Subgroups — C₁₃×#26036 #15712375

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
30	C₁₃×#395	—	2	1	no	—
31	C₁₃×#395	—	2	1	no	—
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#389	—	2	1	no	—
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#388	—	2	1	no	—
39	C₁₃×#384	C₂²	1	1	yes	characteristic
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#381	—	2	1	no	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	4	1	no	—
70	C₁₃×C₄⋊Q₈	—	4	1	no	—
71	C₁₃×C₄⋊Q₈	—	4	4	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	Q₈	1	4	yes	complemented
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	2	no	—
101	C₁₃×#106	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	4	1	no	—
104	C₁₃×C₄⋊C₈	—	4	1	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	4	1	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₁₃×#97	—	2	2	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	D₄	1	1	yes	characteristic
118	C₁₃×#95	D₄	1	1	yes	characteristic
119	#26036	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	4	2	no	—
122	C₂×Q₈×C₁₃	—	4	2	no	—
123	C₂×Q₈×C₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	8	1	no	—
126	C₂×Q₈×C₁₃	—	8	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	8	1	no	—
142	C₂²×C₄×C₁₃	—	8	1	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	4	2	no	—
176	C₁₃×C₄⋊C₄	—	4	2	no	—
177	C₁₃×C₄⋊C₄	—	4	2	no	—
178	C₁₃×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	—	8	1	no	—
181	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
182	C₁₃×C₄⋊C₄	#41	1	2	yes	—
183	C₁₃×C₄⋊C₄	#41	1	2	yes	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	4	2	no	—
186	C₁₃×C₂²⋊C₄	—	4	2	no	—
187	C₁₃×C₂²⋊C₄	—	8	1	no	—
188	C₁₃×C₂²⋊C₄	—	8	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	4	2	no	—
194	C₄²×C₁₃	—	8	1	no	—
195	C₄²×C₁₃	—	8	1	no	—
196	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
197	C₄²×C₁₃	#41	1	2	yes	—
198	#2551	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2357	C₂×C₁₃	1	1	yes	characteristic
200	#2067	C₂×C₁₃	1	1	yes	characteristic
201	#2065	C₂×C₁₃	1	1	yes	characteristic
202	#2023	C₂×C₁₃	1	1	yes	characteristic
203	#2023	C₂×C₁₃	1	1	yes	characteristic
204	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1921	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1836	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1802	C₂×C₁₃	1	1	yes	characteristic
212	#1762	C₂×C₁₃	1	1	yes	characteristic
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃	—	8	4	no	—
222	Q₈×C₁₃	—	8	4	no	—
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	8	4	no	—
263	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
265	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
266	C₂×C₄×C₁₃	#137	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₂×C₄⋊Q₈	—	2	1	no	—
278	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
291	#395	—	2	1	no	—
292	#395	—	2	1	no	—
293	#390	C₂²×C₁₃	1	1	yes	characteristic
294	#390	C₂²×C₁₃	1	1	yes	characteristic
295	#389	—	2	1	no	—
296	#389	C₂²×C₁₃	1	1	yes	characteristic
297	#389	C₂²×C₁₃	1	1	yes	characteristic
298	#388	—	2	1	no	—
299	#388	—	2	1	no	—
300	#384	C₂²×C₁₃	1	1	yes	characteristic
301	#382	C₂²×C₁₃	1	1	yes	characteristic
302	#381	—	2	1	no	—
303	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	—	2	1	no	—
308	#340	C₂²×C₁₃	1	1	yes	characteristic
309	#340	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₃	1	1	yes	characteristic
312	#340	C₂²×C₁₃	1	1	yes	characteristic
313	#340	C₂²×C₁₃	1	1	yes	characteristic
314	#340	C₂²×C₁₃	1	1	yes	characteristic
315	#340	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#336	C₂²×C₁₃	1	1	yes	characteristic
319	#336	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	4	2	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	—	8	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
328	C₂²×C₁₃	#546	1	1	yes	characteristic
329	C₂²×C₁₃	#548	1	1	yes	characteristic
330	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
332	C₂²×C₁₃	#576	1	1	yes	characteristic
333	C₂²×C₁₃	#577	1	1	yes	characteristic
