Subgroups — C₁₃×#61701 #15748040

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3342	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3340	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3304	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3302	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3190	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3091	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	—	2	2	no	—
15	C₁₃×#556	—	2	2	no	—
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#556	C₂²	1	4	yes	—
18	C₁₃×#556	C₂²	1	4	yes	—
19	C₁₃×#556	C₂²	1	2	yes	—
20	C₁₃×#555	C₂²	1	2	yes	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#550	C₂²	1	2	yes	—
23	C₁₃×#547	C₂²	1	2	yes	—
24	C₁₃×#538	—	2	2	no	—
25	C₁₃×#535	—	2	1	no	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#126	—	2	2	no	—
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₁₃×#525	C₂²	1	4	yes	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₁₃×#520	—	2	1	no	—
34	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₁₃×#500	C₂²	1	2	yes	complemented
39	C₁₃×#498	C₂²	1	2	yes	complemented
40	C₁₃×#487	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#485	C₂²	1	8	yes	complemented
43	C₁₃×#485	C₂²	1	8	yes	complemented
44	C₁₃×#484	C₂²	1	2	yes	—
45	C₁₃×#483	C₂²	1	4	yes	—
46	C₁₃×#482	C₂²	1	8	yes	complemented
47	C₁₃×#481	C₂²	1	2	yes	—
48	C₁₃×#480	C₂²	1	4	yes	—
49	C₁₃×#477	C₂²	1	2	yes	complemented
50	C₁₃×#475	C₂²	1	4	yes	complemented
51	C₁₃×#475	C₂²	1	2	yes	complemented
52	C₁₃×#474	C₂²	1	4	yes	complemented
53	C₁₃×#467	C₂²	1	8	yes	complemented
54	C₁₃×#465	C₂²	1	8	yes	complemented
55	C₁₃×#462	C₂²	1	2	yes	complemented
56	C₁₃×#460	C₂²	1	2	yes	complemented
57	C₁₃×#452	C₂²	1	8	yes	complemented
58	C₁₃×#451	C₂²	1	2	yes	—
59	C₁₃×#448	C₂²	1	2	yes	—
60	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
61	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
62	C₈×D₄×C₁₃	C₂²	1	4	yes	—
63	C₈×D₄×C₁₃	C₂²	1	4	yes	—
64	C₁₃×#431	C₂²	1	1	yes	characteristic
65	C₁₃×#431	C₂²	1	1	yes	characteristic
66	C₁₃×#427	C₂²	1	8	yes	complemented
67	C₁₃×#416	C₂²	1	8	yes	complemented
68	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₃	—	2	1	no	—
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	2	8	no	—
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#124	—	2	4	no	—
92	C₁₃×#124	—	2	4	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	—	2	4	no	—
95	C₁₃×#124	—	2	1	no	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×C₂²⋊Q₈	—	2	1	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	—	2	1	no	—
106	C₁₃×#121	—	2	4	no	—
107	C₁₃×#121	C₂³	1	2	yes	—
108	C₁₃×#121	C₂³	1	4	yes	—
109	C₁₃×#120	—	2	4	no	—
110	C₄×Q₈×C₁₃	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×Q₈×C₁₃	—	2	2	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₄×D₄×C₁₃	—	2	4	no	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	1	no	—
123	C₄×D₄×C₁₃	D₄	1	2	yes	—
124	C₄×D₄×C₁₃	D₄	1	2	yes	—
125	C₄×D₄×C₁₃	C₂³	1	2	yes	—
126	C₄×D₄×C₁₃	C₂³	1	2	yes	—
127	C₄×D₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×#117	—	2	4	no	—
129	C₁₃×#117	—	2	1	no	—
130	C₁₃×#117	—	2	2	no	—
131	C₁₃×#117	C₂³	1	8	yes	—
132	C₁₃×#117	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
143	C₂×C₄²×C₁₃	—	2	2	no	—
144	C₂×C₄²×C₁₃	—	2	1	no	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#107	C₂³	1	4	yes	—
147	C₁₃×#107	C₂³	1	8	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×#106	C₂³	1	8	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	8	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	4	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	8	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#61701	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
165	C₁₃×#41	—	4	8	no	—
166	C₁₃×#41	—	4	4	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	2	no	—
170	C₂×Q₈×C₁₃	—	2	2	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	4	2	no	—
