Subgroups — C₁₃×#24132 #15710471

Order 3328.

1336 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₁₃×#547	—	2	4	no	—
15	C₁₃×#547	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#123	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
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	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₁₃×#477	—	2	4	no	—
26	C₁₃×#440	—	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×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₁₃×#398	—	2	1	no	—
38	C₁₃×#394	—	2	1	no	—
39	C₁₃×#388	—	2	2	no	—
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	—	4	8	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
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×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
63	C₁₃×#123	—	2	16	no	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₁₃×C₂²⋊Q₈	—	4	2	no	—
67	C₁₃×#121	—	2	4	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	D₄	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×#107	—	2	4	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×#103	—	2	2	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	4	2	no	—
100	C₁₃×C₂²⋊C₈	—	2	4	no	—
101	C₁₃×C₂²⋊C₈	—	4	2	no	—
102	C₁₃×#97	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	1	no	—
105	C₁₃×#95	—	2	1	no	—
106	#24132	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	1	no	—
108	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
109	C₁₃×#41	—	4	32	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×SD₁₆	—	2	8	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	#41	1	2	yes	complemented
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	4	4	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	4	4	no	—
176	C₁₃×C₂²⋊C₄	—	4	4	no	—
177	C₄²×C₁₃	—	4	2	no	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
181	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2536	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#2033	C₂×C₁₃	1	2	yes	complemented
185	#2000	C₂×C₁₃	1	2	yes	complemented
186	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1955	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1872	C₂×C₁₃	1	2	yes	complemented
189	#1852	C₂×C₁₃	1	2	yes	complemented
190	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	2	no	—
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	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	2	no	—
205	Q₈×C₁₃	—	2	2	no	—
206	Q₈×C₁₃	—	4	8	no	—
207	Q₈×C₁₃	—	4	1	no	—
208	Q₈×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	2	8	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	4	16	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	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	4	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	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	16	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	#120	1	2	yes	—
240	C₂×C₄×C₁₃	#120	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	—	4	1	no	—
249	C₈×C₁₃	—	4	2	no	—
250	C₂²×#41	—	2	1	no	—
251	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
252	#547	—	2	4	no	—
253	#547	—	2	4	no	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#123	—	2	2	no	—
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
258	C₂×#121	C₂²×C₁₃	1	2	yes	—
259	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
263	#477	—	2	4	no	—
264	#440	—	2	4	no	—
265	C₂×#107	C₂²×C₁₃	1	2	yes	—
266	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#103	C₂²×C₁₃	1	2	yes	—
269	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
274	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
275	#398	—	2	1	no	—
276	#394	—	2	1	no	—
277	#388	—	2	2	no	—
278	#382	C₂²×C₁₃	1	1	yes	characteristic
279	#380	C₂²×C₁₃	1	2	yes	—
280	#340	C₂²×C₁₃	1	2	yes	—
281	#340	C₂²×C₁₃	1	2	yes	—
282	#340	C₂²×C₁₃	1	2	yes	—
283	C₂²×C₁₃	—	2	4	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	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	—	8	2	no	—
294	C₂²×C₁₃	—	8	2	no	—
295	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₃	#546	1	1	yes	characteristic
297	C₂²×C₁₃	#547	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
299	C₂²×C₁₃	#578	1	2	yes	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	8	1	no	—
307	C₄×C₁₃	—	8	2	no	—
308	C₄×C₁₃	#525	1	1	yes	characteristic
309	C₄×C₁₃	#537	1	1	yes	characteristic
310	C₄×C₁₃	#548	1	1	yes	characteristic
311	C₄×C₁₃	#550	1	1	yes	characteristic
312	C₂×#41	—	2	8	no	—
313	C₂×#41	—	4	8	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
330	#123	—	2	16	no	—
331	C₂²⋊Q₈	—	2	8	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	4	2	no	—
334	#121	—	2	4	no	—
335	#121	—	2	4	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	D₄×C₁₃	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	#107	—	2	2	no	—
361	#107	—	2	4	no	—
362	C₄⋊C₈	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	4	no	—
365	#102	—	2	2	no	—
366	#102	—	4	2	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	C₂²⋊C₈	—	4	2	no	—
369	#97	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	C₂×C₁₃	—	4	4	no	—
374	C₂×C₁₃	—	8	2	no	—
375	C₂×C₁₃	#2407	1	1	yes	characteristic
376	C₂×C₁₃	#3003	1	1	yes	characteristic
377	C₂×C₁₃	#3011	1	1	yes	characteristic
378	C₂×C₁₃	#3308	1	2	yes	—
379	C₂×C₁₃	#3343	1	2	yes	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
382	#41	—	4	32	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	SD₁₆	—	2	8	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	C₁₃×#41	1	2	yes	complemented
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₄²	—	4	2	no	—
451	C₄²	C₂×D₄×C₁₃	1	2	yes	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₁₃	#24132	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	4	8	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	D₄	—	2	8	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	C₁₃×#120	1	2	yes	—
503	C₂×C₄	C₁₃×#120	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
507	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
508	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
526	C₂²	C₁₃×#546	1	1	yes	characteristic
527	C₂²	C₁₃×#547	1	1	yes	characteristic
528	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
529	C₂²	C₁₃×#578	1	2	yes	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	8	2	no	—
537	C₄	—	8	1	no	—
538	C₄	C₁₃×#525	1	1	yes	characteristic
539	C₄	C₁₃×#537	1	1	yes	characteristic
540	C₄	C₁₃×#548	1	1	yes	characteristic
541	C₄	C₁₃×#550	1	1	yes	characteristic
542	C₂	—	4	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₁₃×#2407	1	1	yes	characteristic
545	C₂	C₁₃×#3003	1	1	yes	characteristic
546	C₂	C₁₃×#3011	1	1	yes	characteristic
547	C₂	C₁₃×#3308	1	2	yes	—
548	C₂	C₁₃×#3343	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#547	C₂
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
2. C₂×C₁₃×#477	C₂	semidirect
3. C₂×C₁₃×#440	C₂	semidirect
4. C₁₃×#2536	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#2000	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1955	C₂	semidirect
9. C₁₃×#1872	C₂	semidirect
10. C₁₃×#1852	C₂	semidirect
11. C₁₃×#1804	C₂	semidirect
106. #24132	C₁₃	direct (N × H)
117. C₂×Q₈×C₁₃	#41	semidirect
158. C₂×C₈×C₁₃	#41	semidirect
181. C₂×#477	C₂×C₁₃	semidirect
182. C₂×#440	C₂×C₁₃	semidirect
183. #2536	C₂×C₁₃	semidirect
184. #2033	C₂×C₁₃	semidirect
185. #2000	C₂×C₁₃	semidirect
186. #1993	C₂×C₁₃	semidirect
187. #1955	C₂×C₁₃	semidirect
188. #1872	C₂×C₁₃	semidirect
189. #1852	C₂×C₁₃	semidirect
190. #1804	C₂×C₁₃	semidirect
390. C₂×Q₈	C₁₃×#41	semidirect
431. C₂×C₈	C₁₃×#41	semidirect
453. C₁₃	#24132	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×#547	2
C₂×C₁₃×#477	2
C₂×C₁₃×#440	2
C₁₃×#2536	2
C₁₃×#2033	2
C₁₃×#2000	2
C₁₃×#1993	2
C₁₃×#1955	2
C₁₃×#1872	2
C₁₃×#1852	2
C₁₃×#1804	2
#24132	13

Subgroups — C13×#24132 #15710471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24132 #15710471