Subgroups — C₁₃×#24171 #15710510

Order 3328.

1106 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2006	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1883	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₁₃×#556	—	2	1	no	—
15	C₁₃×#555	—	2	1	no	—
16	C₁₃×#554	—	2	1	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#548	—	2	2	no	—
19	C₁₃×#547	—	2	1	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#537	C₂²	1	2	yes	—
22	C₁₃×#533	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×#520	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#463	—	2	2	no	—
30	C₁₃×#461	—	2	1	no	—
31	C₁₃×#459	—	2	1	no	—
32	C₁₃×#442	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	1	no	—
35	C₄×C₁₃×D₈	—	2	1	no	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₂×C₁₃×#104	C₂²	1	2	yes	—
40	C₂×C₁₃×#104	C₂²	1	2	yes	—
41	C₁₃×#418	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	2	yes	—
43	C₁₃×#417	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
45	C₁₃×#393	—	2	2	no	—
46	C₁₃×#390	C₂²	1	2	yes	—
47	C₁₃×#382	C₂²	1	2	yes	—
48	C₁₃×#380	—	2	2	no	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₁₃×#343	C₂²	1	2	yes	—
51	C₁₃×#343	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	—	2	1	no	—
59	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
60	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
61	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
62	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	1	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×D₈	—	2	1	no	—
66	C₂×C₁₃×D₈	—	2	2	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	—	2	1	no	—
71	C₁₃×C₄⋊Q₈	—	2	1	no	—
72	C₁₃×C₄⋊Q₈	—	2	1	no	—
73	C₁₃×C₄⋊Q₈	—	2	1	no	—
74	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₃×#127	D₄	1	1	yes	characteristic
76	C₁₃×#126	—	2	4	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	D₄	1	2	yes	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₁₃×#117	—	2	2	no	—
110	C₁₃×#117	—	2	2	no	—
111	C₁₃×#117	—	2	1	no	—
112	C₁₃×#117	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×#104	—	2	4	no	—
128	C₁₃×#104	—	4	2	no	—
129	C₁₃×#104	—	4	2	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#97	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	4	no	—
140	#24171	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₁₃×#41	—	2	2	no	—
143	C₁₃×#41	—	2	2	no	—
144	C₁₃×#41	—	2	1	no	—
145	C₁₃×#41	—	2	1	no	—
146	C₁₃×#41	—	2	1	no	—
147	C₁₃×#41	—	2	2	no	—
148	C₁₃×#41	—	2	2	no	—
149	C₁₃×#41	—	2	1	no	—
150	C₁₃×#41	—	8	4	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	8	2	no	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₃	#41	1	2	yes	complemented
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	4	4	no	—
177	C₂²×C₄×C₁₃	—	4	1	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×SD₁₆	—	2	4	no	—
184	C₁₃×SD₁₆	—	4	4	no	—
185	C₁₃×D₈	—	2	4	no	—
186	C₁₃×D₈	—	4	4	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	2	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	—	2	2	no	—
191	C₁₃×M₁₆	—	2	1	no	—
192	C₁₃×M₁₆	#41	1	2	yes	complemented
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	1	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	2	1	no	—
217	C₁₃×C₂²⋊C₄	—	2	2	no	—
218	C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	1	no	—
220	C₁₃×C₂²⋊C₄	—	4	1	no	—
221	C₁₃×C₂²⋊C₄	—	8	4	no	—
222	C₄²×C₁₃	—	2	4	no	—
223	C₄²×C₁₃	—	2	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	2	no	—
227	C₄²×C₁₃	—	2	2	no	—
228	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
232	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2040	C₂×C₁₃	1	2	yes	complemented
237	#2006	C₂×C₁₃	1	2	yes	complemented
238	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1883	C₂×C₁₃	1	2	yes	complemented
241	#1860	C₂×C₁₃	1	2	yes	complemented
242	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	4	2	no	—
247	C₂³×C₁₃	—	4	2	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	1	no	—
252	Q₈×C₁₃	—	2	1	no	—
253	Q₈×C₁₃	—	2	2	no	—
254	Q₈×C₁₃	—	2	2	no	—
255	Q₈×C₁₃	—	4	4	no	—
256	Q₈×C₁₃	—	8	2	no	—
