Subgroups — C₁₃×#24493 #15710832

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2435	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#485	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
21	C₁₃×#418	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#394	—	2	1	no	—
31	C₁₃×#394	—	2	1	no	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	complemented
34	C₁₃×#388	—	2	2	no	—
35	C₁₃×#383	—	2	1	no	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₁₃×#379	—	2	2	no	—
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	complemented
42	C₁₃×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	4	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	4	2	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	4	2	no	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×#124	—	2	4	no	—
58	C₁₃×#124	—	4	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	2	no	—
61	C₁₃×#117	—	2	2	no	—
62	C₁₃×#117	D₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	4	2	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	4	2	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	2	4	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₁₃×#102	—	4	2	no	—
90	C₁₃×C₂²⋊C₈	—	2	2	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	D₄	1	1	yes	characteristic
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	#24493	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂⁴×C₁₃	—	4	4	no	—
99	C₂⁴×C₁₃	—	4	4	no	—
100	C₂⁴×C₁₃	—	4	2	no	—
101	C₂⁴×C₁₃	—	8	1	no	—
102	C₂⁴×C₁₃	—	8	1	no	—
103	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	8	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	8	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	4	4	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	#41	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	#41	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×M₁₆	—	4	4	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	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	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	4	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	8	2	no	—
156	C₁₃×C₂²⋊C₄	—	8	2	no	—
157	C₁₃×C₂²⋊C₄	—	8	1	no	—
158	C₄²×C₁₃	—	2	4	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	8	2	no	—
162	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
164	#2435	C₂×C₁₃	1	1	yes	characteristic
165	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2065	C₂×C₁₃	1	2	yes	complemented
167	#2042	C₂×C₁₃	1	2	yes	complemented
168	#1983	C₂×C₁₃	1	2	yes	complemented
169	#1925	C₂×C₁₃	1	2	yes	complemented
170	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1786	C₂×C₁₃	1	1	yes	characteristic
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	4	8	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	8	4	no	—
186	C₂³×C₁₃	—	8	4	no	—
187	C₂³×C₁₃	—	8	8	no	—
188	C₂³×C₁₃	—	8	8	no	—
189	C₂³×C₁₃	#121	1	2	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	1	no	—
192	Q₈×C₁₃	—	4	1	no	—
193	Q₈×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	2	4	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	4	8	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	#121	1	2	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#124	C₂²×C₁₃	1	2	yes	—
233	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
235	#485	—	2	4	no	—
236	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
238	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
239	#418	—	2	4	no	—
240	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	2	yes	—
245	C₂×#102	C₂²×C₁₃	1	2	yes	—
246	C₂×#102	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	#394	—	2	1	no	—
249	#394	—	2	1	no	—
250	#390	C₂²×C₁₃	1	2	yes	—
251	#389	C₂²×C₁₃	1	2	yes	complemented
252	#388	—	2	2	no	—
253	#383	—	2	1	no	—
254	#380	C₂²×C₁₃	1	1	yes	characteristic
255	#379	—	2	2	no	—
256	C₄×C₄⋊C₄	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
258	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	#340	C₂²×C₁₃	1	2	yes	complemented
260	#336	C₂²×C₁₃	1	2	yes	complemented
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	8	16	no	—
270	C₂²×C₁₃	—	8	2	no	—
271	C₂²×C₁₃	—	8	2	no	—
272	C₂²×C₁₃	—	8	2	no	—
273	C₂²×C₁₃	—	8	2	no	—
274	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
275	C₂²×C₁₃	#546	1	2	yes	—
276	C₂²×C₁₃	#575	1	2	yes	—
277	C₂²×C₁₃	#576	1	1	yes	characteristic
