Subgroups — C₁₃×#24931 #15711270

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 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×#3013	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1929	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₁₃×#537	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	1	yes	characteristic
22	C₁₃×#520	C₂²	1	1	yes	characteristic
23	C₁₃×#485	—	2	1	no	—
24	C₁₃×#484	—	2	1	no	—
25	C₁₃×#482	—	2	1	no	—
26	C₁₃×#480	—	2	1	no	—
27	C₁₃×#452	—	2	1	no	—
28	C₁₃×#451	—	2	1	no	—
29	C₁₃×#449	—	2	1	no	—
30	C₁₃×#448	—	2	1	no	—
31	C₁₃×#440	—	2	1	no	—
32	C₁₃×#440	—	2	1	no	—
33	C₄×C₁₃×Q₁₆	—	2	1	no	—
34	C₄×C₁₃×D₈	—	2	1	no	—
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
42	C₁₃×#419	—	2	1	no	—
43	C₁₃×#419	C₂²	1	1	yes	characteristic
44	C₁₃×#417	—	2	1	no	—
45	C₁₃×#417	C₂²	1	1	yes	characteristic
46	C₁₃×#417	C₂²	1	1	yes	characteristic
47	C₁₃×#417	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	—	2	1	no	—
51	C₁₃×#416	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	—	2	1	no	—
53	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#408	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#384	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×#341	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
67	C₁₃×2₋¹⁺⁴	—	2	2	no	—
68	C₁₃×2₋¹⁺⁴	—	2	2	no	—
69	C₁₃×2₋¹⁺⁴	—	2	2	no	—
70	C₁₃×2₋¹⁺⁴	—	4	1	no	—
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	—	2	1	no	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#137	—	2	2	no	—
81	C₁₃×#137	—	4	1	no	—
82	C₁₃×#135	—	2	2	no	—
83	C₁₃×#135	—	2	2	no	—
84	C₂×C₁₃×Q₁₆	—	2	1	no	—
85	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
88	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
89	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
90	C₁₃×#131	—	2	2	no	—
91	C₁₃×#131	—	4	1	no	—
92	C₂×C₁₃×M₁₆	—	2	1	no	—
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	C₂²×C₈×C₁₃	—	2	1	no	—
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₂²⋊Q₈	—	2	1	no	—
101	C₁₃×C₂²⋊Q₈	—	2	1	no	—
102	C₁₃×#121	—	2	1	no	—
103	C₁₃×#121	—	2	1	no	—
104	C₁₃×#121	—	4	1	no	—
105	C₄×Q₈×C₁₃	—	2	1	no	—
106	C₄×Q₈×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	—	4	1	no	—
110	C₄×D₄×C₁₃	—	4	1	no	—
111	C₁₃×#117	—	2	1	no	—
112	C₁₃×#117	—	2	1	no	—
113	C₁₃×#117	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#108	—	4	1	no	—
122	C₁₃×#107	—	2	1	no	—
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×#106	—	2	1	no	—
128	C₁₃×#104	—	2	2	no	—
129	C₁₃×#104	—	4	1	no	—
130	C₁₃×#104	—	4	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×#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	—	2	1	no	—
141	C₁₃×#103	—	2	1	no	—
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	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	D₄	1	1	yes	characteristic
150	C₁₃×#102	D₄	1	1	yes	characteristic
151	C₁₃×#101	—	2	2	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	C₄×C₈×C₁₃	—	2	1	no	—
158	C₁₃×#95	—	4	1	no	—
159	#24931	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	4	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	C₁₃×#41	—	2	1	no	—
170	C₁₃×#41	—	2	1	no	—
171	C₁₃×#41	—	4	2	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	4	2	no	—
174	C₁₃×#41	—	4	4	no	—
175	C₁₃×#41	—	4	2	no	—
176	C₁₃×#41	#41	1	2	yes	—
177	C₁₃×#41	#41	1	2	yes	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	4	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	—	4	1	no	—
185	C₂×Q₈×C₁₃	—	4	2	no	—
186	C₂×Q₈×C₁₃	—	4	2	no	—
187	C₂×Q₈×C₁₃	—	4	2	no	—
