Subgroups — C₁₃×#21291 #15707630

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#440	C₄	1	8	yes	complemented
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	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×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#388	—	2	1	no	—
44	C₁₃×#388	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#383	—	2	1	no	—
48	C₁₃×#382	—	2	1	no	—
49	C₁₃×#381	—	2	1	no	—
50	C₁₃×#380	—	2	1	no	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#376	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×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	—	2	2	no	—
97	C₁₃×#107	C₂×C₄	1	4	yes	—
98	C₁₃×#106	—	2	2	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	C₂×C₄	1	4	yes	—
102	C₁₃×#102	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	C₂×C₄	1	4	yes	—
105	C₁₃×#97	—	2	2	no	—
106	C₁₃×#97	—	2	2	no	—
107	C₁₃×#97	C₂×C₄	1	4	yes	—
108	C₄×C₈×C₁₃	—	2	2	no	—
109	C₄×C₈×C₁₃	—	2	2	no	—
110	C₄×C₈×C₁₃	—	2	2	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	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	D₄	1	1	yes	characteristic
122	C₁₃×#95	D₄	1	1	yes	characteristic
123	C₁₃×#95	D₄	1	1	yes	characteristic
124	C₁₃×#95	D₄	1	1	yes	characteristic
125	#21291	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	8	1	no	—
148	C₂²×C₄×C₁₃	—	8	1	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₁₃×SD₁₆	—	2	8	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₁₃	#41	1	2	yes	—
166	C₂×C₈×C₁₃	#41	1	2	yes	—
167	C₂×C₈×C₁₃	#41	1	2	yes	—
168	C₂×C₈×C₁₃	#41	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	8	1	no	—
181	C₁₃×C₄⋊C₄	—	8	1	no	—
182	C₁₃×C₄⋊C₄	—	8	1	no	—
183	C₁₃×C₄⋊C₄	—	8	1	no	—
184	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	8	1	no	—
188	C₁₃×C₂²⋊C₄	—	8	1	no	—
189	C₁₃×C₂²⋊C₄	—	8	1	no	—
190	C₁₃×C₂²⋊C₄	—	8	1	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	8	1	no	—
197	C₄²×C₁₃	—	8	1	no	—
198	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
199	C₄²×C₁₃	#41	1	2	yes	—
200	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
201	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2319	C₂×C₁₃	1	1	yes	characteristic
203	#1973	C₂×C₁₃	1	1	yes	characteristic
204	#1968	C₂×C₁₃	1	1	yes	characteristic
205	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1936	C₂×C₁₃	1	1	yes	characteristic
208	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1934	C₂×C₁₃	1	1	yes	characteristic
210	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1776	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
214	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₃	—	2	2	no	—
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	4	1	no	—
230	D₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	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	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	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	—	8	4	no	—
269	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₈×C₁₃	—	2	2	no	—
278	C₈×C₁₃	—	2	2	no	—
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	#117	1	4	yes	—
281	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
284	#440	C₄×C₁₃	1	8	yes	complemented
285	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
300	#391	C₂²×C₁₃	1	1	yes	characteristic
301	#391	C₂²×C₁₃	1	1	yes	characteristic
302	#390	C₂²×C₁₃	1	1	yes	characteristic
303	#390	C₂²×C₁₃	1	1	yes	characteristic
304	#389	C₂²×C₁₃	1	1	yes	characteristic
305	#389	C₂²×C₁₃	1	1	yes	characteristic
306	#389	C₂²×C₁₃	1	1	yes	characteristic
307	#389	C₂²×C₁₃	1	1	yes	characteristic
308	#388	—	2	1	no	—
309	#388	—	2	1	no	—
310	#387	—	2	1	no	—
311	#387	—	2	1	no	—
312	#383	—	2	1	no	—
313	#382	—	2	1	no	—
314	#381	—	2	1	no	—
315	#380	—	2	1	no	—
316	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
318	#376	C₂²×C₁₃	1	1	yes	characteristic
319	#340	C₂²×C₁₃	1	1	yes	characteristic
320	#340	C₂²×C₁₃	1	1	yes	characteristic
321	#340	C₂²×C₁₃	1	1	yes	characteristic
322	#340	C₂²×C₁₃	1	1	yes	characteristic
323	#340	C₂²×C₁₃	1	1	yes	characteristic
324	#340	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	4	2	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₁₃	#532	1	1	yes	characteristic
334	C₂²×C₁₃	#532	1	1	yes	characteristic
335	C₂²×C₁₃	#576	1	1	yes	characteristic
