Subgroups — C₁₃×#32807 #15719146

Order 3328.

856 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×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2055	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2014	C₂	1	2	yes	maximal
7	C₁₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	—	2	1	no	—
15	C₂×C₁₃×#124	—	2	1	no	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#103	C₂²	1	4	yes	—
18	C₂×C₁₃×#102	C₂²	1	4	yes	—
19	C₁₃×#391	—	2	1	no	—
20	C₁₃×#391	—	2	1	no	—
21	C₁₃×#391	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	2	yes	—
23	C₁₃×#390	—	2	1	no	—
24	C₁₃×#390	—	2	1	no	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	2	yes	—
27	C₁₃×#382	—	2	1	no	—
28	C₁₃×#382	—	2	1	no	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂²×Q₈×C₁₃	—	2	1	no	—
35	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
39	C₂×C₁₃×SD₁₆	—	4	4	no	—
40	C₂×C₁₃×SD₁₆	—	4	4	no	—
41	C₂×C₁₃×SD₁₆	—	4	4	no	—
42	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
43	C₁₃×C₄⋊Q₈	—	4	2	no	—
44	C₁₃×C₄⋊Q₈	—	4	2	no	—
45	C₁₃×C₄⋊Q₈	—	4	2	no	—
46	C₁₃×#127	—	4	2	no	—
47	C₁₃×#124	—	4	4	no	—
48	C₁₃×#124	—	4	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	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×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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	D₄	1	1	yes	characteristic
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	—	4	2	no	—
67	C₁₃×#103	—	4	4	no	—
68	C₁₃×#102	—	4	4	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	—	2	2	no	—
73	#32807	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	4	no	—
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	4	2	no	—
81	C₂×Q₈×C₁₃	—	4	2	no	—
82	C₂×Q₈×C₁₃	—	4	2	no	—
83	C₂×Q₈×C₁₃	—	4	2	no	—
84	C₂×Q₈×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	2	4	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₁₃×SD₁₆	—	4	16	no	—
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₄⋊C₄	—	4	2	no	—
113	C₁₃×C₄⋊C₄	—	4	2	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₂²⋊C₄	—	4	4	no	—
116	C₁₃×C₂²⋊C₄	—	4	4	no	—
117	C₁₃×C₂²⋊C₄	—	4	4	no	—
118	C₁₃×C₂²⋊C₄	—	4	4	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	1	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	—	4	1	no	—
126	C₄²×C₁₃	SD₁₆	1	4	yes	complemented
127	#2862	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#2858	C₂×C₁₃	1	1	yes	characteristic
129	#2055	C₂×C₁₃	1	4	yes	complemented
130	#2024	C₂×C₁₃	1	2	yes	complemented
131	#2023	C₂×C₁₃	1	2	yes	complemented
132	#2014	C₂×C₁₃	1	2	yes	—
133	#2013	C₂×C₁₃	1	2	yes	complemented
134	#1831	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	4	no	—
144	Q₈×C₁₃	—	4	4	no	—
145	Q₈×C₁₃	—	8	4	no	—
146	Q₈×C₁₃	—	8	4	no	—
147	D₄×C₁₃	—	4	4	no	—
148	D₄×C₁₃	—	4	4	no	—
149	D₄×C₁₃	—	8	4	no	—
150	D₄×C₁₃	—	8	4	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	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₁₃	#137	1	2	yes	—
178	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
180	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
181	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₈×C₁₃	—	4	4	no	—
183	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#124	—	2	1	no	—
189	C₂×#124	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
191	C₂×#103	C₂²×C₁₃	1	4	yes	—
192	C₂×#102	C₂²×C₁₃	1	4	yes	—
193	#391	—	2	1	no	—
194	#391	—	2	1	no	—
195	#391	C₂²×C₁₃	1	2	yes	—
196	#391	C₂²×C₁₃	1	2	yes	—
197	#390	—	2	1	no	—
198	#390	—	2	1	no	—
199	#390	C₂²×C₁₃	1	2	yes	—