188	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₃	#41	1	2	yes	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	4	1	no	—
196	C₂×D₄×C₁₃	—	4	1	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	4	1	no	—
209	C₂²×C₄×C₁₃	—	4	1	no	—
210	C₂²×C₄×C₁₃	—	4	1	no	—
211	C₂²×C₄×C₁₃	—	4	1	no	—
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×Q₁₆	—	2	2	no	—
214	C₁₃×Q₁₆	—	4	2	no	—
215	C₁₃×SD₁₆	—	2	2	no	—
216	C₁₃×SD₁₆	—	2	2	no	—
217	C₁₃×SD₁₆	—	4	2	no	—
218	C₁₃×D₈	—	2	2	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	—	2	1	no	—
226	C₁₃×M₁₆	—	2	1	no	—
227	C₁₃×M₁₆	—	4	2	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	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	4	2	no	—
237	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
248	C₁₃×C₄⋊C₄	—	4	1	no	—
249	C₁₃×C₄⋊C₄	—	4	1	no	—
250	C₁₃×C₄⋊C₄	—	8	2	no	—
251	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	4	1	no	—
255	C₁₃×C₂²⋊C₄	—	4	1	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	1	no	—
258	C₄²×C₁₃	—	2	1	no	—
259	C₄²×C₁₃	—	2	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	4	1	no	—
262	C₄²×C₁₃	—	4	1	no	—
263	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3013	C₂×C₁₃	1	1	yes	characteristic
265	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2898	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2078	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1929	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1876	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1793	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
282	Q₈×C₁₃	—	2	1	no	—
283	Q₈×C₁₃	—	2	1	no	—
284	Q₈×C₁₃	—	2	1	no	—
285	Q₈×C₁₃	—	2	2	no	—
286	Q₈×C₁₃	—	2	2	no	—
287	Q₈×C₁₃	—	2	1	no	—
288	Q₈×C₁₃	—	2	1	no	—
289	Q₈×C₁₃	—	4	4	no	—
290	Q₈×C₁₃	—	4	1	no	—
291	Q₈×C₁₃	—	4	1	no	—
292	Q₈×C₁₃	#123	1	2	yes	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	2	no	—
295	D₄×C₁₃	—	2	1	no	—
296	D₄×C₁₃	—	2	1	no	—
297	D₄×C₁₃	—	2	1	no	—
298	D₄×C₁₃	—	2	1	no	—
299	D₄×C₁₃	—	2	1	no	—
300	D₄×C₁₃	—	4	4	no	—
301	D₄×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	16	1	no	—
306	D₄×C₁₃	#123	1	2	yes	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	2	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	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	4	4	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	4	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	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	8	1	no	—
330	C₂×C₄×C₁₃	—	8	1	no	—
331	C₂×C₄×C₁₃	—	8	1	no	—
332	C₂×C₄×C₁₃	—	16	1	no	—
333	C₂×C₄×C₁₃	—	16	1	no	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₁₃	—	2	1	no	—
341	C₈×C₁₃	—	2	1	no	—
342	C₈×C₁₃	—	2	1	no	—
343	C₈×C₁₃	—	2	1	no	—
344	C₈×C₁₃	—	4	1	no	—
345	C₈×C₁₃	—	4	1	no	—
346	C₈×C₁₃	—	4	1	no	—
347	C₈×C₁₃	—	4	1	no	—
348	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
352	#537	C₂²×C₁₃	1	1	yes	characteristic
353	#520	C₂²×C₁₃	1	1	yes	characteristic
354	#520	C₂²×C₁₃	1	1	yes	characteristic
355	#485	—	2	1	no	—
356	#484	—	2	1	no	—
357	#482	—	2	1	no	—
358	#480	—	2	1	no	—
359	#452	—	2	1	no	—
360	#451	—	2	1	no	—
361	#449	—	2	1	no	—
362	#448	—	2	1	no	—
363	#440	—	2	1	no	—
364	#440	—	2	1	no	—
365	C₄×Q₁₆	—	2	1	no	—
366	C₄×D₈	—	2	1	no	—
367	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
368	#428	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
374	#419	—	2	1	no	—
375	#419	C₂²×C₁₃	1	1	yes	characteristic
376	#417	—	2	1	no	—
377	#417	C₂²×C₁₃	1	1	yes	characteristic
378	#417	C₂²×C₁₃	1	1	yes	characteristic
379	#417	C₂²×C₁₃	1	1	yes	characteristic
380	#417	C₂²×C₁₃	1	1	yes	characteristic
381	#417	C₂²×C₁₃	1	1	yes	characteristic
382	#416	—	2	1	no	—
