Subgroups — C₁₃×#24321 #15710660

Order 3328.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2061	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2027	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1883	C₂	1	2	yes	maximal
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	Q₈²×C₁₃	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#554	—	2	1	no	—
16	C₁₃×#554	—	2	2	no	—
17	D₄×Q₈×C₁₃	—	2	2	no	—
18	D₄×Q₈×C₁₃	—	2	1	no	—
19	C₁₃×#544	—	2	2	no	—
20	C₁₃×#544	C₂²	1	2	yes	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#520	C₂²	1	2	yes	—
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#478	—	2	2	no	—
29	C₁₃×#476	—	2	1	no	—
30	C₁₃×#474	—	2	1	no	—
31	C₁₃×#442	—	2	1	no	—
32	C₁₃×#440	—	2	1	no	—
33	C₄×C₁₃×SD₁₆	—	2	1	no	—
34	C₄×C₁₃×D₈	—	2	1	no	—
35	C₁₃×#428	C₂²	1	2	yes	—
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	C₁₃×#418	C₂²	1	1	yes	characteristic
40	C₁₃×#418	C₂²	1	2	yes	—
41	C₁₃×#417	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₃×#393	—	2	2	no	—
44	C₁₃×#390	C₂²	1	2	yes	—
45	C₁₃×#382	C₂²	1	2	yes	—
46	C₁₃×#380	—	2	2	no	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#343	C₂²	1	2	yes	—
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₁₃×#339	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	—	2	2	no	—
55	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
59	C₁₃×AGL(1,ℤ/8)	Q₈	1	4	yes	complemented
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×D₈	—	2	1	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	4	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	2	2	no	—
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×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	D₄	1	2	yes	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₁₃×#117	—	2	2	no	—
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	C₂³	1	1	yes	characteristic
107	C₁₃×#117	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	2	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×#104	—	2	4	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	2	no	—
131	C₁₃×#102	—	2	2	no	—
132	C₁₃×#97	—	2	1	no	—
133	C₄×C₈×C₁₃	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	4	no	—
136	#24321	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₁₃×#41	—	2	1	no	—
139	C₁₃×#41	—	2	1	no	—
140	C₁₃×#41	C₂×Q₈	1	2	yes	—
141	C₁₃×#41	#41	1	2	yes	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	8	2	no	—
148	C₂×Q₈×C₁₃	—	8	4	no	—
149	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	complemented
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×SD₁₆	—	2	4	no	—
172	C₁₃×D₈	—	2	4	no	—
173	C₁₃×M₁₆	—	2	1	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	1	no	—
176	C₁₃×M₁₆	—	2	1	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	C₂×Q₈	1	2	yes	complemented
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	8	4	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	2	no	—
216	C₄²×C₁₃	—	2	2	no	—
217	C₄²×C₁₃	—	2	2	no	—
218	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
222	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
225	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2061	C₂×C₁₃	1	2	yes	complemented
227	#2027	C₂×C₁₃	1	2	yes	complemented
228	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1883	C₂×C₁₃	1	2	yes	—
231	#1860	C₂×C₁₃	1	2	yes	complemented
232	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	1	no	—
241	Q₈×C₁₃	—	4	4	no	—
242	Q₈×C₁₃	—	4	2	no	—
243	Q₈×C₁₃	—	4	2	no	—
244	Q₈×C₁₃	—	8	2	no	—
245	Q₈×C₁₃	—	8	4	no	—
246	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	1	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	8	2	no	—
274	C₂×C₄×C₁₃	—	8	4	no	—
275	C₂×C₄×C₁₃	—	8	2	no	—
276	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
277	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
278	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
286	C₈×C₁₃	—	2	2	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	2	no	—
289	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
290	Q₈²	—	2	1	no	—
291	#557	—	2	1	no	—
292	#554	—	2	1	no	—
293	#554	—	2	2	no	—
294	D₄×Q₈	—	2	2	no	—
295	D₄×Q₈	—	2	1	no	—
296	#544	—	2	2	no	—
297	#544	C₂²×C₁₃	1	2	yes	—
298	#533	—	2	1	no	—
299	#533	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	—	2	1	no	—
301	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	#520	C₂²×C₁₃	1	2	yes	—
303	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
305	#478	—	2	2	no	—
306	#476	—	2	1	no	—
307	#474	—	2	1	no	—
308	#442	—	2	1	no	—
309	#440	—	2	1	no	—
310	C₄×SD₁₆	—	2	1	no	—
311	C₄×D₈	—	2	1	no	—
312	#428	C₂²×C₁₃	1	2	yes	—
313	#428	C₂²×C₁₃	1	1	yes	characteristic
314	#423	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#104	C₂²×C₁₃	1	2	yes	—
316	#418	C₂²×C₁₃	1	2	yes	—
317	#418	C₂²×C₁₃	1	1	yes	characteristic
318	#417	C₂²×C₁₃	1	1	yes	characteristic
319	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	#393	—	2	2	no	—
321	#390	C₂²×C₁₃	1	2	yes	—
322	#382	C₂²×C₁₃	1	2	yes	—
323	#380	—	2	2	no	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
325	#343	C₂²×C₁₃	1	2	yes	—
326	#343	C₂²×C₁₃	1	2	yes	—
327	#339	C₂²×C₁₃	1	2	yes	—
328	#339	C₂²×C₁₃	1	2	yes	—
329	#339	C₂²×C₁₃	1	2	yes	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	8	2	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
341	C₂²×C₁₃	#548	1	1	yes	characteristic
