Subgroups — C₁₃×#61337 #15747676

Order 3328.

1852 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3368	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3366	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	4	yes	—
19	C₁₃×#557	C₂²	1	4	yes	complemented
20	C₁₃×#554	—	2	4	no	—
21	C₁₃×#554	C₂²	1	4	yes	complemented
22	C₁₃×#550	C₂²	1	4	yes	—
23	C₁₃×#546	—	2	4	no	—
24	C₁₃×#544	—	2	2	no	—
25	C₁₃×#544	C₂²	1	2	yes	—
26	C₁₃×#540	—	2	1	no	—
27	C₁₃×#540	—	2	1	no	—
28	C₁₃×#535	C₂²	1	2	yes	—
29	C₁₃×#533	—	2	1	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#532	—	2	2	no	—
32	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#125	—	2	1	no	—
34	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#518	C₂²	1	2	yes	—
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₁₃×#490	C₂²	1	4	yes	—
40	C₁₃×#490	C₂²	1	4	yes	—
41	C₁₃×#490	C₂²	1	4	yes	complemented
42	C₁₃×#489	C₂²	1	4	yes	complemented
43	C₁₃×#488	C₂²	1	4	yes	complemented
44	C₁₃×#486	C₂²	1	4	yes	complemented
45	C₁₃×#479	C₂²	1	4	yes	complemented
46	C₁₃×#478	C₂²	1	4	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#478	C₂²	1	4	yes	complemented
49	C₁₃×#476	C₂²	1	4	yes	complemented
50	C₁₃×#474	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	4	yes	complemented
52	C₁₃×#463	C₂²	1	4	yes	complemented
53	C₁₃×#460	C₂²	1	4	yes	—
54	C₁₃×#460	C₂²	1	4	yes	complemented
55	C₁₃×#459	C₂²	1	4	yes	—
56	C₁₃×#459	C₂²	1	4	yes	complemented
57	C₁₃×#446	C₂²	1	4	yes	complemented
58	C₁₃×#446	C₂²	1	4	yes	complemented
59	C₁₃×#442	C₂²	1	2	yes	complemented
60	C₁₃×#442	C₂²	1	4	yes	complemented
61	C₁₃×#441	C₂²	1	2	yes	complemented
62	C₁₃×#440	C₂²	1	2	yes	complemented
63	C₁₃×#440	C₂²	1	4	yes	complemented
64	C₁₃×#440	C₂²	1	2	yes	complemented
65	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
66	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
67	C₁₃×#428	C₂²	1	2	yes	—
68	C₁₃×#427	C₂²	1	1	yes	characteristic
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#423	C₂²	1	1	yes	characteristic
71	C₁₃×#418	C₂²	1	2	yes	—
72	C₁₃×#417	C₂²	1	2	yes	—
73	C₁₃×#416	C₂²	1	1	yes	characteristic
74	C₁₃×#416	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#102	C₂²	1	2	yes	—
76	C₂×C₁₃×#102	C₂²	1	2	yes	—
77	C₁₃×#405	C₂²	1	2	yes	—
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
79	C₂×C₁₃×#41	—	2	4	no	—
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	—	2	2	no	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
85	C₁₃×#135	—	2	4	no	—
86	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×D₈	C₂³	1	4	yes	—
91	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊Q₈	—	2	4	no	—
96	C₁₃×C₄⋊Q₈	—	2	2	no	—
97	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₃×#127	—	2	1	no	—
100	C₁₃×#127	—	2	1	no	—
101	C₁₃×#127	C₂³	1	4	yes	—
102	C₁₃×#127	C₂³	1	4	yes	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	—	2	4	no	—
106	C₁₃×#125	—	2	1	no	—
107	C₁₃×#125	—	2	1	no	—
108	C₁₃×#125	D₄	1	1	yes	characteristic
109	C₁₃×#125	D₄	1	1	yes	characteristic
110	C₁₃×#125	C₂³	1	4	yes	—
111	C₁₃×#125	C₂³	1	4	yes	—
112	C₁₃×#124	—	2	4	no	—
113	C₁₃×#124	C₂³	1	4	yes	—
