Subgroups — C₁₃×#25054 #15711393

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₁₃×#537	C₂²	1	1	yes	characteristic
19	C₁₃×#537	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	1	yes	characteristic
22	C₁₃×#485	—	2	1	no	—
23	C₁₃×#485	—	2	1	no	—
24	C₁₃×#484	—	2	1	no	—
25	C₁₃×#483	—	2	1	no	—
26	C₁₃×#482	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#481	—	2	1	no	—
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#468	—	2	1	no	—
31	C₁₃×#468	—	2	1	no	—
32	C₁₃×#467	—	2	1	no	—
33	C₁₃×#466	—	2	1	no	—
34	C₁₃×#442	—	2	1	no	—
35	C₁₃×#441	—	2	1	no	—
36	C₄×C₁₃×SD₁₆	—	2	1	no	—
37	C₄×C₁₃×SD₁₆	—	2	1	no	—
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#104	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×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#417	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₁₃×#417	C₂²	1	1	yes	characteristic
54	C₁₃×#416	C₂²	1	1	yes	characteristic
55	C₁₃×#408	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×#384	C₂²	1	1	yes	characteristic
60	C₁₃×#382	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×#343	C₂²	1	1	yes	characteristic
65	C₁₃×#341	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	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₁₃×#135	—	2	2	no	—
71	C₁₃×#135	—	2	2	no	—
72	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
76	C₁₃×#131	—	2	2	no	—
77	C₁₃×#131	—	2	2	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
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	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	—	2	1	no	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	4	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	4	1	no	—
101	C₄×D₄×C₁₃	—	4	1	no	—
102	C₁₃×#117	—	2	1	no	—
103	C₁₃×#117	—	2	1	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#108	—	2	2	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#106	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#104	—	2	2	no	—
127	C₁₃×#104	—	2	2	no	—
128	C₁₃×#104	—	2	2	no	—
129	C₁₃×#103	—	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	D₄	1	1	yes	characteristic
136	C₁₃×#103	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
144	C₁₃×#102	D₄	1	1	yes	characteristic
145	C₁₃×C₂²⋊C₈	—	2	1	no	—
146	C₁₃×C₂²⋊C₈	—	2	1	no	—
147	C₁₃×C₂²⋊C₈	—	2	1	no	—
148	C₁₃×C₂²⋊C₈	—	2	1	no	—
149	C₁₃×#97	—	2	1	no	—
150	C₁₃×#97	—	2	2	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₁₃×#95	—	4	1	no	—
153	#25054	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₁₃×#41	—	2	1	no	—
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	—	2	1	no	—
159	C₁₃×#41	—	2	1	no	—
160	C₁₃×#41	—	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	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
173	C₂×D₄×C₁₃	—	4	1	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	4	1	no	—
186	C₂²×C₄×C₁₃	—	4	1	no	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×Q₁₆	—	2	2	no	—
189	C₁₃×SD₁₆	—	2	2	no	—
190	C₁₃×SD₁₆	—	2	2	no	—
191	C₁₃×D₈	—	2	2	no	—
192	C₁₃×M₁₆	—	2	1	no	—
193	C₁₃×M₁₆	—	2	1	no	—
194	C₁₃×M₁₆	—	2	1	no	—
195	C₁₃×M₁₆	—	2	1	no	—
196	C₁₃×M₁₆	—	2	1	no	—
197	C₁₃×M₁₆	—	2	1	no	—
198	C₁₃×M₁₆	—	2	1	no	—
199	C₁₃×M₁₆	—	2	1	no	—
200	C₁₃×M₁₆	—	4	2	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	4	2	no	—
