Subgroups — C₁₃×#29128 #15715467

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2042	C₂	1	2	yes	maximal
5	C₁₃×#1936	C₂	1	2	yes	maximal
6	C₁₃×#1935	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	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	2	yes	—
22	C₁₃×#391	C₂²	1	1	yes	characteristic
23	C₁₃×#390	C₂²	1	1	yes	characteristic
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#388	—	2	2	no	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#387	—	2	2	no	—
29	C₁₃×#382	C₂²	1	1	yes	characteristic
30	C₁₃×#382	C₂²	1	1	yes	characteristic
31	C₁₃×#382	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
33	C₄³×C₁₃	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	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×#124	—	2	2	no	—
45	C₁₃×#124	—	2	2	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₄×Q₈×C₁₃	—	2	2	no	—
48	C₄×D₄×C₁₃	—	2	2	no	—
49	C₄×D₄×C₁₃	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	—	2	2	no	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×#103	—	2	4	no	—
69	C₁₃×#103	—	4	2	no	—
70	C₁₃×#102	—	2	4	no	—
71	C₁₃×#102	—	4	2	no	—
72	C₁₃×#97	—	4	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	1	no	—
76	C₁₃×#95	—	2	1	no	—
77	C₁₃×#95	—	2	1	no	—
78	C₁₃×#95	—	2	1	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	#29128	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	1	no	—
83	C₂×Q₈×C₁₃	—	2	1	no	—
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	#41	1	2	yes	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	#41	1	2	yes	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	4	4	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	4	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	2	8	no	—
125	C₁₃×C₂²⋊C₄	—	4	4	no	—
126	C₁₃×C₂²⋊C₄	—	4	2	no	—
127	C₄²×C₁₃	—	2	1	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	1	no	—
131	C₄²×C₁₃	—	4	2	no	—
132	C₄²×C₁₃	—	4	2	no	—
133	C₄²×C₁₃	—	4	2	no	—
134	C₄²×C₁₃	#41	1	2	yes	—
135	C₄²×C₁₃	#41	1	2	yes	—
136	#2864	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
138	#2101	C₂×C₁₃	1	2	yes	complemented
139	#2042	C₂×C₁₃	1	2	yes	—
140	#1936	C₂×C₁₃	1	2	yes	—
141	#1935	C₂×C₁₃	1	2	yes	complemented
142	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1804	C₂×C₁₃	1	1	yes	characteristic
145	#1804	C₂×C₁₃	1	1	yes	characteristic
146	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	4	1	no	—
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	2	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	2	2	no	—
159	D₄×C₁₃	—	4	1	no	—
160	D₄×C₁₃	—	4	1	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	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	8	4	no	—
183	C₂×C₄×C₁₃	#124	1	2	yes	—
184	C₂×C₄×C₁₃	#124	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	—	4	2	no	—
193	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#103	C₂²×C₁₃	1	2	yes	—
199	C₂×#103	C₂²×C₁₃	1	2	yes	—
200	C₂×#102	C₂²×C₁₃	1	2	yes	—
201	C₂×#102	C₂²×C₁₃	1	2	yes	—
202	C₂×#97	C₂²×C₁₃	1	2	yes	—
203	#391	C₂²×C₁₃	1	1	yes	characteristic
204	#390	C₂²×C₁₃	1	1	yes	characteristic
205	#389	C₂²×C₁₃	1	2	yes	—
206	#389	C₂²×C₁₃	1	2	yes	—
207	#388	—	2	2	no	—
208	#387	—	2	2	no	—
209	#387	—	2	2	no	—
210	#382	C₂²×C₁₃	1	1	yes	characteristic
211	#382	C₂²×C₁₃	1	1	yes	characteristic
212	#382	C₂²×C₁₃	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	—	2	2	no	—
214	C₄³	C₂²×C₁₃	1	1	yes	characteristic
215	#340	C₂²×C₁₃	1	2	yes	—
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#336	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₁₃	—	4	2	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	#525	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
227	C₂²×C₁₃	#537	1	1	yes	characteristic
228	C₂²×C₁₃	#575	1	2	yes	—
229	C₂²×C₁₃	#575	1	2	yes	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	#552	1	1	yes	characteristic
240	C₄×C₁₃	#552	1	1	yes	characteristic
241	C₄×C₁₃	#553	1	1	yes	characteristic
242	C₄×C₁₃	#553	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	#124	—	2	2	no	—
249	#124	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	D₄×C₁₃	1	2	yes	—
266	C₂×C₄²	D₄×C₁₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#103	—	2	4	no	—
273	#103	—	4	2	no	—
274	#102	—	2	4	no	—
275	#102	—	4	2	no	—
276	#97	—	4	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂×C₁₃	—	8	2	no	—
286	C₂×C₁₃	#2562	1	1	yes	characteristic
287	C₂×C₁₃	#3111	1	2	yes	—
288	C₂×C₁₃	#3135	1	1	yes	characteristic
289	C₂×C₁₃	#3140	1	1	yes	characteristic
290	C₂×C₁₃	#3256	1	2	yes	—
291	C₂⁴	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	C₁₃×#41	1	2	yes	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	C₁₃×#41	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	C₁₃×#41	1	2	yes	—
344	C₄²	C₁₃×#41	1	2	yes	—
345	C₁₃	#29128	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	2	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	4	no	—
382	C₂×C₄	C₁₃×#124	1	2	yes	—
383	C₂×C₄	C₁₃×#124	1	2	yes	—
384	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
388	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₁₃×#525	1	1	yes	characteristic
398	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
399	C₂²	C₁₃×#537	1	1	yes	characteristic
400	C₂²	C₁₃×#575	1	2	yes	—
401	C₂²	C₁₃×#575	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	2	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₃×#552	1	1	yes	characteristic
412	C₄	C₁₃×#552	1	1	yes	characteristic
413	C₄	C₁₃×#553	1	1	yes	characteristic
414	C₄	C₁₃×#553	1	1	yes	characteristic
415	C₂	—	8	2	no	—
416	C₂	C₁₃×#2562	1	1	yes	characteristic
417	C₂	C₁₃×#3111	1	2	yes	—
418	C₂	C₁₃×#3135	1	1	yes	characteristic
419	C₂	C₁₃×#3140	1	1	yes	characteristic
420	C₂	C₁₃×#3256	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2864	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
6. C₁₃×#1935	C₂	semidirect
7. C₁₃×#1805	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
11. C₁₃×#1767	C₂	semidirect
81. #29128	C₁₃	direct (N × H)
136. #2864	C₂×C₁₃	semidirect
138. #2101	C₂×C₁₃	semidirect
141. #1935	C₂×C₁₃	semidirect
142. #1805	C₂×C₁₃	semidirect
143. #1805	C₂×C₁₃	semidirect
146. #1767	C₂×C₁₃	semidirect
345. C₁₃	#29128	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×#2864	2
C₄×C₁₃×#124	2
C₁₃×#2101	2
C₁₃×#2042	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1805	2
C₁₃×#1804	2
C₁₃×#1767	2
#29128	13

Subgroups — C13×#29128 #15715467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29128 #15715467