Subgroups — C₁₃×#22664 #15709003

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2352	C₂	1	2	yes	maximal
4	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1809	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	2	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₁₃×#436	C₄	1	8	yes	complemented
15	C₁₃×#428	—	2	8	no	—
16	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#388	—	2	2	no	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#386	—	2	2	no	—
29	C₁₃×#382	C₂²	1	2	yes	—
30	C₁₃×#380	C₂²	1	2	yes	—
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂×C₁₃×M₁₆	—	2	4	no	—
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	complemented
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
47	C₄×D₄×C₁₃	Q₈	1	4	yes	—
48	C₁₃×#117	—	2	4	no	—
49	C₁₃×#117	—	4	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#107	—	2	2	no	—
66	C₁₃×#107	—	2	4	no	—
67	C₁₃×#107	—	4	1	no	—
68	C₁₃×#107	—	4	1	no	—
69	C₁₃×#107	D₄	1	4	yes	complemented
70	C₁₃×#106	—	2	4	no	—
71	C₁₃×#106	—	2	4	no	—
72	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
74	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	#22664	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
82	C₂×D₄×C₁₃	—	4	1	no	—
83	C₂×D₄×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₃	—	4	4	no	—
95	C₂²×C₄×C₁₃	—	8	2	no	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₁₃×M₁₆	—	2	16	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	4	4	no	—
120	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
121	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	4	4	no	—
124	C₁₃×C₂²⋊C₄	—	8	2	no	—
125	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₄²×C₁₃	—	4	4	no	—
127	C₄²×C₁₃	—	8	2	no	—
128	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
130	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
131	C₂×#428	C₂×C₁₃	1	2	yes	complemented
132	#2352	C₂×C₁₃	1	2	yes	—
133	#1949	C₂×C₁₃	1	2	yes	complemented
134	#1854	C₂×C₁₃	1	2	yes	complemented
135	#1852	C₂×C₁₃	1	2	yes	complemented
136	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1809	C₂×C₁₃	1	2	yes	complemented
138	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂³×C₁₃	—	2	2	no	—
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
146	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
147	D₄×C₁₃	—	4	4	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	1	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	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	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	—	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	—	8	8	no	—
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
180	C₈×C₁₃	—	2	4	no	—
181	C₈×C₁₃	—	2	2	no	—
182	C₈×C₁₃	C₄×D₄	1	4	yes	—
183	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
184	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#117	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
187	#436	C₄×C₁₃	1	8	yes	complemented
188	#428	—	2	8	no	—
189	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#107	C₂²×C₁₃	1	2	yes	—
191	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#106	C₂²×C₁₃	1	2	yes	—
195	C₂×#106	C₂²×C₁₃	1	2	yes	—
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#388	—	2	2	no	—
200	#387	—	2	2	no	—
201	#386	—	2	2	no	—
202	#382	C₂²×C₁₃	1	2	yes	—
203	#380	C₂²×C₁₃	1	2	yes	—
204	#380	C₂²×C₁₃	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
206	C₄×C₂²⋊C₄	—	2	2	no	—
207	#340	C₂²×C₁₃	1	2	yes	—
208	#340	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₁₃	—	2	4	no	—
211	C₂²×C₁₃	—	2	4	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	4	2	no	—
217	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₂²×C₁₃	D₄²	1	1	yes	characteristic
219	C₂²×C₁₃	#547	1	1	yes	characteristic
220	C₂²×C₁₃	#575	1	1	yes	characteristic
221	C₂²×C₁₃	#575	1	1	yes	characteristic
222	C₂²×C₁₃	#576	1	1	yes	characteristic
223	C₂²×C₁₃	#578	1	1	yes	characteristic
224	C₄×C₁₃	—	2	4	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	4	4	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₄×C₁₃	#520	1	1	yes	characteristic
233	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
