Subgroups — C₁₃×#10270 #15696609

Order 3328.

594 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	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#487	—	2	2	no	—
13	C₁₃×#487	—	2	2	no	—
14	C₁₃×#474	—	2	2	no	—
15	C₁₃×#474	—	2	2	no	—
16	C₁₃×#461	—	2	2	no	—
17	C₁₃×#461	—	2	2	no	—
18	C₂×C₁₃×#107	—	2	1	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	—	2	2	no	—
23	C₂×C₁₃×#103	—	2	1	no	—
24	C₂×C₁₃×#102	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#332	—	2	2	no	—
28	C₁₃×#332	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×Q₈×C₁₃	—	2	1	no	—
31	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	—	2	1	no	—
33	C₂×C₁₃×SD₁₆	—	2	4	no	—
34	C₂×C₁₃×SD₁₆	—	4	2	no	—
35	C₂×C₁₃×SD₁₆	—	4	2	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	D₄	1	2	yes	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
48	C₄×D₄×C₁₃	—	2	1	no	—
49	C₄×D₄×C₁₃	—	2	1	no	—
50	C₄×D₄×C₁₃	—	2	1	no	—
51	C₄×D₄×C₁₃	—	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	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#107	—	2	4	no	—
60	C₁₃×C₄⋊C₈	—	2	1	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₃×#103	—	2	4	no	—
67	C₁₃×#103	—	2	8	no	—
68	C₁₃×#102	—	2	4	no	—
69	C₁₃×C₂²⋊C₈	—	4	4	no	—
70	C₄×C₈×C₁₃	—	2	1	no	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	#10270	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	1	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	4	1	no	—
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	C₂×Q₈×C₁₃	—	4	1	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	4	1	no	—
81	C₂×Q₈×C₁₃	—	4	1	no	—
82	C₂×Q₈×C₁₃	—	4	2	no	—
83	C₂×Q₈×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
100	C₁₃×SD₁₆	—	4	8	no	—
101	C₂×C₈×C₁₃	—	2	2	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	—	2	2	no	—
106	C₂×C₈×C₁₃	—	4	1	no	—
107	C₂×C₈×C₁₃	—	4	1	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	—	4	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₂²⋊C₄	—	4	1	no	—
123	C₁₃×C₂²⋊C₄	—	4	1	no	—
124	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
130	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
131	#1954	C₂×C₁₃	1	1	yes	characteristic
132	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#1277	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	2	2	no	—
136	C₂³×C₁₃	—	4	1	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	#121	1	1	yes	characteristic
141	Q₈×C₁₃	—	4	4	no	—
142	Q₈×C₁₃	—	4	2	no	—
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	8	1	no	—
145	Q₈×C₁₃	—	8	1	no	—
146	Q₈×C₁₃	—	8	1	no	—
147	Q₈×C₁₃	—	8	1	no	—
148	D₄×C₁₃	—	2	2	no	—
149	D₄×C₁₃	—	2	2	no	—
150	D₄×C₁₃	—	4	1	no	—
151	D₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	8	2	no	—
158	C₂×C₄×C₁₃	—	8	1	no	—
159	C₂×C₄×C₁₃	—	8	1	no	—
160	C₂×C₄×C₁₃	—	8	2	no	—
161	C₂×C₄×C₁₃	—	8	1	no	—
162	C₂×C₄×C₁₃	—	8	1	no	—
163	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#135	1	2	yes	—
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
175	C₈×C₁₃	—	4	2	no	—
176	C₈×C₁₃	—	4	2	no	—
177	C₈×C₁₃	—	4	2	no	—
178	C₈×C₁₃	—	8	1	no	—
179	C₂²×SD₁₆	—	2	1	no	—
180	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
183	#487	—	2	2	no	—
184	#487	—	2	2	no	—
185	#474	—	2	2	no	—
186	#474	—	2	2	no	—
187	#461	—	2	2	no	—
188	#461	—	2	2	no	—
189	C₂×#107	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#103	—	2	2	no	—
194	C₂×#103	—	2	1	no	—
195	C₂×#102	—	2	1	no	—
196	C₂×C₂²⋊C₈	—	2	2	no	—
197	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
198	#332	—	2	2	no	—
199	#332	—	2	2	no	—
200	C₂²×C₁₃	—	4	4	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	1	no	—
204	C₂²×C₁₃	—	8	1	no	—