383	#416	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#103	—	2	1	no	—
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
388	#408	C₂²×C₁₃	1	1	yes	characteristic
389	#408	C₂²×C₁₃	1	1	yes	characteristic
390	#405	C₂²×C₁₃	1	1	yes	characteristic
391	#391	C₂²×C₁₃	1	1	yes	characteristic
392	#384	C₂²×C₁₃	1	1	yes	characteristic
393	#343	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	#339	C₂²×C₁₃	1	1	yes	characteristic
398	#336	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₁₃	—	2	1	no	—
400	C₂²×C₁₃	—	2	1	no	—
401	C₂²×C₁₃	—	2	2	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	1	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	1	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	1	no	—
409	C₂²×C₁₃	—	4	1	no	—
410	C₂²×C₁₃	#538	1	1	yes	characteristic
411	C₂²×C₁₃	D₄²	1	1	yes	characteristic
412	C₂²×C₁₃	#551	1	1	yes	characteristic
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	—	4	1	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	8	1	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	—	8	1	no	—
423	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
424	C₄×C₁₃	#525	1	1	yes	characteristic
425	C₄×C₁₃	#546	1	1	yes	characteristic
426	C₄×C₁₃	#546	1	1	yes	characteristic
427	2₋¹⁺⁴	—	2	2	no	—
428	2₋¹⁺⁴	—	2	2	no	—
429	2₋¹⁺⁴	—	2	2	no	—
430	2₋¹⁺⁴	—	4	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	4	1	no	—
434	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
440	#137	—	2	2	no	—
441	#137	—	4	1	no	—
442	#135	—	2	2	no	—
443	#135	—	2	2	no	—
444	C₂×Q₁₆	—	2	1	no	—
445	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
448	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
449	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
450	#131	—	2	2	no	—
451	#131	—	4	1	no	—
452	C₂×M₁₆	—	2	1	no	—
453	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
454	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×C₈	—	2	1	no	—
458	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	4	1	no	—
465	C₄×Q₈	—	2	1	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	—	4	1	no	—
470	C₄×D₄	—	4	1	no	—
471	#117	—	2	1	no	—
472	#117	—	2	1	no	—
473	#117	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	4	1	no	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	#108	—	4	1	no	—
482	#107	—	2	1	no	—
483	#107	—	2	1	no	—
484	#107	—	2	1	no	—
485	#107	—	2	1	no	—
486	#107	—	2	1	no	—
487	#106	—	2	1	no	—
488	#104	—	2	2	no	—
489	#104	—	4	1	no	—
490	#104	—	4	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#103	—	2	1	no	—
494	#103	—	2	1	no	—
495	#103	—	2	1	no	—
496	#103	—	2	1	no	—
497	#103	—	2	1	no	—
498	#103	—	2	1	no	—
499	#103	—	2	1	no	—
500	#103	—	2	1	no	—
501	#103	—	2	1	no	—
502	#103	D₄×C₁₃	1	1	yes	characteristic
503	#103	D₄×C₁₃	1	1	yes	characteristic
504	#102	—	2	1	no	—
505	#102	—	2	1	no	—
506	#102	—	2	1	no	—
507	#102	—	2	1	no	—
508	#102	—	2	1	no	—
509	#102	D₄×C₁₃	1	1	yes	characteristic
510	#102	D₄×C₁₃	1	1	yes	characteristic
511	#101	—	2	2	no	—
512	C₂²⋊C₈	—	2	1	no	—
513	C₂²⋊C₈	—	2	1	no	—
514	C₂²⋊C₈	—	2	1	no	—
515	C₂²⋊C₈	—	2	1	no	—
516	#97	—	2	1	no	—
517	C₄×C₈	—	2	1	no	—
518	#95	—	4	1	no	—
519	C₂×C₁₃	—	2	1	no	—
520	C₂×C₁₃	—	2	1	no	—
521	C₂×C₁₃	—	4	2	no	—
522	C₂×C₁₃	—	8	1	no	—
523	C₂×C₁₃	—	8	1	no	—
524	C₂×C₁₃	#2418	1	1	yes	characteristic
525	C₂×C₁₃	#3288	1	1	yes	characteristic
526	C₂×C₁₃	#3293	1	1	yes	characteristic
527	#41	—	2	1	no	—
528	#41	—	2	1	no	—
529	#41	—	2	4	no	—
530	#41	—	2	1	no	—
531	#41	—	2	1	no	—
532	#41	—	2	1	no	—
533	#41	—	2	1	no	—
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	4	2	no	—
539	#41	—	4	4	no	—
