Subgroups — C₁₃×#29139 #15715478

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2023	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1957	C₂	1	2	yes	maximal
5	C₁₃×#1834	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1802	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	8	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#390	—	2	1	no	—
19	C₁₃×#390	—	2	1	no	—
20	C₁₃×#390	C₂²	1	2	yes	—
21	C₁₃×#384	—	2	1	no	—
22	C₁₃×#384	—	2	1	no	—
23	C₁₃×#384	C₂²	1	1	yes	characteristic
24	C₁₃×#384	C₂²	1	2	yes	—
25	C₁₃×#384	C₂²	1	2	yes	—
26	C₄³×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#340	C₂²	1	8	yes	—
28	C₁₃×#336	C₂²	1	2	yes	—
29	C₂²×Q₈×C₁₃	—	2	2	no	—
30	C₂²×D₄×C₁₃	—	2	1	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃	—	2	2	no	—
34	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
35	C₁₃×C₄⋊Q₈	—	4	4	no	—
36	C₁₃×C₄⋊Q₈	—	4	4	no	—
37	C₁₃×C₄⋊Q₈	—	4	4	no	—
38	C₁₃×#127	—	2	2	no	—
39	C₁₃×#127	Q₈	1	4	yes	complemented
40	C₄×D₄×C₁₃	—	2	8	no	—
41	C₄×D₄×C₁₃	—	4	4	no	—
42	C₄×D₄×C₁₃	—	4	4	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊C₈	—	2	4	no	—
63	C₁₃×#102	—	4	8	no	—
64	C₄×C₈×C₁₃	—	2	4	no	—
65	#29139	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	—	2	2	no	—
67	C₂×Q₈×C₁₃	—	4	4	no	—
68	C₂×Q₈×C₁₃	—	4	4	no	—
69	C₂×Q₈×C₁₃	—	4	4	no	—
70	C₂×D₄×C₁₃	—	2	4	no	—
71	C₂×D₄×C₁₃	—	2	4	no	—
72	C₂×D₄×C₁₃	—	2	4	no	—
73	C₂×D₄×C₁₃	—	2	2	no	—
74	C₂×D₄×C₁₃	—	2	4	no	—
75	C₂×D₄×C₁₃	—	4	2	no	—
76	C₂×D₄×C₁₃	—	4	2	no	—
77	C₂×D₄×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	—	4	2	no	—
79	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	4	4	no	—
83	C₂²×C₄×C₁₃	—	4	4	no	—
84	C₂²×C₄×C₁₃	—	4	4	no	—
85	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₃	—	2	4	no	—
93	C₂×C₈×C₁₃	—	2	4	no	—
94	C₂×C₈×C₁₃	—	2	4	no	—
95	C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₁₃×C₄⋊C₄	—	2	8	no	—
97	C₁₃×C₄⋊C₄	—	4	4	no	—
98	C₁₃×C₄⋊C₄	—	4	4	no	—
99	C₁₃×C₄⋊C₄	—	4	2	no	—
100	C₁₃×C₄⋊C₄	—	4	4	no	—
101	C₁₃×C₄⋊C₄	—	4	4	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	4	no	—
104	C₁₃×C₂²⋊C₄	—	4	4	no	—
105	C₁₃×C₂²⋊C₄	—	4	4	no	—
106	C₁₃×C₂²⋊C₄	—	4	4	no	—
107	C₄²×C₁₃	—	2	2	no	—
108	C₄²×C₁₃	—	2	2	no	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	D₈	1	4	yes	—
111	C₄²×C₁₃	SD₁₆	1	4	yes	—
112	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
113	C₄²×C₁₃	#41	1	2	yes	—
114	C₄²×C₁₃	#41	1	4	yes	—
115	#2868	C₂×C₁₃	1	1	yes	characteristic, complemented
116	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
117	#2023	C₂×C₁₃	1	4	yes	complemented
118	#1957	C₂×C₁₃	1	2	yes	—
119	#1834	C₂×C₁₃	1	2	yes	complemented
120	#1802	C₂×C₁₃	1	4	yes	complemented
121	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
122	C₂³×C₁₃	—	2	4	no	—
123	C₂³×C₁₃	—	4	2	no	—
124	C₂³×C₁₃	—	4	2	no	—
125	C₂³×C₁₃	—	4	2	no	—
126	C₂³×C₁₃	—	4	2	no	—
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₁₃	—	8	8	no	—
131	D₄×C₁₃	—	2	8	no	—
132	D₄×C₁₃	—	4	4	no	—
133	D₄×C₁₃	—	4	8	no	—
134	D₄×C₁₃	—	4	8	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	4	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	4	no	—
147	C₂×C₄×C₁₃	—	8	8	no	—
148	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₁₃	#124	1	2	yes	—
151	C₂×C₄×C₁₃	#124	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₁₃	#137	1	2	yes	—
160	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
164	C₈×C₁₃	—	4	4	no	—
165	C₂×C₄⋊Q₈	—	2	1	no	—
166	C₂×C₄⋊Q₈	—	2	1	no	—
167	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
168	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
169	C₂×C₄×D₄	—	2	1	no	—
170	C₂×C₄×D₄	—	2	1	no	—
171	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×#102	C₂²×C₁₃	1	8	yes	—
174	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
175	#390	—	2	1	no	—
176	#390	—	2	1	no	—
177	#390	C₂²×C₁₃	1	2	yes	—
178	#384	—	2	1	no	—
179	#384	—	2	1	no	—
180	#384	C₂²×C₁₃	1	1	yes	characteristic
181	#384	C₂²×C₁₃	1	2	yes	—
182	#384	C₂²×C₁₃	1	2	yes	—
183	C₄³	C₂²×C₁₃	1	1	yes	characteristic
184	#340	C₂²×C₁₃	1	8	yes	—
185	#336	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₁₃	—	4	4	no	—
187	C₂²×C₁₃	—	4	4	no	—
188	C₂²×C₁₃	—	4	4	no	—
189	C₂²×C₁₃	—	8	2	no	—
190	C₂²×C₁₃	—	8	2	no	—
191	C₂²×C₁₃	—	8	2	no	—
