Subgroups — C₁₃×#26997 #15713336

Order 3328.

788 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2006	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1938	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1765	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	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₁₃×#537	C₂²	1	1	yes	characteristic
22	C₁₃×#536	C₂²	1	1	yes	characteristic
23	C₁₃×#520	C₂²	1	1	yes	characteristic
24	C₁₃×#518	C₂²	1	1	yes	characteristic
25	C₁₃×#485	—	2	1	no	—
26	C₁₃×#484	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#480	—	2	1	no	—
29	C₁₃×#470	—	2	1	no	—
30	C₁₃×#468	—	2	1	no	—
31	C₁₃×#467	—	2	1	no	—
32	C₁₃×#465	—	2	1	no	—
33	C₁₃×#463	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#461	—	2	1	no	—
36	C₁₃×#461	—	2	1	no	—
37	C₁₃×#442	—	2	1	no	—
38	C₁₃×#440	—	2	1	no	—
39	C₄×C₁₃×SD₁₆	—	2	1	no	—
40	C₄×C₁₃×D₈	—	2	1	no	—
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#428	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₁₃×#424	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	C₂²	1	1	yes	characteristic
51	C₁₃×#416	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#341	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#137	—	2	2	no	—
72	C₁₃×#137	—	4	1	no	—
73	C₁₃×AGL(1,ℤ/8)	—	2	2	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	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	1	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	4	1	no	—
85	C₂×C₁₃×D₈	—	2	1	no	—
86	C₂×C₁₃×D₈	—	2	1	no	—
87	C₁₃×#131	—	2	2	no	—
88	C₁₃×#131	—	4	1	no	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	—	2	1	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#123	—	4	1	no	—
100	C₁₃×C₂²⋊Q₈	—	2	1	no	—
101	C₁₃×C₂²⋊Q₈	—	2	1	no	—
102	C₁₃×C₂²⋊Q₈	—	2	1	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×#121	—	2	1	no	—
105	C₁₃×#121	—	2	1	no	—
106	C₁₃×#121	—	4	1	no	—
107	C₄×Q₈×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	—	2	1	no	—
113	C₄×D₄×C₁₃	—	4	1	no	—
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	C₂³	1	1	yes	characteristic
116	C₁₃×#117	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	—	2	1	no	—
124	C₁₃×#107	—	2	1	no	—
125	C₁₃×#107	—	2	1	no	—
126	C₁₃×#107	—	2	1	no	—
127	C₁₃×#107	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	—	2	1	no	—
130	C₁₃×#106	—	2	1	no	—
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×#104	—	2	2	no	—
134	C₁₃×#104	—	4	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×#103	—	2	1	no	—
140	C₁₃×#103	D₄	1	1	yes	characteristic
141	C₁₃×#103	D₄	1	1	yes	characteristic
142	C₁₃×#103	D₄	1	1	yes	characteristic
143	C₁₃×#103	D₄	1	1	yes	characteristic
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	D₄	1	1	yes	characteristic
148	C₁₃×#102	D₄	1	1	yes	characteristic
149	C₁₃×#102	D₄	1	1	yes	characteristic
150	C₁₃×#102	D₄	1	1	yes	characteristic
151	C₁₃×#101	—	2	2	no	—
152	C₁₃×#100	—	2	2	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×C₂²⋊C₈	—	2	1	no	—
155	C₁₃×#97	—	2	1	no	—
156	C₁₃×#97	—	4	1	no	—
157	C₄×C₈×C₁₃	—	2	1	no	—
158	C₁₃×#95	—	4	1	no	—
159	#26997	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₃	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	1	no	—
163	C₁₃×#41	—	2	1	no	—
164	C₁₃×#41	—	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×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
185	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₃	#41	1	2	yes	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	1	no	—
