Subgroups — C₁₃×#26443 #15712782

Order 3328.

686 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	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2087	C₂	1	2	yes	maximal
4	C₁₃×#2059	C₂	1	2	yes	maximal
5	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1989	C₂	1	2	yes	maximal
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1919	C₂	1	2	yes	maximal
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#398	—	2	2	no	—
22	C₁₃×#391	—	2	1	no	—
23	C₁₃×#389	—	2	1	no	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#384	—	2	1	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×C₄⋊Q₈	—	2	2	no	—
46	C₁₃×C₄⋊Q₈	Q₈	1	4	yes	—
47	C₁₃×#125	—	2	4	no	—
48	C₁₃×#125	—	4	2	no	—
49	C₄×Q₈×C₁₃	—	4	4	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	—	4	2	no	—
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×#106	Q₈	1	4	yes	complemented
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	4	2	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₁₃×#95	—	2	1	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	1	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	D₄	1	2	yes	—
82	#26443	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	4	2	no	—
85	C₂×Q₈×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	—	2	1	no	—
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₁₃	—	2	1	no	—
98	C₂×C₈×C₁₃	—	2	1	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
106	C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	4	4	no	—
118	C₁₃×C₄⋊C₄	—	4	4	no	—
119	C₁₃×C₄⋊C₄	—	4	4	no	—
120	C₁₃×C₄⋊C₄	—	4	2	no	—
121	C₁₃×C₄⋊C₄	—	8	1	no	—
122	C₁₃×C₄⋊C₄	—	8	2	no	—
123	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
126	C₁₃×C₄⋊C₄	#41	1	2	yes	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	4	4	no	—
130	C₄²×C₁₃	—	4	2	no	—
131	C₄²×C₁₃	—	4	2	no	—
132	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
133	C₄²×C₁₃	#41	1	2	yes	—
134	#2552	C₂×C₁₃	1	1	yes	characteristic
135	#2365	C₂×C₁₃	1	1	yes	characteristic
136	#2087	C₂×C₁₃	1	2	yes	—
137	#2059	C₂×C₁₃	1	2	yes	—
138	#1990	C₂×C₁₃	1	1	yes	characteristic
139	#1989	C₂×C₁₃	1	2	yes	—
140	#1988	C₂×C₁₃	1	1	yes	characteristic
141	#1947	C₂×C₁₃	1	1	yes	characteristic
142	#1939	C₂×C₁₃	1	1	yes	characteristic
143	#1919	C₂×C₁₃	1	2	yes	—
144	C₄×#106	C₂×C₁₃	1	1	yes	characteristic
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	4	8	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	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	1	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₃	#135	1	2	yes	—
176	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	4	1	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#125	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄×Q₈	—	2	1	no	—
189	C₂×#107	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×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
195	#398	—	2	2	no	—
196	#391	—	2	1	no	—
197	#389	—	2	1	no	—
198	#389	C₂²×C₁₃	1	2	yes	—
199	#389	C₂²×C₁₃	1	2	yes	—
200	#387	—	2	2	no	—
201	#384	—	2	1	no	—
202	#384	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	#340	C₂²×C₁₃	1	2	yes	—
208	#340	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	1	yes	characteristic
210	#340	C₂²×C₁₃	1	2	yes	—
211	#340	C₂²×C₁₃	1	2	yes	—
212	#340	C₂²×C₁₃	1	2	yes	—
213	#340	C₂²×C₁₃	1	1	yes	characteristic
214	#336	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₁₃	#546	1	1	yes	characteristic
217	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂²×C₁₃	#577	1	1	yes	characteristic
221	C₂²×C₁₃	#578	1	1	yes	characteristic
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	4	4	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	#478	1	4	yes	—
232	C₄×C₁₃	#533	1	1	yes	characteristic
233	C₄×C₁₃	#542	1	1	yes	characteristic
234	C₄×C₁₃	#557	1	1	yes	characteristic
235	C₄×C₁₃	Q₈²	1	1	yes	characteristic
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	Q₈×C₁₃	1	4	yes	—
242	#125	—	2	4	no	—
243	#125	—	4	2	no	—
244	C₄×Q₈	—	4	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
265	#107	—	4	2	no	—
266	#106	—	2	2	no	—
267	#106	Q₈×C₁₃	1	4	yes	complemented
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	4	2	no	—
270	C₄×C₈	—	2	2	no	—
271	#95	—	2	1	no	—
272	#95	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	D₄×C₁₃	1	2	yes	—
277	C₂×C₁₃	#2451	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
279	C₂×C₁₃	#3082	1	1	yes	characteristic
280	C₂×C₁₃	#3302	1	1	yes	characteristic
281	C₂×C₁₃	#3332	1	1	yes	characteristic
282	C₂×C₁₃	#3381	1	1	yes	characteristic
283	C₂×C₁₃	#3386	1	1	yes	characteristic
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	8	1	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
325	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
326	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
327	C₄⋊C₄	C₁₃×#41	1	2	yes	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	4	no	—
331	C₄²	—	4	2	no	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
334	C₄²	C₁₃×#41	1	2	yes	—
335	C₁₃	#26443	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	Q₈	—	4	8	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
365	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
366	C₂×C₄	C₁₃×#135	1	2	yes	—
367	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
372	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂²	C₁₃×#546	1	1	yes	characteristic
379	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
380	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
381	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂²	C₁₃×#577	1	1	yes	characteristic
383	C₂²	C₁₃×#578	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	C₁₃×#478	1	4	yes	—
394	C₄	C₁₃×#533	1	1	yes	characteristic
395	C₄	C₁₃×#542	1	1	yes	characteristic
396	C₄	C₁₃×#557	1	1	yes	characteristic
397	C₄	Q₈²×C₁₃	1	1	yes	characteristic
398	C₂	C₁₃×#2451	1	1	yes	characteristic
399	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
400	C₂	C₁₃×#3082	1	1	yes	characteristic
401	C₂	C₁₃×#3302	1	1	yes	characteristic
402	C₂	C₁₃×#3332	1	1	yes	characteristic
403	C₂	C₁₃×#3381	1	1	yes	characteristic
404	C₂	C₁₃×#3386	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
72. C₁₃×#106	Q₈	semidirect
82. #26443	C₁₃	direct (N × H)
267. #106	Q₈×C₁₃	semidirect
335. C₁₃	#26443	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×#2552	2
C₁₃×#2365	2
C₁₃×#2087	2
C₁₃×#2059	2
C₁₃×#1990	2
C₁₃×#1989	2
C₁₃×#1988	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1919	2
C₄×C₁₃×#106	2
#26443	13

Subgroups — C13×#26443 #15712782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26443 #15712782