Subgroups — C₁₃×#20844 #15707183

Order 3328.

1862 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#407	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1853	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1852	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1736	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₁₃	—	2	1	no	—
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
14	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₁₃×#428	—	2	8	no	—
19	C₂×C₁₃×#107	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
21	C₁₃×#407	C₄	1	8	yes	complemented
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₁₃×#381	—	2	1	no	—
24	C₁₃×#380	C₂²	1	2	yes	—
25	C₁₃×#380	C₂²	1	2	yes	—
26	C₁₃×#379	—	2	1	no	—
27	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
28	C₁₃×#340	C₂²	1	8	yes	complemented
29	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	—	2	4	no	—
31	C₂³×C₄×C₁₃	—	2	4	no	—
32	C₂³×C₄×C₁₃	—	2	8	no	—
33	C₂³×C₄×C₁₃	—	2	4	no	—
34	C₂³×C₄×C₁₃	—	2	2	no	—
35	C₂³×C₄×C₁₃	—	4	8	no	—
36	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₃	D₄	1	2	yes	—
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	Q₈	1	4	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	—	2	4	no	—
43	C₂×C₁₃×M₁₆	—	2	4	no	—
44	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	complemented
45	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
46	C₁₃×#117	—	2	4	no	—
47	C₁₃×#117	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
54	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₁₃×#107	—	2	8	no	—
66	C₁₃×#106	—	2	8	no	—
67	C₁₃×C₂²⋊C₈	C₂×C₄	1	16	yes	complemented
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	#20844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	2	no	—
72	C₂⁴×C₁₃	—	2	2	no	—
73	C₂⁴×C₁₃	—	2	4	no	—
74	C₂⁴×C₁₃	—	2	4	no	—
75	C₂⁴×C₁₃	C₄⋊C₄	1	4	yes	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	16	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	16	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	16	no	—
87	C₂²×C₄×C₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	4	32	no	—
93	C₂²×C₄×C₁₃	—	4	8	no	—
94	C₂²×C₄×C₁₃	—	4	8	no	—
95	C₂²×C₄×C₁₃	—	4	8	no	—
96	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₃	#41	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×M₁₆	—	2	16	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	complemented
111	C₁₃×C₄⋊C₄	—	2	16	no	—
112	C₁₃×C₄⋊C₄	—	2	8	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
118	C₁₃×C₂²⋊C₄	—	4	2	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	4	no	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₄²×C₁₃	—	4	2	no	—
123	C₄²×C₁₃	—	4	2	no	—
124	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
125	C₂×#428	C₂×C₁₃	1	2	yes	complemented
126	C₂×#407	C₂×C₁₃	1	1	yes	characteristic
127	#2280	C₂×C₁₃	1	1	yes	characteristic
128	#1853	C₂×C₁₃	1	4	yes	complemented
129	#1852	C₂×C₁₃	1	4	yes	complemented
130	#1736	C₂×C₁₃	1	2	yes	complemented
131	C₂³×C₁₃	—	2	8	no	—
132	C₂³×C₁₃	—	2	16	no	—
133	C₂³×C₁₃	—	2	8	no	—
134	C₂³×C₁₃	—	2	2	no	—
135	C₂³×C₁₃	—	2	2	no	—
136	C₂³×C₁₃	—	2	2	no	—
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	2	2	no	—
140	C₂³×C₁₃	—	2	8	no	—
141	C₂³×C₁₃	—	2	16	no	—
142	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
144	C₂³×C₁₃	#120	1	2	yes	—
145	C₂³×C₁₃	#123	1	2	yes	—
146	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
147	C₂³×C₁₃	#137	1	4	yes	—
148	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	16	no	—
155	C₂×C₄×C₁₃	—	2	8	no	—
156	C₂×C₄×C₁₃	—	4	16	no	—
157	C₂×C₄×C₁₃	—	4	32	no	—
158	C₂×C₄×C₁₃	—	4	8	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
169	C₂×C₄×C₁₃	#120	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
171	C₂×C₄×C₁₃	#123	1	2	yes	—
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₈×C₁₃	—	2	8	no	—
177	C₂⁴×C₄	—	2	1	no	—
178	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
179	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
180	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
182	C₂²×C₄⋊C₄	—	2	2	no	—
183	C₂²×C₄⋊C₄	—	2	1	no	—
184	C₂²×C₄⋊C₄	—	2	8	no	—
185	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
187	#428	—	2	8	no	—
188	C₂×#107	C₂²×C₁₃	1	4	yes	complemented
189	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
190	#407	C₄×C₁₃	1	8	yes	complemented
191	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
192	#381	—	2	1	no	—
193	#380	C₂²×C₁₃	1	2	yes	—
194	#380	C₂²×C₁₃	1	2	yes	—
195	#379	—	2	1	no	—
196	C₄×C₂²⋊C₄	—	2	2	no	—
197	#340	C₂²×C₁₃	1	8	yes	complemented
198	C₂²×C₁₃	—	2	32	no	—
199	C₂²×C₁₃	—	2	4	no	—
200	C₂²×C₁₃	—	2	4	no	—
201	C₂²×C₁₃	—	2	4	no	—
202	C₂²×C₁₃	—	2	4	no	—
203	C₂²×C₁₃	—	2	4	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	4	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	2	4	no	—
209	C₂²×C₁₃	#385	1	4	yes	—
210	C₂²×C₁₃	#428	1	8	yes	complemented
211	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