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	#533	1	1	yes	characteristic
348	C₄×C₁₃	#544	1	1	yes	characteristic
349	C₄×C₁₃	#555	1	1	yes	characteristic
350	C₄×C₁₃	#556	1	1	yes	characteristic
351	C₂²×Q₈	—	2	1	no	—
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	4	1	no	—
362	C₄⋊Q₈	—	4	1	no	—
363	C₄⋊Q₈	—	4	4	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	Q₈×C₁₃	1	4	yes	complemented
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	#107	—	2	2	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	4	1	no	—
396	C₄⋊C₈	—	4	1	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	4	1	no	—
400	#102	—	4	1	no	—
401	#97	—	2	2	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	D₄×C₁₃	1	1	yes	characteristic
410	#95	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₁₃	—	8	2	no	—
412	C₂×C₁₃	#2439	1	1	yes	characteristic
413	C₂×C₁₃	#3079	1	1	yes	characteristic
414	C₂×C₁₃	#3081	1	1	yes	characteristic
415	C₂×C₁₃	#3318	1	1	yes	characteristic
416	C₂×C₁₃	#3320	1	1	yes	characteristic
417	C₂×C₁₃	#3373	1	1	yes	characteristic
418	C₂×C₁₃	#3375	1	1	yes	characteristic
419	C₂⁴	—	2	1	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	8	1	no	—
425	C₂×Q₈	—	8	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	8	1	no	—
441	C₂²×C₄	—	8	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	4	2	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	8	1	no	—
480	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
481	C₄⋊C₄	C₁₃×#41	1	2	yes	—
482	C₄⋊C₄	C₁₃×#41	1	2	yes	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₂²⋊C₄	—	8	1	no	—
487	C₂²⋊C₄	—	8	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	2	no	—
493	C₄²	—	8	1	no	—
494	C₄²	—	8	1	no	—
495	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
496	C₄²	C₁₃×#41	1	2	yes	—
497	C₁₃	#26036	1	1	yes	characteristic, direct product factor, Sylow
498	C₂³	—	2	2	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	Q₈	—	8	4	no	—
507	Q₈	—	8	4	no	—
508	D₄	—	2	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
549	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
550	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
551	C₂×C₄	C₁₃×#137	1	2	yes	—
552	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
554	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
556	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
570	C₂²	C₁₃×#546	1	1	yes	characteristic
571	C₂²	C₁₃×#548	1	1	yes	characteristic
572	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
573	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
574	C₂²	C₁₃×#576	1	1	yes	characteristic
575	C₂²	C₁₃×#577	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₁₃×#533	1	1	yes	characteristic
590	C₄	C₁₃×#544	1	1	yes	characteristic
591	C₄	C₁₃×#555	1	1	yes	characteristic
592	C₄	C₁₃×#556	1	1	yes	characteristic
593	C₂	—	8	2	no	—
594	C₂	C₁₃×#2439	1	1	yes	characteristic
595	C₂	C₁₃×#3079	1	1	yes	characteristic
596	C₂	C₁₃×#3081	1	1	yes	characteristic
597	C₂	C₁₃×#3318	1	1	yes	characteristic
598	C₂	C₁₃×#3320	1	1	yes	characteristic
599	C₂	C₁₃×#3373	1	1	yes	characteristic
600	C₂	C₁₃×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
1. C₁₃×#2551	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1987	C₂	semidirect
9. C₁₃×#1949	C₂	semidirect
10. C₁₃×#1940	C₂	semidirect
11. C₁₃×#1921	C₂	semidirect
12. C₁₃×#1919	C₂	semidirect
13. C₁₃×#1836	C₂	semidirect
73. C₄×D₄×C₁₃	Q₈	semidirect
119. #26036	C₁₃	direct (N × H)
198. #2551	C₂×C₁₃	semidirect
204. #1988	C₂×C₁₃	semidirect
205. #1987	C₂×C₁₃	semidirect
206. #1949	C₂×C₁₃	semidirect
207. #1940	C₂×C₁₃	semidirect
208. #1921	C₂×C₁₃	semidirect
209. #1919	C₂×C₁₃	semidirect
210. #1836	C₂×C₁₃	semidirect
365. C₄×D₄	Q₈×C₁₃	semidirect
497. C₁₃	#26036	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×#2551	2
C₁₃×#2357	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#2023	2
C₁₃×#1988	2
C₁₃×#1987	2
C₁₃×#1949	2
C₁₃×#1940	2
C₁₃×#1921	2
C₁₃×#1919	2
C₁₃×#1836	2
C₁₃×#1802	2
C₁₃×#1762	2
#26036	13

Subgroups — C13×#26036 #15712375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26036 #15712375