114	C₁₃×#123	—	2	4	no	—
115	C₁₃×#123	—	2	4	no	—
116	C₁₃×C₂²⋊Q₈	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	4	no	—
124	C₁₃×#121	—	2	4	no	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#120	—	2	4	no	—
127	C₄×Q₈×C₁₃	—	2	4	no	—
128	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	—	2	2	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₄×D₄×C₁₃	C₂³	1	4	yes	—
141	C₄×D₄×C₁₃	C₂³	1	2	yes	—
142	C₄×D₄×C₁₃	C₂³	1	2	yes	—
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	C₂³	1	1	yes	characteristic
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₁₃×#117	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₂×C₄²×C₁₃	—	2	1	no	—
155	C₂×C₄²×C₁₃	—	2	1	no	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₁₃×#107	C₂³	1	2	yes	—
158	C₁₃×#107	C₂³	1	4	yes	—
159	C₁₃×#106	C₂³	1	2	yes	—
160	C₁₃×#106	C₂³	1	4	yes	—
161	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
162	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
163	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₃×#103	C₂³	1	2	yes	—
165	C₁₃×#103	C₂³	1	2	yes	—
166	C₁₃×#103	C₂³	1	4	yes	—
167	C₁₃×#102	C₂³	1	4	yes	—
168	C₁₃×#102	C₂³	1	4	yes	—
169	C₁₃×#102	C₂³	1	4	yes	—
170	C₁₃×#102	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	2	yes	—
172	C₁₃×#102	C₂³	1	2	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	2	yes	—
177	C₁₃×#97	C₂³	1	2	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₄×C₈×C₁₃	C₂³	1	4	yes	—
180	#61337	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂⁴×C₁₃	—	2	2	no	—
182	C₁₃×#41	—	2	2	no	—
183	C₁₃×#41	—	2	2	no	—
184	C₁₃×#41	—	2	2	no	—
185	C₁₃×#41	—	8	8	no	—
186	C₁₃×#41	#41	1	4	yes	complemented
187	C₂×Q₈×C₁₃	—	2	4	no	—
188	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
189	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	8	4	no	—
201	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₁₃×Q₁₆	—	2	2	no	—
215	C₁₃×SD₁₆	—	2	2	no	—
216	C₁₃×SD₁₆	—	2	8	no	—
217	C₁₃×SD₁₆	—	2	2	no	—
218	C₁₃×D₈	—	2	2	no	—
219	C₁₃×D₈	—	2	8	no	—
220	C₁₃×M₁₆	—	2	4	no	—
221	C₂×C₈×C₁₃	—	2	2	no	—
222	C₂×C₈×C₁₃	—	2	2	no	—
223	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
224	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
225	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₁₃×C₂²⋊C₄	—	2	1	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	2	1	no	—
256	C₄²×C₁₃	—	2	2	no	—
257	C₄²×C₁₃	—	2	2	no	—
258	C₄²×C₁₃	—	2	4	no	—
259	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₃	C₂⁴	1	4	yes	—
262	C₄²×C₁₃	C₂⁴	1	2	yes	—
263	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#3371	C₂×C₁₃	1	4	yes	complemented
266	#3370	C₂×C₁₃	1	4	yes	complemented
267	#3368	C₂×C₁₃	1	4	yes	complemented
268	#3366	C₂×C₁₃	1	4	yes	complemented
269	#3136	C₂×C₁₃	1	2	yes	complemented
270	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#3081	C₂×C₁₃	1	2	yes	complemented
272	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3045	C₂×C₁₃	1	2	yes	complemented
274	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2946	C₂×C₁₃	1	2	yes	complemented
277	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	4	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	4	4	no	—
