Subgroups — C₁₃×#60967 #15747306

Order 3328.

1824 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3197	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3183	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3116	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3115	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	2	yes	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#532	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₁₃×#529	—	2	2	no	—
19	C₁₃×#529	—	2	2	no	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	C₂²	1	4	yes	—
23	C₁₃×#529	C₂²	1	4	yes	—
24	C₁₃×#525	—	2	2	no	—
25	C₁₃×#525	—	2	2	no	—
26	C₁₃×#525	C₂²	1	4	yes	—
27	C₄×C₁₃×#41	—	2	2	no	—
28	C₄×C₁₃×#41	—	2	2	no	—
29	C₄×C₁₃×#41	C₂²	1	4	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	4	yes	complemented
32	C₁₃×#495	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#485	C₂²	1	8	yes	—
35	C₁₃×#482	C₂²	1	8	yes	—
36	C₁₃×#477	C₂²	1	4	yes	complemented
37	C₁₃×#476	C₂²	1	4	yes	complemented
38	C₁₃×#475	C₂²	1	4	yes	complemented
39	C₁₃×#474	C₂²	1	4	yes	complemented
40	C₁₃×#470	C₂²	1	4	yes	—
41	C₁₃×#469	C₂²	1	4	yes	—
42	C₁₃×#468	C₂²	1	8	yes	—
43	C₁₃×#462	C₂²	1	4	yes	complemented
44	C₁₃×#461	C₂²	1	4	yes	complemented
45	C₁₃×#460	C₂²	1	4	yes	complemented
46	C₁₃×#459	C₂²	1	4	yes	complemented
47	C₁₃×#452	C₂²	1	8	yes	—
48	C₁₃×#449	C₂²	1	8	yes	—
49	C₁₃×#442	C₂²	1	4	yes	complemented
50	C₁₃×#441	C₂²	1	4	yes	complemented
51	C₁₃×#440	C₂²	1	8	yes	complemented
52	C₁₃×#432	C₂²	1	4	yes	—
53	C₁₃×#431	C₂²	1	4	yes	—
54	C₁₃×#423	C₂²	1	1	yes	characteristic
55	C₁₃×#423	C₂²	1	1	yes	characteristic
56	C₁₃×#407	C₂²	1	2	yes	—
57	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
58	C₂×C₁₃×#41	—	2	2	no	—
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	D₄	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
64	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
65	C₂×C₁₃×D₈	C₂³	1	4	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×#127	C₂³	1	2	yes	—
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	—	2	2	no	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	C₂³	1	4	yes	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×#123	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	C₂³	1	4	yes	—
94	C₁₃×#121	C₂³	1	4	yes	—
95	C₁₃×#120	—	2	4	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
101	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
102	C₄×D₄×C₁₃	—	2	4	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	4	no	—
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₁₃×#117	—	2	2	no	—
115	C₁₃×#117	—	2	2	no	—
116	C₁₃×#117	—	2	4	no	—
117	C₁₃×#117	—	2	4	no	—
118	C₁₃×#117	—	2	4	no	—
119	C₁₃×#117	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	—	2	4	no	—
121	C₂×C₄²×C₁₃	D₄	1	2	yes	—
122	C₂×C₄²×C₁₃	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₁₃×#107	C₂³	1	8	yes	—
129	C₁₃×#106	C₂³	1	4	yes	—
130	C₁₃×#106	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
133	C₁₃×#103	C₂³	1	8	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
138	C₁₃×#97	C₂³	1	4	yes	—
139	C₄×C₈×C₁₃	C₂³	1	4	yes	—
140	#60967	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	8	no	—
145	C₁₃×#41	—	4	8	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×Q₁₆	—	4	4	no	—
172	C₁₃×SD₁₆	—	4	8	no	—
173	C₁₃×D₈	—	4	4	no	—
174	C₁₃×M₁₆	—	4	2	no	—
175	C₁₃×M₁₆	—	4	2	no	—
176	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
177	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	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	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	4	no	—
201	C₄²×C₁₃	—	2	4	no	—
202	C₄²×C₁₃	C₂×D₄	1	2	yes	—
203	C₄²×C₁₃	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃	C₂×D₄	1	2	yes	—
205	C₄²×C₁₃	C₂×D₄	1	2	yes	—
206	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₄²×C₁₃	C₂⁴	1	2	yes	—
212	#3444	C₂×C₁₃	1	2	yes	complemented
213	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3254	C₂×C₁₃	1	2	yes	complemented
215	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3233	C₂×C₁₃	1	4	yes	complemented
217	#3212	C₂×C₁₃	1	4	yes	complemented
218	#3197	C₂×C₁₃	1	4	yes	complemented
219	#3183	C₂×C₁₃	1	4	yes	complemented
220	#3116	C₂×C₁₃	1	4	yes	complemented
