Subgroups — C₁₃×#3318 #13112376

Order 1664.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₃	—	2	1	no	—
17	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₁₃×#126	—	2	1	no	—
26	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#123	—	2	1	no	—
28	C₁₃×#121	—	2	1	no	—
29	C₁₃×#121	—	2	1	no	—
30	C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#120	—	2	1	no	—
35	C₁₃×#120	—	2	1	no	—
36	C₄×D₄×C₁₃	—	2	1	no	—
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₁₃×#102	C₂²	1	1	yes	characteristic
48	C₁₃×#102	C₂²	1	1	yes	characteristic
49	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₁₃	—	2	1	no	—
60	C₂⁴×C₁₃	—	2	1	no	—
61	C₂×D₄×C₁₃	—	2	2	no	—
62	C₂×D₄×C₁₃	—	2	2	no	—
63	C₂×D₄×C₁₃	—	2	1	no	—
64	C₂×D₄×C₁₃	—	2	1	no	—
65	C₂×D₄×C₁₃	—	2	1	no	—
66	C₂×D₄×C₁₃	—	2	1	no	—
67	C₂×D₄×C₁₃	—	2	1	no	—
68	C₂×D₄×C₁₃	—	2	1	no	—
69	C₂×D₄×C₁₃	—	2	1	no	—
70	C₂×D₄×C₁₃	—	2	1	no	—
71	C₂×D₄×C₁₃	—	4	1	no	—
72	C₂×D₄×C₁₃	—	4	1	no	—
73	C₂×D₄×C₁₃	—	4	4	no	—
74	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×D₈	—	2	2	no	—
85	C₁₃×D₈	—	4	1	no	—
86	C₁₃×D₈	—	4	1	no	—
87	C₁₃×M₁₆	—	4	1	no	—
88	C₂×C₈×C₁₃	—	4	1	no	—
89	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	#3318	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	1	no	—
117	C₂³×C₁₃	—	4	2	no	—
118	C₂³×C₁₃	—	4	2	no	—
119	C₂³×C₁₃	—	4	2	no	—
120	C₂³×C₁₃	—	4	2	no	—
121	C₂³×C₁₃	—	8	1	no	—
122	C₂³×C₁₃	—	8	1	no	—
123	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
125	D₄×C₁₃	—	2	2	no	—
126	D₄×C₁₃	—	2	1	no	—
127	D₄×C₁₃	—	2	1	no	—
128	D₄×C₁₃	—	2	1	no	—
129	D₄×C₁₃	—	2	1	no	—
130	D₄×C₁₃	—	2	1	no	—
131	D₄×C₁₃	—	2	1	no	—
132	D₄×C₁₃	—	2	1	no	—
133	D₄×C₁₃	—	4	2	no	—
134	D₄×C₁₃	—	4	2	no	—
135	D₄×C₁₃	—	4	2	no	—
136	D₄×C₁₃	—	4	2	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	4	2	no	—
139	D₄×C₁₃	—	8	1	no	—
140	D₄×C₁₃	—	8	1	no	—
141	D₄×C₁₃	#41	1	2	yes	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	8	1	no	—
152	C₂×C₄×C₁₃	—	8	1	no	—
153	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₈×C₁₃	—	2	1	no	—
159	C₈×C₁₃	—	2	1	no	—
160	C₈×C₁₃	—	2	1	no	—
161	C₈×C₁₃	—	2	1	no	—
162	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
163	D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#490	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#482	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#481	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#478	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#469	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#466	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#459	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#447	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#447	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#442	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#435	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#418	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂²×C₁₃	—	2	1	no	—
178	C₂²×C₁₃	—	2	1	no	—
179	C₂²×C₁₃	—	2	1	no	—
180	C₂²×C₁₃	—	2	2	no	—
181	C₂²×C₁₃	—	2	1	no	—
182	C₂²×C₁₃	—	2	1	no	—
183	C₂²×C₁₃	—	4	1	no	—
184	C₂²×C₁₃	—	4	1	no	—
185	C₂²×C₁₃	—	4	1	no	—
186	C₂²×C₁₃	—	4	1	no	—
187	C₂²×C₁₃	—	4	1	no	—
188	C₂²×C₁₃	—	4	1	no	—
189	C₂²×C₁₃	—	4	1	no	—
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	1	no	—
192	C₂²×C₁₃	—	4	1	no	—
193	C₂²×C₁₃	—	4	1	no	—
194	C₂²×C₁₃	—	8	4	no	—
195	C₂²×C₁₃	—	8	4	no	—
196	C₂²×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	1	no	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	4	1	no	—
203	C₄×C₁₃	—	4	1	no	—
204	C₄×C₁₃	—	4	1	no	—
205	C₄×C₁₃	—	4	1	no	—
206	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²×D₄	—	2	1	no	—
209	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
213	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
215	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	#127	C₂²×C₁₃	1	1	yes	characteristic
217	#126	—	2	1	no	—
218	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	#123	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	—	2	1	no	—
222	#121	C₂²×C₁₃	1	1	yes	characteristic
223	#121	C₂²×C₁₃	1	1	yes	characteristic
224	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
226	#120	—	2	1	no	—
227	#120	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
230	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
233	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
234	#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
235	#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
238	#102	C₂²×C₁₃	1	1	yes	characteristic