282	C₂³×C₁₃	—	8	2	no	—
283	C₂³×C₁₃	—	8	2	no	—
284	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₁₃	—	2	1	no	—
286	Q₈×C₁₃	—	2	1	no	—
287	Q₈×C₁₃	—	2	1	no	—
288	Q₈×C₁₃	—	4	4	no	—
289	Q₈×C₁₃	—	8	4	no	—
290	Q₈×C₁₃	C₂×#41	1	2	yes	—
291	D₄×C₁₃	—	2	4	no	—
292	D₄×C₁₃	—	2	4	no	—
293	D₄×C₁₃	—	2	1	no	—
294	D₄×C₁₃	—	2	1	no	—
295	D₄×C₁₃	—	2	4	no	—
296	D₄×C₁₃	—	2	1	no	—
297	D₄×C₁₃	—	4	8	no	—
298	D₄×C₁₃	—	4	2	no	—
299	D₄×C₁₃	—	4	4	no	—
300	D₄×C₁₃	—	8	4	no	—
301	D₄×C₁₃	—	8	4	no	—
302	D₄×C₁₃	—	8	4	no	—
303	D₄×C₁₃	C₂×#41	1	2	yes	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	4	2	no	—
311	C₂×C₄×C₁₃	—	4	4	no	—
312	C₂×C₄×C₁₃	—	4	2	no	—
313	C₂×C₄×C₁₃	—	8	2	no	—
314	C₂×C₄×C₁₃	—	8	4	no	—
315	C₂×C₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	—	8	4	no	—
317	C₂×C₄×C₁₃	—	8	2	no	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
324	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
325	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
326	C₈×C₁₃	—	2	1	no	—
327	C₈×C₁₃	—	2	1	no	—
328	C₈×C₁₃	—	2	4	no	—
329	C₈×C₁₃	—	2	2	no	—
330	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
331	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
332	#559	C₂²×C₁₃	1	4	yes	—
333	#557	C₂²×C₁₃	1	4	yes	complemented
334	#554	—	2	4	no	—
335	#554	C₂²×C₁₃	1	4	yes	complemented
336	#550	C₂²×C₁₃	1	4	yes	—
337	#546	—	2	4	no	—
338	#544	—	2	2	no	—
339	#544	C₂²×C₁₃	1	2	yes	—
340	#540	—	2	1	no	—
341	#540	—	2	1	no	—
342	#535	C₂²×C₁₃	1	2	yes	—
343	#533	—	2	1	no	—
344	#533	C₂²×C₁₃	1	1	yes	characteristic
345	#532	—	2	2	no	—
346	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#125	—	2	1	no	—
348	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
349	#520	C₂²×C₁₃	1	2	yes	—
350	#518	C₂²×C₁₃	1	2	yes	—
351	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
352	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
353	#490	C₂²×C₁₃	1	4	yes	—
354	#490	C₂²×C₁₃	1	4	yes	—
355	#490	C₂²×C₁₃	1	4	yes	complemented
356	#489	C₂²×C₁₃	1	4	yes	complemented
357	#488	C₂²×C₁₃	1	4	yes	complemented
358	#486	C₂²×C₁₃	1	4	yes	complemented
359	#479	C₂²×C₁₃	1	4	yes	complemented
360	#478	C₂²×C₁₃	1	4	yes	complemented
361	#478	C₂²×C₁₃	1	4	yes	complemented
362	#478	C₂²×C₁₃	1	4	yes	complemented
363	#476	C₂²×C₁₃	1	4	yes	complemented
364	#474	C₂²×C₁₃	1	4	yes	complemented
365	#464	C₂²×C₁₃	1	4	yes	complemented
366	#463	C₂²×C₁₃	1	4	yes	complemented
367	#460	C₂²×C₁₃	1	4	yes	—
368	#460	C₂²×C₁₃	1	4	yes	complemented
369	#459	C₂²×C₁₃	1	4	yes	—
370	#459	C₂²×C₁₃	1	4	yes	complemented
371	#446	C₂²×C₁₃	1	4	yes	complemented
372	#446	C₂²×C₁₃	1	4	yes	complemented
373	#442	C₂²×C₁₃	1	2	yes	complemented
374	#442	C₂²×C₁₃	1	4	yes	complemented
375	#441	C₂²×C₁₃	1	2	yes	complemented
376	#440	C₂²×C₁₃	1	2	yes	complemented
377	#440	C₂²×C₁₃	1	4	yes	complemented
378	#440	C₂²×C₁₃	1	2	yes	complemented
379	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
380	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
381	#428	C₂²×C₁₃	1	2	yes	—
382	#427	C₂²×C₁₃	1	1	yes	characteristic
383	#424	C₂²×C₁₃	1	2	yes	—