213	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₂²×C₁₃	C₂×#137	1	2	yes	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	4	8	no	—
218	C₄×C₁₃	—	8	2	no	—
219	C₄×C₁₃	—	8	1	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	#385	1	4	yes	—
222	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
223	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
224	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	—	2	4	no	—
226	C₂³×C₄	—	2	4	no	—
227	C₂³×C₄	—	2	8	no	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	4	8	no	—
231	C₂³×C₄	C₂×C₄×C₁₃	1	4	yes	—
232	C₂³×C₄	D₄×C₁₃	1	2	yes	—
233	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
234	C₂³×C₄	Q₈×C₁₃	1	4	yes	—
235	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
240	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
241	#117	—	2	4	no	—
242	#117	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	16	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	16	no	—
249	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	#107	—	2	8	no	—
261	#106	—	2	8	no	—
262	C₂²⋊C₈	C₂×C₄×C₁₃	1	16	yes	complemented
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	C₂×C₁₃	—	2	4	no	—
266	C₂×C₁₃	—	2	8	no	—
267	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
268	C₂×C₁₃	C₂×#428	1	2	yes	—
269	C₂×C₁₃	#3003	1	1	yes	characteristic
270	C₂×C₁₃	#3004	1	1	yes	characteristic
271	C₂×C₁₃	#3092	1	2	yes	—
272	C₂⁴	—	2	2	no	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	C₁₃×C₄⋊C₄	1	4	yes	—
277	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	16	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	16	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	32	no	—
294	C₂²×C₄	—	4	8	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	—	4	8	no	—
297	C₂²×C₄	C₁₃×C₄⋊C₄	1	4	yes	—
298	C₂²×C₄	C₁₃×C₄⋊C₄	1	8	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
305	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
306	C₂²×C₄	C₁₃×#41	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	complemented
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₄²	—	4	2	no	—
324	C₄²	—	4	2	no	—
325	C₁₃	#20844	1	1	yes	characteristic, direct product factor, Sylow
326	C₂³	—	2	8	no	—
327	C₂³	—	2	16	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	8	no	—
330	C₂³	—	2	16	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
338	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
339	C₂³	C₁₃×#120	1	2	yes	—
340	C₂³	C₁₃×#123	1	2	yes	—
341	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
342	C₂³	C₁₃×#137	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	32	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
362	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₁₃	1	8	yes	—
364	C₂×C₄	C₁₃×#120	1	2	yes	—
365	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
366	C₂×C₄	C₁₃×#123	1	2	yes	—
367	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
369	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
371	C₈	—	2	8	no	—
372	C₂²	—	2	32	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	C₁₃×#385	1	4	yes	—
384	C₂²	C₁₃×#428	1	8	yes	complemented
385	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
386	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
388	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
389	C₂²	C₂×C₁₃×#137	1	2	yes	—
390	C₄	—	2	4	no	—
391	C₄	—	4	8	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	C₁₃×#385	1	4	yes	—
396	C₄	C₂×C₄×D₄×C₁₃	1	2	yes	—
397	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
398	C₂	—	2	4	no	—
399	C₂	—	2	8	no	—
400	C₂	C₂×C₁₃×#385	1	1	yes	characteristic
401	C₂	C₂×C₁₃×#428	1	2	yes	—
402	C₂	C₁₃×#3003	1	1	yes	characteristic
403	C₂	C₁₃×#3004	1	1	yes	characteristic
404	C₂	C₁₃×#3092	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#428	C₂	semidirect
5. C₁₃×#1853	C₂	semidirect
6. C₁₃×#1852	C₂	semidirect
7. C₁₃×#1736	C₂	semidirect
19. C₂×C₁₃×#107	C₂²	semidirect
20. C₂×C₁₃×#106	C₂²	semidirect
21. C₁₃×#407	C₄	semidirect
28. C₁₃×#340	C₂²	semidirect
44. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
67. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
70. #20844	C₁₃	direct (N × H)
110. C₂×C₈×C₁₃	C₂²×C₄	semidirect
125. C₂×#428	C₂×C₁₃	semidirect
128. #1853	C₂×C₁₃	semidirect
129. #1852	C₂×C₁₃	semidirect
130. #1736	C₂×C₁₃	semidirect
188. C₂×#107	C₂²×C₁₃	semidirect
189. C₂×#106	C₂²×C₁₃	semidirect
190. #407	C₄×C₁₃	semidirect
197. #340	C₂²×C₁₃	semidirect
210. C₂²×C₁₃	#428	semidirect
239. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
262. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
311. C₂×C₈	C₂²×C₄×C₁₃	semidirect
325. C₁₃	#20844	direct (N × H)
384. C₂²	C₁₃×#428	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₃×C₄⋊C₄	2
C₂×C₁₃×#428	2
C₂×C₁₃×#407	2
C₁₃×#2280	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1736	2
#20844	13

Subgroups — C13×#20844 #15707183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20844 #15707183