Subgroups — C₁₃×#24785 #15711124

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2415	C₂	1	2	yes	maximal
6	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1873	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₁₃×#470	—	2	4	no	—
20	C₁₃×#467	—	2	4	no	—
21	C₁₃×#435	—	2	4	no	—
22	C₁₃×#427	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	2	no	—
35	C₁₃×#394	—	2	2	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	—	2	2	no	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#388	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	D₄	1	4	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	4	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₁₃×#117	—	2	4	no	—
67	C₁₃×#117	—	4	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#107	—	2	4	no	—
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×#106	D₄	1	4	yes	complemented
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×#97	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	#24785	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	#41	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×Q₁₆	—	4	4	no	—
131	C₁₃×M₁₆	—	4	4	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	8	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	#41	1	2	yes	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	4	no	—
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	4	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	4	4	no	—
164	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×#435	C₂×C₁₃	1	1	yes	characteristic
167	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2415	C₂×C₁₃	1	2	yes	—
169	#2068	C₂×C₁₃	1	2	yes	complemented
170	#2036	C₂×C₁₃	1	2	yes	complemented
171	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1944	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1873	C₂×C₁₃	1	2	yes	complemented
174	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	#121	1	2	yes	—
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	4	2	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	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	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
220	C₂×C₄×C₁₃	#121	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₈×C₁₃	—	4	1	no	—
230	C₈×C₁₃	#121	1	4	yes	—
231	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#117	C₂²×C₁₃	1	2	yes	—
238	#470	—	2	4	no	—
239	#467	—	2	4	no	—
240	#435	—	2	4	no	—
241	#427	—	2	4	no	—
242	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#107	C₂²×C₁₃	1	2	yes	—
244	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
253	#397	—	2	2	no	—
254	#394	—	2	2	no	—
255	#391	C₂²×C₁₃	1	2	yes	—
256	#389	—	2	2	no	—
257	#389	C₂²×C₁₃	1	2	yes	—
258	#388	—	2	2	no	—
259	#380	C₂²×C₁₃	1	2	yes	—
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
273	C₂²×C₁₃	D₄²	1	1	yes	characteristic
274	C₂²×C₁₃	#547	1	1	yes	characteristic
275	C₂²×C₁₃	#575	1	2	yes	—
276	C₂²×C₁₃	#578	1	2	yes	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
286	C₄×C₁₃	#537	1	1	yes	characteristic
287	C₄×C₁₃	#548	1	1	yes	characteristic
288	C₄×C₁₃	#553	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	D₄×C₁₃	1	4	yes	—
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	4	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	#117	—	2	4	no	—
313	#117	—	4	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	#107	—	2	2	no	—
330	#107	—	2	4	no	—
331	#106	—	2	2	no	—
332	#106	D₄×C₁₃	1	4	yes	complemented
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	4	no	—
335	#103	—	2	4	no	—
336	#103	—	4	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	#97	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂×C₁₃	—	4	2	no	—
345	C₂×C₁₃	—	8	1	no	—
346	C₂×C₁₃	#2416	1	1	yes	characteristic
347	C₂×C₁₃	#3054	1	1	yes	characteristic
348	C₂×C₁₃	#3059	1	1	yes	characteristic
349	C₂×C₁₃	#3269	1	2	yes	—
350	C₂×C₁₃	#3349	1	2	yes	—
351	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	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	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
380	C₂²×C₄	C₁₃×#41	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	Q₁₆	—	4	4	no	—
383	M₁₆	—	4	4	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	8	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
396	C₂×C₈	C₁₃×#41	1	2	yes	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	4	4	no	—
416	C₁₃	#24785	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	C₁₃×#121	1	2	yes	—
427	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	D₄	—	4	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	C₁₃×#121	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
467	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	C₁₃×#121	1	4	yes	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
484	C₂²	D₄²×C₁₃	1	1	yes	characteristic
485	C₂²	C₁₃×#547	1	1	yes	characteristic
486	C₂²	C₁₃×#575	1	2	yes	—
487	C₂²	C₁₃×#578	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	—	8	2	no	—
496	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
497	C₄	C₁₃×#537	1	1	yes	characteristic
498	C₄	C₁₃×#548	1	1	yes	characteristic
499	C₄	C₁₃×#553	1	1	yes	characteristic
500	C₂	—	4	2	no	—
501	C₂	—	8	1	no	—
502	C₂	C₁₃×#2416	1	1	yes	characteristic
503	C₂	C₁₃×#3054	1	1	yes	characteristic
504	C₂	C₁₃×#3059	1	1	yes	characteristic
505	C₂	C₁₃×#3269	1	2	yes	—
506	C₂	C₁₃×#3349	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#470	C₂	semidirect
2. C₂×C₁₃×#467	C₂	semidirect
4. C₂×C₁₃×#427	C₂	semidirect
6. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#1971	C₂	semidirect
9. C₁₃×#1944	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₁₃×#1809	C₂	semidirect
86. C₁₃×#106	D₄	semidirect
98. #24785	C₁₃	direct (N × H)
164. C₂×#470	C₂×C₁₃	semidirect
165. C₂×#467	C₂×C₁₃	semidirect
167. C₂×#427	C₂×C₁₃	semidirect
169. #2068	C₂×C₁₃	semidirect
170. #2036	C₂×C₁₃	semidirect
171. #1971	C₂×C₁₃	semidirect
172. #1944	C₂×C₁₃	semidirect
173. #1873	C₂×C₁₃	semidirect
174. #1809	C₂×C₁₃	semidirect
332. #106	D₄×C₁₃	semidirect
416. C₁₃	#24785	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×#470	2
C₂×C₁₃×#467	2
C₂×C₁₃×#435	2
C₂×C₁₃×#427	2
C₁₃×#2415	2
C₁₃×#2068	2
C₁₃×#2036	2
C₁₃×#1971	2
C₁₃×#1944	2
C₁₃×#1873	2
C₁₃×#1809	2
#24785	13

Subgroups — C13×#24785 #15711124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24785 #15711124