208	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₈×C₁₃	#41	1	2	yes	—
213	C₂×C₈×C₁₃	#41	1	2	yes	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	4	1	no	—
223	C₁₃×C₄⋊C₄	—	4	1	no	—
224	C₁₃×C₄⋊C₄	—	4	1	no	—
225	C₁₃×C₄⋊C₄	—	4	1	no	—
226	C₁₃×C₄⋊C₄	—	8	2	no	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₁₃×C₂²⋊C₄	—	2	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	1	no	—
231	C₁₃×C₂²⋊C₄	—	4	1	no	—
232	C₁₃×C₂²⋊C₄	—	4	1	no	—
233	C₁₃×C₂²⋊C₄	—	4	1	no	—
234	C₁₃×C₂²⋊C₄	—	4	1	no	—
235	C₁₃×C₂²⋊C₄	—	4	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	C₄²×C₁₃	#41	1	2	yes	—
241	#3099	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3061	C₂×C₁₃	1	1	yes	characteristic
244	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2079	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2078	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1975	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#1765	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
260	Q₈×C₁₃	—	2	1	no	—
261	Q₈×C₁₃	—	2	1	no	—
262	Q₈×C₁₃	—	2	1	no	—
263	Q₈×C₁₃	—	2	1	no	—
264	Q₈×C₁₃	—	2	1	no	—
265	Q₈×C₁₃	—	2	1	no	—
266	D₄×C₁₃	—	2	1	no	—
267	D₄×C₁₃	—	2	1	no	—
268	D₄×C₁₃	—	2	1	no	—
269	D₄×C₁₃	—	2	1	no	—
270	D₄×C₁₃	—	2	1	no	—
271	D₄×C₁₃	—	2	1	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	16	1	no	—
279	D₄×C₁₃	—	16	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	2	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	8	1	no	—
299	C₂×C₄×C₁₃	—	8	1	no	—
300	C₂×C₄×C₁₃	—	8	1	no	—
301	C₂×C₄×C₁₃	—	8	1	no	—
302	C₂×C₄×C₁₃	—	16	1	no	—
303	C₂×C₄×C₁₃	—	16	1	no	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
310	C₈×C₁₃	—	2	1	no	—
311	C₈×C₁₃	—	2	1	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₈×C₁₃	—	4	1	no	—
315	C₈×C₁₃	—	4	1	no	—
316	C₈×C₁₃	#123	1	2	yes	—
317	C₈×C₁₃	#123	1	2	yes	—
318	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
320	#537	C₂²×C₁₃	1	1	yes	characteristic
321	#537	C₂²×C₁₃	1	1	yes	characteristic
322	#520	C₂²×C₁₃	1	1	yes	characteristic
323	#520	C₂²×C₁₃	1	1	yes	characteristic
324	#485	—	2	1	no	—
325	#485	—	2	1	no	—
326	#484	—	2	1	no	—
327	#483	—	2	1	no	—
328	#482	—	2	1	no	—
329	#482	—	2	1	no	—
330	#481	—	2	1	no	—
331	#480	—	2	1	no	—
332	#468	—	2	1	no	—
333	#468	—	2	1	no	—
334	#467	—	2	1	no	—
335	#466	—	2	1	no	—
336	#442	—	2	1	no	—
337	#441	—	2	1	no	—
338	C₄×SD₁₆	—	2	1	no	—
339	C₄×SD₁₆	—	2	1	no	—
340	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
341	#428	C₂²×C₁₃	1	1	yes	characteristic
342	#428	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
350	#417	C₂²×C₁₃	1	1	yes	characteristic
351	#417	C₂²×C₁₃	1	1	yes	characteristic
352	#417	C₂²×C₁₃	1	1	yes	characteristic
353	#417	C₂²×C₁₃	1	1	yes	characteristic
354	#417	C₂²×C₁₃	1	1	yes	characteristic
355	#417	C₂²×C₁₃	1	1	yes	characteristic
356	#416	C₂²×C₁₃	1	1	yes	characteristic
357	#408	C₂²×C₁₃	1	1	yes	characteristic
358	#408	C₂²×C₁₃	1	1	yes	characteristic
359	#405	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
361	#384	C₂²×C₁₃	1	1	yes	characteristic
362	#382	C₂²×C₁₃	1	1	yes	characteristic
363	#343	C₂²×C₁₃	1	1	yes	characteristic
364	#343	C₂²×C₁₃	1	1	yes	characteristic
365	#343	C₂²×C₁₃	1	1	yes	characteristic
366	#343	C₂²×C₁₃	1	1	yes	characteristic
367	#341	C₂²×C₁₃	1	1	yes	characteristic
