Subgroups — C₁₃×#29417 #15715756

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1817	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	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	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#387	—	2	1	no	—
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#385	—	2	1	no	—
40	C₁₃×#385	—	2	1	no	—
41	C₁₃×#380	C₂²	1	1	yes	characteristic
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
48	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	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×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×Q₁₆	—	2	2	no	—
65	C₂×C₁₃×Q₁₆	—	2	2	no	—
66	C₂×C₁₃×Q₁₆	—	4	1	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	4	1	no	—
76	C₄×Q₈×C₁₃	—	4	1	no	—
77	C₄×Q₈×C₁₃	—	4	1	no	—
78	C₄×Q₈×C₁₃	—	4	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	—	4	1	no	—
100	C₂×C₄²×C₁₃	—	4	1	no	—
101	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	2	no	—
106	C₁₃×#106	—	2	2	no	—
107	C₁₃×#106	—	4	1	no	—
108	C₁₃×#103	—	2	2	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	4	1	no	—
113	C₁₃×#103	—	4	1	no	—
114	C₁₃×C₂²⋊C₈	—	4	1	no	—
115	C₁₃×C₂²⋊C₈	—	4	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	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	#29417	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	#41	1	2	yes	—
139	C₂×Q₈×C₁₃	#41	1	2	yes	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	4	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₁₃×Q₁₆	—	4	4	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	2	no	—
195	C₁₃×C₄⋊C₄	#41	1	2	yes	—
196	C₁₃×C₄⋊C₄	#41	1	2	yes	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	4	1	no	—
206	C₄²×C₁₃	—	4	1	no	—
207	C₄²×C₁₃	—	4	2	no	—
208	C₄²×C₁₃	—	4	2	no	—
209	C₄²×C₁₃	—	4	2	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
212	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
213	#2077	C₂×C₁₃	1	1	yes	characteristic
214	#2036	C₂×C₁₃	1	1	yes	characteristic
215	#2035	C₂×C₁₃	1	1	yes	characteristic
216	#2001	C₂×C₁₃	1	1	yes	characteristic
217	#1928	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1817	C₂×C₁₃	1	1	yes	characteristic
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	#137	1	2	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	#135	1	2	yes	—
286	C₂×C₄×C₁₃	#137	1	2	yes	—
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
293	C₈×C₁₃	—	4	1	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
314	#391	C₂²×C₁₃	1	1	yes	characteristic
315	#391	C₂²×C₁₃	1	1	yes	characteristic
316	#389	C₂²×C₁₃	1	1	yes	characteristic
317	#389	C₂²×C₁₃	1	1	yes	characteristic
318	#387	—	2	1	no	—
319	#387	—	2	1	no	—
320	#385	—	2	1	no	—
321	#385	—	2	1	no	—
322	#380	C₂²×C₁₃	1	1	yes	characteristic
323	#380	C₂²×C₁₃	1	1	yes	characteristic
324	C₄×C₄⋊C₄	—	2	1	no	—
325	C₄×C₄⋊C₄	—	2	1	no	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₂²⋊C₄	—	2	1	no	—
329	C₄×C₂²⋊C₄	—	2	1	no	—
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#340	C₂²×C₁₃	1	1	yes	characteristic
335	#340	C₂²×C₁₃	1	1	yes	characteristic
336	#336	C₂²×C₁₃	1	1	yes	characteristic
337	#336	C₂²×C₁₃	1	1	yes	characteristic
338	#336	C₂²×C₁₃	1	1	yes	characteristic
339	#336	C₂²×C₁₃	1	1	yes	characteristic
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	#525	1	1	yes	characteristic
348	C₂²×C₁₃	#525	1	1	yes	characteristic
349	C₂²×C₁₃	#534	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
351	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
352	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
353	C₂²×C₁₃	#575	1	1	yes	characteristic
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	4	2	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	#551	1	1	yes	characteristic