195	C₂²×C₄×C₁₃	—	4	1	no	—
196	C₂²×C₄×C₁₃	—	4	1	no	—
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×Q₁₆	—	4	2	no	—
199	C₁₃×SD₁₆	—	2	4	no	—
200	C₁₃×SD₁₆	—	4	2	no	—
201	C₁₃×SD₁₆	—	4	2	no	—
202	C₁₃×SD₁₆	—	4	2	no	—
203	C₁₃×SD₁₆	—	4	2	no	—
204	C₁₃×D₈	—	2	4	no	—
205	C₁₃×D₈	—	4	2	no	—
206	C₁₃×M₁₆	—	2	1	no	—
207	C₁₃×M₁₆	—	2	1	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	2	1	no	—
211	C₁₃×M₁₆	—	2	1	no	—
212	C₁₃×M₁₆	—	4	2	no	—
213	C₁₃×M₁₆	#41	1	2	yes	—
214	C₁₃×M₁₆	#41	1	2	yes	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	4	2	no	—
224	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	4	1	no	—
233	C₁₃×C₄⋊C₄	—	4	1	no	—
234	C₁₃×C₄⋊C₄	—	4	1	no	—
235	C₁₃×C₄⋊C₄	—	4	1	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₂²⋊C₄	—	2	1	no	—
241	C₁₃×C₂²⋊C₄	—	2	1	no	—
242	C₁₃×C₂²⋊C₄	—	4	1	no	—
243	C₁₃×C₂²⋊C₄	—	4	1	no	—
244	C₁₃×C₂²⋊C₄	—	4	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	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	—	8	2	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	—	4	1	no	—
255	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3042	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2006	C₂×C₁₃	1	1	yes	characteristic
263	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1938	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1765	C₂×C₁₃	1	1	yes	characteristic, complemented
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	8	1	no	—
276	C₂³×C₁₃	—	8	1	no	—
277	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
278	Q₈×C₁₃	—	2	1	no	—
279	Q₈×C₁₃	—	2	1	no	—
280	Q₈×C₁₃	—	2	1	no	—
281	Q₈×C₁₃	—	2	1	no	—
282	Q₈×C₁₃	—	4	1	no	—
283	Q₈×C₁₃	—	4	1	no	—
284	Q₈×C₁₃	—	4	1	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	D₄×C₁₃	—	2	1	no	—
287	D₄×C₁₃	—	2	2	no	—
288	D₄×C₁₃	—	2	1	no	—
289	D₄×C₁₃	—	2	1	no	—
290	D₄×C₁₃	—	2	2	no	—
291	D₄×C₁₃	—	2	1	no	—
292	D₄×C₁₃	—	4	1	no	—
293	D₄×C₁₃	—	4	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	16	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
317	C₂×C₄×C₁₃	—	8	1	no	—
318	C₂×C₄×C₁₃	—	8	1	no	—
319	C₂×C₄×C₁₃	—	16	1	no	—
320	C₂×C₄×C₁₃	—	16	1	no	—
321	C₂×C₄×C₁₃	—	16	1	no	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
328	C₈×C₁₃	—	2	2	no	—
329	C₈×C₁₃	—	2	1	no	—
330	C₈×C₁₃	—	2	1	no	—
331	C₈×C₁₃	—	2	1	no	—
332	C₈×C₁₃	—	2	1	no	—
333	C₈×C₁₃	—	2	2	no	—
334	C₈×C₁₃	—	4	1	no	—
335	C₈×C₁₃	—	4	1	no	—
336	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
341	#537	C₂²×C₁₃	1	1	yes	characteristic
342	#536	C₂²×C₁₃	1	1	yes	characteristic
343	#520	C₂²×C₁₃	1	1	yes	characteristic
344	#518	C₂²×C₁₃	1	1	yes	characteristic
345	#485	—	2	1	no	—
346	#484	—	2	1	no	—
347	#482	—	2	1	no	—
348	#480	—	2	1	no	—
349	#470	—	2	1	no	—
350	#468	—	2	1	no	—
351	#467	—	2	1	no	—
352	#465	—	2	1	no	—
353	#463	—	2	1	no	—
354	#463	—	2	1	no	—
355	#461	—	2	1	no	—
356	#461	—	2	1	no	—
357	#442	—	2	1	no	—
358	#440	—	2	1	no	—
359	C₄×SD₁₆	—	2	1	no	—
360	C₄×D₈	—	2	1	no	—
361	#428	C₂²×C₁₃	1	1	yes	characteristic
362	#428	C₂²×C₁₃	1	1	yes	characteristic
363	#428	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
365	#424	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
368	#419	C₂²×C₁₃	1	1	yes	characteristic
369	#417	C₂²×C₁₃	1	1	yes	characteristic
370	#416	C₂²×C₁₃	1	1	yes	characteristic
371	#416	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
376	#408	C₂²×C₁₃	1	1	yes	characteristic
377	#405	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
379	#391	C₂²×C₁₃	1	1	yes	characteristic
380	#390	C₂²×C₁₃	1	1	yes	characteristic