257	D₄×C₁₃	—	2	1	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	1	no	—
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	2	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	4	2	no	—
265	D₄×C₁₃	—	4	1	no	—
266	D₄×C₁₃	—	4	2	no	—
267	D₄×C₁₃	—	4	1	no	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	—	4	2	no	—
271	D₄×C₁₃	—	8	4	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	2	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	4	no	—
286	C₂×C₄×C₁₃	—	4	2	no	—
287	C₂×C₄×C₁₃	—	4	2	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	8	2	no	—
292	C₂×C₄×C₁₃	—	8	4	no	—
293	C₂×C₄×C₁₃	—	8	2	no	—
294	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
304	C₈×C₁₃	—	2	2	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₈×C₁₃	—	4	2	no	—
307	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
309	#556	—	2	1	no	—
310	#555	—	2	1	no	—
311	#554	—	2	1	no	—
312	#553	—	2	2	no	—
313	#548	—	2	2	no	—
314	#547	—	2	1	no	—
315	#542	—	2	2	no	—
316	#537	C₂²×C₁₃	1	2	yes	—
317	#533	—	2	1	no	—
318	#532	—	2	1	no	—
319	#532	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	#520	C₂²×C₁₃	1	2	yes	—
322	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	#463	—	2	2	no	—
325	#461	—	2	1	no	—
326	#459	—	2	1	no	—
327	#442	—	2	1	no	—
328	#440	—	2	1	no	—
329	C₄×SD₁₆	—	2	1	no	—
330	C₄×D₈	—	2	1	no	—
331	#428	C₂²×C₁₃	1	1	yes	characteristic
332	#423	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#104	C₂²×C₁₃	1	2	yes	—
334	C₂×#104	C₂²×C₁₃	1	2	yes	—
335	C₂×#104	C₂²×C₁₃	1	2	yes	—
336	#418	C₂²×C₁₃	1	1	yes	characteristic
337	#417	C₂²×C₁₃	1	2	yes	—
338	#417	C₂²×C₁₃	1	1	yes	characteristic
339	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	#393	—	2	2	no	—
341	#390	C₂²×C₁₃	1	2	yes	—
342	#382	C₂²×C₁₃	1	2	yes	—
343	#380	—	2	2	no	—
344	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
345	#343	C₂²×C₁₃	1	2	yes	—
346	#343	C₂²×C₁₃	1	2	yes	—
347	#339	C₂²×C₁₃	1	2	yes	—
348	C₂²×C₁₃	—	2	1	no	—
349	C₂²×C₁₃	—	2	1	no	—
350	C₂²×C₁₃	—	4	4	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	—	4	2	no	—
356	C₂²×C₁₃	—	4	1	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	8	2	no	—
359	C₂²×C₁₃	—	8	1	no	—
360	C₂²×C₁₃	—	8	1	no	—
361	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
362	C₂²×C₁₃	#548	1	1	yes	characteristic
363	C₂²×C₁₃	#550	1	1	yes	characteristic
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	2	1	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	4	no	—
372	C₄×C₁₃	—	8	2	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	#454	1	2	yes	—
375	C₄×C₁₃	#525	1	1	yes	characteristic
376	C₄×C₁₃	#537	1	1	yes	characteristic
377	C₄×C₁₃	#546	1	1	yes	characteristic
378	C₄×C₁₃	#547	1	1	yes	characteristic
379	C₂×#41	—	2	2	no	—
380	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×#41	C₂³×C₁₃	1	2	yes	—
382	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
383	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	AGL(1,ℤ/8)	—	2	2	no	—
386	AGL(1,ℤ/8)	—	2	4	no	—
387	AGL(1,ℤ/8)	—	2	2	no	—
388	AGL(1,ℤ/8)	—	4	2	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×D₈	—	2	1	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
396	C₄⋊Q₈	—	2	1	no	—
397	C₄⋊Q₈	—	2	1	no	—
398	C₄⋊Q₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
401	#127	D₄×C₁₃	1	1	yes	characteristic
402	#126	—	2	4	no	—
403	#125	—	2	2	no	—
404	#124	—	2	2	no	—
405	#124	—	2	4	no	—
406	#124	D₄×C₁₃	1	2	yes	—
407	#123	—	2	4	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	#121	—	2	2	no	—
413	#121	—	2	2	no	—
414	#121	—	2	2	no	—
415	#121	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	2	4	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
421	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
434	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
435	#117	—	2	2	no	—
436	#117	—	2	2	no	—
437	#117	—	2	1	no	—
438	#117	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	4	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	#107	—	2	1	no	—
450	#106	—	2	1	no	—
451	C₄⋊C₈	—	2	1	no	—
452	C₄⋊C₈	—	2	1	no	—
453	#104	—	2	4	no	—
454	#104	—	4	2	no	—
455	#104	—	4	2	no	—
456	#103	—	2	1	no	—
457	#103	—	2	2	no	—
