Subgroups — C₁₃×#24915 #15711254

Order 3328.

1036 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#449	—	2	4	no	—
24	C₁₃×#442	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#394	—	2	1	no	—
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#386	—	2	1	no	—
46	C₁₃×#386	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#382	C₂²	1	1	yes	characteristic
49	C₁₃×#381	—	2	1	no	—
50	C₁₃×#381	—	2	1	no	—
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#95	—	2	1	no	—
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	—	4	1	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	4	1	no	—
80	C₂×C₁₃×D₈	—	2	2	no	—
81	C₂×C₁₃×D₈	—	2	2	no	—
82	C₂×C₁₃×D₈	D₄	1	4	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	4	1	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	4	1	no	—
93	C₄×D₄×C₁₃	—	4	1	no	—
94	C₄×D₄×C₁₃	—	4	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	—	4	1	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×C₄⋊C₈	—	4	1	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	4	1	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	4	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×C₂²⋊C₈	—	4	1	no	—
126	C₁₃×#97	—	2	2	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	D₄	1	1	yes	characteristic
137	C₁₃×#95	D₄	1	1	yes	characteristic
138	#24915	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	—	2	1	no	—
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	#41	1	2	yes	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	4	2	no	—
162	C₂×D₄×C₁₃	—	4	2	no	—
163	C₂×D₄×C₁₃	—	4	2	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	—	8	1	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂×D₄×C₁₃	#41	1	2	yes	—
169	C₂×D₄×C₁₃	#41	1	2	yes	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	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	—	4	2	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	4	2	no	—
190	C₂²×C₄×C₁₃	—	4	2	no	—
191	C₂²×C₄×C₁₃	—	8	1	no	—
192	C₂²×C₄×C₁₃	—	8	1	no	—
193	C₂²×C₄×C₁₃	—	8	1	no	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₁₃×SD₁₆	—	4	4	no	—
201	C₁₃×D₈	—	2	8	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	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	C₂×D₄	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	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	8	1	no	—
225	C₁₃×C₂²⋊C₄	—	4	1	no	—
226	C₁₃×C₂²⋊C₄	—	4	1	no	—
227	C₁₃×C₂²⋊C₄	—	4	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	2	no	—
229	C₁₃×C₂²⋊C₄	—	4	2	no	—
230	C₁₃×C₂²⋊C₄	—	4	2	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₁₃×C₂²⋊C₄	—	8	1	no	—
233	C₁₃×C₂²⋊C₄	—	8	1	no	—
234	C₁₃×C₂²⋊C₄	—	8	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	2	1	no	—
237	C₄²×C₁₃	—	2	1	no	—
238	C₄²×C₁₃	—	2	1	no	—
239	C₂×#449	C₂×C₁₃	1	1	yes	characteristic
240	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2420	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2097	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1924	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₁₃	—	2	2	no	—
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	—	4	1	no	—
279	Q₈×C₁₃	—	4	1	no	—
280	D₄×C₁₃	—	2	2	no	—
281	D₄×C₁₃	—	2	2	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	2	2	no	—
284	D₄×C₁₃	—	2	2	no	—
285	D₄×C₁₃	—	4	8	no	—
286	D₄×C₁₃	—	4	1	no	—
287	D₄×C₁₃	—	4	1	no	—
288	D₄×C₁₃	—	8	4	no	—
289	D₄×C₁₃	#123	1	4	yes	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	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	—	2	1	no	—
306	C₂×C₄×C₁₃	—	4	8	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	—	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	—	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	—	8	4	no	—