342	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	4	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	8	2	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	#454	1	2	yes	—
355	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
356	C₄×C₁₃	#536	1	1	yes	characteristic
357	C₄×C₁₃	#548	1	1	yes	characteristic
358	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
359	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
360	C₂²×Q₈	—	2	2	no	—
361	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	AGL(1,ℤ/8)	—	2	2	no	—
365	AGL(1,ℤ/8)	Q₈×C₁₃	1	4	yes	complemented
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×D₈	—	2	1	no	—
368	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
370	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	—	2	4	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	—	2	1	no	—
378	C₄⋊Q₈	—	2	1	no	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
381	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
382	#125	—	2	4	no	—
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	#125	D₄×C₁₃	1	2	yes	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	4	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
399	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
409	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
410	#117	—	2	2	no	—
411	#117	—	2	1	no	—
412	#117	C₂³×C₁₃	1	1	yes	characteristic
413	#117	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	2	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	4	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	#107	—	2	1	no	—
426	#107	—	2	2	no	—
427	#106	—	2	1	no	—
428	#106	—	2	2	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	#104	—	2	4	no	—
432	#103	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	#97	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	4	no	—
442	C₂×C₁₃	—	2	1	no	—
443	C₂×C₁₃	—	2	1	no	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	8	2	no	—
446	C₂×C₁₃	#2409	1	1	yes	characteristic
447	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
448	C₂×C₁₃	#3019	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	#41	—	2	1	no	—
451	#41	—	2	1	no	—
452	#41	C₂×Q₈×C₁₃	1	2	yes	—
453	#41	C₁₃×#41	1	2	yes	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	8	2	no	—
460	C₂×Q₈	—	8	4	no	—
461	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	complemented
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
483	SD₁₆	—	2	4	no	—
484	D₈	—	2	4	no	—
485	M₁₆	—	2	1	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	C₂×Q₈×C₁₃	1	2	yes	complemented
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	2	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	8	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₁₃	#24321	1	1	yes	characteristic, direct product factor, Sylow
535	C₂³	—	2	1	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	4	4	no	—
544	Q₈	—	4	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	8	2	no	—
547	Q₈	—	8	4	no	—
548	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	1	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	—	8	4	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
579	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
580	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
581	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
586	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
587	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
588	C₈	—	2	2	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	8	2	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
602	C₂²	C₁₃×#548	1	1	yes	characteristic
603	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	2	no	—
614	C₄	—	8	1	no	—
615	C₄	C₁₃×#454	1	2	yes	—
616	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
617	C₄	C₁₃×#536	1	1	yes	characteristic
618	C₄	C₁₃×#548	1	1	yes	characteristic
619	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	2	no	—
624	C₂	C₁₃×#2409	1	1	yes	characteristic
625	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
626	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
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×#3503	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
4. C₁₃×#2563	C₂	semidirect
5. C₁₃×#2061	C₂	semidirect
6. C₁₃×#2027	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1986	C₂	semidirect
10. C₁₃×#1860	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
59. C₁₃×AGL(1,ℤ/8)	Q₈	semidirect
136. #24321	C₁₃	direct (N × H)
157. C₂×D₄×C₁₃	C₂×Q₈	semidirect
178. C₁₃×M₁₆	C₂×Q₈	semidirect
222. #3503	C₂×C₁₃	semidirect
223. #3077	C₂×C₁₃	semidirect
225. #2563	C₂×C₁₃	semidirect
226. #2061	C₂×C₁₃	semidirect
227. #2027	C₂×C₁₃	semidirect
228. #1997	C₂×C₁₃	semidirect
229. #1986	C₂×C₁₃	semidirect
231. #1860	C₂×C₁₃	semidirect
232. #1806	C₂×C₁₃	semidirect
365. AGL(1,ℤ/8)	Q₈×C₁₃	semidirect
469. C₂×D₄	C₂×Q₈×C₁₃	semidirect
490. M₁₆	C₂×Q₈×C₁₃	semidirect
534. C₁₃	#24321	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×#3503	2
C₁₃×#3077	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2563	2
C₁₃×#2061	2
C₁₃×#2027	2
C₁₃×#1997	2
C₁₃×#1986	2
C₁₃×#1883	2
C₁₃×#1860	2
C₁₃×#1806	2
#24321	13

Subgroups — C13×#24321 #15710660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24321 #15710660