Subgroups — C₁₃×#24775 #15711114

Order 3328.

850 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	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2046	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×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#473	—	2	4	no	—
27	C₁₃×#471	—	2	4	no	—
28	C₁₃×#464	—	2	1	no	—
29	C₁₃×#464	—	2	1	no	—
30	C₁₃×#464	—	2	1	no	—
31	C₁₃×#464	—	2	1	no	—
32	C₁₃×#464	—	2	1	no	—
33	C₁₃×#464	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#463	—	2	1	no	—
36	C₁₃×#441	—	2	1	no	—
37	C₁₃×#440	—	2	1	no	—
38	C₄×C₁₃×Q₁₆	—	2	1	no	—
39	C₄×C₁₃×SD₁₆	—	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×#424	—	2	1	no	—
44	C₁₃×#424	—	2	1	no	—
45	C₁₃×#424	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	1	yes	characteristic
47	C₁₃×#423	—	2	1	no	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₁₃×#423	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₃×#419	C₂²	1	1	yes	characteristic
53	C₁₃×#419	C₂²	1	1	yes	characteristic
54	C₁₃×#418	C₂²	1	1	yes	characteristic
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#341	C₂²	1	1	yes	characteristic
68	C₁₃×#341	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#137	—	2	2	no	—
74	C₁₃×#137	—	2	2	no	—
75	C₁₃×#137	—	2	2	no	—
76	C₁₃×#137	D₄	1	4	yes	—
77	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
79	C₂×C₁₃×Q₁₆	—	2	1	no	—
80	C₂×C₁₃×Q₁₆	—	2	1	no	—
81	C₂×C₁₃×Q₁₆	—	2	2	no	—
82	C₂×C₁₃×Q₁₆	—	2	1	no	—
83	C₂×C₁₃×Q₁₆	—	2	1	no	—
84	C₂×C₁₃×Q₁₆	—	4	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	1	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	—	2	2	no	—
88	C₂×C₁₃×SD₁₆	—	2	1	no	—
89	C₂×C₁₃×SD₁₆	—	2	1	no	—
90	C₂×C₁₃×SD₁₆	—	2	1	no	—
91	C₂×C₁₃×SD₁₆	—	4	1	no	—
92	C₂×C₁₃×D₈	—	2	1	no	—
93	C₁₃×#131	—	2	2	no	—
94	C₁₃×#131	—	2	2	no	—
95	C₁₃×#131	—	4	1	no	—
96	C₁₃×#131	—	4	1	no	—
97	C₂×C₁₃×M₁₆	—	2	1	no	—
98	C₂×C₁₃×M₁₆	—	2	1	no	—
99	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	—	2	1	no	—
106	C₂²×C₈×C₁₃	—	2	1	no	—
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#124	—	2	1	no	—
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#124	—	2	1	no	—
112	C₁₃×#124	—	2	1	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	—	2	1	no	—
117	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
118	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
119	C₄×D₄×C₁₃	—	2	1	no	—
120	C₄×D₄×C₁₃	—	2	1	no	—
121	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
122	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
123	C₁₃×#117	—	2	1	no	—
124	C₁₃×#117	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₄²×C₁₃	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#108	—	2	2	no	—
133	C₁₃×#108	—	2	2	no	—
134	C₁₃×#107	—	2	1	no	—
135	C₁₃×#106	—	2	1	no	—
136	C₁₃×C₄⋊C₈	—	2	1	no	—
137	C₁₃×C₄⋊C₈	—	2	1	no	—
138	C₁₃×C₄⋊C₈	—	2	1	no	—
139	C₁₃×C₄⋊C₈	—	2	1	no	—
140	C₁₃×C₄⋊C₈	—	2	1	no	—
141	C₁₃×C₄⋊C₈	—	2	1	no	—
142	C₁₃×C₄⋊C₈	—	2	1	no	—
143	C₁₃×C₄⋊C₈	—	2	1	no	—
144	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
145	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
147	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#103	—	2	1	no	—
152	C₁₃×#103	—	2	1	no	—
153	C₁₃×#103	—	2	1	no	—
154	C₁₃×#103	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#102	—	2	1	no	—
159	C₁₃×#102	—	2	1	no	—
160	C₁₃×#101	—	2	2	no	—
161	C₁₃×#101	—	2	2	no	—
162	C₁₃×#101	—	2	2	no	—
163	C₁₃×#101	—	4	1	no	—
164	C₁₃×#100	—	2	2	no	—
165	C₁₃×#100	—	4	1	no	—
166	C₁₃×#97	—	2	1	no	—
167	C₄×C₈×C₁₃	—	2	1	no	—
