Subgroups — C₁₃×#24859 #15711198

Order 3328.

736 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#478	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#478	—	2	1	no	—
27	C₁₃×#478	—	2	1	no	—
28	C₁₃×#478	—	2	1	no	—
29	C₁₃×#478	—	2	1	no	—
30	C₁₃×#442	—	2	1	no	—
31	C₁₃×#440	—	2	1	no	—
32	C₄×C₁₃×SD₁₆	—	2	1	no	—
33	C₄×C₁₃×D₈	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
41	C₁₃×#424	—	2	1	no	—
42	C₁₃×#424	—	2	1	no	—
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₁₃×#424	C₂²	1	1	yes	characteristic
45	C₁₃×#423	—	2	1	no	—
46	C₁₃×#423	C₂²	1	1	yes	characteristic
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₁₃×#417	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#343	C₂²	1	1	yes	characteristic
65	C₁₃×#341	C₂²	1	1	yes	characteristic
66	C₁₃×#341	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
71	C₁₃×AGL(1,ℤ/8)	Q₈	1	4	yes	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₁₃×#131	—	2	2	no	—
75	C₁₃×#131	—	2	2	no	—
76	C₁₃×#131	—	4	1	no	—
77	C₁₃×#131	—	4	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂×C₁₃×M₁₆	—	2	1	no	—
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	—	2	1	no	—
87	C₂²×C₈×C₁₃	—	2	1	no	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	—	2	1	no	—
94	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#108	—	4	1	no	—
115	C₁₃×#108	—	4	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×C₄⋊C₈	—	2	1	no	—
130	C₁₃×C₄⋊C₈	—	2	1	no	—
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	—	2	1	no	—
150	C₁₃×#100	—	4	1	no	—
151	C₁₃×#100	—	4	1	no	—
152	C₁₃×#97	—	2	1	no	—
153	C₄×C₈×C₁₃	—	2	1	no	—
154	#24859	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	C₂×Q₈	1	2	yes	—
159	C₁₃×#41	#41	1	2	yes	—
160	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	—	4	1	no	—
177	C₂²×C₄×C₁₃	—	8	2	no	—
178	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×SD₁₆	—	2	4	no	—
182	C₁₃×D₈	—	2	4	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	—	2	1	no	—
191	C₁₃×M₁₆	—	2	1	no	—
192	C₁₃×M₁₆	—	2	1	no	—
193	C₁₃×M₁₆	—	2	1	no	—
194	C₁₃×M₁₆	—	4	2	no	—
195	C₁₃×M₁₆	—	4	2	no	—
196	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	4	2	no	—
208	C₂×C₈×C₁₃	—	4	2	no	—
209	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	4	1	no	—
222	C₁₃×C₄⋊C₄	—	4	1	no	—
223	C₁₃×C₄⋊C₄	—	4	1	no	—
224	C₁₃×C₄⋊C₄	—	4	1	no	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₁₃×C₂²⋊C₄	—	2	1	no	—
228	C₁₃×C₂²⋊C₄	—	2	1	no	—
229	C₁₃×C₂²⋊C₄	—	2	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	1	no	—
231	C₁₃×C₂²⋊C₄	—	4	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
239	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
242	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1907	C₂×C₁₃	1	1	yes	characteristic
250	#1907	C₂×C₁₃	1	1	yes	characteristic
251	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	8	1	no	—
259	C₂³×C₁₃	—	8	1	no	—
260	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
261	Q₈×C₁₃	—	2	1	no	—
262	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
263	D₄×C₁₃	—	2	2	no	—
264	D₄×C₁₃	—	2	2	no	—
265	D₄×C₁₃	—	2	2	no	—
266	D₄×C₁₃	—	2	1	no	—
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	8	1	no	—
283	C₂×C₄×C₁₃	—	8	2	no	—
284	C₂×C₄×C₁₃	—	8	2	no	—
285	C₂×C₄×C₁₃	—	8	1	no	—
286	C₂×C₄×C₁₃	—	8	1	no	—
287	C₂×C₄×C₁₃	—	8	1	no	—
288	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
289	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
290	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
