Subgroups — C₁₃×#24116 #15710455

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 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, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1999	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂²×C₁₃×D₈	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×#121	—	2	1	no	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#474	—	2	4	no	—
27	C₄×C₁₃×D₈	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#394	—	2	2	no	—
39	C₁₃×#384	C₂²	1	1	yes	characteristic
40	C₁₃×#380	—	2	1	no	—
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	4	no	—
47	C₂×C₁₃×#41	—	4	4	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	4	yes	complemented
66	C₁₃×#123	—	2	16	no	—
67	C₁₃×C₂²⋊Q₈	—	2	8	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#121	—	2	4	no	—
70	C₁₃×#121	—	2	4	no	—
71	C₁₃×#121	—	4	2	no	—
72	C₁₃×#121	—	4	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	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#107	—	2	2	no	—
98	C₁₃×#107	—	2	4	no	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#102	—	2	2	no	—
102	C₁₃×#102	—	2	4	no	—
103	C₁₃×#102	—	4	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	4	no	—
105	C₁₃×C₂²⋊C₈	—	4	2	no	—
106	C₄×C₈×C₁₃	—	2	2	no	—
107	C₁₃×#95	—	2	2	no	—
108	#24116	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	1	no	—
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
112	C₁₃×#41	—	4	32	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	4	2	no	—
115	C₂×Q₈×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	8	2	no	—
134	C₂×D₄×C₁₃	D₈	1	4	yes	complemented
135	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₃	#41	1	2	yes	complemented
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×D₈	—	2	8	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	#41	1	2	yes	complemented
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	—	8	1	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	4	4	no	—
187	C₁₃×C₂²⋊C₄	—	4	4	no	—
188	C₁₃×C₂²⋊C₄	—	4	2	no	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2537	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2033	C₂×C₁₃	1	2	yes	complemented
196	#1999	C₂×C₁₃	1	2	yes	complemented
197	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1874	C₂×C₁₃	1	2	yes	complemented
200	#1852	C₂×C₁₃	1	2	yes	complemented
201	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	C₂×D₈	1	4	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	4	8	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	8	no	—
230	D₄×C₁₃	—	4	16	no	—
231	D₄×C₁₃	—	4	1	no	—
232	D₄×C₁₃	—	4	1	no	—
233	D₄×C₁₃	—	4	1	no	—
234	D₄×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	8	8	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	16	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	8	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	8	4	no	—
260	C₂×C₄×C₁₃	#120	1	2	yes	—
261	C₂×C₄×C₁₃	#120	1	2	yes	—
262	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
263	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
269	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₂²×#41	—	2	1	no	—
274	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
275	#547	—	2	4	no	—
276	#547	—	2	4	no	—
277	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#123	—	2	2	no	—
279	C₂×C₂²⋊Q₈	—	2	1	no	—
280	C₂×#121	—	2	1	no	—
281	C₂×#121	C₂²×C₁₃	1	2	yes	—
282	C₂×#121	C₂²×C₁₃	1	2	yes	—
283	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
287	#474	—	2	4	no	—
288	C₄×D₈	—	2	4	no	—
289	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#107	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#102	C₂²×C₁₃	1	2	yes	—
294	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₁₃	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
297	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	#394	—	2	2	no	—
300	#384	C₂²×C₁₃	1	1	yes	characteristic
301	#380	—	2	1	no	—
302	#380	C₂²×C₁₃	1	2	yes	—
303	#340	C₂²×C₁₃	1	2	yes	—
304	#340	C₂²×C₁₃	1	2	yes	—
305	#340	C₂²×C₁₃	1	2	yes	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	4	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	—	8	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
328	C₂²×C₁₃	#546	1	1	yes	characteristic
329	C₂²×C₁₃	#547	1	1	yes	characteristic
330	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₂²×C₁₃	#577	1	1	yes	characteristic
333	C₂²×C₁₃	#578	1	1	yes	characteristic
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	4	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	2	no	—
340	C₄×C₁₃	#447	1	4	yes	—
341	C₄×C₁₃	#525	1	1	yes	characteristic
342	C₄×C₁₃	#537	1	1	yes	characteristic
343	C₄×C₁₃	#548	1	1	yes	characteristic
344	C₄×C₁₃	#550	1	1	yes	characteristic
345	C₂×#41	—	2	8	no	—
346	C₂×#41	—	4	4	no	—