173	C₂×Q₈×C₁₃	—	4	4	no	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₁₃×Q₁₆	—	4	4	no	—
198	C₁₃×SD₁₆	—	4	4	no	—
199	C₂×C₈×C₁₃	—	4	8	no	—
200	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
201	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
222	C₁₃×C₂²⋊C₄	—	2	8	no	—
223	C₁₃×C₂²⋊C₄	—	2	8	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	2	no	—
229	C₁₃×C₂²⋊C₄	—	2	2	no	—
230	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
231	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
232	C₄²×C₁₃	—	2	8	no	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	2	no	—
235	C₄²×C₁₃	—	2	4	no	—
236	C₄²×C₁₃	—	2	2	no	—
237	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
241	#3506	C₂×C₁₃	1	1	yes	characteristic
242	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3342	C₂×C₁₃	1	4	yes	complemented
244	#3340	C₂×C₁₃	1	4	yes	complemented
245	#3304	C₂×C₁₃	1	4	yes	complemented
246	#3302	C₂×C₁₃	1	4	yes	complemented
247	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3190	C₂×C₁₃	1	4	yes	complemented
250	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3091	C₂×C₁₃	1	4	yes	complemented
253	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	4	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	4	2	no	—
257	C₂³×C₁₃	—	4	2	no	—
258	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
259	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₃	—	2	2	no	—
261	Q₈×C₁₃	—	2	2	no	—
262	Q₈×C₁₃	—	2	4	no	—
263	Q₈×C₁₃	—	4	2	no	—
264	Q₈×C₁₃	—	4	4	no	—
265	Q₈×C₁₃	—	4	4	no	—
266	Q₈×C₁₃	—	4	2	no	—
267	Q₈×C₁₃	—	8	1	no	—
268	D₄×C₁₃	—	2	4	no	—
269	D₄×C₁₃	—	2	4	no	—
270	D₄×C₁₃	—	2	4	no	—
271	D₄×C₁₃	—	4	4	no	—
272	D₄×C₁₃	—	4	2	no	—
273	D₄×C₁₃	—	8	1	no	—
274	D₄×C₁₃	—	8	4	no	—
275	D₄×C₁₃	—	8	4	no	—
276	C₂×C₄×C₁₃	—	2	8	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	4	4	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	2	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	4	no	—
290	C₂×C₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	8	4	no	—
292	C₂×C₄×C₁₃	#135	1	4	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
300	C₈×C₁₃	—	2	4	no	—
301	C₈×C₁₃	—	2	4	no	—
302	#559	—	2	2	no	—
303	#556	—	2	2	no	—
304	#556	—	2	2	no	—
305	#556	C₂²×C₁₃	1	4	yes	—
306	#556	C₂²×C₁₃	1	2	yes	—
307	#556	C₂²×C₁₃	1	4	yes	—
308	#555	C₂²×C₁₃	1	2	yes	—
309	#553	—	2	2	no	—
310	#550	C₂²×C₁₃	1	2	yes	—
311	#547	C₂²×C₁₃	1	2	yes	—
312	#538	—	2	2	no	—
313	#535	—	2	1	no	—
314	#533	C₂²×C₁₃	1	1	yes	characteristic
315	#532	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#126	—	2	2	no	—
318	C₂×#124	—	2	1	no	—
319	#525	C₂²×C₁₃	1	4	yes	—
320	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
321	#520	—	2	1	no	—
322	C₂×C₄×Q₈	—	2	1	no	—
323	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#117	C₂²×C₁₃	1	2	yes	—
326	#500	C₂²×C₁₃	1	2	yes	complemented
327	#498	C₂²×C₁₃	1	2	yes	complemented
328	#487	C₂²×C₁₃	1	2	yes	complemented
329	#486	C₂²×C₁₃	1	2	yes	complemented
330	#485	C₂²×C₁₃	1	8	yes	complemented
331	#485	C₂²×C₁₃	1	8	yes	complemented
332	#484	C₂²×C₁₃	1	2	yes	—
333	#483	C₂²×C₁₃	1	4	yes	—
334	#482	C₂²×C₁₃	1	8	yes	complemented
335	#481	C₂²×C₁₃	1	2	yes	—
336	#480	C₂²×C₁₃	1	4	yes	—
337	#477	C₂²×C₁₃	1	2	yes	complemented
338	#475	C₂²×C₁₃	1	2	yes	complemented
339	#475	C₂²×C₁₃	1	4	yes	complemented
340	#474	C₂²×C₁₃	1	4	yes	complemented
341	#467	C₂²×C₁₃	1	8	yes	complemented
342	#465	C₂²×C₁₃	1	8	yes	complemented
343	#462	C₂²×C₁₃	1	2	yes	complemented
344	#460	C₂²×C₁₃	1	2	yes	complemented
345	#452	C₂²×C₁₃	1	8	yes	complemented
346	#451	C₂²×C₁₃	1	2	yes	—
347	#448	C₂²×C₁₃	1	2	yes	—
348	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
349	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
350	C₈×D₄	C₂²×C₁₃	1	4	yes	—
351	C₈×D₄	C₂²×C₁₃	1	4	yes	—
352	#431	C₂²×C₁₃	1	1	yes	characteristic
353	#431	C₂²×C₁₃	1	1	yes	characteristic
