Subgroups — C₁₃×#24742 #15711081

Order 3328.

1104 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#460	—	2	8	no	—
21	C₁₃×#460	—	2	4	no	—
22	C₁₃×#440	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₁₃×#392	—	2	1	no	—
34	C₁₃×#392	—	2	1	no	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#382	—	2	1	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	4	no	—
55	C₂×C₁₃×SD₁₆	—	2	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#127	—	2	4	no	—
62	C₁₃×#127	—	2	2	no	—
63	C₁₃×#127	—	2	2	no	—
64	C₁₃×#127	—	4	2	no	—
65	C₁₃×#121	—	4	8	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	4	2	no	—
69	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
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	2	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	2	no	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×C₄⋊C₈	—	2	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	4	no	—
94	C₁₃×#102	—	4	2	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	D₄	1	1	yes	characteristic
100	C₁₃×#95	D₄	1	1	yes	characteristic
101	#24742	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₃	#41	1	2	yes	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	8	2	no	—
129	C₂×D₄×C₁₃	—	8	2	no	—
130	C₂×D₄×C₁₃	—	8	2	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	4	4	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×SD₁₆	—	2	8	no	—
144	C₁₃×SD₁₆	—	4	8	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₂²⋊C₄	—	4	4	no	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₄²×C₁₃	—	2	4	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	4	4	no	—
171	C₄²×C₁₃	C₂×D₄	1	2	yes	—
172	C₄²×C₁₃	#41	1	2	yes	—
173	C₂×#460	C₂×C₁₃	1	2	yes	complemented
174	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#2541	C₂×C₁₃	1	1	yes	characteristic
177	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2067	C₂×C₁₃	1	2	yes	complemented
179	#2041	C₂×C₁₃	1	2	yes	complemented
180	#1961	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1880	C₂×C₁₃	1	2	yes	complemented
183	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	#121	1	4	yes	complemented
201	D₄×C₁₃	—	2	2	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	1	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	8	8	no	—
210	D₄×C₁₃	—	8	4	no	—
211	D₄×C₁₃	—	8	4	no	—
212	D₄×C₁₃	—	8	8	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	8	4	no	—
231	C₂×C₄×C₁₃	#121	1	2	yes	—
232	C₂×C₄×C₁₃	#121	1	2	yes	—
233	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
240	C₈×C₁₃	—	2	2	no	—
241	C₈×C₁₃	—	4	2	no	—
242	C₈×C₁₃	—	4	1	no	—
243	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
244	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#127	C₂²×C₁₃	1	2	yes	—
247	C₂×#121	—	2	2	no	—
248	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
251	#460	—	2	8	no	—
252	#460	—	2	4	no	—
253	#440	—	2	4	no	—
254	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
257	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#102	C₂²×C₁₃	1	2	yes	—
259	C₂×#102	C₂²×C₁₃	1	2	yes	—
260	C₂×#102	C₂²×C₁₃	1	2	yes	—
261	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#102	C₂²×C₁₃	1	2	yes	—
263	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
264	#392	—	2	1	no	—
265	#392	—	2	1	no	—
266	#390	C₂²×C₁₃	1	2	yes	—
267	#389	—	2	2	no	—
268	#389	C₂²×C₁₃	1	2	yes	—
269	#382	—	2	1	no	—
270	#382	C₂²×C₁₃	1	1	yes	characteristic
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	#340	C₂²×C₁₃	1	2	yes	—
274	#336	C₂²×C₁₃	1	2	yes	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	4	no	—
277	C₂²×C₁₃	—	8	2	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	—	8	2	no	—
281	C₂²×C₁₃	—	8	2	no	—
282	C₂²×C₁₃	—	8	2	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	2	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
288	C₂²×C₁₃	D₄²	1	1	yes	characteristic
289	C₂²×C₁₃	#548	1	1	yes	characteristic
290	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
291	C₂²×C₁₃	#577	1	2	yes	—
292	C₄×C₁₃	—	2	4	no	—
293	C₄×C₁₃	—	2	4	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	2	no	—
