Subgroups — C₁₃×#25914 #15712253

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2621	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2026	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1873	C₂	1	2	yes	maximal
10	C₁₃×#1872	C₂	1	2	yes	maximal
11	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#544	—	2	4	no	—
13	C₁₃×#544	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#491	—	2	4	no	—
28	C₁₃×#487	—	2	4	no	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#398	—	2	1	no	—
37	C₁₃×#398	—	2	1	no	—
38	C₁₃×#397	—	2	1	no	—
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊Q₈	—	2	8	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
61	C₁₃×#125	—	2	8	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×#125	—	2	2	no	—
64	C₁₃×#125	—	2	2	no	—
65	C₁₃×#125	D₄	1	4	yes	—
66	C₁₃×C₂²⋊Q₈	—	2	8	no	—
67	C₁₃×C₂²⋊Q₈	—	2	8	no	—
68	C₁₃×C₂²⋊Q₈	—	2	8	no	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	—	2	2	no	—
71	C₁₃×#117	—	2	2	no	—
72	C₁₃×#117	—	2	2	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	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#103	—	2	4	no	—
100	C₁₃×#103	—	2	4	no	—
101	C₁₃×#103	—	2	4	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×C₂²⋊C₈	—	2	4	no	—
104	C₁₃×#97	—	2	2	no	—
105	C₄×C₈×C₁₃	—	2	2	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	1	no	—
108	C₁₃×#95	—	2	2	no	—
109	C₁₃×#95	—	2	2	no	—
110	#25914	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	8	2	no	—
119	C₂×Q₈×C₁₃	—	8	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	#41	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
158	C₁₃×C₄⋊C₄	—	4	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	—	4	4	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₄²×C₁₃	—	2	4	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×#544	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2621	C₂×C₁₃	1	1	yes	characteristic
178	#2026	C₂×C₁₃	1	2	yes	complemented
179	#2024	C₂×C₁₃	1	2	yes	complemented
180	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1991	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1873	C₂×C₁₃	1	2	yes	—
183	#1872	C₂×C₁₃	1	2	yes	—
184	#1750	C₂×C₁₃	1	1	yes	characteristic
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	#124	1	2	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	4	no	—
192	Q₈×C₁₃	—	4	4	no	—
193	Q₈×C₁₃	—	8	4	no	—
194	Q₈×C₁₃	—	8	4	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	4	no	—
220	C₂×C₄×C₁₃	#120	1	2	yes	—
221	C₂×C₄×C₁₃	#120	1	2	yes	—
222	C₂×C₄×C₁₃	#124	1	2	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
227	C₈×C₁₃	—	4	2	no	—
228	C₈×C₁₃	—	4	2	no	—
229	#544	—	2	4	no	—
230	#544	—	2	4	no	—
231	C₂×C₄⋊Q₈	—	2	1	no	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#125	—	2	1	no	—
236	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	#491	—	2	4	no	—
245	#487	—	2	4	no	—
246	C₂×#103	C₂²×C₁₃	1	2	yes	—
247	C₂×#103	C₂²×C₁₃	1	2	yes	—
248	C₂×#103	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
251	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
253	#398	—	2	1	no	—
254	#398	—	2	1	no	—
255	#397	—	2	1	no	—
256	#397	—	2	1	no	—
257	#391	C₂²×C₁₃	1	2	yes	—
258	#382	C₂²×C₁₃	1	1	yes	characteristic
259	#340	C₂²×C₁₃	1	2	yes	—
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	2	yes	—
262	#340	C₂²×C₁₃	1	2	yes	—
263	#336	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
271	C₂²×C₁₃	#536	1	1	yes	characteristic
272	C₂²×C₁₃	#577	1	2	yes	—
273	C₂²×C₁₃	#578	1	2	yes	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	#548	1	2	yes	—
286	C₄×C₁₃	#548	1	2	yes	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
294	C₄⋊Q₈	—	2	8	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
301	#125	—	2	8	no	—
302	#125	—	2	2	no	—
303	#125	—	2	2	no	—
304	#125	—	2	2	no	—
305	#125	D₄×C₁₃	1	4	yes	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	—	2	8	no	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	2	no	—
312	#117	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	#103	—	2	4	no	—
340	#103	—	2	4	no	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	C₂²⋊C₈	—	2	4	no	—
344	#97	—	2	2	no	—
345	C₄×C₈	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	C₂×C₁₃	—	4	2	no	—
351	C₂×C₁₃	#2436	1	1	yes	characteristic
352	C₂×C₁₃	#3009	1	1	yes	characteristic
353	C₂×C₁₃	#3011	1	1	yes	characteristic
354	C₂×C₁₃	#3137	1	2	yes	—
355	C₂×C₁₃	#3242	1	2	yes	—
356	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	8	2	no	—
364	C₂×Q₈	—	8	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₁₃×#41	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	C₂×D₄×C₁₃	1	2	yes	—
418	C₄²	C₂×D₄×C₁₃	1	2	yes	—
419	C₁₃	#25914	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	C₁₃×#124	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	Q₈	—	4	4	no	—
427	Q₈	—	4	4	no	—
428	Q₈	—	8	4	no	—
429	Q₈	—	8	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	C₁₃×#120	1	2	yes	—
456	C₂×C₄	C₁₃×#120	1	2	yes	—
457	C₂×C₄	C₁₃×#124	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
461	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
470	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
471	C₂²	C₁₃×#536	1	1	yes	characteristic
472	C₂²	C₁₃×#577	1	2	yes	—
473	C₂²	C₁₃×#578	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	2	no	—
485	C₄	C₁₃×#548	1	2	yes	—
486	C₄	C₁₃×#548	1	2	yes	—
487	C₂	—	4	2	no	—
488	C₂	C₁₃×#2436	1	1	yes	characteristic
489	C₂	C₁₃×#3009	1	1	yes	characteristic
490	C₂	C₁₃×#3011	1	1	yes	characteristic
491	C₂	C₁₃×#3137	1	2	yes	—
492	C₂	C₁₃×#3242	1	2	yes	—

	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#491	C₂	semidirect
3. C₂×C₁₃×#487	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2024	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1991	C₂	semidirect
110. #25914	C₁₃	direct (N × H)
175. C₂×#491	C₂×C₁₃	semidirect
176. C₂×#487	C₂×C₁₃	semidirect
178. #2026	C₂×C₁₃	semidirect
179. #2024	C₂×C₁₃	semidirect
180. #1993	C₂×C₁₃	semidirect
181. #1991	C₂×C₁₃	semidirect
419. C₁₃	#25914	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×#544	2
C₂×C₁₃×#491	2
C₂×C₁₃×#487	2
C₁₃×#2621	2
C₁₃×#2026	2
C₁₃×#2024	2
C₁₃×#1993	2
C₁₃×#1991	2
C₁₃×#1873	2
C₁₃×#1872	2
C₁₃×#1750	2
#25914	13

Subgroups — C13×#25914 #15712253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25914 #15712253