Subgroups — C₁₃×#24674 #15711013

Order 3328.

796 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#464	—	2	1	no	—
25	C₁₃×#464	—	2	1	no	—
26	C₁₃×#463	—	2	1	no	—
27	C₁₃×#463	—	2	1	no	—
28	C₁₃×#463	—	2	1	no	—
29	C₁₃×#463	—	2	1	no	—
30	C₁₃×#463	—	2	1	no	—
31	C₁₃×#463	—	2	1	no	—
32	C₁₃×#442	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	1	no	—
35	C₄×C₁₃×D₈	—	2	1	no	—
36	C₁₃×#433	—	2	1	no	—
37	C₁₃×#433	—	2	1	no	—
38	C₁₃×#432	—	2	1	no	—
39	C₁₃×#431	—	2	1	no	—
40	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#423	C₂²	1	1	yes	characteristic
44	C₁₃×#423	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#419	C₂²	1	1	yes	characteristic
47	C₁₃×#418	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₁₃×#408	C₂²	1	1	yes	characteristic
59	C₁₃×#408	C₂²	1	1	yes	characteristic
60	C₁₃×#405	C₂²	1	1	yes	characteristic
61	C₁₃×#405	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×M₁₆	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₁₃×#137	—	4	1	no	—
73	C₁₃×#137	—	4	1	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
76	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
77	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	1	no	—
81	C₂×C₁₃×SD₁₆	—	2	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	4	1	no	—
86	C₂×C₁₃×D₈	—	2	1	no	—
87	C₂×C₁₃×D₈	—	2	1	no	—
88	C₂×C₁₃×D₈	—	2	2	no	—
89	C₂×C₁₃×D₈	—	2	1	no	—
90	C₂×C₁₃×D₈	—	2	1	no	—
91	C₂×C₁₃×D₈	—	4	1	no	—
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	—	2	1	no	—
110	C₄×D₄×C₁₃	—	2	1	no	—
111	C₄×D₄×C₁₃	—	2	1	no	—
112	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
113	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#108	—	4	1	no	—
123	C₁₃×#108	—	4	1	no	—
124	C₁₃×#107	—	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	D₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
133	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	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×#101	—	2	2	no	—
147	C₁₃×#101	—	4	1	no	—
148	C₁₃×#100	—	2	2	no	—
149	C₁₃×#100	—	4	1	no	—
150	C₁₃×#100	—	4	1	no	—
151	C₁₃×#100	—	4	1	no	—
152	C₁₃×C₂²⋊C₈	—	2	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×C₂²⋊C₈	—	2	1	no	—
155	C₁₃×C₂²⋊C₈	—	2	1	no	—
156	C₁₃×#97	—	2	1	no	—
157	C₁₃×#97	—	2	1	no	—
158	C₁₃×#97	—	2	1	no	—
159	C₄×C₈×C₁₃	—	2	1	no	—
160	C₄×C₈×C₁₃	—	2	1	no	—
161	C₄×C₈×C₁₃	—	2	1	no	—
162	#24674	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₁₃×#41	—	2	1	no	—
166	C₁₃×#41	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₁₃×#41	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₁₃	#41	1	2	yes	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	4	1	no	—
196	C₂²×C₄×C₁₃	—	4	1	no	—
197	C₂²×C₄×C₁₃	—	8	2	no	—
198	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₁₃×Q₁₆	—	4	2	no	—
202	C₁₃×SD₁₆	—	2	4	no	—
203	C₁₃×SD₁₆	—	4	2	no	—
204	C₁₃×SD₁₆	—	4	2	no	—
205	C₁₃×SD₁₆	—	4	2	no	—
206	C₁₃×SD₁₆	—	4	2	no	—
207	C₁₃×D₈	—	2	4	no	—
208	C₁₃×D₈	—	4	2	no	—
209	C₁₃×D₈	—	4	2	no	—
210	C₁₃×D₈	—	4	2	no	—
211	C₁₃×M₁₆	—	2	1	no	—
212	C₁₃×M₁₆	—	2	1	no	—
213	C₁₃×M₁₆	—	2	1	no	—
214	C₁₃×M₁₆	—	2	1	no	—
215	C₁₃×M₁₆	—	2	1	no	—
216	C₁₃×M₁₆	—	2	1	no	—
217	C₁₃×M₁₆	—	2	1	no	—
218	C₁₃×M₁₆	—	2	1	no	—
219	C₁₃×M₁₆	—	2	1	no	—
220	C₁₃×M₁₆	—	2	1	no	—
221	C₁₃×M₁₆	—	2	1	no	—
