Subgroups — C₁₃×#24676 #15711015

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2054	C₂	1	2	yes	maximal
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₁₃×#474	—	2	4	no	—
20	C₄×C₁₃×D₈	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#399	—	2	2	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#388	—	2	2	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#384	C₂²	1	2	yes	—
36	C₁₃×#380	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	4	no	—
57	C₁₃×C₂²⋊Q₈	—	4	4	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	D₄	1	4	yes	—
62	C₁₃×#117	—	4	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#107	—	2	4	no	—
85	C₁₃×C₄⋊C₈	—	2	4	no	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₁₃×#102	—	2	4	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	D₄	1	2	yes	—
94	#24676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂⁴×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×D₈	—	2	8	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	#41	1	2	yes	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	4	no	—
149	C₁₃×C₄⋊C₄	—	8	1	no	—
150	C₁₃×C₄⋊C₄	D₈	1	4	yes	complemented
151	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	8	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	4	4	no	—
161	C₄²×C₁₃	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃	#41	1	2	yes	—
163	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
165	#2542	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2071	C₂×C₁₃	1	2	yes	complemented
168	#2054	C₂×C₁₃	1	2	yes	—
169	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1947	C₂×C₁₃	1	2	yes	complemented
171	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1925	C₂×C₁₃	1	2	yes	complemented
173	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₃	—	8	4	no	—
190	D₄×C₁₃	—	2	2	no	—
191	D₄×C₁₃	—	2	2	no	—
192	D₄×C₁₃	—	2	2	no	—
193	D₄×C₁₃	—	2	2	no	—
194	D₄×C₁₃	—	4	1	no	—
195	D₄×C₁₃	—	4	1	no	—
196	D₄×C₁₃	—	4	1	no	—
197	D₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	4	1	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	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	8	4	no	—
219	C₂×C₄×C₁₃	#121	1	2	yes	—
220	C₂×C₄×C₁₃	#121	1	2	yes	—
221	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
222	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	4	2	no	—
232	C₈×C₁₃	—	4	1	no	—
233	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	1	no	—
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#117	—	2	1	no	—
240	#474	—	2	4	no	—
241	C₄×D₈	—	2	4	no	—
242	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#107	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#102	C₂²×C₁₃	1	2	yes	—
247	C₂×#102	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
251	#399	—	2	2	no	—
252	#390	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	2	yes	—
254	#388	—	2	2	no	—
255	#384	C₂²×C₁₃	1	1	yes	characteristic
256	#384	C₂²×C₁₃	1	2	yes	—
257	#380	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	1	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
279	C₂²×C₁₃	#547	1	1	yes	characteristic
280	C₂²×C₁₃	#548	1	1	yes	characteristic
281	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₁₃	#577	1	1	yes	characteristic
284	C₂²×C₁₃	#578	1	1	yes	characteristic
285	C₄×C₁₃	—	2	4	no	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	2	no	—
289	C₄×C₁₃	—	8	2	no	—
290	C₄×C₁₃	—	8	1	no	—
291	C₄×C₁₃	—	8	2	no	—
292	C₄×C₁₃	#459	1	4	yes	—
293	C₄×C₁₃	#525	1	1	yes	characteristic
294	C₄×C₁₃	#536	1	1	yes	characteristic
295	C₄×C₁₃	#552	1	1	yes	characteristic
296	C₄×C₁₃	#556	1	1	yes	characteristic
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	2	2	no	—
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	4	4	no	—
311	C₂²⋊Q₈	—	4	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	D₄×C₁₃	1	4	yes	—
316	#117	—	4	4	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×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	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
337	#107	—	2	2	no	—
338	#107	—	2	4	no	—
339	C₄⋊C₈	—	2	4	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	2	2	no	—
345	C₄×C₈	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	D₄×C₁₃	1	2	yes	—
348	C₂×C₁₃	—	8	2	no	—
349	C₂×C₁₃	—	8	2	no	—
350	C₂×C₁₃	#2415	1	1	yes	characteristic
351	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
352	C₂×C₁₃	#3046	1	1	yes	characteristic
353	C₂×C₁₃	#3334	1	1	yes	characteristic
354	C₂×C₁₃	#3354	1	1	yes	characteristic
355	C₂×C₁₃	#3358	1	1	yes	characteristic
356	C₂×C₁₃	#3367	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	2	1	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂×D₄	C₁₃×#41	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
389	D₈	—	2	8	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	C₁₃×#41	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	8	1	no	—
412	C₄⋊C₄	C₁₃×D₈	1	4	yes	complemented
413	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	8	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	4	no	—
423	C₄²	C₂×D₄×C₁₃	1	2	yes	—
424	C₄²	C₁₃×#41	1	2	yes	—
425	C₁₃	#24676	1	1	yes	characteristic, direct product factor, Sylow
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
441	Q₈	—	8	4	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	C₁₃×#121	1	2	yes	—
472	C₂×C₄	C₁₃×#121	1	2	yes	—
473	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
474	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
475	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
478	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
479	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
480	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
481	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	4	2	no	—
484	C₈	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
500	C₂²	C₁₃×#547	1	1	yes	characteristic
501	C₂²	C₁₃×#548	1	1	yes	characteristic
502	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
503	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₂²	C₁₃×#577	1	1	yes	characteristic
505	C₂²	C₁₃×#578	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	2	no	—
512	C₄	—	8	2	no	—
513	C₄	C₁₃×#459	1	4	yes	—
514	C₄	C₁₃×#525	1	1	yes	characteristic
515	C₄	C₁₃×#536	1	1	yes	characteristic
516	C₄	C₁₃×#552	1	1	yes	characteristic
517	C₄	C₁₃×#556	1	1	yes	characteristic
518	C₂	—	8	2	no	—
519	C₂	—	8	2	no	—
520	C₂	C₁₃×#2415	1	1	yes	characteristic
521	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
522	C₂	C₁₃×#3046	1	1	yes	characteristic
523	C₂	C₁₃×#3334	1	1	yes	characteristic
524	C₂	C₁₃×#3354	1	1	yes	characteristic
525	C₂	C₁₃×#3358	1	1	yes	characteristic
526	C₂	C₁₃×#3367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#474	C₂	semidirect
3. C₁₃×#2542	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2071	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
94. #24676	C₁₃	direct (N × H)
150. C₁₃×C₄⋊C₄	D₈	semidirect
163. C₂×#474	C₂×C₁₃	semidirect
165. #2542	C₂×C₁₃	semidirect
166. #2354	C₂×C₁₃	semidirect
167. #2071	C₂×C₁₃	semidirect
169. #1990	C₂×C₁₃	semidirect
170. #1947	C₂×C₁₃	semidirect
171. #1939	C₂×C₁₃	semidirect
172. #1925	C₂×C₁₃	semidirect
173. #1802	C₂×C₁₃	semidirect
412. C₄⋊C₄	C₁₃×D₈	semidirect
425. C₁₃	#24676	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×#474	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2542	2
C₁₃×#2354	2
C₁₃×#2071	2
C₁₃×#2054	2
C₁₃×#1990	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1925	2
C₁₃×#1802	2
#24676	13

Subgroups — C13×#24676 #15711015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24676 #15711015