168	#24775	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	—	2	1	no	—
170	C₁₃×#41	—	2	1	no	—
171	C₁₃×#41	—	2	1	no	—
172	C₁₃×#41	C₂×D₄	1	2	yes	—
173	C₁₃×#41	#41	1	2	yes	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₁₃×Q₁₆	—	2	4	no	—
205	C₁₃×Q₁₆	—	4	2	no	—
206	C₁₃×Q₁₆	—	4	2	no	—
207	C₁₃×Q₁₆	—	4	2	no	—
208	C₁₃×SD₁₆	—	2	4	no	—
209	C₁₃×SD₁₆	—	4	2	no	—
210	C₁₃×SD₁₆	—	4	2	no	—
211	C₁₃×SD₁₆	—	4	2	no	—
212	C₁₃×SD₁₆	—	4	2	no	—
213	C₁₃×D₈	—	4	2	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	—	2	1	no	—
223	C₁₃×M₁₆	—	2	1	no	—
224	C₁₃×M₁₆	—	2	1	no	—
225	C₁₃×M₁₆	—	4	2	no	—
226	C₁₃×M₁₆	—	4	2	no	—
227	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	4	2	no	—
239	C₂×C₈×C₁₃	—	4	2	no	—
240	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	4	1	no	—
249	C₁₃×C₄⋊C₄	—	4	1	no	—
250	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₁₃×C₂²⋊C₄	—	2	1	no	—
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	2	1	no	—
255	C₁₃×C₂²⋊C₄	—	4	1	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	1	no	—
258	C₁₃×C₂²⋊C₄	—	4	1	no	—
259	C₄²×C₁₃	—	2	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	4	1	no	—
263	C₄²×C₁₃	—	4	1	no	—
264	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂×#471	C₂×C₁₃	1	1	yes	characteristic
270	#3040	C₂×C₁₃	1	1	yes	characteristic
271	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2047	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1907	C₂×C₁₃	1	1	yes	characteristic
282	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂³×C₁₃	—	2	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	8	1	no	—
288	C₂³×C₁₃	—	8	1	no	—
289	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
290	Q₈×C₁₃	—	2	1	no	—
291	Q₈×C₁₃	—	2	2	no	—
292	Q₈×C₁₃	—	2	2	no	—
293	Q₈×C₁₃	—	4	1	no	—
294	Q₈×C₁₃	—	4	1	no	—
295	Q₈×C₁₃	—	4	1	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	#121	1	2	yes	—
300	D₄×C₁₃	—	2	2	no	—
301	D₄×C₁₃	—	2	2	no	—
302	D₄×C₁₃	—	2	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	D₄×C₁₃	#121	1	2	yes	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	2	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	8	1	no	—
324	C₂×C₄×C₁₃	—	8	1	no	—
325	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
326	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
327	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
328	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
335	C₈×C₁₃	—	2	2	no	—
336	C₈×C₁₃	—	2	1	no	—
337	C₈×C₁₃	—	2	1	no	—
338	C₈×C₁₃	—	2	1	no	—
339	C₈×C₁₃	—	2	1	no	—
340	C₈×C₁₃	—	4	1	no	—
341	C₈×C₁₃	—	4	1	no	—
342	C₈×C₁₃	—	4	1	no	—
343	C₈×C₁₃	—	4	1	no	—
344	C₈×C₁₃	—	4	1	no	—
345	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
353	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
355	#473	—	2	4	no	—
356	#471	—	2	4	no	—
357	#464	—	2	1	no	—
358	#464	—	2	1	no	—
359	#464	—	2	1	no	—
360	#464	—	2	1	no	—
361	#464	—	2	1	no	—
362	#464	—	2	1	no	—
363	#463	—	2	1	no	—
364	#463	—	2	1	no	—
365	#441	—	2	1	no	—
366	#440	—	2	1	no	—
367	C₄×Q₁₆	—	2	1	no	—
368	C₄×SD₁₆	—	2	1	no	—
369	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
371	#428	C₂²×C₁₃	1	1	yes	characteristic
372	#424	—	2	1	no	—
373	#424	—	2	1	no	—
374	#424	C₂²×C₁₃	1	1	yes	characteristic
375	#424	C₂²×C₁₃	1	1	yes	characteristic
376	#423	—	2	1	no	—
377	#423	C₂²×C₁₃	1	1	yes	characteristic
378	#423	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₈	—	2	1	no	—
380	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
381	#419	C₂²×C₁₃	1	1	yes	characteristic
382	#419	C₂²×C₁₃	1	1	yes	characteristic
