Subgroups — C₁₃×#32647 #15718986

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2041	C₂	1	2	yes	maximal
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1921	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#124	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#107	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#102	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₁₃×#395	—	2	1	no	—
22	C₁₃×#395	—	2	1	no	—
23	C₁₃×#394	—	2	1	no	—
24	C₁₃×#394	—	2	1	no	—
25	C₁₃×#391	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#384	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	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×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	4	1	no	—
47	C₁₃×C₄⋊Q₈	—	4	1	no	—
48	C₁₃×#127	—	4	1	no	—
49	C₁₃×#127	—	4	1	no	—
50	C₁₃×#124	—	4	4	no	—
51	C₄×Q₈×C₁₃	—	4	1	no	—
52	C₄×Q₈×C₁₃	—	4	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	4	no	—
72	C₁₃×C₄⋊C₈	—	4	1	no	—
73	C₁₃×#102	—	2	4	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#102	—	4	2	no	—
76	C₁₃×#102	—	4	2	no	—
77	C₁₃×#97	—	4	1	no	—
78	C₁₃×#95	—	2	1	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	#32647	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	8	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	8	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	8	2	no	—
126	C₁₃×C₄⋊C₄	—	8	2	no	—
127	C₁₃×C₄⋊C₄	#41	1	4	yes	—
128	C₁₃×C₂²⋊C₄	—	4	4	no	—
129	C₁₃×C₂²⋊C₄	—	4	4	no	—
130	C₁₃×C₂²⋊C₄	—	8	2	no	—
131	C₁₃×C₂²⋊C₄	—	8	2	no	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	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	2	no	—
139	C₄²×C₁₃	—	4	2	no	—
140	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2548	C₂×C₁₃	1	1	yes	characteristic
142	#2067	C₂×C₁₃	1	2	yes	complemented
143	#2041	C₂×C₁₃	1	2	yes	—
144	#2023	C₂×C₁₃	1	2	yes	complemented
145	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1936	C₂×C₁₃	1	2	yes	complemented
147	#1925	C₂×C₁₃	1	2	yes	complemented
148	#1921	C₂×C₁₃	1	2	yes	complemented
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	4	4	no	—
158	Q₈×C₁₃	—	8	4	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	8	4	no	—
164	D₄×C₁₃	—	8	4	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	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	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₁₃	#137	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#124	—	2	1	no	—
198	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#107	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#102	C₂²×C₁₃	1	2	yes	—
202	C₂×#102	C₂²×C₁₃	1	2	yes	—
203	C₂×#102	C₂²×C₁₃	1	2	yes	—
204	C₂×#102	C₂²×C₁₃	1	2	yes	—
205	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
206	#395	—	2	1	no	—
207	#395	—	2	1	no	—
208	#394	—	2	1	no	—
209	#394	—	2	1	no	—
210	#391	—	2	1	no	—
211	#390	—	2	1	no	—
212	#390	C₂²×C₁₃	1	2	yes	—
213	#390	C₂²×C₁₃	1	2	yes	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#389	C₂²×C₁₃	1	2	yes	—
216	#384	—	2	1	no	—
217	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	#340	C₂²×C₁₃	1	2	yes	—
220	#340	C₂²×C₁₃	1	2	yes	—
221	#340	C₂²×C₁₃	1	2	yes	—
222	#336	C₂²×C₁₃	1	2	yes	—
223	#336	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	#534	1	1	yes	characteristic
232	C₂²×C₁₃	#548	1	2	yes	—
233	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
235	C₂²×C₁₃	#576	1	2	yes	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	4	1	no	—
240	C₄×C₁₃	—	4	1	no	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	1	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	#542	1	2	yes	—
246	C₄×C₁₃	#555	1	1	yes	characteristic
247	C₄×C₁₃	#563	1	1	yes	characteristic
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
255	C₄⋊Q₈	—	4	1	no	—
256	C₄⋊Q₈	—	4	1	no	—
257	#127	—	4	1	no	—
258	#127	—	4	1	no	—
259	#124	—	4	4	no	—
260	C₄×Q₈	—	4	1	no	—
261	C₄×Q₈	—	4	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	#107	—	2	4	no	—
281	C₄⋊C₈	—	4	1	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	4	2	no	—
285	#102	—	4	2	no	—
286	#97	—	4	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂×C₁₃	—	16	2	no	—
292	C₂×C₁₃	#2731	1	1	yes	characteristic
293	C₂×C₁₃	#3193	1	1	yes	characteristic
294	C₂×C₁₃	#3199	1	1	yes	characteristic
295	C₂×C₁₃	#3366	1	2	yes	—
296	C₂×C₁₃	#3375	1	2	yes	—
297	C₂⁴	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	—	8	2	no	—
341	C₄⋊C₄	C₁₃×#41	1	4	yes	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₁₃	#32647	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	Q₈	—	4	4	no	—
364	Q₈	—	8	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	8	4	no	—
370	D₄	—	8	4	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
394	C₂×C₄	C₁₃×#137	1	2	yes	—
395	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
396	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	C₁₃×#534	1	1	yes	characteristic
409	C₂²	C₁₃×#548	1	2	yes	—
410	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
412	C₂²	C₁₃×#576	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	2	no	—
422	C₄	C₁₃×#542	1	2	yes	—
423	C₄	C₁₃×#555	1	1	yes	characteristic
424	C₄	C₁₃×#563	1	1	yes	characteristic
425	C₂	—	16	2	no	—
426	C₂	C₁₃×#2731	1	1	yes	characteristic
427	C₂	C₁₃×#3193	1	1	yes	characteristic
428	C₂	C₁₃×#3199	1	1	yes	characteristic
429	C₂	C₁₃×#3366	1	2	yes	—
430	C₂	C₁₃×#3375	1	2	yes	—

	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2567	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
6. C₁₃×#1985	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1925	C₂	semidirect
9. C₁₃×#1921	C₂	semidirect
82. #32647	C₁₃	direct (N × H)
140. #2567	C₂×C₁₃	semidirect
142. #2067	C₂×C₁₃	semidirect
144. #2023	C₂×C₁₃	semidirect
145. #1985	C₂×C₁₃	semidirect
146. #1936	C₂×C₁₃	semidirect
147. #1925	C₂×C₁₃	semidirect
148. #1921	C₂×C₁₃	semidirect
354. C₁₃	#32647	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×#2567	2
C₁₃×#2548	2
C₁₃×#2067	2
C₁₃×#2041	2
C₁₃×#2023	2
C₁₃×#1985	2
C₁₃×#1936	2
C₁₃×#1925	2
C₁₃×#1921	2
#32647	13

Subgroups — C13×#32647 #15718986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32647 #15718986