Subgroups — C₁₃×#26921 #15713260

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#544	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₁₃×#519	C₂²	1	1	yes	characteristic
21	C₁₃×#518	C₂²	1	1	yes	characteristic
22	C₁₃×#518	C₂²	1	1	yes	characteristic
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#479	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#478	—	2	1	no	—
27	C₁₃×#477	—	2	1	no	—
28	C₁₃×#476	—	2	1	no	—
29	C₁₃×#475	—	2	1	no	—
30	C₁₃×#474	—	2	1	no	—
31	C₁₃×#442	—	2	1	no	—
32	C₁₃×#442	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₁₃×#440	—	2	1	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₄×C₁₃×SD₁₆	—	2	1	no	—
37	C₄×C₁₃×D₈	—	2	1	no	—
38	C₄×C₁₃×D₈	—	2	1	no	—
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#427	C₂²	1	1	yes	characteristic
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₁₃×#424	C₂²	1	1	yes	characteristic
45	C₁₃×#419	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×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	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	C₁₃×#405	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#341	C₂²	1	1	yes	characteristic
61	C₁₃×#341	C₂²	1	1	yes	characteristic
62	C₁₃×#339	C₂²	1	1	yes	characteristic
63	C₁₃×#339	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×D₈	—	2	2	no	—
75	C₂×C₁₃×D₈	—	2	2	no	—
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
103	C₁₃×#117	—	4	1	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₁₃×#117	C₂³	1	1	yes	characteristic
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#107	D₄	1	1	yes	characteristic
117	C₁₃×#107	D₄	1	1	yes	characteristic
118	C₁₃×#107	D₄	1	1	yes	characteristic
119	C₁₃×#107	D₄	1	1	yes	characteristic
120	C₁₃×#106	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	D₄	1	1	yes	characteristic
123	C₁₃×#106	D₄	1	1	yes	characteristic
124	C₁₃×#106	D₄	1	1	yes	characteristic
125	C₁₃×#106	D₄	1	1	yes	characteristic
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×#103	—	2	1	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#102	—	2	1	no	—
137	C₁₃×#102	—	2	1	no	—
138	C₁₃×#102	—	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×#100	—	2	2	no	—
148	C₁₃×#100	—	2	2	no	—
149	C₁₃×#97	—	2	1	no	—
150	C₁₃×#97	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₄×C₈×C₁₃	—	2	1	no	—
153	#26921	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	4	1	no	—
162	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	#41	1	2	yes	—
174	C₂×D₄×C₁₃	#41	1	2	yes	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	—	4	1	no	—
180	C₂²×C₄×C₁₃	—	4	1	no	—
181	C₂²×C₄×C₁₃	—	4	1	no	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×SD₁₆	—	2	4	no	—
184	C₁₃×SD₁₆	—	2	4	no	—
185	C₁₃×D₈	—	2	4	no	—
186	C₁₃×D₈	—	2	4	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	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	4	1	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	4	1	no	—
213	C₁₃×C₄⋊C₄	—	4	1	no	—
214	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	4	1	no	—
227	C₁₃×C₂²⋊C₄	—	4	1	no	—
228	C₁₃×C₂²⋊C₄	—	4	1	no	—
229	C₁₃×C₂²⋊C₄	—	4	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	4	no	—
231	C₁₃×C₂²⋊C₄	—	8	2	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	2	1	no	—
237	C₄²×C₁₃	—	2	1	no	—
238	C₄²×C₁₃	—	4	1	no	—
239	C₄²×C₁₃	—	4	1	no	—
240	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2949	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2948	C₂×C₁₃	1	1	yes	characteristic
244	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2045	C₂×C₁₃	1	1	yes	characteristic
246	#2027	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#2012	C₂×C₁₃	1	1	yes	characteristic
248	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1922	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1922	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1888	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1885	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	8	1	no	—
262	C₂³×C₁₃	—	8	1	no	—
263	C₂³×C₁₃	—	8	1	no	—
264	C₂³×C₁₃	—	8	1	no	—