336	C₂²×C₁₃	#577	1	1	yes	characteristic
337	C₂²×C₁₃	#577	1	1	yes	characteristic
338	C₂²×C₁₃	#578	1	1	yes	characteristic
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
353	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
354	C₄×C₁₃	#529	1	1	yes	characteristic
355	C₄×C₁₃	#529	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	—	2	1	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
362	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	#107	—	2	2	no	—
393	#107	C₂×C₄×C₁₃	1	4	yes	—
394	#106	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	C₂×C₄×C₁₃	1	4	yes	—
398	#102	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	C₂×C₄×C₁₃	1	4	yes	—
401	#97	—	2	2	no	—
402	#97	—	2	2	no	—
403	#97	C₂×C₄×C₁₃	1	4	yes	—
404	C₄×C₈	—	2	2	no	—
405	C₄×C₈	—	2	2	no	—
406	C₄×C₈	—	2	2	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	D₄×C₁₃	1	1	yes	characteristic
418	#95	D₄×C₁₃	1	1	yes	characteristic
419	#95	D₄×C₁₃	1	1	yes	characteristic
420	#95	D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₁₃	—	8	2	no	—
422	C₂×C₁₃	#2293	1	1	yes	characteristic
423	C₂×C₁₃	#2946	1	1	yes	characteristic
424	C₂×C₁₃	#2947	1	1	yes	characteristic
425	C₂×C₁₃	#3174	1	1	yes	characteristic
426	C₂×C₁₃	#3175	1	1	yes	characteristic
427	C₂×C₁₃	#3178	1	1	yes	characteristic
428	C₂×C₁₃	#3179	1	1	yes	characteristic
429	C₂⁴	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	—	8	1	no	—
452	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
459	SD₁₆	—	2	8	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
467	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
468	C₂×C₈	C₁₃×#41	1	2	yes	—
469	C₂×C₈	C₁₃×#41	1	2	yes	—
470	C₂×C₈	C₁₃×#41	1	2	yes	—
471	C₂×C₈	C₁₃×#41	1	2	yes	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	—	8	1	no	—
485	C₄⋊C₄	—	8	1	no	—
486	C₄⋊C₄	—	8	1	no	—
487	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
488	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	8	1	no	—
491	C₂²⋊C₄	—	8	1	no	—
492	C₂²⋊C₄	—	8	1	no	—
493	C₂²⋊C₄	—	8	1	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	8	1	no	—
500	C₄²	—	8	1	no	—
501	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
502	C₄²	C₁₃×#41	1	2	yes	—
503	C₁₃	#21291	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	2	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
559	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
560	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
562	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
565	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	C₁₃×#117	1	4	yes	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
578	C₂²	C₁₃×#532	1	1	yes	characteristic
579	C₂²	C₁₃×#532	1	1	yes	characteristic
580	C₂²	C₁₃×#576	1	1	yes	characteristic
581	C₂²	C₁₃×#577	1	1	yes	characteristic
582	C₂²	C₁₃×#577	1	1	yes	characteristic
583	C₂²	C₁₃×#578	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
598	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
599	C₄	C₁₃×#529	1	1	yes	characteristic
600	C₄	C₁₃×#529	1	1	yes	characteristic
601	C₂	—	8	2	no	—
602	C₂	C₁₃×#2293	1	1	yes	characteristic
603	C₂	C₁₃×#2946	1	1	yes	characteristic
604	C₂	C₁₃×#2947	1	1	yes	characteristic
605	C₂	C₁₃×#3174	1	1	yes	characteristic
606	C₂	C₁₃×#3175	1	1	yes	characteristic
607	C₂	C₁₃×#3178	1	1	yes	characteristic
608	C₂	C₁₃×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2320	C₂	semidirect
6. C₁₃×#1943	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1935	C₂	semidirect
11. C₁₃×#1933	C₂	semidirect
12. C₁₃×#1776	C₂	semidirect
13. C₄×C₁₃×#103	C₂	semidirect
15. C₁₃×#1726	C₂	semidirect
19. C₁₃×#440	C₄	semidirect
125. #21291	C₁₃	direct (N × H)
201. #2320	C₂×C₁₃	semidirect
205. #1943	C₂×C₁₃	semidirect
206. #1942	C₂×C₁₃	semidirect
208. #1935	C₂×C₁₃	semidirect
210. #1933	C₂×C₁₃	semidirect
211. #1776	C₂×C₁₃	semidirect
212. C₄×#103	C₂×C₁₃	semidirect
214. #1726	C₂×C₁₃	semidirect
284. #440	C₄×C₁₃	semidirect
503. C₁₃	#21291	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×#440	2
C₁₃×#2320	2
C₁₃×#2319	2
C₁₃×#1973	2
C₁₃×#1968	2
C₁₃×#1943	2
C₁₃×#1942	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1934	2
C₁₃×#1933	2
C₁₃×#1776	2
C₄×C₁₃×#103	2
C₄×C₁₃×#102	2
C₁₃×#1726	2
#21291	13

Subgroups — C13×#21291 #15707630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21291 #15707630