291	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₃	—	2	2	no	—
299	C₈×C₁₃	—	2	1	no	—
300	C₈×C₁₃	—	2	1	no	—
301	C₈×C₁₃	—	2	1	no	—
302	C₈×C₁₃	—	2	1	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₈×C₁₃	—	4	1	no	—
307	C₈×C₁₃	—	4	1	no	—
308	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
312	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
314	#479	—	2	1	no	—
315	#479	—	2	1	no	—
316	#478	—	2	1	no	—
317	#478	—	2	1	no	—
318	#478	—	2	1	no	—
319	#478	—	2	1	no	—
320	#478	—	2	1	no	—
321	#478	—	2	1	no	—
322	#442	—	2	1	no	—
323	#440	—	2	1	no	—
324	C₄×SD₁₆	—	2	1	no	—
325	C₄×D₈	—	2	1	no	—
326	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
328	#428	C₂²×C₁₃	1	1	yes	characteristic
329	#428	C₂²×C₁₃	1	1	yes	characteristic
330	#428	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
333	#424	—	2	1	no	—
334	#424	—	2	1	no	—
335	#424	C₂²×C₁₃	1	1	yes	characteristic
336	#424	C₂²×C₁₃	1	1	yes	characteristic
337	#423	—	2	1	no	—
338	#423	C₂²×C₁₃	1	1	yes	characteristic
339	#423	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₈	—	2	1	no	—
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	#418	C₂²×C₁₃	1	1	yes	characteristic
343	#417	C₂²×C₁₃	1	1	yes	characteristic
344	#417	C₂²×C₁₃	1	1	yes	characteristic
345	#417	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
350	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
351	#343	C₂²×C₁₃	1	1	yes	characteristic
352	#343	C₂²×C₁₃	1	1	yes	characteristic
353	#343	C₂²×C₁₃	1	1	yes	characteristic
354	#343	C₂²×C₁₃	1	1	yes	characteristic
355	#343	C₂²×C₁₃	1	1	yes	characteristic
356	#343	C₂²×C₁₃	1	1	yes	characteristic
357	#341	C₂²×C₁₃	1	1	yes	characteristic
358	#341	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×C₁₃	—	2	1	no	—
360	C₂²×C₁₃	—	2	1	no	—
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	8	2	no	—
366	C₂²×C₁₃	—	8	2	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
370	C₂²×C₁₃	#552	1	1	yes	characteristic
371	C₂²×C₁₃	#554	1	1	yes	characteristic
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	2	1	no	—
374	C₄×C₁₃	—	2	1	no	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	2	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	—	8	1	no	—
381	C₄×C₁₃	—	8	1	no	—
382	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
383	C₄×C₁₃	#537	1	1	yes	characteristic
384	C₄×C₁₃	#546	1	1	yes	characteristic
385	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
386	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	AGL(1,ℤ/8)	—	2	2	no	—
390	AGL(1,ℤ/8)	Q₈×C₁₃	1	4	yes	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×D₈	—	2	1	no	—
393	#131	—	2	2	no	—
394	#131	—	2	2	no	—
395	#131	—	4	1	no	—
396	#131	—	4	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
409	#125	—	2	1	no	—
410	#125	—	2	1	no	—
411	#125	—	2	1	no	—
412	#125	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
422	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
423	#117	—	2	1	no	—
424	#117	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	#108	—	4	1	no	—
434	#108	—	4	1	no	—
435	#107	—	2	1	no	—
436	#107	—	2	1	no	—
437	#107	—	2	1	no	—
438	#107	—	2	1	no	—
439	#107	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	#106	—	2	1	no	—
443	#106	—	2	1	no	—
444	#106	—	2	1	no	—
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	C₄⋊C₈	—	2	1	no	—
449	C₄⋊C₈	—	2	1	no	—
450	C₄⋊C₈	—	2	1	no	—
451	C₄⋊C₈	—	2	1	no	—
452	C₄⋊C₈	—	2	1	no	—
453	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
454	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