265	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	2	no	—
267	Q₈×C₁₃	—	2	2	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	16	1	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	2	2	no	—
273	D₄×C₁₃	—	2	2	no	—
274	D₄×C₁₃	—	2	2	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	8	1	no	—
295	C₂×C₄×C₁₃	—	16	1	no	—
296	C₂×C₄×C₁₃	—	16	1	no	—
297	C₂×C₄×C₁₃	—	16	1	no	—
298	C₂×C₄×C₁₃	—	16	1	no	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
305	C₈×C₁₃	—	2	1	no	—
306	C₈×C₁₃	—	2	1	no	—
307	C₈×C₁₃	—	2	1	no	—
308	C₈×C₁₃	—	2	1	no	—
309	C₈×C₁₃	—	4	1	no	—
310	C₈×C₁₃	—	4	1	no	—
311	C₈×C₁₃	—	4	1	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
314	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
315	#544	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
317	#519	C₂²×C₁₃	1	1	yes	characteristic
318	#518	C₂²×C₁₃	1	1	yes	characteristic
319	#518	C₂²×C₁₃	1	1	yes	characteristic
320	#479	—	2	1	no	—
321	#479	—	2	1	no	—
322	#478	—	2	1	no	—
323	#478	—	2	1	no	—
324	#477	—	2	1	no	—
325	#476	—	2	1	no	—
326	#475	—	2	1	no	—
327	#474	—	2	1	no	—
328	#442	—	2	1	no	—
329	#442	—	2	1	no	—
330	#440	—	2	1	no	—
331	#440	—	2	1	no	—
332	C₄×SD₁₆	—	2	1	no	—
333	C₄×SD₁₆	—	2	1	no	—
334	C₄×D₈	—	2	1	no	—
335	C₄×D₈	—	2	1	no	—
336	#428	C₂²×C₁₃	1	1	yes	characteristic
337	#428	C₂²×C₁₃	1	1	yes	characteristic
338	#427	C₂²×C₁₃	1	1	yes	characteristic
339	#427	C₂²×C₁₃	1	1	yes	characteristic
340	#424	C₂²×C₁₃	1	1	yes	characteristic
341	#424	C₂²×C₁₃	1	1	yes	characteristic
342	#419	C₂²×C₁₃	1	1	yes	characteristic
343	#419	C₂²×C₁₃	1	1	yes	characteristic
344	#418	C₂²×C₁₃	1	1	yes	characteristic
345	#418	C₂²×C₁₃	1	1	yes	characteristic
346	#418	C₂²×C₁₃	1	1	yes	characteristic
347	#418	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
353	#405	C₂²×C₁₃	1	1	yes	characteristic
354	#405	C₂²×C₁₃	1	1	yes	characteristic
355	#390	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	#339	C₂²×C₁₃	1	1	yes	characteristic
360	#339	C₂²×C₁₃	1	1	yes	characteristic
361	#339	C₂²×C₁₃	1	1	yes	characteristic
362	#339	C₂²×C₁₃	1	1	yes	characteristic
363	#336	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₁₃	—	2	1	no	—
365	C₂²×C₁₃	—	2	1	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	8	2	no	—
369	C₂²×C₁₃	—	8	2	no	—
370	C₂²×C₁₃	—	8	1	no	—
371	C₂²×C₁₃	—	8	1	no	—
372	C₂²×C₁₃	—	8	1	no	—
373	C₂²×C₁₃	—	8	1	no	—
374	C₂²×C₁₃	—	16	1	no	—
375	C₂²×C₁₃	—	16	1	no	—
376	C₂²×C₁₃	#539	1	1	yes	characteristic
377	C₂²×C₁₃	D₄²	1	1	yes	characteristic
378	C₂²×C₁₃	#551	1	1	yes	characteristic
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	1	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	1	no	—
385	C₄×C₁₃	—	4	1	no	—
386	C₄×C₁₃	—	4	1	no	—
387	C₄×C₁₃	—	4	1	no	—
388	C₄×C₁₃	—	8	1	no	—
389	C₄×C₁₃	—	8	1	no	—
390	C₄×C₁₃	#525	1	1	yes	characteristic
391	C₄×C₁₃	#525	1	1	yes	characteristic
392	C₄×C₁₃	#548	1	1	yes	characteristic
393	C₄×C₁₃	#548	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	1	no	—
400	C₂×SD₁₆	—	2	1	no	—
401	C₂×D₈	—	2	2	no	—
402	C₂×D₈	—	2	2	no	—
403	C₂×D₈	—	2	1	no	—
404	C₂×D₈	—	2	1	no	—
405	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊Q₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	1	no	—
413	#125	—	2	1	no	—
414	#125	—	2	1	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	C₂²⋊Q₈	—	4	1	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	1	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	#117	—	4	1	no	—
431	#117	C₂³×C₁₃	1	1	yes	characteristic
432	#117	C₂³×C₁₃	1	1	yes	characteristic
433	#117	C₂³×C₁₃	1	1	yes	characteristic
434	#117	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	—	4	1	no	—
437	C₂×C₂²⋊C₄	—	4	1	no	—
438	C₂×C₂²⋊C₄	—	4	1	no	—
439	C₂×C₂²⋊C₄	—	4	1	no	—
440	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
441	#107	—	2	1	no	—
442	#107	—	2	1	no	—
443	#107	D₄×C₁₃	1	1	yes	characteristic
444	#107	D₄×C₁₃	1	1	yes	characteristic
445	#107	D₄×C₁₃	1	1	yes	characteristic
446	#107	D₄×C₁₃	1	1	yes	characteristic
447	#106	—	2	1	no	—
448	#106	—	2	1	no	—
449	#106	D₄×C₁₃	1	1	yes	characteristic
450	#106	D₄×C₁₃	1	1	yes	characteristic
