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊C₈	—	2	4	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₁₃×#102	—	4	2	no	—
70	C₁₃×#102	—	4	2	no	—
71	C₁₃×#102	—	4	2	no	—
72	C₁₃×#97	—	2	2	no	—
73	C₄×C₈×C₁₃	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	D₄	1	2	yes	—
78	C₁₃×#95	D₄	1	2	yes	—
79	#29152	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	4	2	no	—
82	C₂×Q₈×C₁₃	—	8	2	no	—
83	C₂×D₄×C₁₃	—	2	8	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	8	2	no	—
90	C₂×D₄×C₁₃	—	8	2	no	—
91	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	4	4	no	—
98	C₂²×C₄×C₁₃	—	8	2	no	—
99	C₂²×C₄×C₁₃	—	8	2	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	—	8	2	no	—
121	C₁₃×C₄⋊C₄	—	8	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	8	2	no	—
124	C₁₃×C₂²⋊C₄	—	8	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
127	C₄²×C₁₃	#41	1	2	yes	—
128	C₄²×C₁₃	#41	1	4	yes	—
129	#2660	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2328	C₂×C₁₃	1	1	yes	characteristic
131	#2025	C₂×C₁₃	1	2	yes	complemented
132	#2023	C₂×C₁₃	1	2	yes	complemented
133	#1961	C₂×C₁₃	1	1	yes	characteristic
134	#1957	C₂×C₁₃	1	1	yes	characteristic
135	#1836	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1835	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1804	C₂×C₁₃	1	2	yes	complemented
138	#1802	C₂×C₁₃	1	2	yes	complemented
139	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	2	4	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	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	—	8	4	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	—	2	4	no	—
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	8	8	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	8	8	no	—
174	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₃	#124	1	4	yes	—
176	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
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×#102	C₂²×C₁₃	1	2	yes	—
191	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	#398	—	2	2	no	—
194	#395	—	2	2	no	—
195	#390	C₂²×C₁₃	1	2	yes	—
196	#386	—	2	2	no	—
197	#386	—	2	2	no	—
198	#384	C₂²×C₁₃	1	1	yes	characteristic
199	#384	C₂²×C₁₃	1	1	yes	characteristic
200	#382	C₂²×C₁₃	1	1	yes	characteristic
201	#382	C₂²×C₁₃	1	1	yes	characteristic
202	#382	C₂²×C₁₃	1	1	yes	characteristic
203	#376	C₂²×C₁₃	1	1	yes	characteristic
204	#340	C₂²×C₁₃	1	2	yes	—
205	#340	C₂²×C₁₃	1	2	yes	—
206	#340	C₂²×C₁₃	1	2	yes	—
207	#340	C₂²×C₁₃	1	2	yes	—
208	#336	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₁₃	—	4	4	no	—
210	C₂²×C₁₃	—	4	4	no	—
211	C₂²×C₁₃	—	4	4	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
218	C₂²×C₁₃	#535	1	1	yes	characteristic
219	C₂²×C₁₃	#576	1	2	yes	—
220	C₂²×C₁₃	#577	1	2	yes	—
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	4	no	—
223	C₄×C₁₃	—	4	1	no	—
224	C₄×C₁₃	—	4	1	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	—	8	1	no	—
227	C₄×C₁₃	—	8	1	no	—
228	C₄×C₁₃	—	8	1	no	—
229	C₄×C₁₃	—	8	1	no	—
230	C₄×C₁₃	#554	1	2	yes	—
231	C₄×C₁₃	#555	1	2	yes	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
235	C₂³×C₄	—	2	2	no	—
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
238	C₄⋊Q₈	—	4	2	no	—
239	#127	—	2	2	no	—
240	#127	Q₈×C₁₃	1	4	yes	complemented
241	#125	—	4	2	no	—
242	C₄×D₄	—	2	4	no	—
243	C₄×D₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₄⋊C₈	—	2	4	no	—
261	#102	—	4	2	no	—
262	#102	—	4	2	no	—
263	#102	—	4	2	no	—
264	#102	—	4	2	no	—
265	#97	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	D₄×C₁₃	1	2	yes	—
271	#95	D₄×C₁₃	1	2	yes	—
272	C₂×C₁₃	—	8	4	no	—
273	C₂×C₁₃	#2563	1	1	yes	characteristic
274	C₂×C₁₃	#3081	1	2	yes	—
275	C₂×C₁₃	#3136	1	2	yes	—
276	C₂×C₁₃	#3220	1	1	yes	characteristic
277	C₂×C₁₃	#3221	1	1	yes	characteristic
278	C₂⁴	—	2	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	8	2	no	—
281	C₂×D₄	—	2	8	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	—	2	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂×D₄	—	8	2	no	—
289	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	—	8	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	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	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	8	2	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
325	C₄²	C₁₃×#41	1	2	yes	—
326	C₄²	C₁₃×#41	1	4	yes	—
327	C₁₃	#29152	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	—	8	4	no	—
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	8	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	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×C₂²⋊Q₈	1	4	yes	—
363	C₂×C₄	C₁₃×#124	1	4	yes	—
364	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
367	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
379	C₂²	C₁₃×#535	1	1	yes	characteristic
380	C₂²	C₁₃×#576	1	2	yes	—
381	C₂²	C₁₃×#577	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₄	C₁₃×#554	1	2	yes	—
392	C₄	C₁₃×#555	1	2	yes	—
393	C₂	—	8	4	no	—
394	C₂	C₁₃×#2563	1	1	yes	characteristic
395	C₂	C₁₃×#3081	1	2	yes	—
396	C₂	C₁₃×#3136	1	2	yes	—
397	C₂	C₁₃×#3220	1	1	yes	characteristic
398	C₂	C₁₃×#3221	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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×#2660	C₂	semidirect
3. C₁₃×#2025	C₂	semidirect
4. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1836	C₂	semidirect
8. C₁₃×#1835	C₂	semidirect
9. C₁₃×#1804	C₂	semidirect
10. C₁₃×#1802	C₂	semidirect
11. C₁₃×#1768	C₂	semidirect
47. C₁₃×#127	Q₈	semidirect
79. #29152	C₁₃	direct (N × H)
129. #2660	C₂×C₁₃	semidirect
131. #2025	C₂×C₁₃	semidirect
132. #2023	C₂×C₁₃	semidirect
135. #1836	C₂×C₁₃	semidirect
136. #1835	C₂×C₁₃	semidirect
137. #1804	C₂×C₁₃	semidirect
138. #1802	C₂×C₁₃	semidirect
139. #1768	C₂×C₁₃	semidirect
240. #127	Q₈×C₁₃	semidirect
327. C₁₃	#29152	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×#2660	2
C₁₃×#2328	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#1961	2
C₁₃×#1957	2
C₁₃×#1836	2
C₁₃×#1835	2
C₁₃×#1804	2
C₁₃×#1802	2
C₁₃×#1768	2
#29152	13

Subgroups — C13×#29152 #15715491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29152 #15715491