222	C₁₃×M₁₆	#41	1	2	yes	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₁₃×C₂²⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₁₃×C₂²⋊C₄	—	2	1	no	—
246	C₁₃×C₂²⋊C₄	—	4	1	no	—
247	C₁₃×C₂²⋊C₄	—	4	1	no	—
248	C₁₃×C₂²⋊C₄	—	4	1	no	—
249	C₁₃×C₂²⋊C₄	—	4	1	no	—
250	C₁₃×C₂²⋊C₄	—	4	1	no	—
251	C₁₃×C₂²⋊C₄	—	4	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
259	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2018	C₂×C₁₃	1	1	yes	characteristic
267	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	—	4	1	no	—
280	C₂³×C₁₃	—	4	1	no	—
281	C₂³×C₁₃	—	8	1	no	—
282	C₂³×C₁₃	—	8	1	no	—
283	C₂³×C₁₃	—	8	1	no	—
284	C₂³×C₁₃	—	8	1	no	—
285	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
286	Q₈×C₁₃	—	2	1	no	—
287	Q₈×C₁₃	—	2	1	no	—
288	Q₈×C₁₃	—	4	1	no	—
289	Q₈×C₁₃	—	4	1	no	—
290	Q₈×C₁₃	—	4	1	no	—
291	Q₈×C₁₃	—	4	1	no	—
292	D₄×C₁₃	—	2	1	no	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	1	no	—
295	D₄×C₁₃	—	2	2	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	4	1	no	—
299	D₄×C₁₃	—	4	1	no	—
300	D₄×C₁₃	—	4	1	no	—
301	D₄×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	2	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	8	1	no	—
317	C₂×C₄×C₁₃	—	8	2	no	—
318	C₂×C₄×C₁₃	—	8	2	no	—
319	C₂×C₄×C₁₃	—	8	1	no	—
320	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
321	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
322	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
323	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₈×C₁₃	—	2	2	no	—
331	C₈×C₁₃	—	2	1	no	—
332	C₈×C₁₃	—	2	1	no	—
333	C₈×C₁₃	—	2	1	no	—
334	C₈×C₁₃	—	2	1	no	—
335	C₈×C₁₃	—	4	1	no	—
336	C₈×C₁₃	—	4	1	no	—
337	C₈×C₁₃	—	4	1	no	—
338	C₈×C₁₃	—	4	1	no	—
339	C₈×C₁₃	—	4	1	no	—
340	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
343	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
348	#464	—	2	1	no	—
349	#464	—	2	1	no	—
350	#463	—	2	1	no	—
351	#463	—	2	1	no	—
352	#463	—	2	1	no	—
353	#463	—	2	1	no	—
354	#463	—	2	1	no	—
355	#463	—	2	1	no	—
356	#442	—	2	1	no	—
357	#440	—	2	1	no	—
358	C₄×SD₁₆	—	2	1	no	—
359	C₄×D₈	—	2	1	no	—
360	#433	—	2	1	no	—
361	#433	—	2	1	no	—
362	#432	—	2	1	no	—
363	#431	—	2	1	no	—
364	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
366	#428	C₂²×C₁₃	1	1	yes	characteristic
367	#423	C₂²×C₁₃	1	1	yes	characteristic
368	#423	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
370	#419	C₂²×C₁₃	1	1	yes	characteristic
371	#418	C₂²×C₁₃	1	1	yes	characteristic
372	#418	C₂²×C₁₃	1	1	yes	characteristic
373	#417	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
382	#408	C₂²×C₁₃	1	1	yes	characteristic
383	#408	C₂²×C₁₃	1	1	yes	characteristic
384	#405	C₂²×C₁₃	1	1	yes	characteristic
385	#405	C₂²×C₁₃	1	1	yes	characteristic
386	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
387	#343	C₂²×C₁₃	1	1	yes	characteristic
388	#343	C₂²×C₁₃	1	1	yes	characteristic
389	#341	C₂²×C₁₃	1	1	yes	characteristic
390	#341	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×C₁₃	—	2	1	no	—
392	C₂²×C₁₃	—	2	1	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	1	no	—
397	C₂²×C₁₃	—	8	2	no	—
398	C₂²×C₁₃	—	8	2	no	—
399	C₂²×C₁₃	—	8	1	no	—
400	C₂²×C₁₃	—	8	1	no	—
401	C₂²×C₁₃	—	8	1	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	16	1	no	—
405	C₂²×C₁₃	—	16	1	no	—
406	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