354	#427	C₂²×C₁₃	1	8	yes	complemented
355	#416	C₂²×C₁₃	1	8	yes	complemented
356	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	2	4	no	—
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	2	4	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	8	4	no	—
366	C₂²×C₁₃	C₂×#135	1	2	yes	—
367	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₁₃	—	2	1	no	—
369	C₄×C₁₃	—	2	1	no	—
370	C₄×C₁₃	—	2	1	no	—
371	C₄×C₁₃	—	2	4	no	—
372	C₄×C₁₃	—	4	2	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₄×C₁₃	C₂×#135	1	2	yes	—
379	C₄×C₁₃	C₂×#135	1	2	yes	—
380	C₄×C₁₃	#585	1	2	yes	—
381	C₂×#41	—	2	1	no	—
382	C₂×#41	C₂³×C₁₃	1	4	yes	—
383	C₂²×Q₈	—	2	1	no	—
384	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
388	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
389	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
390	C₄⋊Q₈	—	2	1	no	—
391	C₄⋊Q₈	—	2	1	no	—
392	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
394	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
395	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
397	#127	—	2	2	no	—
398	#127	C₂³×C₁₃	1	1	yes	characteristic
399	#126	—	2	8	no	—
400	#126	—	2	8	no	—
401	#126	—	2	4	no	—
402	#125	—	2	1	no	—
403	#124	—	2	4	no	—
404	#124	—	2	4	no	—
405	#124	—	2	2	no	—
406	#124	—	2	4	no	—
407	#124	—	2	1	no	—
408	#123	—	2	4	no	—
409	#123	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
413	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
414	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	4	no	—
419	#121	C₂³×C₁₃	1	2	yes	—
420	#121	C₂³×C₁₃	1	4	yes	—
421	#120	—	2	4	no	—
422	C₄×Q₈	—	2	4	no	—
423	C₄×Q₈	—	2	4	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	—	2	1	no	—
428	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
429	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
430	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
431	C₄×D₄	—	2	4	no	—
432	C₄×D₄	—	2	4	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	D₄×C₁₃	1	2	yes	—
436	C₄×D₄	D₄×C₁₃	1	2	yes	—
437	C₄×D₄	C₂³×C₁₃	1	2	yes	—
438	C₄×D₄	C₂³×C₁₃	1	2	yes	—
439	C₄×D₄	C₂³×C₁₃	1	2	yes	—
440	#117	—	2	4	no	—
441	#117	—	2	1	no	—
442	#117	—	2	2	no	—
443	#117	C₂³×C₁₃	1	8	yes	—
444	#117	C₂³×C₁₃	1	4	yes	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	2	no	—
449	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
455	C₂×C₄²	—	2	2	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
458	#107	C₂³×C₁₃	1	4	yes	—
459	#107	C₂³×C₁₃	1	8	yes	—
460	#106	C₂³×C₁₃	1	4	yes	—
461	#106	C₂³×C₁₃	1	8	yes	—
462	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
463	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
464	#103	C₂³×C₁₃	1	4	yes	—
465	#103	C₂³×C₁₃	1	8	yes	—
466	#103	C₂³×C₁₃	1	4	yes	—
467	#103	C₂³×C₁₃	1	4	yes	—
468	#102	C₂³×C₁₃	1	4	yes	—
469	#102	C₂³×C₁₃	1	8	yes	—
470	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
471	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
472	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
473	C₄×C₈	C₂³×C₁₃	1	2	yes	—
474	C₄×C₈	C₂³×C₁₃	1	2	yes	—
475	C₂×C₁₃	—	2	2	no	—
476	C₂×C₁₃	—	4	4	no	—
477	C₂×C₁₃	—	8	2	no	—
478	C₂×C₁₃	#3485	1	1	yes	characteristic
479	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
480	C₂×C₁₃	#3586	1	1	yes	characteristic
481	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
482	#41	—	4	8	no	—
483	#41	—	4	4	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	4	2	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
492	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	4	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	2	yes	—
501	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
511	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
514	Q₁₆	—	4	4	no	—
515	SD₁₆	—	4	4	no	—
516	C₂×C₈	—	4	8	no	—
517	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
518	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