384	#423	C₂²×C₁₃	1	1	yes	characteristic
385	#418	C₂²×C₁₃	1	2	yes	—
386	#417	C₂²×C₁₃	1	2	yes	—
387	#416	C₂²×C₁₃	1	1	yes	characteristic
388	#416	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₃	1	2	yes	—
390	C₂×#102	C₂²×C₁₃	1	2	yes	—
391	#405	C₂²×C₁₃	1	2	yes	—
392	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×C₁₃	—	2	2	no	—
394	C₂²×C₁₃	—	2	2	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	4	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	4	no	—
401	C₂²×C₁₃	—	16	4	no	—
402	C₂²×C₁₃	#548	1	2	yes	—
403	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₁₃	—	2	2	no	—
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	—	2	4	no	—
407	C₄×C₁₃	—	2	4	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	4	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	1	no	—
413	C₄×C₁₃	#548	1	2	yes	—
414	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
415	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂×#41	—	2	4	no	—
417	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×D₄	—	2	2	no	—
420	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
421	AGL(1,ℤ/8)	—	2	8	no	—
422	#135	—	2	4	no	—
423	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
427	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×D₈	C₂³×C₁₃	1	4	yes	—
429	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄⋊Q₈	—	2	4	no	—
433	C₄⋊Q₈	—	2	2	no	—
434	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
435	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
436	#127	—	2	1	no	—
437	#127	—	2	1	no	—
438	#127	C₂³×C₁₃	1	4	yes	—
439	#127	C₂³×C₁₃	1	4	yes	—
440	#125	—	2	2	no	—
441	#125	—	2	4	no	—
442	#125	—	2	4	no	—
443	#125	—	2	1	no	—
444	#125	—	2	1	no	—
445	#125	D₄×C₁₃	1	1	yes	characteristic
446	#125	D₄×C₁₃	1	1	yes	characteristic
447	#125	C₂³×C₁₃	1	4	yes	—
448	#125	C₂³×C₁₃	1	4	yes	—
449	#124	—	2	4	no	—
450	#124	C₂³×C₁₃	1	4	yes	—
451	#123	—	2	4	no	—
452	#123	—	2	4	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₂²⋊Q₈	—	2	4	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	—	2	4	no	—
457	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
458	#121	—	2	2	no	—
459	#121	—	2	2	no	—
460	#121	—	2	4	no	—
461	#121	—	2	4	no	—
462	#121	—	2	4	no	—
463	#120	—	2	4	no	—
464	C₄×Q₈	—	2	4	no	—
465	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
466	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
467	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
468	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	C₂³×C₁₃	1	2	yes	—
476	C₄×D₄	C₂³×C₁₃	1	2	yes	—
477	C₄×D₄	C₂³×C₁₃	1	4	yes	—
478	C₄×D₄	C₂³×C₁₃	1	4	yes	—
479	C₄×D₄	C₂³×C₁₃	1	4	yes	—
480	#117	—	2	2	no	—
481	#117	—	2	1	no	—
482	#117	—	2	1	no	—
483	#117	C₂³×C₁₃	1	1	yes	characteristic
484	#117	C₂³×C₁₃	1	1	yes	characteristic
485	#117	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄⋊C₄	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	4	no	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
494	#107	C₂³×C₁₃	1	2	yes	—
495	#107	C₂³×C₁₃	1	4	yes	—
496	#106	C₂³×C₁₃	1	2	yes	—
497	#106	C₂³×C₁₃	1	4	yes	—