407	C₂²×C₁₃	#553	1	1	yes	characteristic
408	C₂²×C₁₃	#555	1	1	yes	characteristic
409	C₄×C₁₃	—	2	1	no	—
410	C₄×C₁₃	—	2	1	no	—
411	C₄×C₁₃	—	2	1	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	4	1	no	—
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	1	no	—
416	C₄×C₁₃	—	8	1	no	—
417	C₄×C₁₃	—	8	1	no	—
418	C₄×C₁₃	#525	1	1	yes	characteristic
419	C₄×C₁₃	#535	1	1	yes	characteristic
420	C₄×C₁₃	#546	1	1	yes	characteristic
421	C₄×C₁₃	#550	1	1	yes	characteristic
422	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	#137	—	4	1	no	—
428	#137	—	4	1	no	—
429	AGL(1,ℤ/8)	—	2	2	no	—
430	AGL(1,ℤ/8)	—	2	2	no	—
431	AGL(1,ℤ/8)	—	4	1	no	—
432	AGL(1,ℤ/8)	—	4	1	no	—
433	C₂×Q₁₆	—	2	1	no	—
434	C₂×SD₁₆	—	2	1	no	—
435	C₂×SD₁₆	—	2	1	no	—
436	C₂×SD₁₆	—	2	1	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	2	1	no	—
439	C₂×SD₁₆	—	2	1	no	—
440	C₂×SD₁₆	—	4	1	no	—
441	C₂×D₈	—	2	1	no	—
442	C₂×D₈	—	2	1	no	—
443	C₂×D₈	—	2	2	no	—
444	C₂×D₈	—	2	1	no	—
445	C₂×D₈	—	2	1	no	—
446	C₂×D₈	—	4	1	no	—
447	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
455	#124	—	2	1	no	—
456	#124	—	2	1	no	—
457	#124	—	2	1	no	—
458	#124	—	2	1	no	—
459	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
460	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
468	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
469	#117	—	2	1	no	—
470	#117	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₄²	—	2	1	no	—
476	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
477	#108	—	4	1	no	—
478	#108	—	4	1	no	—
479	#107	—	2	1	no	—
480	#106	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	C₄⋊C₈	—	2	1	no	—
483	C₄⋊C₈	—	2	1	no	—
484	C₄⋊C₈	—	2	1	no	—
485	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
486	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
487	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
489	#103	—	2	1	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#103	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#102	—	2	1	no	—
500	#102	—	2	1	no	—
501	#101	—	2	2	no	—
502	#101	—	4	1	no	—
503	#100	—	2	2	no	—
504	#100	—	4	1	no	—
505	#100	—	4	1	no	—
506	#100	—	4	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	C₂²⋊C₈	—	2	1	no	—
509	C₂²⋊C₈	—	2	1	no	—
510	C₂²⋊C₈	—	2	1	no	—
511	#97	—	2	1	no	—
512	#97	—	2	1	no	—
513	#97	—	2	1	no	—
514	C₄×C₈	—	2	1	no	—
515	C₄×C₈	—	2	1	no	—
516	C₄×C₈	—	2	1	no	—
517	C₂×C₁₃	—	2	1	no	—
518	C₂×C₁₃	—	2	1	no	—
519	C₂×C₁₃	—	8	1	no	—
520	C₂×C₁₃	—	8	2	no	—
521	C₂×C₁₃	—	16	1	no	—
522	C₂×C₁₃	#2414	1	1	yes	characteristic
523	C₂×C₁₃	#3067	1	1	yes	characteristic
524	C₂×C₁₃	#3068	1	1	yes	characteristic
525	C₂⁴	—	2	1	no	—
526	C₂⁴	—	2	1	no	—
527	#41	—	2	1	no	—
528	#41	—	2	1	no	—
529	#41	—	2	1	no	—
530	#41	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂×D₄	C₁₃×#41	1	2	yes	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	—	8	2	no	—
560	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
561	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
563	Q₁₆	—	4	2	no	—
564	SD₁₆	—	2	4	no	—
565	SD₁₆	—	4	2	no	—
566	SD₁₆	—	4	2	no	—
567	SD₁₆	—	4	2	no	—
568	SD₁₆	—	4	2	no	—
569	D₈	—	2	4	no	—
570	D₈	—	4	2	no	—
571	D₈	—	4	2	no	—
572	D₈	—	4	2	no	—
573	M₁₆	—	2	1	no	—
574	M₁₆	—	2	1	no	—
575	M₁₆	—	2	1	no	—
576	M₁₆	—	2	1	no	—
577	M₁₆	—	2	1	no	—