329	C₂×C₄×C₁₃	—	8	4	no	—
330	C₂×C₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
337	C₈×C₁₃	—	2	2	no	—
338	C₈×C₁₃	—	4	1	no	—
339	C₈×C₁₃	—	4	1	no	—
340	C₈×C₁₃	—	4	1	no	—
341	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
343	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
348	#449	—	2	4	no	—
349	#442	—	2	4	no	—
350	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
364	#397	—	2	1	no	—
365	#394	—	2	1	no	—
366	#391	C₂²×C₁₃	1	1	yes	characteristic
367	#391	C₂²×C₁₃	1	1	yes	characteristic
368	#390	C₂²×C₁₃	1	1	yes	characteristic
369	#389	C₂²×C₁₃	1	1	yes	characteristic
370	#386	—	2	1	no	—
371	#386	—	2	1	no	—
372	#386	—	2	1	no	—
373	#382	C₂²×C₁₃	1	1	yes	characteristic
374	#381	—	2	1	no	—
375	#381	—	2	1	no	—
376	#380	C₂²×C₁₃	1	1	yes	characteristic
377	#380	C₂²×C₁₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#95	—	2	1	no	—
380	#340	C₂²×C₁₃	1	1	yes	characteristic
381	#340	C₂²×C₁₃	1	1	yes	characteristic
382	#340	C₂²×C₁₃	1	1	yes	characteristic
383	#340	C₂²×C₁₃	1	1	yes	characteristic
384	#336	C₂²×C₁₃	1	1	yes	characteristic
385	#336	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₁₃	—	2	4	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	2	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	2	no	—
398	C₂²×C₁₃	—	4	1	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	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	—	8	1	no	—
407	C₂²×C₁₃	#525	1	1	yes	characteristic
408	C₂²×C₁₃	D₄²	1	1	yes	characteristic
409	C₂²×C₁₃	#546	1	1	yes	characteristic
410	C₂²×C₁₃	#575	1	1	yes	characteristic
411	C₂²×C₁₃	#575	1	1	yes	characteristic
412	C₂²×C₁₃	#576	1	1	yes	characteristic
413	C₂²×C₁₃	#577	1	1	yes	characteristic
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	1	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	—	8	1	no	—
424	C₄×C₁₃	—	8	1	no	—
425	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
426	C₄×C₁₃	#538	1	1	yes	characteristic
427	C₄×C₁₃	#546	1	1	yes	characteristic
428	C₄×C₁₃	#551	1	1	yes	characteristic
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	2	2	no	—
431	C₂×#41	—	2	2	no	—
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	4	1	no	—
434	C₂×#41	—	4	1	no	—
435	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	—	2	1	no	—
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	4	1	no	—
448	C₂×D₈	—	2	2	no	—
449	C₂×D₈	—	2	2	no	—
450	C₂×D₈	D₄×C₁₃	1	4	yes	—
451	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
455	#121	—	2	2	no	—
456	#121	—	4	1	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	4	1	no	—
461	C₄×D₄	—	4	1	no	—
462	C₄×D₄	—	4	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	#107	—	4	1	no	—
482	#106	—	2	2	no	—
483	C₄⋊C₈	—	4	1	no	—
484	#103	—	2	2	no	—
485	#103	—	2	2	no	—
486	#103	—	4	1	no	—
487	#102	—	2	2	no	—
488	#102	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	4	1	no	—
492	C₂²⋊C₈	—	2	2	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	#97	—	2	2	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	D₄×C₁₃	1	1	yes	characteristic
505	#95	D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₁₃	—	4	4	no	—
507	C₂×C₁₃	—	8	1	no	—
508	C₂×C₁₃	—	8	2	no	—
509	C₂×C₁₃	#2418	1	1	yes	characteristic
510	C₂×C₁₃	#3111	1	1	yes	characteristic
511	C₂×C₁₃	#3119	1	1	yes	characteristic
512	C₂×C₁₃	#3267	1	1	yes	characteristic
513	C₂×C₁₃	#3273	1	1	yes	characteristic
514	C₂×C₁₃	#3307	1	1	yes	characteristic
515	C₂×C₁₃	#3319	1	1	yes	characteristic
516	C₂⁴	—	2	1	no	—
517	C₂⁴	—	2	1	no	—
518	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
519	#41	—	4	4	no	—
520	#41	—	4	4	no	—
521	#41	—	4	4	no	—
