Subgroups — C₁₃×#29203 #15715542

Order 3328.

706 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	C₁₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1959	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1958	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#124	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	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	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×#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×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#400	—	2	1	no	—
36	C₁₃×#400	—	2	1	no	—
37	C₁₃×#398	—	2	1	no	—
38	C₁₃×#398	—	2	1	no	—
39	C₁₃×#391	C₂²	1	1	yes	characteristic
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×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#384	C₂²	1	1	yes	characteristic
51	C₁₃×#382	C₂²	1	1	yes	characteristic
52	C₁₃×#376	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#124	Q₈	1	4	yes	—
68	C₄×Q₈×C₁₃	—	4	1	no	—
69	C₄×Q₈×C₁₃	—	4	1	no	—
70	C₄×D₄×C₁₃	—	4	1	no	—
71	C₄×D₄×C₁₃	—	4	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	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	—	4	1	no	—
97	C₁₃×#107	—	4	1	no	—
98	C₁₃×#106	—	4	1	no	—
99	C₁₃×#106	—	4	1	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×#103	—	2	2	no	—
103	C₁₃×#103	—	2	2	no	—
104	C₁₃×#103	—	4	1	no	—
105	C₁₃×#103	—	4	1	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₁₃×#102	—	4	1	no	—
110	C₁₃×#97	—	2	2	no	—
111	C₄×C₈×C₁₃	—	2	2	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	D₄	1	1	yes	characteristic
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	#29203	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂×Q₈×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	C₂×Q₈	1	2	yes	—
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	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
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	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	8	1	no	—
147	C₂²×C₄×C₁₃	—	8	1	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	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	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	#41	1	2	yes	—
166	C₂×C₈×C₁₃	#41	1	2	yes	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	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	—	8	1	no	—
185	C₁₃×C₄⋊C₄	—	8	1	no	—
186	C₁₃×C₄⋊C₄	—	8	1	no	—
187	C₁₃×C₄⋊C₄	—	8	1	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	4	2	no	—
191	C₁₃×C₂²⋊C₄	—	8	1	no	—
192	C₁₃×C₂²⋊C₄	—	8	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	4	2	no	—
198	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
199	C₄²×C₁₃	#41	1	2	yes	—
200	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2326	C₂×C₁₃	1	1	yes	characteristic
202	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2067	C₂×C₁₃	1	1	yes	characteristic
204	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2065	C₂×C₁₃	1	1	yes	characteristic
206	#1959	C₂×C₁₃	1	1	yes	characteristic
207	#1958	C₂×C₁₃	1	1	yes	characteristic
208	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1864	C₂×C₁₃	1	1	yes	characteristic
210	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1862	C₂×C₁₃	1	1	yes	characteristic
212	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1768	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	1	no	—
237	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	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	C₂²⋊Q₈	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×Q₈	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	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₈×C₁₃	—	2	2	no	—
278	C₈×C₁₃	—	2	2	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₂×#124	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	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#398	—	2	1	no	—
303	#398	—	2	1	no	—
304	#391	C₂²×C₁₃	1	1	yes	characteristic
305	#390	C₂²×C₁₃	1	1	yes	characteristic
306	#389	C₂²×C₁₃	1	1	yes	characteristic
307	#389	C₂²×C₁₃	1	1	yes	characteristic
308	#389	C₂²×C₁₃	1	1	yes	characteristic
309	#389	C₂²×C₁₃	1	1	yes	characteristic
310	#388	—	2	1	no	—
311	#388	—	2	1	no	—
312	#385	—	2	1	no	—
313	#385	—	2	1	no	—
314	#384	C₂²×C₁₃	1	1	yes	characteristic
315	#384	C₂²×C₁₃	1	1	yes	characteristic
316	#382	C₂²×C₁₃	1	1	yes	characteristic
317	#376	C₂²×C₁₃	1	1	yes	characteristic
318	#340	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	#336	C₂²×C₁₃	1	1	yes	characteristic
323	#336	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
332	C₂²×C₁₃	#532	1	1	yes	characteristic
333	C₂²×C₁₃	#535	1	1	yes	characteristic
