Subgroups — C₁₃×#32785 #15719124

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2620	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2034	C₂	1	2	yes	maximal
9	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₃×#398	—	2	2	no	—
25	C₁₃×#396	—	2	2	no	—
26	C₁₃×#396	—	2	2	no	—
27	C₁₃×#394	—	2	2	no	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×#125	—	4	2	no	—
46	C₁₃×#124	—	4	2	no	—
47	C₁₃×C₂²⋊Q₈	—	4	2	no	—
48	C₁₃×#121	—	4	2	no	—
49	C₁₃×#117	—	4	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#106	—	4	2	no	—
69	C₁₃×#106	—	4	2	no	—
70	C₁₃×#103	—	4	2	no	—
71	C₁₃×#103	—	4	2	no	—
72	C₁₃×#102	—	4	2	no	—
73	C₁₃×#102	—	4	2	no	—
74	C₁₃×C₂²⋊C₈	—	4	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	#32785	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	2	1	no	—
80	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	1	no	—
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	8	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	4	no	—
119	C₁₃×C₄⋊C₄	—	8	2	no	—
120	C₁₃×C₄⋊C₄	—	8	2	no	—
121	C₁₃×C₄⋊C₄	—	8	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	4	no	—
125	C₁₃×C₂²⋊C₄	—	4	2	no	—
126	C₁₃×C₂²⋊C₄	—	8	2	no	—
127	C₁₃×C₂²⋊C₄	—	8	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	#2629	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#2620	C₂×C₁₃	1	1	yes	characteristic
132	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2084	C₂×C₁₃	1	2	yes	complemented
135	#2042	C₂×C₁₃	1	2	yes	complemented
136	#2035	C₂×C₁₃	1	2	yes	complemented
137	#2034	C₂×C₁₃	1	2	yes	—
138	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1818	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	4	1	no	—
147	C₂³×C₁₃	—	4	1	no	—
148	C₂³×C₁₃	—	4	1	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	8	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	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	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	—	4	2	no	—
187	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#106	C₂²×C₁₃	1	2	yes	—
193	C₂×#106	C₂²×C₁₃	1	2	yes	—
194	C₂×#103	C₂²×C₁₃	1	2	yes	—
195	C₂×#103	C₂²×C₁₃	1	2	yes	—
196	C₂×#102	C₂²×C₁₃	1	2	yes	—
197	C₂×#102	C₂²×C₁₃	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
199	#398	—	2	2	no	—
200	#396	—	2	2	no	—
201	#396	—	2	2	no	—
202	#394	—	2	2	no	—
203	#391	C₂²×C₁₃	1	1	yes	characteristic
204	#390	C₂²×C₁₃	1	1	yes	characteristic
205	#389	C₂²×C₁₃	1	2	yes	—
206	#384	C₂²×C₁₃	1	1	yes	characteristic
207	#384	C₂²×C₁₃	1	1	yes	characteristic
208	#380	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	#340	C₂²×C₁₃	1	2	yes	—
211	#336	C₂²×C₁₃	1	2	yes	—
212	#336	C₂²×C₁₃	1	1	yes	characteristic
213	#336	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₁₃	—	4	1	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	8	1	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	1	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	#534	1	1	yes	characteristic
225	C₂²×C₁₃	#535	1	1	yes	characteristic
226	C₂²×C₁₃	#536	1	1	yes	characteristic
227	C₂²×C₁₃	#577	1	2	yes	—
228	C₂²×C₁₃	#577	1	2	yes	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	—	8	1	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	#562	1	2	yes	—
238	C₄×C₁₃	#562	1	2	yes	—
239	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
245	#125	—	4	2	no	—
246	#124	—	4	2	no	—
247	C₂²⋊Q₈	—	4	2	no	—
248	#121	—	4	2	no	—
249	#117	—	4	2	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	#106	—	4	2	no	—
269	#106	—	4	2	no	—
270	#103	—	4	2	no	—
271	#103	—	4	2	no	—
272	#102	—	4	2	no	—
273	#102	—	4	2	no	—
274	C₂²⋊C₈	—	4	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₂×C₁₃	—	8	1	no	—
279	C₂×C₁₃	—	16	1	no	—
280	C₂×C₁₃	#2816	1	1	yes	characteristic
281	C₂×C₁₃	#3204	1	2	yes	—
282	C₂×C₁₃	#3221	1	1	yes	characteristic
283	C₂×C₁₃	#3222	1	1	yes	characteristic
284	C₂×C₁₃	#3244	1	2	yes	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	8	2	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₁₃	#32785	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
380	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₁₃×#534	1	1	yes	characteristic
394	C₂²	C₁₃×#535	1	1	yes	characteristic
395	C₂²	C₁₃×#536	1	1	yes	characteristic
396	C₂²	C₁₃×#577	1	2	yes	—
397	C₂²	C₁₃×#577	1	2	yes	—
398	C₄	—	4	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	1	no	—
406	C₄	C₁₃×#562	1	2	yes	—
407	C₄	C₁₃×#562	1	2	yes	—
408	C₂	—	8	1	no	—
409	C₂	—	16	1	no	—
410	C₂	C₁₃×#2816	1	1	yes	characteristic
411	C₂	C₁₃×#3204	1	2	yes	—
412	C₂	C₁₃×#3221	1	1	yes	characteristic
413	C₂	C₁₃×#3222	1	1	yes	characteristic
414	C₂	C₁₃×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2629	C₂	semidirect
3. C₁₃×#2096	C₂	semidirect
4. C₁₃×#2094	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2026	C₂	semidirect
10. C₁₃×#2025	C₂	semidirect
11. C₁₃×#1818	C₂	semidirect
78. #32785	C₁₃	direct (N × H)
130. #2629	C₂×C₁₃	semidirect
132. #2096	C₂×C₁₃	semidirect
133. #2094	C₂×C₁₃	semidirect
134. #2084	C₂×C₁₃	semidirect
135. #2042	C₂×C₁₃	semidirect
136. #2035	C₂×C₁₃	semidirect
138. #2026	C₂×C₁₃	semidirect
139. #2025	C₂×C₁₃	semidirect
140. #1818	C₂×C₁₃	semidirect
336. C₁₃	#32785	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×#2629	2
C₁₃×#2620	2
C₁₃×#2096	2
C₁₃×#2094	2
C₁₃×#2084	2
C₁₃×#2042	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1818	2
#32785	13

Subgroups — C13×#32785 #15719124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32785 #15719124