298	C₄×C₁₃	—	8	2	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
301	C₄×C₁₃	#537	1	1	yes	characteristic
302	C₄×C₁₃	#547	1	1	yes	characteristic
303	C₄×C₁₃	#553	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
310	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂³×C₄	—	2	1	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	4	no	—
315	C₂×SD₁₆	—	2	4	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
318	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	#127	—	2	4	no	—
322	#127	—	2	2	no	—
323	#127	—	2	2	no	—
324	#127	—	4	2	no	—
325	#121	—	4	8	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	4	2	no	—
329	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	#107	—	2	2	no	—
347	C₄⋊C₈	—	2	4	no	—
348	C₄⋊C₈	—	2	2	no	—
349	#103	—	2	2	no	—
350	#102	—	2	4	no	—
351	#102	—	2	4	no	—
352	#102	—	2	2	no	—
353	#102	—	2	4	no	—
354	#102	—	4	2	no	—
355	#97	—	2	2	no	—
356	#95	—	2	1	no	—
357	#95	—	2	2	no	—
358	#95	—	2	1	no	—
359	#95	D₄×C₁₃	1	1	yes	characteristic
360	#95	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₁₃	—	8	2	no	—
362	C₂×C₁₃	—	16	2	no	—
363	C₂×C₁₃	#2416	1	1	yes	characteristic
364	C₂×C₁₃	#3038	1	1	yes	characteristic
365	C₂×C₁₃	#3043	1	1	yes	characteristic
366	C₂×C₁₃	#3265	1	2	yes	—
367	C₂×C₁₃	#3368	1	2	yes	—
368	C₂⁴	—	2	1	no	—
369	C₂⁴	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
375	C₂×Q₈	C₁₃×#41	1	2	yes	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	8	2	no	—
395	C₂×D₄	—	8	2	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	SD₁₆	—	2	8	no	—
410	SD₁₆	—	4	8	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	4	4	no	—
437	C₄²	C₂×D₄×C₁₃	1	2	yes	—
438	C₄²	C₁₃×#41	1	2	yes	—
439	C₁₃	#24742	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	C₁₃×#121	1	4	yes	complemented
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	8	no	—
466	D₄	—	8	4	no	—
467	D₄	—	8	4	no	—
468	D₄	—	8	8	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	8	4	no	—
487	C₂×C₄	C₁₃×#121	1	2	yes	—
488	C₂×C₄	C₁₃×#121	1	2	yes	—
489	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
494	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₈	—	4	1	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
512	C₂²	D₄²×C₁₃	1	1	yes	characteristic
513	C₂²	C₁₃×#548	1	1	yes	characteristic
514	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
515	C₂²	C₁₃×#577	1	2	yes	—
516	C₄	—	2	4	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	1	no	—
524	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
525	C₄	C₁₃×#537	1	1	yes	characteristic
526	C₄	C₁₃×#547	1	1	yes	characteristic
527	C₄	C₁₃×#553	1	1	yes	characteristic
528	C₂	—	8	2	no	—
529	C₂	—	16	2	no	—
530	C₂	C₁₃×#2416	1	1	yes	characteristic
531	C₂	C₁₃×#3038	1	1	yes	characteristic
532	C₂	C₁₃×#3043	1	1	yes	characteristic
533	C₂	C₁₃×#3265	1	2	yes	—
534	C₂	C₁₃×#3368	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2541	C₂
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×#460	C₂	semidirect
2. C₂×C₁₃×#460	C₂	semidirect
3. C₂×C₁₃×#440	C₂	semidirect
5. C₁₃×#2351	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2041	C₂	semidirect
8. C₁₃×#1961	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1880	C₂	semidirect
11. C₁₃×#1804	C₂	semidirect
57. C₂×C₁₃×SD₁₆	D₄	semidirect
69. C₄×Q₈×C₁₃	D₄	semidirect
101. #24742	C₁₃	direct (N × H)
173. C₂×#460	C₂×C₁₃	semidirect
174. C₂×#460	C₂×C₁₃	semidirect
175. C₂×#440	C₂×C₁₃	semidirect
177. #2351	C₂×C₁₃	semidirect
178. #2067	C₂×C₁₃	semidirect
179. #2041	C₂×C₁₃	semidirect
180. #1961	C₂×C₁₃	semidirect
181. #1940	C₂×C₁₃	semidirect
182. #1880	C₂×C₁₃	semidirect
183. #1804	C₂×C₁₃	semidirect
200. Q₈×C₁₃	#121	semidirect
317. C₂×SD₁₆	D₄×C₁₃	semidirect
329. C₄×Q₈	D₄×C₁₃	semidirect
439. C₁₃	#24742	direct (N × H)
456. Q₈	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#460	2
C₂×C₁₃×#440	2
C₁₃×#2541	2
C₁₃×#2351	2
C₁₃×#2067	2
C₁₃×#2041	2
C₁₃×#1961	2
C₁₃×#1940	2
C₁₃×#1880	2
C₁₃×#1804	2
#24742	13

Subgroups — C13×#24742 #15711081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24742 #15711081