381	#343	C₂²×C₁₃	1	1	yes	characteristic
382	#343	C₂²×C₁₃	1	1	yes	characteristic
383	#341	C₂²×C₁₃	1	1	yes	characteristic
384	#341	C₂²×C₁₃	1	1	yes	characteristic
385	#339	C₂²×C₁₃	1	1	yes	characteristic
386	#339	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	2	1	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	—	4	1	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	8	2	no	—
397	C₂²×C₁₃	—	8	1	no	—
398	C₂²×C₁₃	—	8	1	no	—
399	C₂²×C₁₃	—	16	1	no	—
400	C₂²×C₁₃	#540	1	1	yes	characteristic
401	C₂²×C₁₃	D₄²	1	1	yes	characteristic
402	C₂²×C₁₃	#553	1	1	yes	characteristic
403	C₄×C₁₃	—	4	1	no	—
404	C₄×C₁₃	—	4	1	no	—
405	C₄×C₁₃	—	4	1	no	—
406	C₄×C₁₃	—	4	1	no	—
407	C₄×C₁₃	—	4	1	no	—
408	C₄×C₁₃	—	4	1	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	—	8	1	no	—
411	C₄×C₁₃	—	8	1	no	—
412	C₄×C₁₃	—	8	1	no	—
413	C₄×C₁₃	#525	1	1	yes	characteristic
414	C₄×C₁₃	#532	1	1	yes	characteristic
415	C₄×C₁₃	#546	1	1	yes	characteristic
416	C₄×C₁₃	#546	1	1	yes	characteristic
417	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
421	#137	—	2	2	no	—
422	#137	—	4	1	no	—
423	AGL(1,ℤ/8)	—	2	2	no	—
424	AGL(1,ℤ/8)	—	2	2	no	—
425	AGL(1,ℤ/8)	—	2	2	no	—
426	AGL(1,ℤ/8)	—	4	1	no	—
427	C₂×Q₁₆	—	2	1	no	—
428	C₂×SD₁₆	—	2	1	no	—
429	C₂×SD₁₆	—	2	1	no	—
430	C₂×SD₁₆	—	2	1	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×SD₁₆	—	2	1	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×D₈	—	2	1	no	—
436	C₂×D₈	—	2	1	no	—
437	#131	—	2	2	no	—
438	#131	—	4	1	no	—
439	C₂×M₁₆	—	2	1	no	—
440	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×C₈	—	2	1	no	—
445	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄⋊Q₈	—	2	1	no	—
448	#124	—	2	1	no	—
449	#123	—	4	1	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂²⋊Q₈	—	2	1	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	#121	—	2	1	no	—
455	#121	—	2	1	no	—
456	#121	—	4	1	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	4	1	no	—
464	#117	—	2	1	no	—
465	#117	C₂³×C₁₃	1	1	yes	characteristic
466	#117	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	4	1	no	—
471	C₂×C₂²⋊C₄	—	4	1	no	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	#107	—	2	1	no	—
474	#107	—	2	1	no	—
475	#107	—	2	1	no	—
476	#107	—	2	1	no	—
477	#107	—	2	1	no	—
478	#106	—	2	1	no	—
479	#106	—	2	1	no	—
480	#106	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	C₄⋊C₈	—	2	1	no	—
483	#104	—	2	2	no	—
484	#104	—	4	1	no	—
485	#103	—	2	1	no	—
486	#103	—	2	1	no	—
487	#103	—	2	1	no	—
488	#103	—	2	1	no	—
489	#103	—	2	1	no	—
490	#103	D₄×C₁₃	1	1	yes	characteristic
491	#103	D₄×C₁₃	1	1	yes	characteristic
492	#103	D₄×C₁₃	1	1	yes	characteristic
493	#103	D₄×C₁₃	1	1	yes	characteristic
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	D₄×C₁₃	1	1	yes	characteristic
498	#102	D₄×C₁₃	1	1	yes	characteristic
499	#102	D₄×C₁₃	1	1	yes	characteristic
500	#102	D₄×C₁₃	1	1	yes	characteristic
501	#101	—	2	2	no	—
502	#100	—	2	2	no	—
503	C₂²⋊C₈	—	2	1	no	—
504	C₂²⋊C₈	—	2	1	no	—
505	#97	—	2	1	no	—
506	#97	—	4	1	no	—
507	C₄×C₈	—	2	1	no	—
508	#95	—	4	1	no	—
509	C₂×C₁₃	—	2	1	no	—
510	C₂×C₁₃	—	2	1	no	—
511	C₂×C₁₃	—	8	1	no	—
512	C₂×C₁₃	—	8	1	no	—
513	C₂×C₁₃	—	8	2	no	—
514	C₂×C₁₃	#2464	1	1	yes	characteristic
515	C₂×C₁₃	#3288	1	1	yes	characteristic
516	C₂×C₁₃	#3289	1	1	yes	characteristic
517	C₂⁴	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	1	no	—
521	#41	—	2	1	no	—
522	#41	—	2	1	no	—
523	#41	—	2	1	no	—
524	#41	—	2	1	no	—
525	#41	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	4	1	no	—