522	#41	—	4	4	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	C₁₃×#41	1	2	yes	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	8	1	no	—
543	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
544	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
545	C₂×D₄	C₁₃×#41	1	2	yes	—
546	C₂×D₄	C₁₃×#41	1	2	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	8	1	no	—
569	C₂²×C₄	—	8	1	no	—
570	C₂²×C₄	—	8	1	no	—
571	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
577	SD₁₆	—	4	4	no	—
578	D₈	—	2	8	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	8	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₂²⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₂²⋊C₄	—	8	1	no	—
610	C₂²⋊C₄	—	8	1	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₁₃	#24915	1	1	yes	characteristic, direct product factor, Sylow
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	4	8	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	8	4	no	—
652	D₄	C₁₃×#123	1	4	yes	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	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	1	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	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	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
696	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
697	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
698	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
700	C₈	—	2	2	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	C₁₃×#525	1	1	yes	characteristic
726	C₂²	D₄²×C₁₃	1	1	yes	characteristic
727	C₂²	C₁₃×#546	1	1	yes	characteristic
728	C₂²	C₁₃×#575	1	1	yes	characteristic
729	C₂²	C₁₃×#575	1	1	yes	characteristic
730	C₂²	C₁₃×#576	1	1	yes	characteristic
731	C₂²	C₁₃×#577	1	1	yes	characteristic
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	2	no	—
738	C₄	—	8	1	no	—
739	C₄	—	8	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	—	8	1	no	—
743	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
744	C₄	C₁₃×#538	1	1	yes	characteristic
745	C₄	C₁₃×#546	1	1	yes	characteristic
746	C₄	C₁₃×#551	1	1	yes	characteristic
747	C₂	—	4	4	no	—
748	C₂	—	8	1	no	—
749	C₂	—	8	2	no	—
750	C₂	C₁₃×#2418	1	1	yes	characteristic
751	C₂	C₁₃×#3111	1	1	yes	characteristic
752	C₂	C₁₃×#3119	1	1	yes	characteristic
753	C₂	C₁₃×#3267	1	1	yes	characteristic
754	C₂	C₁₃×#3273	1	1	yes	characteristic
755	C₂	C₁₃×#3307	1	1	yes	characteristic
756	C₂	C₁₃×#3319	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#442	C₂	semidirect
3. C₁₃×#2420	C₂	semidirect
4. C₁₃×#2339	C₂	semidirect
5. C₁₃×#2097	C₂	semidirect
6. C₁₃×#2077	C₂	semidirect
7. C₁₃×#2055	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1935	C₂	semidirect
10. C₁₃×#1924	C₂	semidirect
11. C₁₃×#1879	C₂	semidirect
12. C₁₃×#1877	C₂	semidirect
13. C₁₃×#1862	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
138. #24915	C₁₃	direct (N × H)
240. C₂×#442	C₂×C₁₃	semidirect
241. #2420	C₂×C₁₃	semidirect
242. #2339	C₂×C₁₃	semidirect
243. #2097	C₂×C₁₃	semidirect
244. #2077	C₂×C₁₃	semidirect
245. #2055	C₂×C₁₃	semidirect
246. #2033	C₂×C₁₃	semidirect
247. #1935	C₂×C₁₃	semidirect
248. #1924	C₂×C₁₃	semidirect
249. #1879	C₂×C₁₃	semidirect
250. #1877	C₂×C₁₃	semidirect
251. #1862	C₂×C₁₃	semidirect
252. #1804	C₂×C₁₃	semidirect
253. #1788	C₂×C₁₃	semidirect
616. C₁₃	#24915	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×#449	2
C₂×C₁₃×#442	2
C₁₃×#2420	2
C₁₃×#2339	2
C₁₃×#2097	2
C₁₃×#2077	2
C₁₃×#2055	2
C₁₃×#2033	2
C₁₃×#1935	2
C₁₃×#1924	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1862	2
C₁₃×#1804	2
C₁₃×#1788	2
#24915	13

Subgroups — C13×#24915 #15711254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24915 #15711254