Subgroups — C₁₃×#25953 #15712292

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₃×#416	—	2	4	no	—
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	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×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#399	—	2	1	no	—
40	C₁₃×#396	—	2	1	no	—
41	C₁₃×#390	—	2	1	no	—
42	C₁₃×#390	—	2	1	no	—
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#389	—	2	1	no	—
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#387	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#380	—	2	1	no	—
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	—	4	1	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	Q₈	1	4	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	—	4	1	no	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	—	4	1	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	—	4	1	no	—
84	C₄×Q₈×C₁₃	—	4	1	no	—
85	C₁₃×#117	—	2	2	no	—
86	C₁₃×#117	—	4	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#107	—	2	2	no	—
116	C₁₃×#106	—	2	2	no	—
117	C₁₃×#106	—	4	1	no	—
118	C₁₃×#106	—	4	1	no	—
119	C₁₃×C₄⋊C₈	—	2	2	no	—
120	C₁₃×C₄⋊C₈	—	4	1	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	2	2	no	—
123	C₁₃×#103	—	2	2	no	—
124	C₁₃×#103	D₄	1	4	yes	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	4	1	no	—
128	C₁₃×#102	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	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	D₄	1	1	yes	characteristic
135	C₁₃×#95	D₄	1	1	yes	characteristic
136	#25953	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₁₃×#41	—	2	8	no	—
140	C₁₃×#41	—	4	4	no	—
141	C₁₃×#41	—	4	4	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
148	C₂×Q₈×C₁₃	#41	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	2	no	—
156	C₂×D₄×C₁₃	—	4	2	no	—
157	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
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	4	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	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
178	C₂²×C₄×C₁₃	#41	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	4	4	no	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	2	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	8	1	no	—
211	C₁₃×C₄⋊C₄	—	8	1	no	—
212	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
213	C₁₃×C₂²⋊C₄	—	2	2	no	—
214	C₁₃×C₂²⋊C₄	—	4	1	no	—
215	C₁₃×C₂²⋊C₄	—	4	2	no	—
216	C₁₃×C₂²⋊C₄	—	4	2	no	—
217	C₁₃×C₂²⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	8	1	no	—
219	C₁₃×C₂²⋊C₄	—	8	1	no	—
220	C₁₃×C₂²⋊C₄	—	8	1	no	—
221	C₁₃×C₂²⋊C₄	—	8	1	no	—
222	C₄²×C₁₃	—	2	1	no	—
223	C₄²×C₁₃	—	2	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	4	2	no	—
227	C₄²×C₁₃	—	4	2	no	—
228	C₄²×C₁₃	—	4	2	no	—
229	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
231	#2441	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2341	C₂×C₁₃	1	1	yes	characteristic
233	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1788	C₂×C₁₃	1	1	yes	characteristic
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	—	2	2	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	—	4	1	no	—
257	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
258	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₁₃	—	2	2	no	—
260	Q₈×C₁₃	—	2	2	no	—
261	Q₈×C₁₃	—	2	2	no	—
262	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
263	D₄×C₁₃	—	2	2	no	—
264	D₄×C₁₃	—	2	2	no	—
265	D₄×C₁₃	—	4	8	no	—
266	D₄×C₁₃	—	4	1	no	—
267	D₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	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	2	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	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	4	8	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	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
308	C₂×C₄×C₁₃	#135	1	2	yes	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₈×C₁₃	—	4	1	no	—
319	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
320	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
325	#479	—	2	4	no	—
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
332	#416	—	2	4	no	—
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	#399	—	2	1	no	—
343	#396	—	2	1	no	—
344	#390	—	2	1	no	—
345	#390	—	2	1	no	—
346	#390	C₂²×C₁₃	1	1	yes	characteristic
347	#390	C₂²×C₁₃	1	1	yes	characteristic
348	#389	—	2	1	no	—
349	#389	C₂²×C₁₃	1	1	yes	characteristic
350	#389	C₂²×C₁₃	1	1	yes	characteristic
351	#387	—	2	1	no	—
352	#384	C₂²×C₁₃	1	1	yes	characteristic
353	#380	—	2	1	no	—
354	#380	C₂²×C₁₃	1	1	yes	characteristic
355	#380	C₂²×C₁₃	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	—	2	1	no	—
357	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#340	C₂²×C₁₃	1	1	yes	characteristic
360	#340	C₂²×C₁₃	1	1	yes	characteristic
361	#340	C₂²×C₁₃	1	1	yes	characteristic
362	#336	C₂²×C₁₃	1	1	yes	characteristic
363	#336	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₁₃	—	2	2	no	—
365	C₂²×C₁₃	—	2	2	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	1	no	—
371	C₂²×C₁₃	—	4	2	no	—
372	C₂²×C₁₃	—	4	2	no	—
373	C₂²×C₁₃	—	4	2	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	C₂×C₂²⋊Q₈	1	1	yes	characteristic
379	C₂²×C₁₃	D₄²	1	1	yes	characteristic
380	C₂²×C₁₃	#546	1	1	yes	characteristic
381	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
382	C₂²×C₁₃	#575	1	1	yes	characteristic
383	C₂²×C₁₃	#577	1	1	yes	characteristic
384	C₂²×C₁₃	#577	1	1	yes	characteristic
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	—	2	4	no	—
387	C₄×C₁₃	—	2	2	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	2	no	—