334	C₂²×C₁₃	#576	1	1	yes	characteristic
335	C₂²×C₁₃	#577	1	1	yes	characteristic
336	C₂²×C₁₃	#577	1	1	yes	characteristic
337	C₂²×C₁₃	#578	1	1	yes	characteristic
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	4	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	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	#553	1	1	yes	characteristic
352	C₄×C₁₃	#553	1	1	yes	characteristic
353	C₄×C₁₃	#554	1	1	yes	characteristic
354	C₄×C₁₃	#554	1	1	yes	characteristic
355	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	#124	—	2	2	no	—
363	#124	Q₈×C₁₃	1	4	yes	—
364	C₄×Q₈	—	4	1	no	—
365	C₄×Q₈	—	4	1	no	—
366	C₄×D₄	—	4	1	no	—
367	C₄×D₄	—	4	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	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	—	4	1	no	—
393	#107	—	4	1	no	—
394	#106	—	4	1	no	—
395	#106	—	4	1	no	—
396	C₄⋊C₈	—	2	2	no	—
397	C₄⋊C₈	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	4	1	no	—
401	#103	—	4	1	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	4	1	no	—
405	#102	—	4	1	no	—
406	#97	—	2	2	no	—
407	C₄×C₈	—	2	2	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	D₄×C₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	8	2	no	—
421	C₂×C₁₃	#2566	1	1	yes	characteristic
422	C₂×C₁₃	#3083	1	1	yes	characteristic
423	C₂×C₁₃	#3084	1	1	yes	characteristic
424	C₂×C₁₃	#3178	1	1	yes	characteristic
425	C₂×C₁₃	#3179	1	1	yes	characteristic
426	C₂×C₁₃	#3224	1	1	yes	characteristic
427	C₂×C₁₃	#3225	1	1	yes	characteristic
428	C₂⁴	—	2	1	no	—
429	C₂×Q₈	—	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	C₂×Q₈×C₁₃	1	2	yes	—
435	C₂×D₄	—	2	1	no	—
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	C₂×Q₈×C₁₃	1	2	yes	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁴×C₁₃	1	1	yes	characteristic
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	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	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	C₁₃×#41	1	2	yes	—
469	C₂×C₈	C₁₃×#41	1	2	yes	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	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	—	4	2	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	—	8	1	no	—
488	C₄⋊C₄	—	8	1	no	—
489	C₄⋊C₄	—	8	1	no	—
490	C₄⋊C₄	—	8	1	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	8	1	no	—
495	C₂²⋊C₄	—	8	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	2	no	—
501	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
502	C₄²	C₁₃×#41	1	2	yes	—
503	C₁₃	#29203	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	1	no	—
526	C₂×C₄	—	2	1	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	—	4	1	no	—
538	C₂×C₄	—	4	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	C₁₃×C₂²⋊Q₈	1	2	yes	—
559	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
560	C₂×C₄	C₂²×Q₈×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	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
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×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
578	C₂²	C₁₃×#532	1	1	yes	characteristic
579	C₂²	C₁₃×#535	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	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₁₃×#553	1	1	yes	characteristic
598	C₄	C₁₃×#553	1	1	yes	characteristic
599	C₄	C₁₃×#554	1	1	yes	characteristic
600	C₄	C₁₃×#554	1	1	yes	characteristic
601	C₂	—	8	2	no	—
602	C₂	C₁₃×#2566	1	1	yes	characteristic
603	C₂	C₁₃×#3083	1	1	yes	characteristic
604	C₂	C₁₃×#3084	1	1	yes	characteristic
605	C₂	C₁₃×#3178	1	1	yes	characteristic
606	C₂	C₁₃×#3179	1	1	yes	characteristic
607	C₂	C₁₃×#3224	1	1	yes	characteristic
608	C₂	C₁₃×#3225	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 ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2647	C₂	semidirect
3. C₁₃×#2068	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
9. C₁₃×#1865	C₂	semidirect
11. C₁₃×#1863	C₂	semidirect
13. C₁₃×#1847	C₂	semidirect
14. C₁₃×#1834	C₂	semidirect
15. C₁₃×#1768	C₂	semidirect
124. #29203	C₁₃	direct (N × H)
200. #2647	C₂×C₁₃	semidirect
202. #2068	C₂×C₁₃	semidirect
204. #2066	C₂×C₁₃	semidirect
208. #1865	C₂×C₁₃	semidirect
210. #1863	C₂×C₁₃	semidirect
212. #1847	C₂×C₁₃	semidirect
213. #1834	C₂×C₁₃	semidirect
214. #1768	C₂×C₁₃	semidirect
503. C₁₃	#29203	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×#2647	2
C₁₃×#2326	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2065	2
C₁₃×#1959	2
C₁₃×#1958	2
C₁₃×#1865	2
C₁₃×#1864	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1847	2
C₁₃×#1834	2
C₁₃×#1768	2
#29203	13

Subgroups — C13×#29203 #15715542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29203 #15715542