Subgroups — C₁₃×#29130 #15715469

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2100	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2041	C₂	1	2	yes	maximal
5	C₁₃×#1936	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1802	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1802	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#125	—	2	1	no	—
11	C₂×C₄×D₄×C₁₃	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#102	C₂²	1	4	yes	—
16	C₂×C₁₃×#102	C₂²	1	4	yes	—
17	C₂×C₁₃×#97	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×#389	—	2	1	no	—
22	C₁₃×#389	—	2	1	no	—
23	C₁₃×#389	C₂²	1	2	yes	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#384	C₂²	1	1	yes	characteristic
26	C₁₃×#384	C₂²	1	1	yes	characteristic
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#382	—	2	1	no	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃	—	2	2	no	—
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₁₃×#127	—	2	4	no	—
39	C₁₃×#125	—	4	4	no	—
40	C₄×D₄×C₁₃	—	2	4	no	—
41	C₄×D₄×C₁₃	—	2	4	no	—
42	C₄×D₄×C₁₃	—	4	4	no	—
43	C₄×D₄×C₁₃	—	4	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	4	no	—
66	C₁₃×#102	—	2	8	no	—
67	C₁₃×#102	—	4	4	no	—
68	C₁₃×#97	—	4	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	#29130	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	2	no	—
73	C₂×D₄×C₁₃	—	2	4	no	—
74	C₂×D₄×C₁₃	—	2	4	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	#41	1	4	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₁₃×C₄⋊C₄	—	2	4	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	4	2	no	—
107	C₁₃×C₄⋊C₄	—	4	2	no	—
108	C₁₃×C₄⋊C₄	—	4	2	no	—
109	C₁₃×C₄⋊C₄	—	4	2	no	—
110	C₁₃×C₄⋊C₄	—	4	4	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₄⋊C₄	—	4	2	no	—
113	C₁₃×C₄⋊C₄	—	4	4	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₁₃×C₂²⋊C₄	—	4	4	no	—
116	C₁₃×C₂²⋊C₄	—	4	4	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	2	1	no	—
124	C₄²×C₁₃	#41	1	4	yes	—
125	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
126	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
127	#2100	C₂×C₁₃	1	2	yes	complemented
128	#2041	C₂×C₁₃	1	2	yes	—
129	#1936	C₂×C₁₃	1	4	yes	complemented
130	#1802	C₂×C₁₃	1	2	yes	complemented
131	#1802	C₂×C₁₃	1	2	yes	complemented
132	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	—	2	4	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₁₃	—	2	4	no	—
142	D₄×C₁₃	—	2	4	no	—
143	D₄×C₁₃	—	4	8	no	—
144	D₄×C₁₃	—	4	8	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	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	#124	1	2	yes	—
170	C₂×C₄×C₁₃	#124	1	2	yes	—
171	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₁₃	#137	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₁₃	—	4	4	no	—
180	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×#125	—	2	1	no	—
182	C₂×C₄×D₄	—	2	1	no	—
183	C₂×C₄×D₄	—	2	1	no	—
184	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
185	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
186	C₂×#102	C₂²×C₁₃	1	4	yes	—
187	C₂×#102	C₂²×C₁₃	1	4	yes	—
188	C₂×#97	C₂²×C₁₃	1	2	yes	—
189	#390	—	2	1	no	—
190	#390	—	2	1	no	—
191	#390	C₂²×C₁₃	1	2	yes	—
192	#389	—	2	1	no	—
193	#389	—	2	1	no	—
194	#389	C₂²×C₁₃	1	2	yes	—
195	#389	C₂²×C₁₃	1	2	yes	—
196	#384	C₂²×C₁₃	1	1	yes	characteristic
197	#384	C₂²×C₁₃	1	1	yes	characteristic
198	#384	C₂²×C₁₃	1	1	yes	characteristic
199	#382	—	2	1	no	—
200	C₄³	C₂²×C₁₃	1	1	yes	characteristic
201	#340	C₂²×C₁₃	1	4	yes	—
202	#340	C₂²×C₁₃	1	4	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	#525	1	1	yes	characteristic
212	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
213	C₂²×C₁₃	#537	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	#490	1	4	yes	—
227	C₄×C₁₃	#552	1	2	yes	—
228	C₄×C₁₃	#553	1	2	yes	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
234	#127	—	2	4	no	—
235	#125	—	4	4	no	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₄×D₄	—	4	4	no	—
239	C₄×D₄	—	4	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	C₄⋊C₈	—	2	4	no	—
262	#102	—	2	8	no	—
263	#102	—	4	4	no	—
264	#97	—	4	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	C₂×C₁₃	—	8	4	no	—
268	C₂×C₁₃	#2562	1	1	yes	characteristic
269	C₂×C₁₃	#3109	1	1	yes	characteristic
270	C₂×C₁₃	#3110	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#490	1	1	yes	characteristic
272	C₂×C₁₃	#3141	1	1	yes	characteristic
273	C₂×C₁₃	#3253	1	1	yes	characteristic
274	C₂×C₁₃	#3254	1	1	yes	characteristic
275	C₂⁴	—	2	2	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	C₁₃×#41	1	4	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	C₁₃×#41	1	4	yes	—
328	C₁₃	#29130	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	2	4	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	—	4	2	no	—
336	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	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	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	8	no	—
365	C₂×C₄	C₁₃×#124	1	2	yes	—
366	C₂×C₄	C₁₃×#124	1	2	yes	—
367	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
370	C₂×C₄	C₁₃×#137	1	2	yes	—
371	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
372	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
373	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
375	C₈	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	C₁₃×#525	1	1	yes	characteristic
384	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
385	C₂²	C₁₃×#537	1	1	yes	characteristic
386	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	C₁₃×#490	1	4	yes	—
399	C₄	C₁₃×#552	1	2	yes	—
400	C₄	C₁₃×#553	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	C₁₃×#2562	1	1	yes	characteristic
403	C₂	C₁₃×#3109	1	1	yes	characteristic
404	C₂	C₁₃×#3110	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#490	1	1	yes	characteristic
406	C₂	C₁₃×#3141	1	1	yes	characteristic
407	C₂	C₁₃×#3253	1	1	yes	characteristic
408	C₂	C₁₃×#3254	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×#2859	C₂	semidirect
3. C₁₃×#2100	C₂	semidirect
5. C₁₃×#1936	C₂	semidirect
6. C₁₃×#1802	C₂	semidirect
7. C₁₃×#1802	C₂	semidirect
8. C₁₃×#1767	C₂	semidirect
71. #29130	C₁₃	direct (N × H)
125. #2859	C₂×C₁₃	semidirect
127. #2100	C₂×C₁₃	semidirect
129. #1936	C₂×C₁₃	semidirect
130. #1802	C₂×C₁₃	semidirect
131. #1802	C₂×C₁₃	semidirect
132. #1767	C₂×C₁₃	semidirect
328. C₁₃	#29130	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×#2859	2
C₄×C₁₃×#127	2
C₁₃×#2100	2
C₁₃×#2041	2
C₁₃×#1936	2
C₁₃×#1802	2
C₁₃×#1767	2
#29130	13

Subgroups — C13×#29130 #15715469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29130 #15715469