498	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
499	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
500	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
501	#103	C₂³×C₁₃	1	2	yes	—
502	#103	C₂³×C₁₃	1	2	yes	—
503	#103	C₂³×C₁₃	1	4	yes	—
504	#102	C₂³×C₁₃	1	4	yes	—
505	#102	C₂³×C₁₃	1	4	yes	—
506	#102	C₂³×C₁₃	1	4	yes	—
507	#102	C₂³×C₁₃	1	4	yes	—
508	#102	C₂³×C₁₃	1	2	yes	—
509	#102	C₂³×C₁₃	1	2	yes	—
510	#102	C₂³×C₁₃	1	4	yes	—
511	#102	C₂³×C₁₃	1	4	yes	—
512	#102	C₂³×C₁₃	1	4	yes	—
513	#97	C₂³×C₁₃	1	2	yes	—
514	#97	C₂³×C₁₃	1	2	yes	—
515	#97	C₂³×C₁₃	1	4	yes	—
516	C₄×C₈	C₂³×C₁₃	1	4	yes	—
517	C₂×C₁₃	—	2	2	no	—
518	C₂×C₁₃	—	4	2	no	—
519	C₂×C₁₃	—	8	1	no	—
520	C₂×C₁₃	—	8	4	no	—
521	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
522	C₂×C₁₃	#3585	1	2	yes	—
523	C₂⁴	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	2	no	—
527	#41	—	8	8	no	—
528	#41	C₁₃×#41	1	4	yes	complemented
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
531	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
544	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
556	Q₁₆	—	2	2	no	—
557	SD₁₆	—	2	2	no	—
558	SD₁₆	—	2	8	no	—
559	SD₁₆	—	2	2	no	—
560	D₈	—	2	2	no	—
561	D₈	—	2	8	no	—
562	M₁₆	—	2	4	no	—
563	C₂×C₈	—	2	2	no	—
564	C₂×C₈	—	2	2	no	—
565	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
566	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
567	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
568	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
580	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
582	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
583	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
584	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	4	no	—
601	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₄²	C₂⁴×C₁₃	1	4	yes	—
604	C₄²	C₂⁴×C₁₃	1	2	yes	—
605	C₁₃	#61337	1	1	yes	characteristic, direct product factor, Sylow
606	C₂³	—	2	1	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	8	2	no	—
611	C₂³	—	8	2	no	—
612	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	Q₈	—	2	1	no	—
616	Q₈	—	4	4	no	—
617	Q₈	—	8	4	no	—
618	Q₈	C₂×C₁₃×#41	1	2	yes	—
619	D₄	—	2	4	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	1	no	—
622	D₄	—	2	1	no	—
623	D₄	—	2	4	no	—
624	D₄	—	2	1	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	4	no	—
628	D₄	—	8	4	no	—
629	D₄	—	8	4	no	—
630	D₄	—	8	4	no	—
631	D₄	C₂×C₁₃×#41	1	2	yes	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	—	8	4	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	—	8	2	no	—
646	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
652	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
653	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
654	C₈	—	2	1	no	—
655	C₈	—	2	1	no	—
656	C₈	—	2	4	no	—
657	C₈	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	16	4	no	—
667	C₂²	C₁₃×#548	1	2	yes	—
668	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
669	C₄	—	2	2	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	4	no	—
673	C₄	—	2	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	4	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	C₁₃×#548	1	2	yes	—