205	C₂²×C₁₃	#392	1	1	yes	characteristic
206	C₂²×C₁₃	#463	1	2	yes	—
207	C₂²×C₁₃	#465	1	1	yes	characteristic
208	C₂²×C₁₃	#468	1	1	yes	characteristic
209	C₂²×C₁₃	#473	1	2	yes	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	8	2	no	—
213	C₄×C₁₃	—	8	1	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	#448	1	1	yes	characteristic
216	C₄×C₁₃	#449	1	1	yes	characteristic
217	C₄×C₁₃	#449	1	2	yes	—
218	C₄×C₁₃	#450	1	1	yes	characteristic
219	C₄×C₁₃	#452	1	1	yes	characteristic
220	C₄×C₁₃	#495	1	1	yes	characteristic
221	C₄×C₁₃	#496	1	1	yes	characteristic
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	—	2	1	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	4	2	no	—
228	C₂×SD₁₆	—	4	2	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	D₄×C₁₃	1	2	yes	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
240	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	#107	—	2	4	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
258	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
259	#103	—	2	4	no	—
260	#103	—	2	8	no	—
261	#102	—	2	4	no	—
262	C₂²⋊C₈	—	4	4	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	2	1	no	—
265	C₂×C₁₃	—	8	2	no	—
266	C₂×C₁₃	#1679	1	2	yes	—
267	C₂×C₁₃	#1699	1	2	yes	—
268	C₂×C₁₃	#2000	1	1	yes	characteristic
269	C₂×C₁₃	#2012	1	1	yes	characteristic
270	C₂×C₁₃	#2020	1	1	yes	characteristic
271	C₂⁴	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
298	SD₁₆	—	4	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₁₃	#10270	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₁₃×#121	1	1	yes	characteristic
333	Q₈	—	4	4	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	1	no	—
337	Q₈	—	8	1	no	—
338	Q₈	—	8	1	no	—
339	Q₈	—	8	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
356	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
357	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
358	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
359	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
360	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
362	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
363	C₂×C₄	C₁₃×#135	1	2	yes	—
364	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
366	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
367	C₈	—	4	2	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	8	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₁₃×#392	1	1	yes	characteristic
377	C₂²	C₁₃×#463	1	2	yes	—
378	C₂²	C₁₃×#465	1	1	yes	characteristic
379	C₂²	C₁₃×#468	1	1	yes	characteristic
380	C₂²	C₁₃×#473	1	2	yes	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	C₁₃×#448	1	1	yes	characteristic
387	C₄	C₁₃×#449	1	1	yes	characteristic
388	C₄	C₁₃×#449	1	2	yes	—
389	C₄	C₁₃×#450	1	1	yes	characteristic
390	C₄	C₁₃×#452	1	1	yes	characteristic
391	C₄	C₁₃×#495	1	1	yes	characteristic
392	C₄	C₁₃×#496	1	1	yes	characteristic
393	C₂	—	8	2	no	—
394	C₂	C₁₃×#1679	1	2	yes	—
395	C₂	C₁₃×#1699	1	2	yes	—
396	C₂	C₁₃×#2000	1	1	yes	characteristic
397	C₂	C₁₃×#2012	1	1	yes	characteristic
398	C₂	C₁₃×#2020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#487	C₂	semidirect
5. C₂×C₁₃×#332	C₂	semidirect
6. C₂×C₁₃×#332	C₂	semidirect
7. C₁₃×#1277	C₂	semidirect
72. #10270	C₁₃	direct (N × H)
128. C₂×#487	C₂×C₁₃	semidirect
132. C₂×#332	C₂×C₁₃	semidirect
133. C₂×#332	C₂×C₁₃	semidirect
134. #1277	C₂×C₁₃	semidirect
326. C₁₃	#10270	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×#487	2
C₂×C₁₃×#474	2
C₂×C₁₃×#461	2
C₁₃×#1954	2
C₂×C₁₃×#332	2
C₁₃×#1277	2
#10270	13

Subgroups — C13×#10270 #15696609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10270 #15696609