383	#418	C₂²×C₁₃	1	1	yes	characteristic
384	#417	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
393	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
394	#343	C₂²×C₁₃	1	1	yes	characteristic
395	#343	C₂²×C₁₃	1	1	yes	characteristic
396	#341	C₂²×C₁₃	1	1	yes	characteristic
397	#341	C₂²×C₁₃	1	1	yes	characteristic
398	C₂²×C₁₃	—	2	1	no	—
399	C₂²×C₁₃	—	2	1	no	—
400	C₂²×C₁₃	—	2	2	no	—
401	C₂²×C₁₃	—	4	1	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	—	8	1	no	—
406	C₂²×C₁₃	—	16	1	no	—
407	C₂²×C₁₃	—	16	1	no	—
408	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
409	C₂²×C₁₃	#547	1	1	yes	characteristic
410	C₂²×C₁₃	#553	1	1	yes	characteristic
411	C₄×C₁₃	—	2	2	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	1	no	—
415	C₄×C₁₃	—	2	1	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	8	1	no	—
420	C₄×C₁₃	—	8	1	no	—
421	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
422	C₄×C₁₃	#537	1	1	yes	characteristic
423	C₄×C₁₃	D₄²	1	1	yes	characteristic
424	C₄×C₁₃	#548	1	1	yes	characteristic
425	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
429	#137	—	2	2	no	—
430	#137	—	2	2	no	—
431	#137	—	2	2	no	—
432	#137	D₄×C₁₃	1	4	yes	—
433	AGL(1,ℤ/8)	—	2	2	no	—
434	AGL(1,ℤ/8)	—	2	2	no	—
435	C₂×Q₁₆	—	2	1	no	—
436	C₂×Q₁₆	—	2	2	no	—
437	C₂×Q₁₆	—	2	1	no	—
438	C₂×Q₁₆	—	2	1	no	—
439	C₂×Q₁₆	—	2	1	no	—
440	C₂×Q₁₆	—	4	1	no	—
441	C₂×SD₁₆	—	2	1	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	1	no	—
444	C₂×SD₁₆	—	2	1	no	—
445	C₂×SD₁₆	—	2	1	no	—
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×SD₁₆	—	4	1	no	—
448	C₂×D₈	—	2	1	no	—
449	#131	—	2	2	no	—
450	#131	—	2	2	no	—
451	#131	—	4	1	no	—
452	#131	—	4	1	no	—
453	C₂×M₁₆	—	2	1	no	—
454	C₂×M₁₆	—	2	1	no	—
455	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×C₈	—	2	1	no	—
462	C₂²×C₈	—	2	1	no	—
463	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
465	#124	—	2	1	no	—
466	#124	—	2	1	no	—
467	#124	—	2	1	no	—
468	#124	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
474	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
478	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
479	#117	—	2	1	no	—
480	#117	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
488	#108	—	2	2	no	—
489	#108	—	2	2	no	—
490	#107	—	2	1	no	—
491	#106	—	2	1	no	—
492	C₄⋊C₈	—	2	1	no	—
493	C₄⋊C₈	—	2	1	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	—	2	1	no	—
496	C₄⋊C₈	—	2	1	no	—
497	C₄⋊C₈	—	2	1	no	—
498	C₄⋊C₈	—	2	1	no	—
499	C₄⋊C₈	—	2	1	no	—
500	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
501	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
504	#103	—	2	1	no	—
505	#103	—	2	1	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#103	—	2	1	no	—
509	#103	—	2	1	no	—
510	#103	—	2	1	no	—
511	#102	—	2	1	no	—
512	#102	—	2	1	no	—
513	#102	—	2	1	no	—
514	#102	—	2	1	no	—
515	#102	—	2	1	no	—
516	#101	—	2	2	no	—
517	#101	—	2	2	no	—
518	#101	—	2	2	no	—
519	#101	—	4	1	no	—
520	#100	—	2	2	no	—
521	#100	—	4	1	no	—
522	#97	—	2	1	no	—
523	C₄×C₈	—	2	1	no	—
524	C₂×C₁₃	—	2	1	no	—
525	C₂×C₁₃	—	2	1	no	—
526	C₂×C₁₃	—	4	2	no	—
527	C₂×C₁₃	—	16	1	no	—
528	C₂×C₁₃	#2416	1	1	yes	characteristic
529	C₂×C₁₃	#3067	1	1	yes	characteristic
530	C₂×C₁₃	#3069	1	1	yes	characteristic
531	C₂⁴	—	2	1	no	—
532	#41	—	2	1	no	—
533	#41	—	2	1	no	—
534	#41	C₂×D₄×C₁₃	1	2	yes	—
535	#41	C₁₃×#41	1	2	yes	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
548	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
564	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
566	Q₁₆	—	2	4	no	—
567	Q₁₆	—	4	2	no	—
