Subgroups — C₁₃×#26400 #15712739

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₁₃×#544	C₂²	1	1	yes	characteristic
19	C₁₃×#520	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#518	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#478	—	2	1	no	—
24	C₁₃×#478	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#477	—	2	1	no	—
27	C₁₃×#476	—	2	1	no	—
28	C₁₃×#474	—	2	1	no	—
29	C₁₃×#474	—	2	1	no	—
30	C₁₃×#442	—	2	1	no	—
31	C₁₃×#440	—	2	1	no	—
32	C₄×C₁₃×SD₁₆	—	2	1	no	—
33	C₄×C₁₃×D₈	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	—	2	1	no	—
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	—	2	1	no	—
43	C₁₃×#427	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#107	—	2	1	no	—
45	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#424	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#416	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₁₃×#405	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#384	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#341	C₂²	1	1	yes	characteristic
63	C₁₃×#339	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
70	C₁₃×AGL(1,ℤ/8)	Q₈	1	4	yes	complemented
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×D₈	—	2	1	no	—
73	C₁₃×#131	—	2	2	no	—
74	C₁₃×#131	—	2	2	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	4	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	4	1	no	—
97	C₄×D₄×C₁₃	—	4	1	no	—
98	C₁₃×#117	—	2	1	no	—
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	C₂³	1	1	yes	characteristic
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#108	—	2	2	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#107	—	2	1	no	—
122	C₁₃×#107	D₄	1	1	yes	characteristic
123	C₁₃×#107	D₄	1	1	yes	characteristic
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#106	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	D₄	1	1	yes	characteristic
130	C₁₃×#106	D₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×C₄⋊C₈	—	2	1	no	—
135	C₁₃×#104	—	2	2	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	D₄	1	1	yes	characteristic
138	C₁₃×#103	D₄	1	1	yes	characteristic
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	D₄	1	1	yes	characteristic
147	C₁₃×#102	D₄	1	1	yes	characteristic
148	C₁₃×#100	—	2	2	no	—
149	C₁₃×#97	—	2	1	no	—
150	C₄×C₈×C₁₃	—	2	1	no	—
151	#26400	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₁₃×#41	—	2	1	no	—
154	C₁₃×#41	—	2	1	no	—
155	C₁₃×#41	C₂×Q₈	1	2	yes	—
156	C₁₃×#41	#41	1	2	yes	—
157	C₂×Q₈×C₁₃	—	4	1	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×D₈	—	2	4	no	—
179	C₁₃×M₁₆	—	2	4	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
187	C₁₃×M₁₆	#41	1	2	yes	—
188	C₂×C₈×C₁₃	—	2	4	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	4	1	no	—
208	C₁₃×C₄⋊C₄	—	4	1	no	—
209	C₁₃×C₄⋊C₄	—	4	1	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	8	2	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₁₃×C₂²⋊C₄	—	4	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	1	no	—
224	C₁₃×C₂²⋊C₄	—	4	1	no	—
225	C₁₃×C₂²⋊C₄	—	4	1	no	—
226	C₁₃×C₂²⋊C₄	—	8	2	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	4	1	no	—
233	C₄²×C₁₃	—	4	1	no	—
234	#3083	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2946	C₂×C₁₃	1	1	yes	characteristic
237	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1922	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1907	C₂×C₁₃	1	1	yes	characteristic
245	#1883	C₂×C₁₃	1	1	yes	characteristic
246	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	—	2	2	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	8	1	no	—
254	C₂³×C₁₃	—	8	1	no	—
255	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	16	1	no	—
258	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	1	no	—
263	D₄×C₁₃	—	2	2	no	—
