Subgroups — C₁₃×#32475 #15718814

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2513	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#398	—	2	1	no	—
30	C₁₃×#397	—	2	1	no	—
31	C₁₃×#397	—	2	1	no	—
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#388	—	2	1	no	—
41	C₁₃×#388	—	2	1	no	—
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#382	—	2	1	no	—
44	C₁₃×#382	C₂²	1	1	yes	characteristic
45	C₁₃×#382	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×#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	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#107	—	2	2	no	—
90	C₁₃×#107	—	4	1	no	—
91	C₁₃×#106	—	2	2	no	—
92	C₁₃×#106	—	4	1	no	—
93	C₁₃×C₄⋊C₈	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×C₄⋊C₈	—	4	1	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	4	1	no	—
99	C₁₃×#102	—	4	1	no	—
100	C₄×C₈×C₁₃	—	4	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	—	2	1	no	—
105	C₁₃×#95	—	2	1	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	1	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	D₄	1	1	yes	characteristic
113	C₁₃×#95	D₄	1	1	yes	characteristic
114	#32475	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	#41	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	4	1	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	8	1	no	—
165	C₁₃×C₄⋊C₄	—	8	1	no	—
166	C₁₃×C₄⋊C₄	—	8	1	no	—
167	C₁₃×C₄⋊C₄	—	8	1	no	—
168	C₁₃×C₄⋊C₄	#41	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	8	1	no	—
172	C₁₃×C₂²⋊C₄	—	8	1	no	—
173	C₁₃×C₂²⋊C₄	—	8	1	no	—
174	C₁₃×C₂²⋊C₄	—	8	1	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	4	2	no	—
182	C₄²×C₁₃	—	8	1	no	—
183	#2513	C₂×C₁₃	1	1	yes	characteristic
184	#2508	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2073	C₂×C₁₃	1	1	yes	characteristic
188	#2067	C₂×C₁₃	1	1	yes	characteristic
189	#2067	C₂×C₁₃	1	1	yes	characteristic
190	#2065	C₂×C₁₃	1	1	yes	characteristic
191	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1934	C₂×C₁₃	1	1	yes	characteristic
196	#1926	C₂×C₁₃	1	1	yes	characteristic
197	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	#135	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
255	C₈×C₁₃	—	2	2	no	—
256	C₈×C₁₃	—	4	1	no	—
257	C₈×C₁₃	—	4	1	no	—
258	C₈×C₁₃	—	4	1	no	—
259	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#400	—	2	1	no	—
272	#398	—	2	1	no	—
273	#397	—	2	1	no	—
274	#397	—	2	1	no	—
275	#390	C₂²×C₁₃	1	1	yes	characteristic
276	#390	C₂²×C₁₃	1	1	yes	characteristic
277	#390	C₂²×C₁₃	1	1	yes	characteristic
278	#389	C₂²×C₁₃	1	1	yes	characteristic
279	#389	C₂²×C₁₃	1	1	yes	characteristic
280	#389	C₂²×C₁₃	1	1	yes	characteristic
281	#389	C₂²×C₁₃	1	1	yes	characteristic
282	#389	C₂²×C₁₃	1	1	yes	characteristic
283	#388	—	2	1	no	—
284	#388	—	2	1	no	—
285	#387	—	2	1	no	—
286	#382	—	2	1	no	—
287	#382	C₂²×C₁₃	1	1	yes	characteristic
288	#382	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	#340	C₂²×C₁₃	1	1	yes	characteristic
293	#340	C₂²×C₁₃	1	1	yes	characteristic
294	#340	C₂²×C₁₃	1	1	yes	characteristic
295	#340	C₂²×C₁₃	1	1	yes	characteristic
296	#340	C₂²×C₁₃	1	1	yes	characteristic
297	#340	C₂²×C₁₃	1	1	yes	characteristic
298	#340	C₂²×C₁₃	1	1	yes	characteristic
299	#340	C₂²×C₁₃	1	1	yes	characteristic
300	#336	C₂²×C₁₃	1	1	yes	characteristic
301	#336	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₁₃	—	8	1	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	8	1	no	—
306	C₂²×C₁₃	—	8	1	no	—
307	C₂²×C₁₃	—	8	1	no	—
308	C₂²×C₁₃	—	8	1	no	—
309	C₂²×C₁₃	#537	1	1	yes	characteristic
310	C₂²×C₁₃	#547	1	1	yes	characteristic
311	C₂²×C₁₃	#548	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
313	C₂²×C₁₃	#575	1	1	yes	characteristic