458	#102	—	2	1	no	—
459	#102	—	2	2	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	#97	—	2	1	no	—
463	C₄×C₈	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	4	no	—
466	C₂×C₁₃	—	2	1	no	—
467	C₂×C₁₃	—	2	1	no	—
468	C₂×C₁₃	—	8	1	no	—
469	C₂×C₁₃	—	8	2	no	—
470	C₂×C₁₃	—	8	2	no	—
471	C₂×C₁₃	#2407	1	1	yes	characteristic
472	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
473	C₂×C₁₃	#3019	1	1	yes	characteristic
474	C₂⁴	—	2	1	no	—
475	#41	—	2	2	no	—
476	#41	—	2	2	no	—
477	#41	—	2	1	no	—
478	#41	—	2	1	no	—
479	#41	—	2	1	no	—
480	#41	—	2	2	no	—
481	#41	—	2	2	no	—
482	#41	—	2	1	no	—
483	#41	—	8	4	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	2	2	no	—
486	C₂×Q₈	—	8	2	no	—
487	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
488	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
500	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂×D₄	C₁₃×#41	1	2	yes	complemented
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
514	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
516	SD₁₆	—	2	4	no	—
517	SD₁₆	—	4	4	no	—
518	D₈	—	2	4	no	—
519	D₈	—	4	4	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	2	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	2	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	C₁₃×#41	1	2	yes	complemented
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	4	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	8	4	no	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	2	no	—
561	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₁₃	#24171	1	1	yes	characteristic, direct product factor, Sylow
566	C₂³	—	2	1	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	Q₈	—	2	1	no	—
575	Q₈	—	2	1	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	2	2	no	—
578	Q₈	—	4	4	no	—
579	Q₈	—	8	2	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	1	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	8	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
618	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
619	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
620	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
624	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
625	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
644	C₂²	C₁₃×#548	1	1	yes	characteristic
645	C₂²	C₁₃×#550	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	4	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	2	no	—
655	C₄	—	8	1	no	—
656	C₄	C₁₃×#454	1	2	yes	—
657	C₄	C₁₃×#525	1	1	yes	characteristic
658	C₄	C₁₃×#537	1	1	yes	characteristic
659	C₄	C₁₃×#546	1	1	yes	characteristic
660	C₄	C₁₃×#547	1	1	yes	characteristic
661	C₂	—	2	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	8	2	no	—
664	C₂	—	8	1	no	—
665	C₂	—	8	2	no	—
666	C₂	C₁₃×#2407	1	1	yes	characteristic
667	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
668	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3036	C₂	semidirect
3. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₃×#2563	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2006	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1980	C₂	semidirect
9. C₁₃×#1883	C₂	semidirect
10. C₁₃×#1860	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
140. #24171	C₁₃	direct (N × H)
168. C₂×D₄×C₁₃	#41	semidirect
192. C₁₃×M₁₆	#41	semidirect
232. #3511	C₂×C₁₃	semidirect
233. #3036	C₂×C₁₃	semidirect
234. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
235. #2563	C₂×C₁₃	semidirect
236. #2040	C₂×C₁₃	semidirect
237. #2006	C₂×C₁₃	semidirect
238. #1997	C₂×C₁₃	semidirect
239. #1980	C₂×C₁₃	semidirect
240. #1883	C₂×C₁₃	semidirect
241. #1860	C₂×C₁₃	semidirect
242. #1806	C₂×C₁₃	semidirect
501. C₂×D₄	C₁₃×#41	semidirect
525. M₁₆	C₁₃×#41	semidirect
565. C₁₃	#24171	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3036	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2563	2
C₁₃×#2040	2
C₁₃×#2006	2
C₁₃×#1997	2
C₁₃×#1980	2
C₁₃×#1883	2
C₁₃×#1860	2
C₁₃×#1806	2
#24171	13

Subgroups — C13×#24171 #15710510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24171 #15710510