391	C₄×C₁₃	—	4	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	—	8	1	no	—
394	C₄×C₁₃	—	8	1	no	—
395	C₄×C₁₃	—	8	1	no	—
396	C₄×C₁₃	—	8	1	no	—
397	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
398	C₄×C₁₃	#543	1	1	yes	characteristic
399	C₄×C₁₃	#546	1	1	yes	characteristic
400	C₄×C₁₃	#551	1	1	yes	characteristic
401	C₂×#41	—	2	2	no	—
402	C₂×#41	—	2	2	no	—
403	C₂×#41	—	2	2	no	—
404	C₂×#41	—	4	1	no	—
405	C₂×#41	—	4	1	no	—
406	C₂×#41	Q₈×C₁₃	1	4	yes	—
407	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×D₄	—	2	1	no	—
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	—	2	2	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	#125	—	2	2	no	—
420	#125	—	4	1	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	4	1	no	—
424	C₄×Q₈	—	4	1	no	—
425	#117	—	2	2	no	—
426	#117	—	4	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	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	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
448	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
455	#107	—	2	2	no	—
456	#106	—	2	2	no	—
457	#106	—	4	1	no	—
458	#106	—	4	1	no	—
459	C₄⋊C₈	—	2	2	no	—
460	C₄⋊C₈	—	4	1	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	D₄×C₁₃	1	4	yes	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	4	1	no	—
468	#102	—	4	1	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	D₄×C₁₃	1	1	yes	characteristic
475	#95	D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₁₃	—	4	2	no	—
477	C₂×C₁₃	—	8	2	no	—
478	C₂×C₁₃	#2437	1	1	yes	characteristic
479	C₂×C₁₃	#3076	1	1	yes	characteristic
480	C₂×C₁₃	#3084	1	1	yes	characteristic
481	C₂×C₁₃	#3271	1	1	yes	characteristic
482	C₂×C₁₃	#3284	1	1	yes	characteristic
483	C₂×C₁₃	#3301	1	1	yes	characteristic
484	C₂×C₁₃	#3317	1	1	yes	characteristic
485	C₂⁴	—	2	1	no	—
486	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
487	#41	—	2	8	no	—
488	#41	—	4	4	no	—
489	#41	—	4	4	no	—
490	#41	—	4	4	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
495	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
496	C₂×Q₈	C₁₃×#41	1	2	yes	—
497	C₂×D₄	—	2	4	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	—	4	2	no	—
504	C₂×D₄	—	4	2	no	—
505	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	4	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	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
526	C₂²×C₄	C₁₃×#41	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	4	4	no	—
540	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	8	1	no	—
559	C₄⋊C₄	—	8	1	no	—
560	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	8	1	no	—
567	C₂²⋊C₄	—	8	1	no	—
568	C₂²⋊C₄	—	8	1	no	—
569	C₂²⋊C₄	—	8	1	no	—
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	C₄²	—	4	2	no	—
576	C₄²	—	4	2	no	—
577	C₁₃	#25953	1	1	yes	characteristic, direct product factor, Sylow
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	2	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	C₁₃×C₂²⋊Q₈	1	2	yes	—
592	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	4	8	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	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	8	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	C₁₃×C₂²⋊Q₈	1	2	yes	—
642	C₂×C₄	C₁₃×#135	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
644	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
645	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
646	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
647	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
649	C₈	—	2	2	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
668	C₂²	D₄²×C₁₃	1	1	yes	characteristic
669	C₂²	C₁₃×#546	1	1	yes	characteristic
670	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
671	C₂²	C₁₃×#575	1	1	yes	characteristic
672	C₂²	C₁₃×#577	1	1	yes	characteristic
673	C₂²	C₁₃×#577	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	4	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	1	no	—
681	C₄	—	8	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
687	C₄	C₁₃×#543	1	1	yes	characteristic
688	C₄	C₁₃×#546	1	1	yes	characteristic
689	C₄	C₁₃×#551	1	1	yes	characteristic
690	C₂	—	4	2	no	—
691	C₂	—	8	2	no	—
692	C₂	C₁₃×#2437	1	1	yes	characteristic
693	C₂	C₁₃×#3076	1	1	yes	characteristic
694	C₂	C₁₃×#3084	1	1	yes	characteristic
695	C₂	C₁₃×#3271	1	1	yes	characteristic
696	C₂	C₁₃×#3284	1	1	yes	characteristic
697	C₂	C₁₃×#3301	1	1	yes	characteristic
698	C₂	C₁₃×#3317	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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. C₂×C₁₃×#479	C₂	semidirect
3. C₁₃×#2441	C₂	semidirect
5. C₁₃×#2094	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2025	C₂	semidirect
9. C₁₃×#1865	C₂	semidirect
10. C₁₃×#1865	C₂	semidirect
11. C₁₃×#1854	C₂	semidirect
12. C₁₃×#1850	C₂	semidirect
13. C₁₃×#1807	C₂	semidirect
14. C₁₃×#1803	C₂	semidirect
136. #25953	C₁₃	direct (N × H)
229. C₂×#479	C₂×C₁₃	semidirect
231. #2441	C₂×C₁₃	semidirect
233. #2094	C₂×C₁₃	semidirect
234. #2067	C₂×C₁₃	semidirect
235. #2065	C₂×C₁₃	semidirect
236. #2025	C₂×C₁₃	semidirect
237. #1865	C₂×C₁₃	semidirect
238. #1865	C₂×C₁₃	semidirect
239. #1854	C₂×C₁₃	semidirect
240. #1850	C₂×C₁₃	semidirect
241. #1807	C₂×C₁₃	semidirect
242. #1803	C₂×C₁₃	semidirect
577. C₁₃	#25953	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×#479	2
C₂×C₁₃×#416	2
C₁₃×#2441	2
C₁₃×#2341	2
C₁₃×#2094	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#2025	2
C₁₃×#1865	2
C₁₃×#1854	2
C₁₃×#1850	2
C₁₃×#1807	2
C₁₃×#1803	2
C₁₃×#1788	2
#25953	13

Subgroups — C13×#25953 #15712292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25953 #15712292