578	M₁₆	—	2	1	no	—
579	M₁₆	—	2	1	no	—
580	M₁₆	—	2	1	no	—
581	M₁₆	—	2	1	no	—
582	M₁₆	—	2	1	no	—
583	M₁₆	—	2	1	no	—
584	M₁₆	C₁₃×#41	1	2	yes	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₁₃	#24674	1	1	yes	characteristic, direct product factor, Sylow
622	C₂³	—	2	1	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	8	1	no	—
630	C₂³	—	8	1	no	—
631	C₂³	—	8	1	no	—
632	C₂³	—	8	1	no	—
633	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	D₄	—	2	1	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	1	no	—
643	D₄	—	2	2	no	—
644	D₄	—	4	1	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	8	1	no	—
665	C₂×C₄	—	8	2	no	—
666	C₂×C₄	—	8	2	no	—
667	C₂×C₄	—	8	1	no	—
668	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
669	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
670	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
671	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
674	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
675	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
676	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
678	C₈	—	2	2	no	—
679	C₈	—	2	1	no	—
680	C₈	—	2	1	no	—
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	8	2	no	—
695	C₂²	—	8	2	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	16	1	no	—
702	C₂²	—	16	1	no	—
703	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
704	C₂²	C₁₃×#553	1	1	yes	characteristic
705	C₂²	C₁₃×#555	1	1	yes	characteristic
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₁₃×#525	1	1	yes	characteristic
716	C₄	C₁₃×#535	1	1	yes	characteristic
717	C₄	C₁₃×#546	1	1	yes	characteristic
718	C₄	C₁₃×#550	1	1	yes	characteristic
719	C₂	—	2	1	no	—
720	C₂	—	2	1	no	—
721	C₂	—	8	1	no	—
722	C₂	—	8	2	no	—
723	C₂	—	16	1	no	—
724	C₂	C₁₃×#2414	1	1	yes	characteristic
725	C₂	C₁₃×#3067	1	1	yes	characteristic
726	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	C₁₃×#2018	C₂
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×#3040	C₂	semidirect
2. C₂×C₁₃×#463	C₂	semidirect
3. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₃×#2925	C₂	semidirect
5. C₁₃×#2052	C₂	semidirect
6. C₁₃×#2051	C₂	semidirect
7. C₁₃×#2019	C₂	semidirect
9. C₁₃×#1978	C₂	semidirect
10. C₁₃×#1977	C₂	semidirect
11. C₁₃×#1967	C₂	semidirect
12. C₁₃×#1950	C₂	semidirect
13. C₁₃×#1931	C₂	semidirect
14. C₁₃×#1930	C₂	semidirect
15. C₁₃×#1800	C₂	semidirect
162. #24674	C₁₃	direct (N × H)
259. #3040	C₂×C₁₃	semidirect
260. C₂×#463	C₂×C₁₃	semidirect
261. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
262. #2925	C₂×C₁₃	semidirect
263. #2052	C₂×C₁₃	semidirect
264. #2051	C₂×C₁₃	semidirect
265. #2019	C₂×C₁₃	semidirect
267. #1978	C₂×C₁₃	semidirect
268. #1977	C₂×C₁₃	semidirect
269. #1967	C₂×C₁₃	semidirect
270. #1950	C₂×C₁₃	semidirect
271. #1931	C₂×C₁₃	semidirect
272. #1930	C₂×C₁₃	semidirect
273. #1800	C₂×C₁₃	semidirect
621. C₁₃	#24674	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×#3040	2
C₂×C₁₃×#463	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2925	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#2019	2
C₁₃×#2018	2
C₁₃×#1978	2
C₁₃×#1977	2
C₁₃×#1967	2
C₁₃×#1950	2
C₁₃×#1931	2
C₁₃×#1930	2
C₁₃×#1800	2
#24674	13

Subgroups — C13×#24674 #15711013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24674 #15711013