368	#339	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₁₃	—	2	1	no	—
370	C₂²×C₁₃	—	2	1	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	1	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	1	no	—
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	#542	1	1	yes	characteristic
381	C₂²×C₁₃	D₄²	1	1	yes	characteristic
382	C₂²×C₁₃	#553	1	1	yes	characteristic
383	C₄×C₁₃	—	4	2	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	—	4	1	no	—
389	C₄×C₁₃	—	8	1	no	—
390	C₄×C₁₃	—	8	1	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
394	C₄×C₁₃	#532	1	1	yes	characteristic
395	C₄×C₁₃	#547	1	1	yes	characteristic
396	C₄×C₁₃	#547	1	1	yes	characteristic
397	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
400	#135	—	2	2	no	—
401	#135	—	2	2	no	—
402	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
403	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
404	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
405	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
406	#131	—	2	2	no	—
407	#131	—	2	2	no	—
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×C₈	—	2	1	no	—
414	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²⋊Q₈	—	2	1	no	—
417	C₂²⋊Q₈	—	2	1	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	#121	—	2	1	no	—
421	#121	—	2	1	no	—
422	#121	—	2	1	no	—
423	#121	—	2	1	no	—
424	#121	—	4	1	no	—
425	#121	—	4	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	4	1	no	—
431	C₄×D₄	—	4	1	no	—
432	#117	—	2	1	no	—
433	#117	—	2	1	no	—
434	#117	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	4	1	no	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	#108	—	2	2	no	—
444	#107	—	2	1	no	—
445	#107	—	2	1	no	—
446	#107	—	2	1	no	—
447	#107	—	2	1	no	—
448	#107	—	2	1	no	—
449	#107	—	2	1	no	—
450	#106	—	2	1	no	—
451	#106	—	2	1	no	—
452	#106	—	2	1	no	—
453	#106	—	2	1	no	—
454	#106	—	2	1	no	—
455	#106	—	2	1	no	—
456	#104	—	2	2	no	—
457	#104	—	2	2	no	—
458	#104	—	2	2	no	—
459	#103	—	2	1	no	—
460	#103	—	2	1	no	—
461	#103	—	2	1	no	—
462	#103	—	2	1	no	—
463	#103	—	2	1	no	—
464	#103	—	2	1	no	—
465	#103	D₄×C₁₃	1	1	yes	characteristic
466	#103	D₄×C₁₃	1	1	yes	characteristic
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	#102	D₄×C₁₃	1	1	yes	characteristic
474	#102	D₄×C₁₃	1	1	yes	characteristic
475	C₂²⋊C₈	—	2	1	no	—
476	C₂²⋊C₈	—	2	1	no	—
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	#97	—	2	1	no	—
480	#97	—	2	2	no	—
481	C₄×C₈	—	2	1	no	—
482	#95	—	4	1	no	—
483	C₂×C₁₃	—	2	1	no	—
484	C₂×C₁₃	—	2	1	no	—
485	C₂×C₁₃	—	8	1	no	—
486	C₂×C₁₃	—	8	1	no	—
487	C₂×C₁₃	—	8	1	no	—
488	C₂×C₁₃	#2422	1	1	yes	characteristic
489	C₂×C₁₃	#3288	1	1	yes	characteristic
490	C₂×C₁₃	#3289	1	1	yes	characteristic
491	#41	—	2	1	no	—
492	#41	—	2	1	no	—
493	#41	—	2	1	no	—
494	#41	—	2	1	no	—
495	#41	—	2	1	no	—
496	#41	—	2	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	—	2	1	no	—
503	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	4	1	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	Q₁₆	—	2	2	no	—
526	SD₁₆	—	2	2	no	—
527	SD₁₆	—	2	2	no	—
528	D₈	—	2	2	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	4	2	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	4	2	no	—
545	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₈	C₁₃×#41	1	2	yes	—
