Subgroups — C₁₃×#29039 #15715378

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2428	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#126	—	2	1	no	—
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#400	—	2	1	no	—
37	C₁₃×#397	—	2	1	no	—
38	C₁₃×#394	—	2	1	no	—
39	C₁₃×#392	—	2	1	no	—
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#386	—	2	1	no	—
46	C₁₃×#384	C₂²	1	1	yes	characteristic
47	C₁₃×#380	C₂²	1	1	yes	characteristic
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	—	2	2	no	—
68	C₂²×C₈×C₁₃	—	4	1	no	—
69	C₂²×C₈×C₁₃	—	4	1	no	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#127	—	2	2	no	—
75	C₁₃×#127	—	4	1	no	—
76	C₁₃×#126	—	4	4	no	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	4	1	no	—
80	C₁₃×#121	—	4	1	no	—
81	C₁₃×#121	—	4	4	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	4	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#107	—	4	1	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×#102	—	4	1	no	—
115	C₁₃×#102	—	4	1	no	—
116	C₁₃×#102	—	4	1	no	—
117	C₁₃×C₂²⋊C₈	—	2	2	no	—
118	C₄×C₈×C₁₃	—	4	1	no	—
119	C₄×C₈×C₁₃	—	4	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	D₄	1	1	yes	characteristic
127	C₁₃×#95	D₄	1	1	yes	characteristic
128	#29039	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₂⁴×C₁₃	—	2	1	no	—
131	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	4	2	no	—
144	C₂×D₄×C₁₃	—	4	2	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	—	4	2	no	—
147	C₂×D₄×C₁₃	—	4	2	no	—
148	C₂×D₄×C₁₃	—	4	2	no	—
149	C₂×D₄×C₁₃	—	4	2	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	8	1	no	—
152	C₂×D₄×C₁₃	—	8	1	no	—
153	C₂×D₄×C₁₃	—	8	1	no	—
154	C₂×D₄×C₁₃	—	8	1	no	—
155	C₂×D₄×C₁₃	#41	1	2	yes	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	8	1	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	4	4	no	—
188	C₂×C₈×C₁₃	#41	1	2	yes	—
189	C₂×C₈×C₁₃	#41	1	2	yes	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	4	2	no	—
203	C₁₃×C₄⋊C₄	—	4	2	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	#41	1	2	yes	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	—	4	2	no	—
212	C₁₃×C₂²⋊C₄	—	4	2	no	—
213	C₁₃×C₂²⋊C₄	—	4	2	no	—
214	C₁₃×C₂²⋊C₄	—	8	1	no	—
215	C₁₃×C₂²⋊C₄	D₈	1	4	yes	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	2	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	4	2	no	—
221	#2496	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2428	C₂×C₁₃	1	1	yes	characteristic
223	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	C₂×D₈	1	2	yes	—
257	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	1	no	—
265	D₄×C₁₃	—	4	1	no	—
266	D₄×C₁₃	—	8	4	no	—
267	D₄×C₁₃	—	8	4	no	—
268	D₄×C₁₃	—	8	4	no	—
269	D₄×C₁₃	—	8	4	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	8	4	no	—
305	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
306	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
307	C₂×C₄×C₁₃	#135	1	2	yes	—
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
314	C₈×C₁₃	—	2	2	no	—
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#126	—	2	1	no	—
321	C₂×#121	—	2	1	no	—
322	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
338	#400	—	2	1	no	—
339	#397	—	2	1	no	—
340	#394	—	2	1	no	—
341	#392	—	2	1	no	—
342	#390	C₂²×C₁₃	1	1	yes	characteristic
343	#389	C₂²×C₁₃	1	1	yes	characteristic
344	#389	C₂²×C₁₃	1	1	yes	characteristic
345	#389	C₂²×C₁₃	1	1	yes	characteristic
346	#387	—	2	1	no	—
347	#386	—	2	1	no	—
348	#384	C₂²×C₁₃	1	1	yes	characteristic
349	#380	C₂²×C₁₃	1	1	yes	characteristic
350	#380	C₂²×C₁₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
353	#340	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#340	C₂²×C₁₃	1	1	yes	characteristic
356	#340	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#336	C₂²×C₁₃	1	1	yes	characteristic
360	#336	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	2	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	—	4	2	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	8	1	no	—
372	C₂²×C₁₃	—	8	1	no	—
373	C₂²×C₁₃	—	8	1	no	—
374	C₂²×C₁₃	—	8	1	no	—
375	C₂²×C₁₃	—	8	1	no	—
376	C₂²×C₁₃	—	8	1	no	—
377	C₂²×C₁₃	—	8	1	no	—
378	C₂²×C₁₃	—	8	1	no	—
379	C₂²×C₁₃	—	8	1	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	#532	1	1	yes	characteristic
383	C₂²×C₁₃	#546	1	1	yes	characteristic
384	C₂²×C₁₃	#546	1	1	yes	characteristic
385	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
386	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
387	C₂²×C₁₃	#577	1	1	yes	characteristic
388	C₂²×C₁₃	#577	1	1	yes	characteristic
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	2	2	no	—
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	4	2	no	—
393	C₄×C₁₃	—	4	1	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	8	1	no	—
396	C₄×C₁₃	—	8	1	no	—
397	C₄×C₁₃	—	8	1	no	—
398	C₄×C₁₃	—	8	1	no	—
399	C₄×C₁₃	—	8	1	no	—
400	C₄×C₁₃	#529	1	1	yes	characteristic
401	C₄×C₁₃	#538	1	1	yes	characteristic