200	#390	C₂²×C₁₃	1	2	yes	—
201	#382	—	2	1	no	—
202	#382	—	2	1	no	—
203	C₄³	C₂²×C₁₃	1	1	yes	characteristic
204	#340	C₂²×C₁₃	1	4	yes	—
205	#336	C₂²×C₁₃	1	2	yes	—
206	#336	C₂²×C₁₃	1	2	yes	—
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	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	#535	1	1	yes	characteristic
215	C₂²×C₁₃	#535	1	1	yes	characteristic
216	C₂²×C₁₃	#537	1	1	yes	characteristic
217	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
220	C₂²×C₁₃	#575	1	1	yes	characteristic
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	4	1	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	H(3,𝔽₄)	1	2	yes	—
231	C₄×C₁₃	#562	1	2	yes	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
238	C₂×SD₁₆	—	4	4	no	—
239	C₂×SD₁₆	—	4	4	no	—
240	C₂×SD₁₆	—	4	4	no	—
241	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
242	C₄⋊Q₈	—	4	2	no	—
243	C₄⋊Q₈	—	4	2	no	—
244	C₄⋊Q₈	—	4	2	no	—
245	#127	—	4	2	no	—
246	#124	—	4	4	no	—
247	#124	—	4	4	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
265	C₄⋊C₈	—	4	2	no	—
266	#103	—	4	4	no	—
267	#102	—	4	4	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	C₂×C₁₃	—	16	2	no	—
273	C₂×C₁₃	#2819	1	1	yes	characteristic
274	C₂×C₁₃	#3206	1	1	yes	characteristic
275	C₂×C₁₃	#3208	1	1	yes	characteristic
276	C₂×C₁₃	#3213	1	1	yes	characteristic
277	C₂×C₁₃	#3215	1	1	yes	characteristic
278	C₂×C₁₃	#3246	1	1	yes	characteristic
279	C₂×C₁₃	#3254	1	1	yes	characteristic
280	C₂⁴	—	2	2	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
311	SD₁₆	—	4	16	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	C₁₃×SD₁₆	1	4	yes	complemented
333	C₁₃	#32807	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	8	4	no	—
345	Q₈	—	8	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	4	no	—
349	D₄	—	8	4	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	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
375	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
376	C₂×C₄	C₁₃×#137	1	2	yes	—
377	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
381	C₈	—	4	4	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₁₃×#535	1	1	yes	characteristic
390	C₂²	C₁₃×#535	1	1	yes	characteristic
391	C₂²	C₁₃×#537	1	1	yes	characteristic
392	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
393	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
395	C₂²	C₁₃×#575	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₃×H(3,𝔽₄)	1	2	yes	—
406	C₄	C₁₃×#562	1	2	yes	—
407	C₂	—	16	2	no	—
408	C₂	C₁₃×#2819	1	1	yes	characteristic
409	C₂	C₁₃×#3206	1	1	yes	characteristic
410	C₂	C₁₃×#3208	1	1	yes	characteristic
411	C₂	C₁₃×#3213	1	1	yes	characteristic
412	C₂	C₁₃×#3215	1	1	yes	characteristic
413	C₂	C₁₃×#3246	1	1	yes	characteristic
414	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×#2862	C₂	semidirect
3. C₁₃×#2055	C₂	semidirect
4. C₁₃×#2024	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
7. C₁₃×#2013	C₂	semidirect
8. C₁₃×#1831	C₂	semidirect
73. #32807	C₁₃	direct (N × H)
126. C₄²×C₁₃	SD₁₆	semidirect
127. #2862	C₂×C₁₃	semidirect
129. #2055	C₂×C₁₃	semidirect
130. #2024	C₂×C₁₃	semidirect
131. #2023	C₂×C₁₃	semidirect
133. #2013	C₂×C₁₃	semidirect
134. #1831	C₂×C₁₃	semidirect
332. C₄²	C₁₃×SD₁₆	semidirect
333. C₁₃	#32807	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×#2862	2
C₁₃×#2858	2
C₁₃×#2055	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#2014	2
C₁₃×#2013	2
C₁₃×#1831	2
#32807	13

Subgroups — C13×#32807 #15719146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32807 #15719146