550	C₂×C₈	C₁₃×#41	1	2	yes	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	4	1	no	—
560	C₄⋊C₄	—	4	1	no	—
561	C₄⋊C₄	—	4	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	—	8	2	no	—
564	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	4	1	no	—
576	C₄²	—	4	1	no	—
577	C₄²	C₁₃×#41	1	2	yes	—
578	C₁₃	#25054	1	1	yes	characteristic, direct product factor, Sylow
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
583	Q₈	—	2	1	no	—
584	Q₈	—	2	1	no	—
585	Q₈	—	2	1	no	—
586	Q₈	—	2	1	no	—
587	Q₈	—	2	1	no	—
588	Q₈	—	2	1	no	—
589	D₄	—	2	1	no	—
590	D₄	—	2	1	no	—
591	D₄	—	2	1	no	—
592	D₄	—	2	1	no	—
593	D₄	—	2	1	no	—
594	D₄	—	2	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	16	1	no	—
602	D₄	—	16	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	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	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	1	no	—
622	C₂×C₄	—	8	1	no	—
623	C₂×C₄	—	8	1	no	—
624	C₂×C₄	—	8	1	no	—
625	C₂×C₄	—	16	1	no	—
626	C₂×C₄	—	16	1	no	—
627	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
630	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
631	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
632	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
633	C₈	—	2	1	no	—
634	C₈	—	2	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₈	C₁₃×#123	1	2	yes	—
640	C₈	C₁₃×#123	1	2	yes	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	C₁₃×#542	1	1	yes	characteristic
653	C₂²	D₄²×C₁₃	1	1	yes	characteristic
654	C₂²	C₁₃×#553	1	1	yes	characteristic
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
666	C₄	C₁₃×#532	1	1	yes	characteristic
667	C₄	C₁₃×#547	1	1	yes	characteristic
668	C₄	C₁₃×#547	1	1	yes	characteristic
669	C₂	—	2	1	no	—
670	C₂	—	2	1	no	—
671	C₂	—	8	1	no	—
672	C₂	—	8	1	no	—
673	C₂	—	8	1	no	—
674	C₂	C₁₃×#2422	1	1	yes	characteristic
675	C₂	C₁₃×#3288	1	1	yes	characteristic
676	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×#3061	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×#3099	C₂	semidirect
2. C₁₃×#3098	C₂	semidirect
4. C₁₃×#2952	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2078	C₂	semidirect
7. C₁₃×#2040	C₂	semidirect
8. C₁₃×#2039	C₂	semidirect
9. C₁₃×#1975	C₂	semidirect
10. C₁₃×#1952	C₂	semidirect
11. C₁₃×#1860	C₂	semidirect
12. C₁₃×#1859	C₂	semidirect
13. C₁₃×#1847	C₂	semidirect
14. C₁₃×#1815	C₂	semidirect
15. C₁₃×#1765	C₂	semidirect
153. #25054	C₁₃	direct (N × H)
241. #3099	C₂×C₁₃	semidirect
242. #3098	C₂×C₁₃	semidirect
244. #2952	C₂×C₁₃	semidirect
245. #2079	C₂×C₁₃	semidirect
246. #2078	C₂×C₁₃	semidirect
247. #2040	C₂×C₁₃	semidirect
248. #2039	C₂×C₁₃	semidirect
249. #1975	C₂×C₁₃	semidirect
250. #1952	C₂×C₁₃	semidirect
251. #1860	C₂×C₁₃	semidirect
252. #1859	C₂×C₁₃	semidirect
253. #1847	C₂×C₁₃	semidirect
254. #1815	C₂×C₁₃	semidirect
255. #1765	C₂×C₁₃	semidirect
578. C₁₃	#25054	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×#3099	2
C₁₃×#3098	2
C₁₃×#3061	2
C₁₃×#2952	2
C₁₃×#2079	2
C₁₃×#2078	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#1975	2
C₁₃×#1952	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1847	2
C₁₃×#1815	2
C₁₃×#1765	2
#25054	13

Subgroups — C13×#25054 #15711393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25054 #15711393