402	C₄×C₁₃	#553	1	1	yes	characteristic
403	C₄×C₁₃	#553	1	1	yes	characteristic
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×C₈	—	2	2	no	—
413	C₂²×C₈	—	4	1	no	—
414	C₂²×C₈	—	4	1	no	—
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	#127	—	2	2	no	—
420	#127	—	4	1	no	—
421	#126	—	4	4	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#121	—	4	1	no	—
425	#121	—	4	1	no	—
426	#121	—	4	4	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	4	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
452	#107	—	2	2	no	—
453	#107	—	4	1	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	#102	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	4	1	no	—
460	#102	—	4	1	no	—
461	#102	—	4	1	no	—
462	C₂²⋊C₈	—	2	2	no	—
463	C₄×C₈	—	4	1	no	—
464	C₄×C₈	—	4	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	D₄×C₁₃	1	1	yes	characteristic
472	#95	D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₁₃	—	4	2	no	—
474	C₂×C₁₃	—	8	2	no	—
475	C₂×C₁₃	—	16	1	no	—
476	C₂×C₁₃	#2559	1	1	yes	characteristic
477	C₂×C₁₃	#3169	1	1	yes	characteristic
478	C₂×C₁₃	#3174	1	1	yes	characteristic
479	C₂×C₁₃	#3294	1	1	yes	characteristic
480	C₂×C₁₃	#3294	1	1	yes	characteristic
481	C₂×C₁₃	#3296	1	1	yes	characteristic
482	C₂×C₁₃	#3304	1	1	yes	characteristic
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	4	2	no	—
505	C₂×D₄	—	8	1	no	—
506	C₂×D₄	—	8	1	no	—
507	C₂×D₄	—	8	1	no	—
508	C₂×D₄	—	8	1	no	—
509	C₂×D₄	C₁₃×#41	1	2	yes	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
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	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	4	4	no	—
542	C₂×C₈	C₁₃×#41	1	2	yes	—
543	C₂×C₈	C₁₃×#41	1	2	yes	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	C₁₃×#41	1	2	yes	—
561	C₂²⋊C₄	—	2	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	C₁₃×D₈	1	4	yes	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	4	2	no	—
575	C₁₃	#29039	1	1	yes	characteristic, direct product factor, Sylow
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	C₂×C₁₃×D₈	1	2	yes	—
597	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	D₄	—	2	2	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	8	4	no	—
607	D₄	—	8	4	no	—
608	D₄	—	8	4	no	—
609	D₄	—	8	4	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
646	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
647	C₂×C₄	C₁₃×#135	1	2	yes	—
648	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
649	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
650	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
651	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
652	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	C₁₃×#532	1	1	yes	characteristic
680	C₂²	C₁₃×#546	1	1	yes	characteristic
681	C₂²	C₁₃×#546	1	1	yes	characteristic
682	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
683	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
684	C₂²	C₁₃×#577	1	1	yes	characteristic
685	C₂²	C₁₃×#577	1	1	yes	characteristic
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	C₁₃×#529	1	1	yes	characteristic
698	C₄	C₁₃×#538	1	1	yes	characteristic
699	C₄	C₁₃×#553	1	1	yes	characteristic
700	C₄	C₁₃×#553	1	1	yes	characteristic
701	C₂	—	4	2	no	—
702	C₂	—	8	2	no	—
703	C₂	—	16	1	no	—
704	C₂	C₁₃×#2559	1	1	yes	characteristic
705	C₂	C₁₃×#3169	1	1	yes	characteristic
706	C₂	C₁₃×#3174	1	1	yes	characteristic
707	C₂	C₁₃×#3294	1	1	yes	characteristic
708	C₂	C₁₃×#3294	1	1	yes	characteristic
709	C₂	C₁₃×#3296	1	1	yes	characteristic
710	C₂	C₁₃×#3304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2428	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
1. C₁₃×#2496	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2041	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#2033	C₂	semidirect
7. C₁₃×#1957	C₂	semidirect
8. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1934	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1893	C₂	semidirect
12. C₁₃×#1893	C₂	semidirect
13. C₁₃×#1862	C₂	semidirect
14. C₄×C₁₃×#102	C₂	semidirect
15. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
128. #29039	C₁₃	direct (N × H)
221. #2496	C₂×C₁₃	semidirect
223. #2099	C₂×C₁₃	semidirect
224. #2041	C₂×C₁₃	semidirect
225. #2033	C₂×C₁₃	semidirect
226. #2033	C₂×C₁₃	semidirect
227. #1957	C₂×C₁₃	semidirect
228. #1942	C₂×C₁₃	semidirect
229. #1934	C₂×C₁₃	semidirect
230. #1925	C₂×C₁₃	semidirect
231. #1893	C₂×C₁₃	semidirect
232. #1893	C₂×C₁₃	semidirect
233. #1862	C₂×C₁₃	semidirect
234. C₄×#102	C₂×C₁₃	semidirect
235. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
575. C₁₃	#29039	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×#2496	2
C₁₃×#2428	2
C₁₃×#2099	2
C₁₃×#2041	2
C₁₃×#2033	2
C₁₃×#1957	2
C₁₃×#1942	2
C₁₃×#1934	2
C₁₃×#1925	2
C₁₃×#1893	2
C₁₃×#1862	2
C₄×C₁₃×#102	2
C₈×C₁₃×C₂²⋊C₄	2
#29039	13

Subgroups — C13×#29039 #15715378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29039 #15715378