234	C₄×C₁₃	#554	1	1	yes	characteristic
235	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
245	C₄×D₄	Q₈×C₁₃	1	4	yes	—
246	#117	—	2	4	no	—
247	#117	—	4	2	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	4	2	no	—
251	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#107	—	2	4	no	—
265	#107	—	4	1	no	—
266	#107	—	4	1	no	—
267	#107	D₄×C₁₃	1	4	yes	complemented
268	#106	—	2	4	no	—
269	#106	—	2	4	no	—
270	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
271	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
272	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₂×C₁₃	—	4	4	no	—
279	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₁₃	#2911	1	1	yes	characteristic
281	C₂×C₁₃	#2913	1	1	yes	characteristic
282	C₂×C₁₃	#3273	1	1	yes	characteristic
283	C₂×C₁₃	#3277	1	1	yes	characteristic
284	C₂×C₁₃	#3352	1	1	yes	characteristic
285	C₂×C₁₃	#3355	1	1	yes	characteristic
286	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	M₁₆	—	2	16	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
315	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
316	C₂×C₈	C₁₃×#41	1	2	yes	—
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	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
326	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
331	C₄²	—	4	4	no	—
332	C₄²	—	8	2	no	—
333	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
334	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
335	C₁₃	#22664	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	D₄	—	4	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	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	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	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	—	4	2	no	—
362	C₂×C₄	—	4	2	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	—	8	8	no	—
368	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
369	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
370	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
371	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	2	no	—
379	C₈	C₄×D₄×C₁₃	1	4	yes	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
388	C₂²	D₄²×C₁₃	1	1	yes	characteristic
389	C₂²	C₁₃×#547	1	1	yes	characteristic
390	C₂²	C₁₃×#575	1	1	yes	characteristic
391	C₂²	C₁₃×#575	1	1	yes	characteristic
392	C₂²	C₁₃×#576	1	1	yes	characteristic
393	C₂²	C₁₃×#578	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
402	C₄	C₁₃×#520	1	1	yes	characteristic
403	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
404	C₄	C₁₃×#554	1	1	yes	characteristic
405	C₂	—	4	4	no	—
406	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
407	C₂	C₁₃×#2911	1	1	yes	characteristic
408	C₂	C₁₃×#2913	1	1	yes	characteristic
409	C₂	C₁₃×#3273	1	1	yes	characteristic
410	C₂	C₁₃×#3277	1	1	yes	characteristic
411	C₂	C₁₃×#3352	1	1	yes	characteristic
412	C₂	C₁₃×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#428	C₂	semidirect
4. C₁₃×#1949	C₂	semidirect
5. C₁₃×#1854	C₂	semidirect
6. C₁₃×#1852	C₂	semidirect
7. C₁₃×#1846	C₂	semidirect
8. C₁₃×#1809	C₂	semidirect
9. C₄×C₁₃×#107	C₂	semidirect
14. C₁₃×#436	C₄	semidirect
42. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
69. C₁₃×#107	D₄	semidirect
72. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
74. C₄×C₈×C₁₃	C₂×C₄	semidirect
80. #22664	C₁₃	direct (N × H)
131. C₂×#428	C₂×C₁₃	semidirect
133. #1949	C₂×C₁₃	semidirect
134. #1854	C₂×C₁₃	semidirect
135. #1852	C₂×C₁₃	semidirect
136. #1846	C₂×C₁₃	semidirect
137. #1809	C₂×C₁₃	semidirect
138. C₄×#107	C₂×C₁₃	semidirect
187. #436	C₄×C₁₃	semidirect
240. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
267. #107	D₄×C₁₃	semidirect
270. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
271. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
272. C₄×C₈	C₂×C₄×C₁₃	semidirect
335. C₁₃	#22664	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#436	2
C₂×C₁₃×#428	2
C₁₃×#2352	2
C₁₃×#1949	2
C₁₃×#1854	2
C₁₃×#1852	2
C₁₃×#1846	2
C₁₃×#1809	2
C₄×C₁₃×#107	2
#22664	13

Subgroups — C13×#22664 #15709003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22664 #15709003