Subgroups — C₁₃×#25926 #15712265

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 602 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×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2028	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×#1995	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1883	C₂	1	2	yes	maximal
10	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₃	—	2	1	no	—
15	C₁₃×#557	—	2	1	no	—
16	C₁₃×#554	—	2	1	no	—
17	C₁₃×#554	—	2	2	no	—
18	D₄×Q₈×C₁₃	—	2	2	no	—
19	D₄×Q₈×C₁₃	—	2	1	no	—
20	C₁₃×#544	—	2	2	no	—
21	C₁₃×#544	C₂²	1	2	yes	—
22	C₁₃×#533	—	2	1	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₁₃×#520	C₂²	1	2	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#489	—	2	1	no	—
30	C₁₃×#489	—	2	1	no	—
31	C₁₃×#488	—	2	2	no	—
32	C₁₃×#464	—	2	1	no	—
33	C₁₃×#464	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#463	—	2	1	no	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#104	C₂²	1	2	yes	—
38	C₁₃×#419	C₂²	1	1	yes	characteristic
39	C₁₃×#419	C₂²	1	2	yes	—
40	C₁₃×#418	C₂²	1	1	yes	characteristic
41	C₁₃×#418	C₂²	1	2	yes	—
42	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₃×#397	—	2	2	no	—
44	C₁₃×#393	—	2	2	no	—
45	C₁₃×#391	C₂²	1	2	yes	—
46	C₁₃×#390	C₂²	1	2	yes	—
47	C₁₃×#376	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#137	—	2	4	no	—
59	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
60	C₂×C₁₃×Q₁₆	—	2	1	no	—
61	C₂×C₁₃×SD₁₆	—	2	1	no	—
62	C₂×C₁₃×SD₁₆	—	2	1	no	—
63	C₂×C₁₃×D₈	—	2	1	no	—
64	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	2	4	no	—
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	—	2	1	no	—
73	C₁₃×C₄⋊Q₈	—	2	1	no	—
74	C₁₃×C₄⋊Q₈	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
78	C₁₃×#125	—	2	4	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	D₄	1	2	yes	—
82	C₁₃×#124	—	2	1	no	—
83	C₁₃×#124	—	2	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	4	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	4	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₁₃×#117	C₂³	1	1	yes	characteristic
109	C₁₃×#117	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₄²×C₁₃	—	2	1	no	—
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	—	2	1	no	—
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×#104	—	2	4	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	2	no	—
126	C₁₃×#103	—	2	2	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	2	no	—
130	C₁₃×#102	—	2	2	no	—
131	C₁₃×#97	—	2	1	no	—
132	C₄×C₈×C₁₃	—	2	1	no	—
133	C₁₃×#95	—	2	4	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	#25926	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₁₃×#41	—	2	2	no	—
139	C₁₃×#41	#41	1	4	yes	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	2	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	1	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	8	2	no	—
150	C₂×Q₈×C₁₃	—	8	4	no	—
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×Q₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	4	2	no	—
171	C₁₃×D₈	—	4	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	8	4	no	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	2	no	—
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#3040	C₂×C₁₃	1	1	yes	characteristic
221	#2640	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2028	C₂×C₁₃	1	2	yes	complemented
223	#2027	C₂×C₁₃	1	2	yes	complemented
224	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1995	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1883	C₂×C₁₃	1	2	yes	—
227	#1882	C₂×C₁₃	1	2	yes	complemented
228	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	4	2	no	—
237	Q₈×C₁₃	—	4	4	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	Q₈×C₁₃	—	8	2	no	—
243	Q₈×C₁₃	—	8	4	no	—
244	Q₈×C₁₃	#124	1	2	yes	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	#124	1	2	yes	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	8	4	no	—
269	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	2	no	—
280	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
282	Q₈²	—	2	1	no	—
283	#557	—	2	1	no	—
284	#554	—	2	1	no	—
285	#554	—	2	2	no	—
286	D₄×Q₈	—	2	2	no	—
287	D₄×Q₈	—	2	1	no	—
288	#544	—	2	2	no	—
289	#544	C₂²×C₁₃	1	2	yes	—
290	#533	—	2	1	no	—
291	#533	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	—	2	1	no	—
293	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
295	#520	C₂²×C₁₃	1	2	yes	—
296	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
297	#489	—	2	1	no	—
298	#489	—	2	1	no	—
299	#488	—	2	2	no	—
300	#464	—	2	1	no	—
301	#464	—	2	1	no	—
302	#463	—	2	1	no	—
303	#463	—	2	1	no	—
304	#423	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#104	C₂²×C₁₃	1	2	yes	—
306	#419	C₂²×C₁₃	1	2	yes	—
307	#419	C₂²×C₁₃	1	1	yes	characteristic