455	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
456	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
457	#103	—	2	1	no	—
458	#103	—	2	1	no	—
459	#103	—	2	1	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	1	no	—
466	#102	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#100	—	4	1	no	—
470	#100	—	4	1	no	—
471	#97	—	2	1	no	—
472	C₄×C₈	—	2	1	no	—
473	C₂×C₁₃	—	2	1	no	—
474	C₂×C₁₃	—	2	1	no	—
475	C₂×C₁₃	—	4	2	no	—
476	C₂×C₁₃	—	8	2	no	—
477	C₂×C₁₃	#2417	1	1	yes	characteristic
478	C₂×C₁₃	#3067	1	1	yes	characteristic
479	C₂×C₁₃	#3068	1	1	yes	characteristic
480	C₂⁴	—	2	1	no	—
481	#41	—	2	1	no	—
482	#41	—	2	1	no	—
483	#41	C₂×Q₈×C₁₃	1	2	yes	—
484	#41	C₁₃×#41	1	2	yes	—
485	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	8	2	no	—
503	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
504	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
506	SD₁₆	—	2	4	no	—
507	D₈	—	2	4	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	4	2	no	—
520	M₁₆	—	4	2	no	—
521	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	4	2	no	—
533	C₂×C₈	—	4	2	no	—
534	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	4	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₁₃	#24859	1	1	yes	characteristic, direct product factor, Sylow
565	C₂³	—	2	1	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	8	1	no	—
570	C₂³	—	8	1	no	—
571	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
572	Q₈	—	2	1	no	—
573	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	1	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	8	1	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	8	1	no	—
599	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
600	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
601	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
602	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
607	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	2	1	no	—
613	C₈	—	2	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
630	C₂²	C₁₃×#552	1	1	yes	characteristic
631	C₂²	C₁₃×#554	1	1	yes	characteristic
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
643	C₄	C₁₃×#537	1	1	yes	characteristic
644	C₄	C₁₃×#546	1	1	yes	characteristic
645	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	8	2	no	—
650	C₂	C₁₃×#2417	1	1	yes	characteristic
651	C₂	C₁₃×#3067	1	1	yes	characteristic
652	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3080	C₂	semidirect
2. C₂×C₁₃×#478	C₂	semidirect
4. C₁₃×#2906	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#1998	C₂	semidirect
10. C₁₃×#1950	C₂	semidirect
13. C₁₃×#1816	C₂	semidirect
14. C₁₃×#1815	C₂	semidirect
15. C₁₃×#1800	C₂	semidirect
154. #24859	C₁₃	direct (N × H)
239. #3080	C₂×C₁₃	semidirect
240. C₂×#478	C₂×C₁₃	semidirect
242. #2906	C₂×C₁₃	semidirect
243. #2090	C₂×C₁₃	semidirect
244. #2089	C₂×C₁₃	semidirect
245. #2063	C₂×C₁₃	semidirect
246. #2063	C₂×C₁₃	semidirect
247. #1998	C₂×C₁₃	semidirect
248. #1950	C₂×C₁₃	semidirect
251. #1816	C₂×C₁₃	semidirect
252. #1815	C₂×C₁₃	semidirect
253. #1800	C₂×C₁₃	semidirect
564. C₁₃	#24859	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×#3080	2
C₂×C₁₃×#478	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2906	2
C₁₃×#2090	2
C₁₃×#2089	2
C₁₃×#2063	2
C₁₃×#1998	2
C₁₃×#1950	2
C₁₃×#1907	2
C₁₃×#1816	2
C₁₃×#1815	2
C₁₃×#1800	2
#24859	13

Subgroups — C13×#24859 #15711198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24859 #15711198