534	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
537	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
538	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
539	C₂²⋊C₄	—	2	8	no	—
540	C₂²⋊C₄	—	2	8	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
548	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
549	C₄²	—	2	8	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	2	no	—
554	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₁₃	#61701	1	1	yes	characteristic, direct product factor, Sylow
559	C₂³	—	2	4	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
564	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	4	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	4	no	—
570	Q₈	—	4	4	no	—
571	Q₈	—	4	2	no	—
572	Q₈	—	8	1	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	4	no	—
576	D₄	—	4	4	no	—
577	D₄	—	4	2	no	—
578	D₄	—	8	1	no	—
579	D₄	—	8	4	no	—
580	D₄	—	8	4	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	8	4	no	—
597	C₂×C₄	C₁₃×#135	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
599	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
605	C₈	—	2	4	no	—
606	C₈	—	2	4	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	8	4	no	—
616	C₂²	C₂×C₁₃×#135	1	2	yes	—
617	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	4	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	C₂×C₁₃×#135	1	2	yes	—
629	C₄	C₂×C₁₃×#135	1	2	yes	—
630	C₄	C₁₃×#585	1	2	yes	—
631	C₂	—	2	2	no	—
632	C₂	—	4	4	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₃×#3485	1	1	yes	characteristic
635	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
636	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3342	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#3304	C₂	semidirect
6. C₁₃×#3302	C₂	semidirect
7. C₁₃×#3229	C₂	semidirect
8. C₁₃×#3226	C₂	semidirect
9. C₁₃×#3190	C₂	semidirect
10. C₁₃×#3104	C₂	semidirect
11. C₁₃×#3103	C₂	semidirect
12. C₁₃×#3091	C₂	semidirect
13. C₁₃×#2972	C₂	semidirect
38. C₁₃×#500	C₂²	semidirect
39. C₁₃×#498	C₂²	semidirect
40. C₁₃×#487	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#485	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
49. C₁₃×#477	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
51. C₁₃×#475	C₂²	semidirect
52. C₁₃×#474	C₂²	semidirect
53. C₁₃×#467	C₂²	semidirect
54. C₁₃×#465	C₂²	semidirect
55. C₁₃×#462	C₂²	semidirect
56. C₁₃×#460	C₂²	semidirect
57. C₁₃×#452	C₂²	semidirect
60. C₄×C₁₃×Q₁₆	C₂²	semidirect
61. C₄×C₁₃×SD₁₆	C₂²	semidirect
66. C₁₃×#427	C₂²	semidirect
67. C₁₃×#416	C₂²	semidirect
163. #61701	C₁₃	direct (N × H)
242. C₂×#556	C₂×C₁₃	semidirect
243. #3342	C₂×C₁₃	semidirect
244. #3340	C₂×C₁₃	semidirect
245. #3304	C₂×C₁₃	semidirect
246. #3302	C₂×C₁₃	semidirect
247. #3229	C₂×C₁₃	semidirect
248. #3226	C₂×C₁₃	semidirect
249. #3190	C₂×C₁₃	semidirect
250. #3104	C₂×C₁₃	semidirect
251. #3103	C₂×C₁₃	semidirect
252. #3091	C₂×C₁₃	semidirect
253. #2972	C₂×C₁₃	semidirect
326. #500	C₂²×C₁₃	semidirect
327. #498	C₂²×C₁₃	semidirect
328. #487	C₂²×C₁₃	semidirect
329. #486	C₂²×C₁₃	semidirect
330. #485	C₂²×C₁₃	semidirect
331. #485	C₂²×C₁₃	semidirect
334. #482	C₂²×C₁₃	semidirect
337. #477	C₂²×C₁₃	semidirect
338. #475	C₂²×C₁₃	semidirect
339. #475	C₂²×C₁₃	semidirect
340. #474	C₂²×C₁₃	semidirect
341. #467	C₂²×C₁₃	semidirect
342. #465	C₂²×C₁₃	semidirect
343. #462	C₂²×C₁₃	semidirect
344. #460	C₂²×C₁₃	semidirect
345. #452	C₂²×C₁₃	semidirect
348. C₄×Q₁₆	C₂²×C₁₃	semidirect
349. C₄×SD₁₆	C₂²×C₁₃	semidirect
354. #427	C₂²×C₁₃	semidirect
355. #416	C₂²×C₁₃	semidirect
558. C₁₃	#61701	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×#3506	2
C₂×C₁₃×#556	2
C₁₃×#3342	2
C₁₃×#3340	2
C₁₃×#3304	2
C₁₃×#3302	2
C₁₃×#3229	2
C₁₃×#3226	2
C₁₃×#3190	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#3091	2
C₁₃×#2972	2
#61701	13

Subgroups — C13×#61701 #15748040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61701 #15748040