308	#418	C₂²×C₁₃	1	2	yes	—
309	#418	C₂²×C₁₃	1	1	yes	characteristic
310	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
311	#397	—	2	2	no	—
312	#393	—	2	2	no	—
313	#391	C₂²×C₁₃	1	2	yes	—
314	#390	C₂²×C₁₃	1	2	yes	—
315	#376	C₂²×C₁₃	1	1	yes	characteristic
316	#343	C₂²×C₁₃	1	2	yes	—
317	#343	C₂²×C₁₃	1	2	yes	—
318	#339	C₂²×C₁₃	1	2	yes	—
319	#339	C₂²×C₁₃	1	2	yes	—
320	#339	C₂²×C₁₃	1	2	yes	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	8	4	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₃	#548	1	2	yes	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	4	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	8	2	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
345	C₄×C₁₃	#536	1	1	yes	characteristic
346	C₄×C₁₃	#548	1	2	yes	—
347	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×Q₈	—	2	2	no	—
349	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
350	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
352	#137	—	2	4	no	—
353	AGL(1,ℤ/8)	—	2	4	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×D₈	—	2	1	no	—
358	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	—	2	2	no	—
363	C₄⋊Q₈	—	2	4	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
372	#125	—	2	4	no	—
373	#125	—	2	2	no	—
374	#125	—	2	2	no	—
375	#125	D₄×C₁₃	1	2	yes	—
376	#124	—	2	1	no	—
377	#124	—	2	1	no	—
378	#124	—	2	1	no	—
379	#124	—	2	1	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	4	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
393	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
399	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
400	#117	—	2	2	no	—
401	#117	—	2	1	no	—
402	#117	C₂³×C₁₃	1	1	yes	characteristic
403	#117	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	#104	—	2	4	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	2	no	—
424	#102	—	2	2	no	—
425	#97	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	4	no	—
430	C₂×C₁₃	—	2	2	no	—
431	C₂×C₁₃	—	4	2	no	—
432	C₂×C₁₃	—	16	1	no	—
433	C₂×C₁₃	#2436	1	1	yes	characteristic
434	C₂×C₁₃	#3019	1	1	yes	characteristic
435	C₂×C₁₃	#3020	1	1	yes	characteristic
436	C₂⁴	—	2	1	no	—
437	#41	—	2	2	no	—
438	#41	C₁₃×#41	1	4	yes	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	8	2	no	—
449	C₂×Q₈	—	8	4	no	—
450	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
467	Q₁₆	—	4	2	no	—
468	SD₁₆	—	4	2	no	—
469	SD₁₆	—	4	2	no	—
470	D₈	—	4	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
493	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	8	4	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₁₃	#25926	1	1	yes	characteristic, direct product factor, Sylow
518	C₂³	—	2	1	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	2	no	—
523	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	Q₈	—	2	1	no	—
525	Q₈	—	4	4	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	2	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	8	2	no	—
532	Q₈	—	8	4	no	—
533	Q₈	C₁₃×#124	1	2	yes	—
534	D₄	—	2	4	no	—
535	D₄	—	2	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	2	no	—
539	D₄	C₁₃×#124	1	2	yes	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
559	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
560	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
561	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
565	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	8	4	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
579	C₂²	C₁₃×#548	1	2	yes	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	2	no	—
591	C₄	—	8	1	no	—
592	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
593	C₄	C₁₃×#536	1	1	yes	characteristic
594	C₄	C₁₃×#548	1	2	yes	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	16	1	no	—
598	C₂	C₁₃×#2436	1	1	yes	characteristic
599	C₂	C₁₃×#3019	1	1	yes	characteristic
600	C₂	C₁₃×#3020	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×#3140	C₂	semidirect
4. C₁₃×#2640	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#2027	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1995	C₂	semidirect
10. C₁₃×#1882	C₂	semidirect
11. C₁₃×#1759	C₂	semidirect
136. #25926	C₁₃	direct (N × H)
218. #3503	C₂×C₁₃	semidirect
219. #3140	C₂×C₁₃	semidirect
221. #2640	C₂×C₁₃	semidirect
222. #2028	C₂×C₁₃	semidirect
223. #2027	C₂×C₁₃	semidirect
224. #1997	C₂×C₁₃	semidirect
225. #1995	C₂×C₁₃	semidirect
227. #1882	C₂×C₁₃	semidirect
228. #1759	C₂×C₁₃	semidirect
517. C₁₃	#25926	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×#3140	2
C₁₃×#3040	2
C₁₃×#2640	2
C₁₃×#2028	2
C₁₃×#2027	2
C₁₃×#1997	2
C₁₃×#1995	2
C₁₃×#1883	2
C₁₃×#1882	2
C₁₃×#1759	2
#25926	13

Subgroups — C13×#25926 #15712265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25926 #15712265