542	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂×D₄	C₁₃×#41	1	2	yes	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	Q₁₆	—	4	2	no	—
556	SD₁₆	—	2	4	no	—
557	SD₁₆	—	4	2	no	—
558	SD₁₆	—	4	2	no	—
559	SD₁₆	—	4	2	no	—
560	SD₁₆	—	4	2	no	—
561	D₈	—	2	4	no	—
562	D₈	—	4	2	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	2	1	no	—
565	M₁₆	—	2	1	no	—
566	M₁₆	—	2	1	no	—
567	M₁₆	—	2	1	no	—
568	M₁₆	—	2	1	no	—
569	M₁₆	—	4	2	no	—
570	M₁₆	C₁₃×#41	1	2	yes	—
571	M₁₆	C₁₃×#41	1	2	yes	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	4	2	no	—
581	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	—	4	1	no	—
593	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	—	8	2	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	4	1	no	—
612	C₁₃	#26997	1	1	yes	characteristic, direct product factor, Sylow
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	8	1	no	—
619	C₂³	—	8	1	no	—
620	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	2	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	1	no	—
632	D₄	—	2	1	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	16	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	8	1	no	—
661	C₂×C₄	—	8	1	no	—
662	C₂×C₄	—	16	1	no	—
663	C₂×C₄	—	16	1	no	—
664	C₂×C₄	—	16	1	no	—
665	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
667	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
668	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
669	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
670	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
671	C₈	—	2	2	no	—
672	C₈	—	2	1	no	—
673	C₈	—	2	1	no	—
674	C₈	—	2	1	no	—
675	C₈	—	2	1	no	—
676	C₈	—	2	2	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	16	1	no	—
692	C₂²	C₁₃×#540	1	1	yes	characteristic
693	C₂²	D₄²×C₁₃	1	1	yes	characteristic
694	C₂²	C₁₃×#553	1	1	yes	characteristic
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	C₁₃×#525	1	1	yes	characteristic
706	C₄	C₁₃×#532	1	1	yes	characteristic
707	C₄	C₁₃×#546	1	1	yes	characteristic
708	C₄	C₁₃×#546	1	1	yes	characteristic
709	C₂	—	2	1	no	—
710	C₂	—	2	1	no	—
711	C₂	—	8	1	no	—
712	C₂	—	8	1	no	—
713	C₂	—	8	2	no	—
714	C₂	C₁₃×#2464	1	1	yes	characteristic
715	C₂	C₁₃×#3288	1	1	yes	characteristic
716	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3098	C₂	semidirect
2. C₁₃×#3063	C₂	semidirect
3. C₁₃×#3042	C₂	semidirect
4. C₁₃×#2946	C₂	semidirect
5. C₁₃×#2089	C₂	semidirect
6. C₁₃×#2038	C₂	semidirect
7. C₁₃×#2019	C₂	semidirect
9. C₁₃×#1973	C₂	semidirect
10. C₁₃×#1938	C₂	semidirect
11. C₁₃×#1930	C₂	semidirect
12. C₁₃×#1907	C₂	semidirect
13. C₁₃×#1882	C₂	semidirect
14. C₁₃×#1856	C₂	semidirect
15. C₁₃×#1765	C₂	semidirect
159. #26997	C₁₃	direct (N × H)
255. #3098	C₂×C₁₃	semidirect
256. #3063	C₂×C₁₃	semidirect
257. #3042	C₂×C₁₃	semidirect
258. #2946	C₂×C₁₃	semidirect
259. #2089	C₂×C₁₃	semidirect
260. #2038	C₂×C₁₃	semidirect
261. #2019	C₂×C₁₃	semidirect
263. #1973	C₂×C₁₃	semidirect
264. #1938	C₂×C₁₃	semidirect
265. #1930	C₂×C₁₃	semidirect
266. #1907	C₂×C₁₃	semidirect
267. #1882	C₂×C₁₃	semidirect
268. #1856	C₂×C₁₃	semidirect
269. #1765	C₂×C₁₃	semidirect
612. C₁₃	#26997	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×#3098	2
C₁₃×#3063	2
C₁₃×#3042	2
C₁₃×#2946	2
C₁₃×#2089	2
C₁₃×#2038	2
C₁₃×#2019	2
C₁₃×#2006	2
C₁₃×#1973	2
C₁₃×#1938	2
C₁₃×#1930	2
C₁₃×#1907	2
C₁₃×#1882	2
C₁₃×#1856	2
C₁₃×#1765	2
#26997	13

Subgroups — C13×#26997 #15713336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26997 #15713336