451	#106	D₄×C₁₃	1	1	yes	characteristic
452	#106	D₄×C₁₃	1	1	yes	characteristic
453	C₄⋊C₈	—	2	1	no	—
454	C₄⋊C₈	—	2	1	no	—
455	C₄⋊C₈	—	2	1	no	—
456	C₄⋊C₈	—	2	1	no	—
457	#103	—	2	1	no	—
458	#103	—	2	1	no	—
459	#103	—	2	1	no	—
460	#103	—	2	1	no	—
461	#103	—	2	1	no	—
462	#103	—	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	#102	—	2	1	no	—
470	#102	—	2	1	no	—
471	#102	—	2	1	no	—
472	#102	—	2	1	no	—
473	#101	—	2	2	no	—
474	#100	—	2	2	no	—
475	#100	—	2	2	no	—
476	#97	—	2	1	no	—
477	#97	—	2	1	no	—
478	C₄×C₈	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	C₂×C₁₃	—	2	1	no	—
481	C₂×C₁₃	—	2	1	no	—
482	C₂×C₁₃	—	8	2	no	—
483	C₂×C₁₃	—	8	2	no	—
484	C₂×C₁₃	#2463	1	1	yes	characteristic
485	C₂×C₁₃	#3288	1	1	yes	characteristic
486	C₂×C₁₃	#3290	1	1	yes	characteristic
487	C₂⁴	—	2	1	no	—
488	C₂⁴	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	4	1	no	—
495	C₂×Q₈	C₁₃×#41	1	2	yes	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	C₁₃×#41	1	2	yes	—
507	C₂×D₄	C₁₃×#41	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
516	SD₁₆	—	2	4	no	—
517	SD₁₆	—	2	4	no	—
518	D₈	—	2	4	no	—
519	D₈	—	2	4	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	2	1	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	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	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	1	no	—
547	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	4	1	no	—
560	C₂²⋊C₄	—	4	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	8	2	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	4	1	no	—
572	C₄²	—	4	1	no	—
573	C₁₃	#26921	1	1	yes	characteristic, direct product factor, Sylow
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	8	1	no	—
581	C₂³	—	8	1	no	—
582	C₂³	—	8	1	no	—
583	C₂³	—	8	1	no	—
584	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	16	1	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	8	1	no	—
614	C₂×C₄	—	16	1	no	—
615	C₂×C₄	—	16	1	no	—
616	C₂×C₄	—	16	1	no	—
617	C₂×C₄	—	16	1	no	—
618	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
622	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
623	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
624	C₈	—	2	1	no	—
625	C₈	—	2	1	no	—
626	C₈	—	2	1	no	—
627	C₈	—	2	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	16	1	no	—
643	C₂²	—	16	1	no	—
644	C₂²	C₁₃×#539	1	1	yes	characteristic
645	C₂²	D₄²×C₁₃	1	1	yes	characteristic
646	C₂²	C₁₃×#551	1	1	yes	characteristic
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	2	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	C₁₃×#525	1	1	yes	characteristic
659	C₄	C₁₃×#525	1	1	yes	characteristic
660	C₄	C₁₃×#548	1	1	yes	characteristic
661	C₄	C₁₃×#548	1	1	yes	characteristic
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	8	2	no	—
665	C₂	—	8	2	no	—
666	C₂	C₁₃×#2463	1	1	yes	characteristic
667	C₂	C₁₃×#3288	1	1	yes	characteristic
668	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
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×#3082	C₂	semidirect
2. C₁₃×#3081	C₂	semidirect
3. C₁₃×#2949	C₂	semidirect
5. C₁₃×#2046	C₂	semidirect
7. C₁₃×#2027	C₂	semidirect
9. C₁₃×#1931	C₂	semidirect
10. C₁₃×#1930	C₂	semidirect
11. C₁₃×#1922	C₂	semidirect
12. C₁₃×#1922	C₂	semidirect
13. C₁₃×#1888	C₂	semidirect
14. C₁₃×#1885	C₂	semidirect
15. C₁₃×#1856	C₂	semidirect
153. #26921	C₁₃	direct (N × H)
240. #3082	C₂×C₁₃	semidirect
241. #3081	C₂×C₁₃	semidirect
242. #2949	C₂×C₁₃	semidirect
244. #2046	C₂×C₁₃	semidirect
246. #2027	C₂×C₁₃	semidirect
248. #1931	C₂×C₁₃	semidirect
249. #1930	C₂×C₁₃	semidirect
250. #1922	C₂×C₁₃	semidirect
251. #1922	C₂×C₁₃	semidirect
252. #1888	C₂×C₁₃	semidirect
253. #1885	C₂×C₁₃	semidirect
254. #1856	C₂×C₁₃	semidirect
573. C₁₃	#26921	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×#3082	2
C₁₃×#3081	2
C₁₃×#2949	2
C₁₃×#2948	2
C₁₃×#2046	2
C₁₃×#2045	2
C₁₃×#2027	2
C₁₃×#2012	2
C₁₃×#1931	2
C₁₃×#1930	2
C₁₃×#1922	2
C₁₃×#1888	2
C₁₃×#1885	2
C₁₃×#1856	2
#26921	13

Subgroups — C13×#26921 #15713260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26921 #15713260