Subgroups — C₁₃×#24326 #15710665

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1879	C₂	1	2	yes	maximal
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	—	2	1	no	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	D₄×Q₈×C₁₃	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#474	—	2	4	no	—
26	C₄×C₁₃×D₈	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	2	yes	—
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#390	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#384	C₂²	1	1	yes	characteristic
39	C₁₃×#380	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	8	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	4	4	no	—
49	C₂²×Q₈×C₁₃	—	4	4	no	—
50	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	Q₈	1	4	yes	complemented
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	—	2	4	no	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
66	C₁₃×C₂²⋊Q₈	—	2	8	no	—
67	C₁₃×C₂²⋊Q₈	—	2	16	no	—
68	C₁₃×C₂²⋊Q₈	—	4	4	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	4	no	—
72	C₄×D₄×C₁₃	—	2	4	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	D₄	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#107	—	2	2	no	—
96	C₁₃×#107	—	2	4	no	—
97	C₁₃×C₄⋊C₈	—	2	2	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	4	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#102	—	2	4	no	—
102	C₄×C₈×C₁₃	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	#24326	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	—	2	1	no	—
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	8	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	4	4	no	—
112	C₂×Q₈×C₁₃	—	4	32	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	—	4	2	no	—
115	C₂×Q₈×C₁₃	—	4	2	no	—
116	C₂×Q₈×C₁₃	D₈	1	4	yes	complemented
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
127	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	complemented
128	C₂×D₄×C₁₃	#41	1	2	yes	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	4	4	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×D₈	—	2	8	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	complemented
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	4	no	—
169	C₁₃×C₄⋊C₄	—	8	1	no	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	4	2	no	—
175	C₁₃×C₂²⋊C₄	—	4	4	no	—
176	C₁₃×C₂²⋊C₄	—	8	2	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
184	#2538	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2057	C₂×C₁₃	1	2	yes	complemented
186	#2023	C₂×C₁₃	1	2	yes	complemented
187	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1879	C₂×C₁₃	1	2	yes	—
190	#1862	C₂×C₁₃	1	2	yes	complemented
191	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₃	—	2	8	no	—
208	Q₈×C₁₃	—	4	16	no	—
209	Q₈×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	4	1	no	—
216	D₄×C₁₃	—	4	1	no	—
217	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	4	16	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	8	4	no	—
240	C₂×C₄×C₁₃	#120	1	2	yes	—
241	C₂×C₄×C₁₃	#120	1	2	yes	—
242	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
243	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
244	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₁₃	—	2	2	no	—
252	C₈×C₁₃	—	4	1	no	—
253	C₈×C₁₃	—	4	2	no	—
254	C₂³×Q₈	—	2	1	no	—
255	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
256	D₄×Q₈	—	2	4	no	—
257	D₄×Q₈	—	2	4	no	—
258	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	—	2	1	no	—
261	C₂×C₂²⋊Q₈	—	2	1	no	—
262	C₂×C₂²⋊Q₈	—	2	2	no	—
263	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
267	#474	—	2	4	no	—
268	C₄×D₈	—	2	4	no	—
269	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#107	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#102	C₂²×C₁₃	1	2	yes	—
273	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₃	1	2	yes	—
275	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
277	#396	—	2	2	no	—
278	#390	C₂²×C₁₃	1	2	yes	—
279	#389	C₂²×C₁₃	1	2	yes	—
280	#384	C₂²×C₁₃	1	1	yes	characteristic
281	#380	—	2	1	no	—
282	#340	C₂²×C₁₃	1	2	yes	—
283	#340	C₂²×C₁₃	1	2	yes	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	#336	C₂²×C₁₃	1	2	yes	—
286	#336	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₁₃	—	2	4	no	—
288	C₂²×C₁₃	—	4	2	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	8	1	no	—
298	C₂²×C₁₃	—	8	1	no	—
299	C₂²×C₁₃	—	8	1	no	—
300	C₂²×C₁₃	—	8	1	no	—
301	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
302	C₂²×C₁₃	#548	1	1	yes	characteristic
303	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
304	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
305	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂²×C₁₃	#577	1	1	yes	characteristic
307	C₂²×C₁₃	#578	1	1	yes	characteristic