347	C₂×#41	—	4	4	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	—	2	2	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	2	2	no	—
360	C₂×D₈	—	2	2	no	—
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	D₄×C₁₃	1	4	yes	complemented
366	#123	—	2	16	no	—
367	C₂²⋊Q₈	—	2	8	no	—
368	#121	—	2	4	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	4	2	no	—
372	#121	—	4	4	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
397	#107	—	2	2	no	—
398	#107	—	2	4	no	—
399	C₄⋊C₈	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	4	no	—
403	#102	—	4	2	no	—
404	C₂²⋊C₈	—	2	4	no	—
405	C₂²⋊C₈	—	4	2	no	—
406	C₄×C₈	—	2	2	no	—
407	#95	—	2	2	no	—
408	C₂×C₁₃	—	4	4	no	—
409	C₂×C₁₃	—	8	2	no	—
410	C₂×C₁₃	—	8	2	no	—
411	C₂×C₁₃	#2407	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
413	C₂×C₁₃	#3013	1	1	yes	characteristic
414	C₂×C₁₃	#3294	1	1	yes	characteristic
415	C₂×C₁₃	#3330	1	1	yes	characteristic
416	C₂×C₁₃	#3334	1	1	yes	characteristic
417	C₂×C₁₃	#3354	1	1	yes	characteristic
418	C₂⁴	—	2	1	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
421	#41	—	4	32	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	8	2	no	—
443	C₂×D₄	C₁₃×D₈	1	4	yes	complemented
444	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂×D₄	C₁₃×#41	1	2	yes	complemented
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	D₈	—	2	8	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	C₁₃×#41	1	2	yes	complemented
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	8	1	no	—
490	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
491	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	4	4	no	—
496	C₂²⋊C₄	—	4	4	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₄²	C₂×D₄×C₁₃	1	2	yes	—
499	C₄²	C₂×D₄×C₁₃	1	2	yes	—
500	C₁₃	#24116	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	C₂×C₁₃×D₈	1	4	yes	—
522	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	Q₈	—	4	8	no	—
524	D₄	—	2	8	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	16	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	8	8	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	16	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	C₁₃×#120	1	2	yes	—
560	C₂×C₄	C₁₃×#120	1	2	yes	—
561	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
562	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
566	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
567	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
594	C₂²	C₁₃×#546	1	1	yes	characteristic
595	C₂²	C₁₃×#547	1	1	yes	characteristic
596	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
597	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
598	C₂²	C₁₃×#577	1	1	yes	characteristic
599	C₂²	C₁₃×#578	1	1	yes	characteristic
600	C₄	—	2	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	4	no	—
604	C₄	—	8	2	no	—
605	C₄	—	8	1	no	—
606	C₄	C₁₃×#447	1	4	yes	—
607	C₄	C₁₃×#525	1	1	yes	characteristic
608	C₄	C₁₃×#537	1	1	yes	characteristic
609	C₄	C₁₃×#548	1	1	yes	characteristic
610	C₄	C₁₃×#550	1	1	yes	characteristic
611	C₂	—	4	4	no	—
612	C₂	—	8	2	no	—
613	C₂	—	8	2	no	—
614	C₂	C₁₃×#2407	1	1	yes	characteristic
615	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
616	C₂	C₁₃×#3013	1	1	yes	characteristic
617	C₂	C₁₃×#3294	1	1	yes	characteristic
618	C₂	C₁₃×#3330	1	1	yes	characteristic
619	C₂	C₁₃×#3334	1	1	yes	characteristic
620	C₂	C₁₃×#3354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₂×C₁₃×#547	C₂	semidirect
2. C₂×C₁₃×#474	C₂	semidirect
3. C₂×C₄×C₁₃×D₈	C₂	semidirect
4. C₁₃×#2537	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1999	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1954	C₂	semidirect
9. C₁₃×#1874	C₂	semidirect
10. C₁₃×#1852	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
65. C₁₃×C₄⋊Q₈	D₄	semidirect
78. C₄×D₄×C₁₃	D₄	semidirect
108. #24116	C₁₃	direct (N × H)
134. C₂×D₄×C₁₃	D₈	semidirect
136. C₂×D₄×C₁₃	#41	semidirect
169. C₂×C₈×C₁₃	#41	semidirect
191. C₂×#547	C₂×C₁₃	semidirect
192. C₂×#474	C₂×C₁₃	semidirect
193. C₂×C₄×D₈	C₂×C₁₃	semidirect
194. #2537	C₂×C₁₃	semidirect
195. #2033	C₂×C₁₃	semidirect
196. #1999	C₂×C₁₃	semidirect
197. #1990	C₂×C₁₃	semidirect
198. #1954	C₂×C₁₃	semidirect
199. #1874	C₂×C₁₃	semidirect
200. #1852	C₂×C₁₃	semidirect
201. #1802	C₂×C₁₃	semidirect
365. C₄⋊Q₈	D₄×C₁₃	semidirect
378. C₄×D₄	D₄×C₁₃	semidirect
443. C₂×D₄	C₁₃×D₈	semidirect
445. C₂×D₄	C₁₃×#41	semidirect
478. C₂×C₈	C₁₃×#41	semidirect
500. C₁₃	#24116	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×#474	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2537	2
C₁₃×#2033	2
C₁₃×#1999	2
C₁₃×#1990	2
C₁₃×#1954	2
C₁₃×#1874	2
C₁₃×#1852	2
C₁₃×#1802	2
#24116	13

Subgroups — C13×#24116 #15710455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24116 #15710455