264	D₄×C₁₃	—	4	1	no	—
265	D₄×C₁₃	—	4	1	no	—
266	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	8	1	no	—
283	C₂×C₄×C₁₃	—	8	1	no	—
284	C₂×C₄×C₁₃	—	8	1	no	—
285	C₂×C₄×C₁₃	—	16	1	no	—
286	C₂×C₄×C₁₃	—	16	1	no	—
287	C₂×C₄×C₁₃	—	16	1	no	—
288	C₂×C₄×C₁₃	—	16	1	no	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₁₃	—	2	2	no	—
296	C₈×C₁₃	—	2	1	no	—
297	C₈×C₁₃	—	2	2	no	—
298	C₈×C₁₃	—	2	1	no	—
299	C₈×C₁₃	—	2	1	no	—
300	C₈×C₁₃	—	2	1	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
305	#544	C₂²×C₁₃	1	1	yes	characteristic
306	#520	C₂²×C₁₃	1	1	yes	characteristic
307	#520	C₂²×C₁₃	1	1	yes	characteristic
308	#518	C₂²×C₁₃	1	1	yes	characteristic
309	#479	—	2	1	no	—
310	#478	—	2	1	no	—
311	#478	—	2	1	no	—
312	#478	—	2	1	no	—
313	#477	—	2	1	no	—
314	#476	—	2	1	no	—
315	#474	—	2	1	no	—
316	#474	—	2	1	no	—
317	#442	—	2	1	no	—
318	#440	—	2	1	no	—
319	C₄×SD₁₆	—	2	1	no	—
320	C₄×D₈	—	2	1	no	—
321	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
322	#428	—	2	1	no	—
323	#428	—	2	1	no	—
324	#428	C₂²×C₁₃	1	1	yes	characteristic
325	#428	C₂²×C₁₃	1	1	yes	characteristic
326	#428	C₂²×C₁₃	1	1	yes	characteristic
327	#428	C₂²×C₁₃	1	1	yes	characteristic
328	#428	C₂²×C₁₃	1	1	yes	characteristic
329	#427	—	2	1	no	—
330	#427	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#107	—	2	1	no	—
332	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
334	#424	C₂²×C₁₃	1	1	yes	characteristic
335	#424	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
337	#418	C₂²×C₁₃	1	1	yes	characteristic
338	#417	C₂²×C₁₃	1	1	yes	characteristic
339	#416	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
343	#405	C₂²×C₁₃	1	1	yes	characteristic
344	#390	C₂²×C₁₃	1	1	yes	characteristic
345	#384	C₂²×C₁₃	1	1	yes	characteristic
346	#343	C₂²×C₁₃	1	1	yes	characteristic
347	#343	C₂²×C₁₃	1	1	yes	characteristic
348	#343	C₂²×C₁₃	1	1	yes	characteristic
349	#341	C₂²×C₁₃	1	1	yes	characteristic
350	#339	C₂²×C₁₃	1	1	yes	characteristic
351	#339	C₂²×C₁₃	1	1	yes	characteristic
352	#339	C₂²×C₁₃	1	1	yes	characteristic
353	#336	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×C₁₃	—	2	1	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	8	2	no	—
361	C₂²×C₁₃	—	8	1	no	—
362	C₂²×C₁₃	—	8	1	no	—
363	C₂²×C₁₃	—	16	1	no	—
364	C₂²×C₁₃	#539	1	1	yes	characteristic
365	C₂²×C₁₃	D₄²	1	1	yes	characteristic
366	C₂²×C₁₃	#554	1	1	yes	characteristic
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	1	no	—
374	C₄×C₁₃	—	4	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
379	C₄×C₁₃	#525	1	1	yes	characteristic
380	C₄×C₁₃	#547	1	1	yes	characteristic
381	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
382	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
384	AGL(1,ℤ/8)	—	2	2	no	—
385	AGL(1,ℤ/8)	Q₈×C₁₃	1	4	yes	complemented
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×D₈	—	2	1	no	—
388	#131	—	2	2	no	—
389	#131	—	2	2	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊Q₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	#125	—	2	1	no	—
401	#125	—	2	1	no	—
402	C₂²⋊Q₈	—	4	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	4	1	no	—
412	C₄×D₄	—	4	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	C₂³×C₁₃	1	1	yes	characteristic
416	#117	C₂³×C₁₃	1	1	yes	characteristic
417	#117	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	4	1	no	—
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	4	1	no	—
425	C₂×C₂²⋊C₄	—	4	1	no	—
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	#108	—	2	2	no	—
428	#107	—	2	1	no	—
429	#107	—	2	1	no	—
430	#107	—	2	1	no	—
431	#107	—	2	1	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#107	—	2	1	no	—
435	#107	—	2	1	no	—
436	#107	—	2	1	no	—
437	#107	D₄×C₁₃	1	1	yes	characteristic
438	#107	D₄×C₁₃	1	1	yes	characteristic