679	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
680	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	8	4	no	—
684	C₂	—	8	1	no	—
685	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
686	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3371	C₂	semidirect
4. C₁₃×#3370	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3136	C₂	semidirect
8. C₂×C₁₃×#490	C₂	semidirect
9. C₁₃×#3081	C₂	semidirect
10. C₁₃×#3080	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3038	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2946	C₂	semidirect
15. C₁₃×#2943	C₂	semidirect
19. C₁₃×#557	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
41. C₁₃×#490	C₂²	semidirect
42. C₁₃×#489	C₂²	semidirect
43. C₁₃×#488	C₂²	semidirect
44. C₁₃×#486	C₂²	semidirect
45. C₁₃×#479	C₂²	semidirect
46. C₁₃×#478	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#478	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#474	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
54. C₁₃×#460	C₂²	semidirect
56. C₁₃×#459	C₂²	semidirect
57. C₁₃×#446	C₂²	semidirect
58. C₁₃×#446	C₂²	semidirect
59. C₁₃×#442	C₂²	semidirect
60. C₁₃×#442	C₂²	semidirect
61. C₁₃×#441	C₂²	semidirect
62. C₁₃×#440	C₂²	semidirect
63. C₁₃×#440	C₂²	semidirect
64. C₁₃×#440	C₂²	semidirect
65. C₄×C₁₃×SD₁₆	C₂²	semidirect
66. C₄×C₁₃×D₈	C₂²	semidirect
180. #61337	C₁₃	direct (N × H)
186. C₁₃×#41	#41	semidirect
263. #3508	C₂×C₁₃	semidirect
264. #3504	C₂×C₁₃	semidirect
265. #3371	C₂×C₁₃	semidirect
266. #3370	C₂×C₁₃	semidirect
267. #3368	C₂×C₁₃	semidirect
268. #3366	C₂×C₁₃	semidirect
269. #3136	C₂×C₁₃	semidirect
270. C₂×#490	C₂×C₁₃	semidirect
271. #3081	C₂×C₁₃	semidirect
272. #3080	C₂×C₁₃	semidirect
273. #3045	C₂×C₁₃	semidirect
274. #3038	C₂×C₁₃	semidirect
275. #2961	C₂×C₁₃	semidirect
276. #2946	C₂×C₁₃	semidirect
277. #2943	C₂×C₁₃	semidirect
333. #557	C₂²×C₁₃	semidirect
335. #554	C₂²×C₁₃	semidirect
355. #490	C₂²×C₁₃	semidirect
356. #489	C₂²×C₁₃	semidirect
357. #488	C₂²×C₁₃	semidirect
358. #486	C₂²×C₁₃	semidirect
359. #479	C₂²×C₁₃	semidirect
360. #478	C₂²×C₁₃	semidirect
361. #478	C₂²×C₁₃	semidirect
362. #478	C₂²×C₁₃	semidirect
363. #476	C₂²×C₁₃	semidirect
364. #474	C₂²×C₁₃	semidirect
365. #464	C₂²×C₁₃	semidirect
366. #463	C₂²×C₁₃	semidirect
368. #460	C₂²×C₁₃	semidirect
370. #459	C₂²×C₁₃	semidirect
371. #446	C₂²×C₁₃	semidirect
372. #446	C₂²×C₁₃	semidirect
373. #442	C₂²×C₁₃	semidirect
374. #442	C₂²×C₁₃	semidirect
375. #441	C₂²×C₁₃	semidirect
376. #440	C₂²×C₁₃	semidirect
377. #440	C₂²×C₁₃	semidirect
378. #440	C₂²×C₁₃	semidirect
379. C₄×SD₁₆	C₂²×C₁₃	semidirect
380. C₄×D₈	C₂²×C₁₃	semidirect
528. #41	C₁₃×#41	semidirect
605. C₁₃	#61337	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×#3508	2
C₁₃×#3504	2
C₁₃×#3371	2
C₁₃×#3370	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3136	2
C₂×C₁₃×#490	2
C₁₃×#3081	2
C₁₃×#3080	2
C₁₃×#3045	2
C₁₃×#3038	2
C₁₃×#2961	2
C₁₃×#2946	2
C₁₃×#2943	2
#61337	13

Subgroups — C13×#61337 #15747676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61337 #15747676