368	C₄×C₁₃	#553	1	1	yes	characteristic
369	C₄×C₁₃	#553	1	1	yes	characteristic
370	C₄×C₁₃	#559	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×Q₁₆	—	2	2	no	—
377	C₂×Q₁₆	—	2	2	no	—
378	C₂×Q₁₆	—	4	1	no	—
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₄×Q₈	—	4	1	no	—
388	C₄×Q₈	—	4	1	no	—
389	C₄×Q₈	—	4	1	no	—
390	C₄×Q₈	—	4	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	4	1	no	—
412	C₂×C₄²	—	4	1	no	—
413	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	#107	—	2	2	no	—
418	#106	—	2	2	no	—
419	#106	—	4	1	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#103	—	4	1	no	—
425	#103	—	4	1	no	—
426	C₂²⋊C₈	—	4	1	no	—
427	C₂²⋊C₈	—	4	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	C₂×C₁₃	—	4	2	no	—
439	C₂×C₁₃	#2600	1	1	yes	characteristic
440	C₂×C₁₃	#3102	1	1	yes	characteristic
441	C₂×C₁₃	#3107	1	1	yes	characteristic
442	C₂×C₁₃	#3113	1	1	yes	characteristic
443	C₂×C₁₃	#3117	1	1	yes	characteristic
444	C₂×C₁₃	#3190	1	1	yes	characteristic
445	C₂×C₁₃	#3196	1	1	yes	characteristic
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	C₁₃×#41	1	2	yes	—
458	C₂×Q₈	C₁₃×#41	1	2	yes	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
485	Q₁₆	—	4	4	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	C₁₃×#41	1	2	yes	—
515	C₄⋊C₄	C₁₃×#41	1	2	yes	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	1	no	—
526	C₄²	—	4	2	no	—
527	C₄²	—	4	2	no	—
528	C₄²	—	4	2	no	—
529	C₄²	—	4	2	no	—
530	C₁₃	#29417	1	1	yes	characteristic, direct product factor, Sylow
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	C₁₃×#137	1	2	yes	—
538	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	C₁₃×#135	1	2	yes	—
591	C₂×C₄	C₁₃×#137	1	2	yes	—
592	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
594	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
595	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
596	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₁₃×#525	1	1	yes	characteristic
610	C₂²	C₁₃×#525	1	1	yes	characteristic
611	C₂²	C₁₃×#534	1	1	yes	characteristic
612	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
613	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
614	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
615	C₂²	C₁₃×#575	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	C₁₃×#551	1	1	yes	characteristic
630	C₄	C₁₃×#553	1	1	yes	characteristic
631	C₄	C₁₃×#553	1	1	yes	characteristic
632	C₄	C₁₃×#559	1	1	yes	characteristic
633	C₂	—	4	2	no	—
634	C₂	C₁₃×#2600	1	1	yes	characteristic
635	C₂	C₁₃×#3102	1	1	yes	characteristic
636	C₂	C₁₃×#3107	1	1	yes	characteristic
637	C₂	C₁₃×#3113	1	1	yes	characteristic
638	C₂	C₁₃×#3117	1	1	yes	characteristic
639	C₂	C₁₃×#3190	1	1	yes	characteristic
640	C₂	C₁₃×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₃×#1928	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
9. C₁₃×#1919	C₂	semidirect
10. C₁₃×#1918	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
12. C₁₃×#1878	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
14. C₁₃×#1865	C₂	semidirect
126. #29417	C₁₃	direct (N × H)
217. #1928	C₂×C₁₃	semidirect
218. #1927	C₂×C₁₃	semidirect
219. #1919	C₂×C₁₃	semidirect
220. #1918	C₂×C₁₃	semidirect
221. #1878	C₂×C₁₃	semidirect
222. #1878	C₂×C₁₃	semidirect
223. #1865	C₂×C₁₃	semidirect
224. #1865	C₂×C₁₃	semidirect
530. C₁₃	#29417	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2077	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2001	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1919	2
C₁₃×#1918	2
C₁₃×#1878	2
C₁₃×#1865	2
C₁₃×#1817	2
#29417	13

Subgroups — C13×#29417 #15715756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29417 #15715756