439	#106	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	#106	—	2	1	no	—
443	#106	—	2	1	no	—
444	#106	D₄×C₁₃	1	1	yes	characteristic
445	#106	D₄×C₁₃	1	1	yes	characteristic
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	C₄⋊C₈	—	2	1	no	—
449	C₄⋊C₈	—	2	1	no	—
450	#104	—	2	2	no	—
451	#103	—	2	1	no	—
452	#103	D₄×C₁₃	1	1	yes	characteristic
453	#103	D₄×C₁₃	1	1	yes	characteristic
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	#102	—	2	1	no	—
459	#102	—	2	1	no	—
460	#102	—	2	1	no	—
461	#102	D₄×C₁₃	1	1	yes	characteristic
462	#102	D₄×C₁₃	1	1	yes	characteristic
463	#100	—	2	2	no	—
464	#97	—	2	1	no	—
465	C₄×C₈	—	2	1	no	—
466	C₂×C₁₃	—	2	1	no	—
467	C₂×C₁₃	—	2	1	no	—
468	C₂×C₁₃	—	4	2	no	—
469	C₂×C₁₃	—	8	2	no	—
470	C₂×C₁₃	#2449	1	1	yes	characteristic
471	C₂×C₁₃	#3289	1	1	yes	characteristic
472	C₂×C₁₃	#3292	1	1	yes	characteristic
473	C₂⁴	—	2	1	no	—
474	#41	—	2	1	no	—
475	#41	—	2	1	no	—
476	#41	C₂×Q₈×C₁₃	1	2	yes	—
477	#41	C₁₃×#41	1	2	yes	—
478	C₂×Q₈	—	4	1	no	—
479	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
498	SD₁₆	—	2	4	no	—
499	D₈	—	2	4	no	—
500	M₁₆	—	2	4	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
508	M₁₆	C₁₃×#41	1	2	yes	—
509	C₂×C₈	—	2	4	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	8	2	no	—
534	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	8	2	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₁₃	#26400	1	1	yes	characteristic, direct product factor, Sylow
556	C₂³	—	2	1	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	8	1	no	—
561	C₂³	—	8	1	no	—
562	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
563	Q₈	—	2	1	no	—
564	Q₈	—	16	1	no	—
565	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	8	1	no	—
590	C₂×C₄	—	8	1	no	—
591	C₂×C₄	—	8	1	no	—
592	C₂×C₄	—	16	1	no	—
593	C₂×C₄	—	16	1	no	—
594	C₂×C₄	—	16	1	no	—
595	C₂×C₄	—	16	1	no	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
601	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	2	1	no	—
604	C₈	—	2	2	no	—
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	16	1	no	—
620	C₂²	C₁₃×#539	1	1	yes	characteristic
621	C₂²	D₄²×C₁₃	1	1	yes	characteristic
622	C₂²	C₁₃×#554	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
635	C₄	C₁₃×#525	1	1	yes	characteristic
636	C₄	C₁₃×#547	1	1	yes	characteristic
637	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	4	2	no	—
641	C₂	—	8	2	no	—
642	C₂	C₁₃×#2449	1	1	yes	characteristic
643	C₂	C₁₃×#3289	1	1	yes	characteristic
644	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
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 ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3083	C₂	semidirect
2. C₁₃×#3081	C₂	semidirect
4. C₁₃×#2913	C₂	semidirect
5. C₁₃×#2093	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2060	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1922	C₂	semidirect
13. C₁₃×#1866	C₂	semidirect
14. C₁₃×#1859	C₂	semidirect
15. C₁₃×#1856	C₂	semidirect
70. C₁₃×AGL(1,ℤ/8)	Q₈	semidirect
151. #26400	C₁₃	direct (N × H)
234. #3083	C₂×C₁₃	semidirect
235. #3081	C₂×C₁₃	semidirect
237. #2913	C₂×C₁₃	semidirect
238. #2093	C₂×C₁₃	semidirect
239. #2089	C₂×C₁₃	semidirect
240. #2063	C₂×C₁₃	semidirect
241. #2060	C₂×C₁₃	semidirect
242. #1952	C₂×C₁₃	semidirect
243. #1922	C₂×C₁₃	semidirect
246. #1866	C₂×C₁₃	semidirect
247. #1859	C₂×C₁₃	semidirect
248. #1856	C₂×C₁₃	semidirect
385. AGL(1,ℤ/8)	Q₈×C₁₃	semidirect
555. C₁₃	#26400	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×#3083	2
C₁₃×#3081	2
C₁₃×#2946	2
C₁₃×#2913	2
C₁₃×#2093	2
C₁₃×#2089	2
C₁₃×#2063	2
C₁₃×#2060	2
C₁₃×#1952	2
C₁₃×#1922	2
C₁₃×#1907	2
C₁₃×#1883	2
C₁₃×#1866	2
C₁₃×#1859	2
C₁₃×#1856	2
#26400	13

Subgroups — C13×#26400 #15712739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26400 #15712739