Subgroups — C₁₃×#22666 #15709005

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 400 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×#1853	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×#106	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	2	yes	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
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	4	no	—
66	C₁₃×#107	—	2	4	no	—
67	C₁₃×#106	—	2	2	no	—
68	C₁₃×#106	—	2	4	no	—
69	C₁₃×#106	—	4	1	no	—
70	C₁₃×#106	—	4	1	no	—
71	C₁₃×#106	D₄	1	4	yes	complemented
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	#22666	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
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	—	4	4	no	—
93	C₂²×C₄×C₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₃	—	8	2	no	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×M₁₆	—	2	16	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₁₃	#41	1	2	yes	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	4	4	no	—
119	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
120	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	8	2	no	—
124	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
125	C₄²×C₁₃	—	4	4	no	—
126	C₄²×C₁₃	—	8	2	no	—
127	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
129	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
130	C₂×#428	C₂×C₁₃	1	2	yes	complemented
131	#2352	C₂×C₁₃	1	2	yes	—
132	#1949	C₂×C₁₃	1	2	yes	complemented
133	#1854	C₂×C₁₃	1	2	yes	complemented
134	#1853	C₂×C₁₃	1	2	yes	complemented
135	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1809	C₂×C₁₃	1	2	yes	complemented
137	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	2	no	—
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	C₂×C₄⋊C₄	1	4	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	D₄×C₁₃	—	4	4	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	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	—	8	8	no	—
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₁₃	—	2	4	no	—
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	C₄×D₄	1	4	yes	—
180	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
181	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#117	C₂²×C₁₃	1	2	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
184	#436	C₄×C₁₃	1	8	yes	complemented
185	#428	—	2	8	no	—
186	C₂×#107	C₂²×C₁₃	1	2	yes	—
187	C₂×#107	C₂²×C₁₃	1	2	yes	—
188	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#106	C₂²×C₁₃	1	2	yes	—
190	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
196	#388	—	2	2	no	—
197	#387	—	2	2	no	—
198	#386	—	2	2	no	—
199	#382	C₂²×C₁₃	1	2	yes	—
200	#380	C₂²×C₁₃	1	2	yes	—
201	#380	C₂²×C₁₃	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
203	C₄×C₂²⋊C₄	—	2	2	no	—
204	#340	C₂²×C₁₃	1	2	yes	—
205	#340	C₂²×C₁₃	1	2	yes	—
206	#340	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	2	4	no	—
209	C₂²×C₁₃	—	2	4	no	—
210	C₂²×C₁₃	—	4	2	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₃	D₄²	1	1	yes	characteristic
216	C₂²×C₁₃	#547	1	1	yes	characteristic
217	C₂²×C₁₃	#575	1	2	yes	—
218	C₂²×C₁₃	#577	1	2	yes	—
219	C₄×C₁₃	—	2	4	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	4	4	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₁₃	#520	1	1	yes	characteristic
228	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
229	C₄×C₁₃	#554	1	1	yes	characteristic
230	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
240	C₄×D₄	Q₈×C₁₃	1	4	yes	—
241	#117	—	2	4	no	—
242	#117	—	4	2	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	4	2	no	—
246	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	#107	—	2	4	no	—
259	#107	—	2	4	no	—
260	#106	—	2	2	no	—
261	#106	—	2	4	no	—
262	#106	—	4	1	no	—
263	#106	—	4	1	no	—
264	#106	D₄×C₁₃	1	4	yes	complemented
265	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
266	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
267	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	C₂×C₁₃	—	4	4	no	—
274	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₁₃	#2911	1	1	yes	characteristic
276	C₂×C₁₃	#2912	1	1	yes	characteristic
277	C₂×C₁₃	#3275	1	2	yes	—
278	C₂×C₁₃	#3351	1	2	yes	—
279	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	8	2	no	—
293	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
299	M₁₆	—	2	16	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
305	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
306	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
308	C₂×C₈	C₁₃×#41	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
318	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
323	C₄²	—	4	4	no	—
324	C₄²	—	8	2	no	—
325	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
326	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
327	C₁₃	#22666	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
335	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	D₄	—	4	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	8	no	—
358	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
359	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
360	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
361	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
365	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
367	C₈	—	2	4	no	—
368	C₈	—	2	2	no	—
369	C₈	C₄×D₄×C₁₃	1	4	yes	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
378	C₂²	D₄²×C₁₃	1	1	yes	characteristic
379	C₂²	C₁₃×#547	1	1	yes	characteristic
380	C₂²	C₁₃×#575	1	2	yes	—
381	C₂²	C₁₃×#577	1	2	yes	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	4	4	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
390	C₄	C₁₃×#520	1	1	yes	characteristic
391	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
392	C₄	C₁₃×#554	1	1	yes	characteristic
393	C₂	—	4	4	no	—
394	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
395	C₂	C₁₃×#2911	1	1	yes	characteristic
396	C₂	C₁₃×#2912	1	1	yes	characteristic
397	C₂	C₁₃×#3275	1	2	yes	—
398	C₂	C₁₃×#3351	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	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×#1853	C₂	semidirect
7. C₁₃×#1846	C₂	semidirect
8. C₁₃×#1809	C₂	semidirect
9. C₄×C₁₃×#106	C₂	semidirect
14. C₁₃×#436	C₄	semidirect
42. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
71. C₁₃×#106	D₄	semidirect
72. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
74. C₄×C₈×C₁₃	C₂×C₄	semidirect
80. #22666	C₁₃	direct (N × H)
130. C₂×#428	C₂×C₁₃	semidirect
132. #1949	C₂×C₁₃	semidirect
133. #1854	C₂×C₁₃	semidirect
134. #1853	C₂×C₁₃	semidirect
135. #1846	C₂×C₁₃	semidirect
136. #1809	C₂×C₁₃	semidirect
137. C₄×#106	C₂×C₁₃	semidirect
184. #436	C₄×C₁₃	semidirect
235. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
264. #106	D₄×C₁₃	semidirect
265. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
266. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
267. C₄×C₈	C₂×C₄×C₁₃	semidirect
327. C₁₃	#22666	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×#1853	2
C₁₃×#1846	2
C₁₃×#1809	2
C₄×C₁₃×#106	2
#22666	13

Subgroups — C13×#22666 #15709005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22666 #15709005