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	—	8	1	no	—
315	C₄×C₁₃	#447	1	4	yes	—
316	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
317	C₄×C₁₃	#536	1	1	yes	characteristic
318	C₄×C₁₃	#548	1	1	yes	characteristic
319	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
320	C₂²×Q₈	—	2	8	no	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	—	4	4	no	—
324	C₂²×Q₈	—	4	4	no	—
325	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	—	2	1	no	—
331	C₂×D₈	—	2	2	no	—
332	C₂×D₈	—	2	2	no	—
333	C₂×D₈	Q₈×C₁₃	1	4	yes	complemented
334	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊Q₈	—	2	4	no	—
338	C₄⋊Q₈	—	2	4	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
341	C₂²⋊Q₈	—	2	8	no	—
342	C₂²⋊Q₈	—	2	16	no	—
343	C₂²⋊Q₈	—	4	4	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	D₄×C₁₃	1	4	yes	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
369	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
370	#107	—	2	2	no	—
371	#107	—	2	4	no	—
372	C₄⋊C₈	—	2	2	no	—
373	#102	—	2	2	no	—
374	#102	—	2	4	no	—
375	#102	—	2	2	no	—
376	#102	—	2	4	no	—
377	C₄×C₈	—	2	2	no	—
378	#95	—	2	2	no	—
379	C₂×C₁₃	—	4	4	no	—
380	C₂×C₁₃	—	8	2	no	—
381	C₂×C₁₃	#2409	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
383	C₂×C₁₃	#3013	1	1	yes	characteristic
384	C₂×C₁₃	#3358	1	1	yes	characteristic
385	C₂×C₁₃	#3367	1	1	yes	characteristic
386	C₂×C₁₃	Q₈×D₈	1	1	yes	characteristic
387	C₂×C₁₃	#3384	1	1	yes	characteristic
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	2	1	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	32	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	C₁₃×D₈	1	4	yes	complemented
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
410	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	complemented
411	C₂×D₄	C₁₃×#41	1	2	yes	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
430	D₈	—	2	8	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	complemented
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	8	1	no	—
453	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	8	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	C₂×D₄×C₁₃	1	2	yes	—
463	C₄²	C₂×D₄×C₁₃	1	2	yes	—
464	C₁₃	#24326	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	Q₈	—	2	8	no	—
481	Q₈	—	4	16	no	—
482	Q₈	—	4	8	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	C₁₃×#120	1	2	yes	—
514	C₂×C₄	C₁₃×#120	1	2	yes	—
515	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
516	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
517	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
522	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
542	C₂²	C₁₃×#548	1	1	yes	characteristic
543	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
544	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
545	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
546	C₂²	C₁₃×#577	1	1	yes	characteristic
547	C₂²	C₁₃×#578	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	2	no	—
554	C₄	—	8	1	no	—
555	C₄	C₁₃×#447	1	4	yes	—
556	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
557	C₄	C₁₃×#536	1	1	yes	characteristic
558	C₄	C₁₃×#548	1	1	yes	characteristic
559	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
560	C₂	—	4	4	no	—
561	C₂	—	8	2	no	—
562	C₂	C₁₃×#2409	1	1	yes	characteristic
563	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
564	C₂	C₁₃×#3013	1	1	yes	characteristic
565	C₂	C₁₃×#3358	1	1	yes	characteristic
566	C₂	C₁₃×#3367	1	1	yes	characteristic
567	C₂	Q₈×C₁₃×D₈	1	1	yes	characteristic
568	C₂	C₁₃×#3384	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₁₃	C₂	semidirect
2. C₂×C₁₃×#474	C₂	semidirect
4. C₁₃×#2538	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1984	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
58. C₂×C₁₃×D₈	Q₈	semidirect
104. #24326	C₁₃	direct (N × H)
116. C₂×Q₈×C₁₃	D₈	semidirect
127. C₂×D₄×C₁₃	C₂×Q₈	semidirect
156. C₂×C₈×C₁₃	C₂×Q₈	semidirect
181. C₂×D₄×Q₈	C₂×C₁₃	semidirect
182. C₂×#474	C₂×C₁₃	semidirect
184. #2538	C₂×C₁₃	semidirect
185. #2057	C₂×C₁₃	semidirect
186. #2023	C₂×C₁₃	semidirect
187. #1990	C₂×C₁₃	semidirect
188. #1984	C₂×C₁₃	semidirect
190. #1862	C₂×C₁₃	semidirect
191. #1802	C₂×C₁₃	semidirect
217. D₄×C₁₃	C₂²⋊Q₈	semidirect
333. C₂×D₈	Q₈×C₁₃	semidirect
399. C₂×Q₈	C₁₃×D₈	semidirect
410. C₂×D₄	C₂×Q₈×C₁₃	semidirect
439. C₂×C₈	C₂×Q₈×C₁₃	semidirect
464. C₁₃	#24326	direct (N × H)
490. D₄	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#474	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2538	2
C₁₃×#2057	2
C₁₃×#2023	2
C₁₃×#1990	2
C₁₃×#1984	2
C₁₃×#1879	2
C₁₃×#1862	2
C₁₃×#1802	2
#24326	13

Subgroups — C13×#24326 #15710665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24326 #15710665