239	#102	C₂²×C₁₃	1	1	yes	characteristic
240	#102	C₂²×C₁₃	1	1	yes	characteristic
241	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
244	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
246	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
247	#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
250	#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
251	C₂×C₁₃	—	2	2	no	—
252	C₂×C₁₃	—	4	1	no	—
253	C₂×C₁₃	—	4	2	no	—
254	C₂×C₁₃	—	8	1	no	—
255	C₂×C₁₃	—	8	1	no	—
256	C₂×C₁₃	—	8	1	no	—
257	C₂×C₁₃	#546	1	1	yes	characteristic
258	C₂×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂×C₁₃	#576	1	1	yes	characteristic
260	C₂⁴	—	2	1	no	—
261	C₂⁴	—	2	1	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
285	D₈	—	2	2	no	—
286	D₈	—	4	1	no	—
287	D₈	—	4	1	no	—
288	M₁₆	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
310	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
311	C₄²	—	2	1	no	—
312	C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	C₁₃	#3318	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	8	1	no	—
323	C₂³	—	8	1	no	—
324	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
326	D₄	—	2	2	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	2	1	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	8	1	no	—
341	D₄	—	8	1	no	—
342	D₄	C₁₃×#41	1	2	yes	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	8	4	no	—
381	C₂²	—	8	4	no	—
382	C₂²	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
383	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
393	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	4	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	8	1	no	—
398	C₂	—	8	1	no	—
399	C₂	—	8	1	no	—
400	C₂	C₁₃×#546	1	1	yes	characteristic
401	C₂	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂	C₁₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. D₄²×C₁₃	C₂	semidirect
3. C₁₃×#490	C₂	semidirect
4. C₁₃×#482	C₂	semidirect
5. C₁₃×#481	C₂	semidirect
6. C₁₃×#478	C₂	semidirect
7. C₁₃×#469	C₂	semidirect
8. C₁₃×#466	C₂	semidirect
9. C₁₃×#459	C₂	semidirect
10. C₁₃×#447	C₂	semidirect
11. C₁₃×#447	C₂	semidirect
12. C₁₃×#442	C₂	semidirect
13. C₁₃×#435	C₂	semidirect
14. C₁₃×#418	C₂	semidirect
15. C₂×C₁₃×#102	C₂	semidirect
20. C₂×C₁₃×D₈	C₂²	semidirect
21. C₂×C₁₃×D₈	C₂²	semidirect
22. C₂×C₁₃×M₁₆	C₂²	semidirect
23. C₂²×C₈×C₁₃	C₂²	semidirect
26. C₁₃×#125	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
33. C₁₃×#121	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
41. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. C₁₃×#107	C₂²	semidirect
43. C₁₃×#106	C₂²	semidirect
44. C₁₃×#106	C₂²	semidirect
45. C₁₃×C₄⋊C₈	C₂²	semidirect
49. C₁₃×#102	C₂²	semidirect
50. C₁₃×#102	C₂²	semidirect
51. C₁₃×#102	C₂²	semidirect
52. C₁₃×#102	C₂²	semidirect
53. C₁₃×#102	C₂²	semidirect
54. C₁₃×#102	C₂²	semidirect
55. C₁₃×#102	C₂²	semidirect
56. C₁₃×C₂²⋊C₈	C₂²	semidirect
57. C₁₃×C₂²⋊C₈	C₂²	semidirect
58. C₁₃×#97	C₂²	semidirect
112. #3318	C₁₃	direct (N × H)
162. #553	C₂×C₁₃	semidirect
163. D₄²	C₂×C₁₃	semidirect
164. #490	C₂×C₁₃	semidirect
165. #482	C₂×C₁₃	semidirect
166. #481	C₂×C₁₃	semidirect
167. #478	C₂×C₁₃	semidirect
168. #469	C₂×C₁₃	semidirect
169. #466	C₂×C₁₃	semidirect
170. #459	C₂×C₁₃	semidirect
171. #447	C₂×C₁₃	semidirect
172. #447	C₂×C₁₃	semidirect
173. #442	C₂×C₁₃	semidirect
174. #435	C₂×C₁₃	semidirect
175. #418	C₂×C₁₃	semidirect
176. C₂×#102	C₂×C₁₃	semidirect
212. C₂×D₈	C₂²×C₁₃	semidirect
213. C₂×D₈	C₂²×C₁₃	semidirect
214. C₂×M₁₆	C₂²×C₁₃	semidirect
215. C₂²×C₈	C₂²×C₁₃	semidirect
218. #125	C₂²×C₁₃	semidirect
224. #121	C₂²×C₁₃	semidirect
225. #121	C₂²×C₁₃	semidirect
231. C₄×D₄	C₂²×C₁₃	semidirect
232. #117	C₂²×C₁₃	semidirect
233. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
234. #107	C₂²×C₁₃	semidirect
235. #106	C₂²×C₁₃	semidirect
236. #106	C₂²×C₁₃	semidirect
237. C₄⋊C₈	C₂²×C₁₃	semidirect
241. #102	C₂²×C₁₃	semidirect
242. #102	C₂²×C₁₃	semidirect
243. #102	C₂²×C₁₃	semidirect
244. #102	C₂²×C₁₃	semidirect
245. #102	C₂²×C₁₃	semidirect
246. #102	C₂²×C₁₃	semidirect
247. #102	C₂²×C₁₃	semidirect
248. C₂²⋊C₈	C₂²×C₁₃	semidirect
249. C₂²⋊C₈	C₂²×C₁₃	semidirect
250. #97	C₂²×C₁₃	semidirect
313. C₁₃	#3318	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×#553	2
D₄²×C₁₃	2
C₁₃×#490	2
C₁₃×#482	2
C₁₃×#481	2
C₁₃×#478	2
C₁₃×#469	2
C₁₃×#466	2
C₁₃×#459	2
C₁₃×#447	2
C₁₃×#442	2
C₁₃×#435	2
C₁₃×#418	2
C₂×C₁₃×#102	2
#3318	13

Subgroups — C13×#3318 #13112376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3318 #13112376