540	#41	—	4	2	no	—
541	#41	—	4	4	no	—
542	#41	—	4	2	no	—
543	#41	C₁₃×#41	1	2	yes	—
544	#41	C₁₃×#41	1	2	yes	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	4	1	no	—
552	C₂×Q₈	—	4	2	no	—
553	C₂×Q₈	—	4	2	no	—
554	C₂×Q₈	—	4	2	no	—
555	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
558	C₂×Q₈	C₁₃×#41	1	2	yes	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
580	Q₁₆	—	2	2	no	—
581	Q₁₆	—	4	2	no	—
582	SD₁₆	—	2	2	no	—
583	SD₁₆	—	2	2	no	—
584	SD₁₆	—	4	2	no	—
585	D₈	—	2	2	no	—
586	M₁₆	—	2	1	no	—
587	M₁₆	—	2	1	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	2	1	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	1	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	4	2	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	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	4	2	no	—
604	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	4	1	no	—
615	C₄⋊C₄	—	4	1	no	—
616	C₄⋊C₄	—	4	1	no	—
617	C₄⋊C₄	—	8	2	no	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	1	no	—
624	C₂²⋊C₄	—	4	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	4	1	no	—
629	C₄²	—	4	1	no	—
630	C₁₃	#24931	1	1	yes	characteristic, direct product factor, Sylow
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	1	no	—
641	Q₈	—	2	1	no	—
642	Q₈	—	4	4	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	C₁₃×#123	1	2	yes	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	1	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	16	1	no	—
659	D₄	C₁₃×#123	1	2	yes	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	—	16	1	no	—
686	C₂×C₄	—	16	1	no	—
687	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
690	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
691	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
692	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
693	C₈	—	2	1	no	—
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	C₁₃×#538	1	1	yes	characteristic
713	C₂²	D₄²×C₁₃	1	1	yes	characteristic
714	C₂²	C₁₃×#551	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
726	C₄	C₁₃×#525	1	1	yes	characteristic
727	C₄	C₁₃×#546	1	1	yes	characteristic
728	C₄	C₁₃×#546	1	1	yes	characteristic
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	8	1	no	—
734	C₂	C₁₃×#2418	1	1	yes	characteristic
735	C₂	C₁₃×#3288	1	1	yes	characteristic
736	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3013	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
3. C₁₃×#2951	C₂	semidirect
4. C₁₃×#2898	C₂	semidirect
5. C₁₃×#2095	C₂	semidirect
6. C₁₃×#2078	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#2039	C₂	semidirect
9. C₁₃×#1930	C₂	semidirect
10. C₁₃×#1929	C₂	semidirect
11. C₁₃×#1882	C₂	semidirect
12. C₁₃×#1876	C₂	semidirect
13. C₁₃×#1859	C₂	semidirect
14. C₁₃×#1816	C₂	semidirect
15. C₁₃×#1793	C₂	semidirect
159. #24931	C₁₃	direct (N × H)
263. #3098	C₂×C₁₃	semidirect
265. #2951	C₂×C₁₃	semidirect
266. #2898	C₂×C₁₃	semidirect
267. #2095	C₂×C₁₃	semidirect
268. #2078	C₂×C₁₃	semidirect
269. #2052	C₂×C₁₃	semidirect
270. #2039	C₂×C₁₃	semidirect
271. #1930	C₂×C₁₃	semidirect
272. #1929	C₂×C₁₃	semidirect
273. #1882	C₂×C₁₃	semidirect
274. #1876	C₂×C₁₃	semidirect
275. #1859	C₂×C₁₃	semidirect
276. #1816	C₂×C₁₃	semidirect
277. #1793	C₂×C₁₃	semidirect
630. C₁₃	#24931	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×#3013	2
C₁₃×#2951	2
C₁₃×#2898	2
C₁₃×#2095	2
C₁₃×#2078	2
C₁₃×#2052	2
C₁₃×#2039	2
C₁₃×#1930	2
C₁₃×#1929	2
C₁₃×#1882	2
C₁₃×#1876	2
C₁₃×#1859	2
C₁₃×#1816	2
C₁₃×#1793	2
#24931	13

Subgroups — C13×#24931 #15711270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24931 #15711270