Subgroups — C₁₃×#24065 #15710404

Order 3328.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#485	C₂	1	2	yes	maximal
3	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1873	C₂	1	2	yes	maximal
9	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1817	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	—	2	8	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂×C₁₃×#117	—	2	1	no	—
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#485	—	2	8	no	—
25	C₂×C₁₃×#107	C₂²	1	2	yes	—
26	C₂×C₁₃×#106	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#385	—	2	1	no	—
37	C₁₃×#385	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₁₃×#336	C₂²	1	1	yes	characteristic
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	2	4	no	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×#125	—	2	8	no	—
55	C₁₃×C₂²⋊Q₈	—	2	8	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	D₄	1	8	yes	—
58	C₄×Q₈×C₁₃	—	2	8	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	—	2	4	no	—
61	C₁₃×#117	—	2	8	no	—
62	C₁₃×#117	—	2	2	no	—
63	C₁₃×#117	—	2	2	no	—
64	C₁₃×#117	—	2	4	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	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	—	2	4	no	—
84	C₂×C₄²×C₁₃	—	2	2	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#107	—	2	4	no	—
91	C₁₃×#106	—	2	4	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#103	—	2	4	no	—
96	C₁₃×C₂²⋊C₈	—	2	4	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	#24065	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	4	2	no	—
110	C₂×Q₈×C₁₃	—	4	2	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	4	1	no	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
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	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
155	C₁₃×C₄⋊C₄	#41	1	2	yes	—
156	C₁₃×C₄⋊C₄	#41	1	2	yes	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₁₃	—	2	4	no	—
161	C₄²×C₁₃	—	2	8	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	4	2	no	—
167	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
168	C₂×#485	C₂×C₁₃	1	2	yes	—
169	#2296	C₂×C₁₃	1	1	yes	characteristic
170	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1873	C₂×C₁₃	1	2	yes	—
175	#1865	C₂×C₁₃	1	2	yes	complemented
176	#1863	C₂×C₁₃	1	2	yes	complemented
177	#1817	C₂×C₁₃	1	1	yes	characteristic
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	#120	1	2	yes	—
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	2	4	no	—
187	Q₈×C₁₃	—	2	4	no	—
188	Q₈×C₁₃	—	4	8	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	#120	1	2	yes	—
225	C₂×C₄×C₁₃	#135	1	2	yes	—
226	C₂×C₄×C₁₃	#137	1	2	yes	—
227	C₂×C₄×C₁₃	#137	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
232	C₈×C₁₃	—	4	2	no	—
233	C₈×C₁₃	—	4	2	no	—
234	#533	—	2	8	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#125	—	2	1	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄×Q₈	—	2	1	no	—
241	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
242	C₂×#117	—	2	1	no	—
243	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
246	#485	—	2	8	no	—
247	C₂×#107	C₂²×C₁₃	1	2	yes	—
248	C₂×#106	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×#103	C₂²×C₁₃	1	2	yes	—
251	C₂×#103	C₂²×C₁₃	1	2	yes	—
252	C₂×#103	C₂²×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
254	#389	C₂²×C₁₃	1	1	yes	characteristic
255	#389	C₂²×C₁₃	1	1	yes	characteristic
256	#389	C₂²×C₁₃	1	1	yes	characteristic
257	#389	C₂²×C₁₃	1	1	yes	characteristic
258	#385	—	2	1	no	—
259	#385	—	2	1	no	—
260	C₄×C₄⋊C₄	—	2	1	no	—
261	C₄×C₄⋊C₄	—	2	1	no	—
262	#340	C₂²×C₁₃	1	2	yes	—
263	#340	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	1	yes	characteristic
265	#336	C₂²×C₁₃	1	1	yes	characteristic
266	#336	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
275	C₂²×C₁₃	#525	1	1	yes	characteristic
276	C₂²×C₁₃	#536	1	1	yes	characteristic
277	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
280	C₂²×C₁₃	#575	1	1	yes	characteristic
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	8	1	no	—
291	C₄×C₁₃	—	8	1	no	—
292	C₄×C₁₃	#547	1	2	yes	—
293	C₄×C₁₃	#547	1	2	yes	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
296	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
300	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
301	C₄⋊Q₈	—	2	4	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	#125	—	2	8	no	—
304	C₂²⋊Q₈	—	2	8	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	D₄×C₁₃	1	8	yes	—
307	C₄×Q₈	—	2	8	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	#117	—	2	8	no	—
311	#117	—	2	2	no	—
312	#117	—	2	2	no	—
313	#117	—	2	4	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	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	#107	—	2	4	no	—
340	#106	—	2	4	no	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	#103	—	2	4	no	—
344	#103	—	2	4	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	C₂×C₁₃	—	4	2	no	—
351	C₂×C₁₃	#2406	1	1	yes	characteristic
352	C₂×C₁₃	#3002	1	1	yes	characteristic
353	C₂×C₁₃	#3004	1	1	yes	characteristic
354	C₂×C₁₃	#3107	1	1	yes	characteristic
355	C₂×C₁₃	#3116	1	1	yes	characteristic
356	C₂×C₁₃	#3231	1	1	yes	characteristic
357	C₂×C₁₃	#3237	1	1	yes	characteristic
358	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₄⋊C₄	C₁₃×#41	1	2	yes	—
412	C₄⋊C₄	C₁₃×#41	1	2	yes	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₄²	—	2	8	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	2	no	—
423	C₁₃	#24065	1	1	yes	characteristic, direct product factor, Sylow
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	C₁₃×#120	1	2	yes	—
431	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	C₁₃×#120	1	2	yes	—
471	C₂×C₄	C₁₃×#135	1	2	yes	—
472	C₂×C₄	C₁₃×#137	1	2	yes	—
473	C₂×C₄	C₁₃×#137	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
475	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
477	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
488	C₂²	C₁₃×#525	1	1	yes	characteristic
489	C₂²	C₁₃×#536	1	1	yes	characteristic
490	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
491	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
492	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
493	C₂²	C₁₃×#575	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	4	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	C₁₃×#547	1	2	yes	—
506	C₄	C₁₃×#547	1	2	yes	—
507	C₂	—	4	2	no	—
508	C₂	C₁₃×#2406	1	1	yes	characteristic
509	C₂	C₁₃×#3002	1	1	yes	characteristic
510	C₂	C₁₃×#3004	1	1	yes	characteristic
511	C₂	C₁₃×#3107	1	1	yes	characteristic
512	C₂	C₁₃×#3116	1	1	yes	characteristic
513	C₂	C₁₃×#3231	1	1	yes	characteristic
514	C₂	C₁₃×#3237	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
4. C₁₃×#2058	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#2043	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
9. C₁₃×#1865	C₂	semidirect
10. C₁₃×#1863	C₂	semidirect
101. #24065	C₁₃	direct (N × H)
170. #2058	C₂×C₁₃	semidirect
171. #2057	C₂×C₁₃	semidirect
172. #2043	C₂×C₁₃	semidirect
173. #2043	C₂×C₁₃	semidirect
175. #1865	C₂×C₁₃	semidirect
176. #1863	C₂×C₁₃	semidirect
423. C₁₃	#24065	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×#533	2
C₂×C₁₃×#485	2
C₁₃×#2296	2
C₁₃×#2058	2
C₁₃×#2057	2
C₁₃×#2043	2
C₁₃×#1873	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1817	2
#24065	13

Subgroups — C13×#24065 #15710404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24065 #15710404