568	Q₁₆	—	4	2	no	—
569	Q₁₆	—	4	2	no	—
570	SD₁₆	—	2	4	no	—
571	SD₁₆	—	4	2	no	—
572	SD₁₆	—	4	2	no	—
573	SD₁₆	—	4	2	no	—
574	SD₁₆	—	4	2	no	—
575	D₈	—	4	2	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	—	2	1	no	—
585	M₁₆	—	2	1	no	—
586	M₁₆	—	2	1	no	—
587	M₁₆	—	4	2	no	—
588	M₁₆	—	4	2	no	—
589	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
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	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	4	2	no	—
601	C₂×C₈	—	4	2	no	—
602	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	1	no	—
612	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₂²⋊C₄	—	4	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	4	1	no	—
625	C₄²	—	4	1	no	—
626	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₁₃	#24775	1	1	yes	characteristic, direct product factor, Sylow
631	C₂³	—	2	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	8	1	no	—
636	C₂³	—	8	1	no	—
637	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
638	Q₈	—	2	1	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	C₁₃×#121	1	2	yes	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	C₁₃×#121	1	2	yes	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	8	1	no	—
672	C₂×C₄	—	8	1	no	—
673	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
674	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
675	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
676	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
680	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
681	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
683	C₈	—	2	2	no	—
684	C₈	—	2	1	no	—
685	C₈	—	2	1	no	—
686	C₈	—	2	1	no	—
687	C₈	—	2	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	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×#547	1	1	yes	characteristic
705	C₂²	C₁₃×#553	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	—	2	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	8	1	no	—
715	C₄	—	8	1	no	—
716	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
717	C₄	C₁₃×#537	1	1	yes	characteristic
718	C₄	D₄²×C₁₃	1	1	yes	characteristic
719	C₄	C₁₃×#548	1	1	yes	characteristic
720	C₂	—	2	1	no	—
721	C₂	—	2	1	no	—
722	C₂	—	4	2	no	—
723	C₂	—	16	1	no	—
724	C₂	C₁₃×#2416	1	1	yes	characteristic
725	C₂	C₁₃×#3067	1	1	yes	characteristic
726	C₂	C₁₃×#3069	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. C₂×C₁₃×#473	C₂	semidirect
4. C₂×C₁₃×#464	C₂	semidirect
5. C₄×C₁₃×#137	C₂	semidirect
6. C₁₃×#2906	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#2047	C₂	semidirect
10. C₁₃×#2046	C₂	semidirect
11. C₁₃×#1967	C₂	semidirect
12. C₁₃×#1950	C₂	semidirect
13. C₁₃×#1908	C₂	semidirect
15. C₁₃×#1801	C₂	semidirect
168. #24775	C₁₃	direct (N × H)
268. C₂×#473	C₂×C₁₃	semidirect
271. C₂×#464	C₂×C₁₃	semidirect
272. C₄×#137	C₂×C₁₃	semidirect
273. #2906	C₂×C₁₃	semidirect
274. #2064	C₂×C₁₃	semidirect
275. #2063	C₂×C₁₃	semidirect
276. #2047	C₂×C₁₃	semidirect
277. #2046	C₂×C₁₃	semidirect
278. #1967	C₂×C₁₃	semidirect
279. #1950	C₂×C₁₃	semidirect
280. #1908	C₂×C₁₃	semidirect
282. #1801	C₂×C₁₃	semidirect
630. C₁₃	#24775	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×#473	2
C₂×C₁₃×#471	2
C₁₃×#3040	2
C₂×C₁₃×#464	2
C₄×C₁₃×#137	2
C₁₃×#2906	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2047	2
C₁₃×#2046	2
C₁₃×#1967	2
C₁₃×#1950	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1801	2
#24775	13

Subgroups — C13×#24775 #15711114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24775 #15711114