278	C₂²×C₁₃	#577	1	1	yes	characteristic
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	8	1	no	—
285	C₄×C₁₃	—	8	1	no	—
286	C₄×C₁₃	—	8	2	no	—
287	C₄×C₁₃	#525	1	1	yes	characteristic
288	C₄×C₁₃	#535	1	1	yes	characteristic
289	C₄×C₁₃	#551	1	2	yes	—
290	C₂⁵	—	2	1	no	—
291	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×D₄	—	2	4	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	4	2	no	—
297	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	4	2	no	—
301	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	#124	—	2	4	no	—
305	#124	—	4	2	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	D₄×C₁₃	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
327	#107	—	2	2	no	—
328	#106	—	2	2	no	—
329	C₄⋊C₈	—	4	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	2	no	—
332	#103	—	4	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	4	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	D₄×C₁₃	1	1	yes	characteristic
342	#95	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₁₃	—	4	2	no	—
344	C₂×C₁₃	—	8	4	no	—
345	C₂×C₁₃	#2411	1	1	yes	characteristic
346	C₂×C₁₃	#3040	1	1	yes	characteristic
347	C₂×C₁₃	#3045	1	1	yes	characteristic
348	C₂×C₁₃	#3311	1	2	yes	—
349	C₂×C₁₃	#3322	1	2	yes	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	4	4	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	8	1	no	—
355	C₂⁴	—	8	1	no	—
356	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	8	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	C₁₃×#41	1	4	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₁₃×#41	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	M₁₆	—	4	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₂²⋊C₄	—	8	1	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	8	2	no	—
415	C₁₃	#24493	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	4	no	—
430	C₂³	—	8	8	no	—
431	C₂³	—	8	8	no	—
432	C₂³	C₁₃×#121	1	2	yes	—
433	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	C₁₃×#121	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
468	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
469	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	2	no	—
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	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	8	16	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
487	C₂²	C₁₃×#546	1	2	yes	—
488	C₂²	C₁₃×#575	1	2	yes	—
489	C₂²	C₁₃×#576	1	1	yes	characteristic
490	C₂²	C₁₃×#577	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	C₁₃×#525	1	1	yes	characteristic
500	C₄	C₁₃×#535	1	1	yes	characteristic
501	C₄	C₁₃×#551	1	2	yes	—
502	C₂	—	4	2	no	—
503	C₂	—	8	4	no	—
504	C₂	C₁₃×#2411	1	1	yes	characteristic
505	C₂	C₁₃×#3040	1	1	yes	characteristic
506	C₂	C₁₃×#3045	1	1	yes	characteristic
507	C₂	C₁₃×#3311	1	2	yes	—
508	C₂	C₁₃×#3322	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#485	C₂	semidirect
4. C₁₃×#2347	C₂	semidirect
5. C₁₃×#2065	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1925	C₂	semidirect
9. C₁₃×#1894	C₂	semidirect
10. C₁₃×#1851	C₂	semidirect
18. C₂×C₁₃×#107	C₂²	semidirect
19. C₂×C₁₃×#106	C₂²	semidirect
20. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₃×#103	C₂²	semidirect
23. C₂×C₁₃×#103	C₂²	semidirect
24. C₂×C₁₃×#103	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
39. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
41. C₁₃×#340	C₂²	semidirect
42. C₁₃×#336	C₂²	semidirect
96. #24493	C₁₃	direct (N × H)
162. C₂×#485	C₂×C₁₃	semidirect
165. #2347	C₂×C₁₃	semidirect
166. #2065	C₂×C₁₃	semidirect
167. #2042	C₂×C₁₃	semidirect
168. #1983	C₂×C₁₃	semidirect
169. #1925	C₂×C₁₃	semidirect
170. #1894	C₂×C₁₃	semidirect
171. #1851	C₂×C₁₃	semidirect
236. C₂×#107	C₂²×C₁₃	semidirect
237. C₂×#106	C₂²×C₁₃	semidirect
238. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
240. C₂×#103	C₂²×C₁₃	semidirect
241. C₂×#103	C₂²×C₁₃	semidirect
242. C₂×#103	C₂²×C₁₃	semidirect
251. #389	C₂²×C₁₃	semidirect
257. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
259. #340	C₂²×C₁₃	semidirect
260. #336	C₂²×C₁₃	semidirect
415. C₁₃	#24493	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×#485	2
C₂×C₁₃×#418	2
C₁₃×#2435	2
C₁₃×#2347	2
C₁₃×#2065	2
C₁₃×#2042	2
C₁₃×#1983	2
C₁₃×#1925	2
C₁₃×#1894	2
C₁₃×#1851	2
C₁₃×#1786	2
#24493	13

Subgroups — C13×#24493 #15710832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24493 #15710832