314	C₂²×C₁₃	#576	1	1	yes	characteristic
315	C₂²×C₁₃	#577	1	1	yes	characteristic
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	1	no	—
321	C₄×C₁₃	—	4	2	no	—
322	C₄×C₁₃	—	4	1	no	—
323	C₄×C₁₃	—	8	1	no	—
324	C₄×C₁₃	—	8	1	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	—	8	1	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	—	8	1	no	—
329	C₄×C₁₃	#541	1	1	yes	characteristic
330	C₄×C₁₃	#541	1	1	yes	characteristic
331	C₄×C₁₃	#553	1	1	yes	characteristic
332	C₄×C₁₃	#563	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	#107	—	2	2	no	—
364	#107	—	4	1	no	—
365	#106	—	2	2	no	—
366	#106	—	4	1	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	4	1	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	4	1	no	—
373	#102	—	4	1	no	—
374	C₄×C₈	—	4	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	D₄×C₁₃	1	1	yes	characteristic
387	#95	D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₁₃	—	16	1	no	—
389	C₂×C₁₃	#2725	1	1	yes	characteristic
390	C₂×C₁₃	#3250	1	1	yes	characteristic
391	C₂×C₁₃	#3257	1	1	yes	characteristic
392	C₂×C₁₃	#3341	1	1	yes	characteristic
393	C₂×C₁₃	#3351	1	1	yes	characteristic
394	C₂×C₁₃	#3365	1	1	yes	characteristic
395	C₂×C₁₃	#3370	1	1	yes	characteristic
396	C₂⁴	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	C₁₃×#41	1	2	yes	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	8	1	no	—
446	C₄⋊C₄	—	8	1	no	—
447	C₄⋊C₄	—	8	1	no	—
448	C₄⋊C₄	—	8	1	no	—
449	C₄⋊C₄	C₁₃×#41	1	2	yes	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₂²⋊C₄	—	8	1	no	—
453	C₂²⋊C₄	—	8	1	no	—
454	C₂²⋊C₄	—	8	1	no	—
455	C₂²⋊C₄	—	8	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	4	2	no	—
463	C₄²	—	8	1	no	—
464	C₁₃	#32475	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	C₁₃×#135	1	2	yes	—
516	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
517	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
518	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	C₁₃×#537	1	1	yes	characteristic
534	C₂²	C₁₃×#547	1	1	yes	characteristic
535	C₂²	C₁₃×#548	1	1	yes	characteristic
536	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
537	C₂²	C₁₃×#575	1	1	yes	characteristic
538	C₂²	C₁₃×#576	1	1	yes	characteristic
539	C₂²	C₁₃×#577	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	C₁₃×#541	1	1	yes	characteristic
554	C₄	C₁₃×#541	1	1	yes	characteristic
555	C₄	C₁₃×#553	1	1	yes	characteristic
556	C₄	C₁₃×#563	1	1	yes	characteristic
557	C₂	—	16	1	no	—
558	C₂	C₁₃×#2725	1	1	yes	characteristic
559	C₂	C₁₃×#3250	1	1	yes	characteristic
560	C₂	C₁₃×#3257	1	1	yes	characteristic
561	C₂	C₁₃×#3341	1	1	yes	characteristic
562	C₂	C₁₃×#3351	1	1	yes	characteristic
563	C₂	C₁₃×#3365	1	1	yes	characteristic
564	C₂	C₁₃×#3370	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2508	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2088	C₂	semidirect
9. C₁₃×#1949	C₂	semidirect
10. C₁₃×#1949	C₂	semidirect
11. C₁₃×#1942	C₂	semidirect
12. C₁₃×#1939	C₂	semidirect
15. C₁₃×#1920	C₂	semidirect
114. #32475	C₁₃	direct (N × H)
184. #2508	C₂×C₁₃	semidirect
185. #2101	C₂×C₁₃	semidirect
186. #2088	C₂×C₁₃	semidirect
191. #1949	C₂×C₁₃	semidirect
192. #1949	C₂×C₁₃	semidirect
193. #1942	C₂×C₁₃	semidirect
194. #1939	C₂×C₁₃	semidirect
197. #1920	C₂×C₁₃	semidirect
464. C₁₃	#32475	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×#2513	2
C₁₃×#2508	2
C₁₃×#2101	2
C₁₃×#2088	2
C₁₃×#2073	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1949	2
C₁₃×#1942	2
C₁₃×#1939	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1920	2
#32475	13

Subgroups — C13×#32475 #15718814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32475 #15718814