Subgroups — C₁₃×#25049 #15711388

Order 3328.

776 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	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2421	C₂	1	2	yes	maximal
4	C₁₃×#2074	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2036	C₂	1	2	yes	maximal
6	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#470	—	2	4	no	—
17	C₁₃×#441	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#400	—	2	2	no	—
29	C₁₃×#397	—	2	2	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#387	—	2	2	no	—
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#107	—	2	2	no	—
70	C₁₃×#107	—	4	2	no	—
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×#103	—	2	4	no	—
74	C₁₃×#103	—	2	4	no	—
75	C₁₃×#103	—	2	4	no	—
76	C₁₃×C₂²⋊C₈	—	2	2	no	—
77	C₁₃×#97	—	2	2	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	D₄	1	2	yes	—
86	#25049	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×Q₁₆	—	2	8	no	—
109	C₁₃×M₁₆	—	4	4	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃	#41	1	2	yes	—
120	C₂×C₈×C₁₃	#41	1	2	yes	—
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	4	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	4	4	no	—
139	C₂×#470	C₂×C₁₃	1	1	yes	characteristic
140	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2421	C₂×C₁₃	1	2	yes	—
142	#2074	C₂×C₁₃	1	2	yes	complemented
143	#2036	C₂×C₁₃	1	2	yes	—
144	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1863	C₂×C₁₃	1	2	yes	complemented
147	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1809	C₂×C₁₃	1	1	yes	characteristic
149	#1753	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	—	2	1	no	—
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	2	1	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	2	4	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	1	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	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	C₂²×D₄	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	—	2	2	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	1	no	—
194	C₈×C₁₃	#123	1	4	yes	—
195	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
199	#470	—	2	4	no	—
200	#441	—	2	4	no	—
201	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#107	C₂²×C₁₃	1	2	yes	—
203	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#103	C₂²×C₁₃	1	2	yes	—
206	C₂×#103	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	#400	—	2	2	no	—
212	#397	—	2	2	no	—
213	#391	C₂²×C₁₃	1	2	yes	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#388	—	2	2	no	—
216	#387	—	2	2	no	—
217	#382	C₂²×C₁₃	1	2	yes	—
218	#380	C₂²×C₁₃	1	2	yes	—
219	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	#340	C₂²×C₁₃	1	2	yes	—
221	#340	C₂²×C₁₃	1	2	yes	—
222	#336	C₂²×C₁₃	1	1	yes	characteristic
223	#336	C₂²×C₁₃	1	1	yes	characteristic
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	4	1	no	—
226	C₂²×C₁₃	—	4	1	no	—
227	C₂²×C₁₃	—	4	1	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	#532	1	1	yes	characteristic
230	C₂²×C₁₃	D₄²	1	1	yes	characteristic
231	C₂²×C₁₃	#547	1	1	yes	characteristic
232	C₂²×C₁₃	#575	1	2	yes	—
233	C₂²×C₁₃	#578	1	2	yes	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	1	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
242	C₄×C₁₃	#542	1	1	yes	characteristic
243	C₄×C₁₃	#547	1	1	yes	characteristic
244	C₄×C₁₃	#553	1	1	yes	characteristic
245	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	4	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
273	#107	—	2	2	no	—
274	#107	—	4	2	no	—
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	#103	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	D₄×C₁₃	1	2	yes	—
290	C₂×C₁₃	—	8	1	no	—
291	C₂×C₁₃	#2422	1	1	yes	characteristic
292	C₂×C₁₃	#3177	1	1	yes	characteristic
293	C₂×C₁₃	#3183	1	1	yes	characteristic
294	C₂×C₁₃	#3277	1	2	yes	—
295	C₂×C₁₃	#3349	1	2	yes	—
296	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
317	Q₁₆	—	2	8	no	—
318	M₁₆	—	4	4	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
328	C₂×C₈	C₁₃×#41	1	2	yes	—
329	C₂×C₈	C₁₃×#41	1	2	yes	—
330	C₂×C₈	C₁₃×#41	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	4	4	no	—
348	C₁₃	#25049	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	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	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	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	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂²×D₄×C₁₃	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	—	2	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	C₁₃×#123	1	4	yes	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	C₁₃×#532	1	1	yes	characteristic
400	C₂²	D₄²×C₁₃	1	1	yes	characteristic
401	C₂²	C₁₃×#547	1	1	yes	characteristic
402	C₂²	C₁₃×#575	1	2	yes	—
403	C₂²	C₁₃×#578	1	2	yes	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
412	C₄	C₁₃×#542	1	1	yes	characteristic
413	C₄	C₁₃×#547	1	1	yes	characteristic
414	C₄	C₁₃×#553	1	1	yes	characteristic
415	C₂	—	8	1	no	—
416	C₂	C₁₃×#2422	1	1	yes	characteristic
417	C₂	C₁₃×#3177	1	1	yes	characteristic
418	C₂	C₁₃×#3183	1	1	yes	characteristic
419	C₂	C₁₃×#3277	1	2	yes	—
420	C₂	C₁₃×#3349	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#441	C₂	semidirect
4. C₁₃×#2074	C₂	semidirect
6. C₁₃×#1969	C₂	semidirect
7. C₁₃×#1943	C₂	semidirect
8. C₁₃×#1863	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
86. #25049	C₁₃	direct (N × H)
140. C₂×#441	C₂×C₁₃	semidirect
142. #2074	C₂×C₁₃	semidirect
144. #1969	C₂×C₁₃	semidirect
145. #1943	C₂×C₁₃	semidirect
146. #1863	C₂×C₁₃	semidirect
147. #1846	C₂×C₁₃	semidirect
348. C₁₃	#25049	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×#470	2
C₂×C₁₃×#441	2
C₁₃×#2421	2
C₁₃×#2074	2
C₁₃×#2036	2
C₁₃×#1969	2
C₁₃×#1943	2
C₁₃×#1863	2
C₁₃×#1846	2
C₁₃×#1809	2
C₁₃×#1753	2
#25049	13

Subgroups — C13×#25049 #15711388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25049 #15711388