192	C₂²×C₁₃	—	8	2	no	—
193	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
195	C₂²×C₁₃	#535	1	1	yes	characteristic
196	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
197	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	8	2	no	—
204	C₄×C₁₃	—	8	4	no	—
205	C₄×C₁₃	#474	1	4	yes	—
206	C₄×C₁₃	#476	1	4	yes	—
207	C₄×C₁₃	#486	1	4	yes	—
208	C₄×C₁₃	#554	1	2	yes	—
209	C₄×C₁₃	#555	1	2	yes	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
214	C₂³×C₄	—	2	2	no	—
215	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
216	C₄⋊Q₈	—	4	4	no	—
217	C₄⋊Q₈	—	4	4	no	—
218	C₄⋊Q₈	—	4	4	no	—
219	#127	—	2	2	no	—
220	#127	Q₈×C₁₃	1	4	yes	complemented
221	C₄×D₄	—	2	8	no	—
222	C₄×D₄	—	4	4	no	—
223	C₄×D₄	—	4	4	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
243	C₄⋊C₈	—	2	4	no	—
244	#102	—	4	8	no	—
245	C₄×C₈	—	2	4	no	—
246	C₂×C₁₃	—	8	4	no	—
247	C₂×C₁₃	#2563	1	1	yes	characteristic
248	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
249	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
250	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
251	C₂×C₁₃	#3141	1	1	yes	characteristic
252	C₂×C₁₃	#3205	1	1	yes	characteristic
253	C₂×C₁₃	#3206	1	1	yes	characteristic
254	C₂⁴	—	2	2	no	—
255	C₂×Q₈	—	4	4	no	—
256	C₂×Q₈	—	4	4	no	—
257	C₂×Q₈	—	4	4	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₁₃×D₈	1	4	yes	—
299	C₄²	C₁₃×SD₁₆	1	4	yes	—
300	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
301	C₄²	C₁₃×#41	1	2	yes	—
302	C₄²	C₁₃×#41	1	4	yes	—
303	C₁₃	#29139	1	1	yes	characteristic, direct product factor, Sylow
304	C₂³	—	2	4	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	2	no	—
311	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	Q₈	—	8	8	no	—
313	D₄	—	2	8	no	—
314	D₄	—	4	8	no	—
315	D₄	—	4	8	no	—
316	D₄	—	4	4	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	8	8	no	—
330	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
331	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
332	C₂×C₄	C₁₃×#124	1	2	yes	—
333	C₂×C₄	C₁₃×#124	1	2	yes	—
334	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
335	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
336	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
337	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
338	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
339	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
340	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
341	C₂×C₄	C₁₃×#137	1	2	yes	—
342	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
344	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
345	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
346	C₈	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
355	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
356	C₂²	C₁₃×#535	1	1	yes	characteristic
357	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
358	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
359	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	4	no	—
366	C₄	C₁₃×#474	1	4	yes	—
367	C₄	C₁₃×#476	1	4	yes	—
368	C₄	C₁₃×#486	1	4	yes	—
369	C₄	C₁₃×#554	1	2	yes	—
370	C₄	C₁₃×#555	1	2	yes	—
371	C₂	—	8	4	no	—
372	C₂	C₁₃×#2563	1	1	yes	characteristic
373	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
374	C₂	C₂×C₁₃×#476	1	1	yes	characteristic
375	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
376	C₂	C₁₃×#3141	1	1	yes	characteristic
377	C₂	C₁₃×#3205	1	1	yes	characteristic
378	C₂	C₁₃×#3206	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2868	C₂	semidirect
3. C₁₃×#2023	C₂	semidirect
5. C₁₃×#1834	C₂	semidirect
6. C₁₃×#1802	C₂	semidirect
7. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
39. C₁₃×#127	Q₈	semidirect
65. #29139	C₁₃	direct (N × H)
115. #2868	C₂×C₁₃	semidirect
117. #2023	C₂×C₁₃	semidirect
119. #1834	C₂×C₁₃	semidirect
120. #1802	C₂×C₁₃	semidirect
121. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
220. #127	Q₈×C₁₃	semidirect
303. C₁₃	#29139	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×#2868	2
C₄×C₁₃×#127	2
C₁₃×#2023	2
C₁₃×#1957	2
C₁₃×#1834	2
C₁₃×#1802	2
C₄×C₁₃×C₄⋊C₈	2
#29139	13

Subgroups — C13×#29139 #15715478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29139 #15715478