221	#3115	C₂×C₁₃	1	4	yes	complemented
222	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₁₃	—	2	4	no	—
229	Q₈×C₁₃	—	2	4	no	—
230	Q₈×C₁₃	—	4	4	no	—
231	Q₈×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	2	4	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	8	no	—
236	D₄×C₁₃	—	4	8	no	—
237	D₄×C₁₃	—	4	8	no	—
238	D₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	8	no	—
255	C₂×C₄×C₁₃	—	4	8	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
264	C₈×C₁₃	—	2	4	no	—
265	C₈×C₁₃	—	2	4	no	—
266	#533	C₂²×C₁₃	1	2	yes	—
267	#533	C₂²×C₁₃	1	2	yes	—
268	#533	C₂²×C₁₃	1	2	yes	—
269	#532	C₂²×C₁₃	1	2	yes	—
270	#532	C₂²×C₁₃	1	2	yes	—
271	#532	C₂²×C₁₃	1	2	yes	—
272	#529	—	2	2	no	—
273	#529	—	2	2	no	—
274	#529	—	2	2	no	—
275	#529	—	2	2	no	—
276	#529	C₂²×C₁₃	1	4	yes	—
277	#529	C₂²×C₁₃	1	4	yes	—
278	#525	—	2	2	no	—
279	#525	—	2	2	no	—
280	#525	C₂²×C₁₃	1	4	yes	—
281	C₄×#41	—	2	2	no	—
282	C₄×#41	—	2	2	no	—
283	C₄×#41	C₂²×C₁₃	1	4	yes	—
284	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
285	#499	C₂²×C₁₃	1	4	yes	complemented
286	#495	C₂²×C₁₃	1	4	yes	complemented
287	#488	C₂²×C₁₃	1	8	yes	complemented
288	#485	C₂²×C₁₃	1	8	yes	—
289	#482	C₂²×C₁₃	1	8	yes	—
290	#477	C₂²×C₁₃	1	4	yes	complemented
291	#476	C₂²×C₁₃	1	4	yes	complemented
292	#475	C₂²×C₁₃	1	4	yes	complemented
293	#474	C₂²×C₁₃	1	4	yes	complemented
294	#470	C₂²×C₁₃	1	4	yes	—
295	#469	C₂²×C₁₃	1	4	yes	—
296	#468	C₂²×C₁₃	1	8	yes	—
297	#462	C₂²×C₁₃	1	4	yes	complemented
298	#461	C₂²×C₁₃	1	4	yes	complemented
299	#460	C₂²×C₁₃	1	4	yes	complemented
300	#459	C₂²×C₁₃	1	4	yes	complemented
301	#452	C₂²×C₁₃	1	8	yes	—
302	#449	C₂²×C₁₃	1	8	yes	—
303	#442	C₂²×C₁₃	1	4	yes	complemented
304	#441	C₂²×C₁₃	1	4	yes	complemented
305	#440	C₂²×C₁₃	1	8	yes	complemented
306	#432	C₂²×C₁₃	1	4	yes	—
307	#431	C₂²×C₁₃	1	4	yes	—
308	#423	C₂²×C₁₃	1	1	yes	characteristic
309	#423	C₂²×C₁₃	1	1	yes	characteristic
310	#407	C₂²×C₁₃	1	2	yes	—
311	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	4	no	—
321	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	4	4	no	—
328	C₄×C₁₃	—	4	4	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	#575	1	4	yes	—
331	C₄×C₁₃	#585	1	1	yes	characteristic
332	C₄×C₁₃	#585	1	1	yes	characteristic
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	C₂³×C₁₃	1	4	yes	—
336	C₂³×C₄	D₄×C₁₃	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
339	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
340	C₂×D₈	C₂³×C₁₃	1	4	yes	—
341	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
342	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
343	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
344	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
345	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
346	#127	C₂³×C₁₃	1	2	yes	—
347	#126	—	2	4	no	—
348	#126	—	2	4	no	—
349	#125	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	C₂³×C₁₃	1	4	yes	—
352	#124	—	2	2	no	—
353	#124	—	2	2	no	—
354	#124	C₂³×C₁₃	1	4	yes	—
355	#123	—	2	4	no	—
356	#123	—	2	4	no	—
357	#123	—	2	4	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
363	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
364	#121	—	2	2	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	C₂³×C₁₃	1	4	yes	—
369	#121	C₂³×C₁₃	1	4	yes	—
370	#120	—	2	4	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
376	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	4	no	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	C₂³×C₁₃	1	4	yes	—
388	C₄×D₄	C₂³×C₁₃	1	4	yes	—
389	#117	—	2	2	no	—
390	#117	—	2	2	no	—
391	#117	—	2	4	no	—
392	#117	—	2	4	no	—
393	#117	—	2	4	no	—
394	#117	C₂³×C₁₃	1	4	yes	—
395	C₂×C₄²	—	2	4	no	—
396	C₂×C₄²	D₄×C₁₃	1	2	yes	—
397	C₂×C₄²	D₄×C₁₃	1	2	yes	—
398	C₂×C₄²	D₄×C₁₃	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	#107	C₂³×C₁₃	1	8	yes	—
404	#106	C₂³×C₁₃	1	4	yes	—
405	#106	C₂³×C₁₃	1	4	yes	—
406	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
407	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
408	#103	C₂³×C₁₃	1	8	yes	—
409	#103	C₂³×C₁₃	1	8	yes	—
410	#102	C₂³×C₁₃	1	8	yes	—
411	#102	C₂³×C₁₃	1	8	yes	—
412	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
413	#97	C₂³×C₁₃	1	4	yes	—
414	C₄×C₈	C₂³×C₁₃	1	4	yes	—
415	C₂×C₁₃	—	4	2	no	—
416	C₂×C₁₃	—	4	1	no	—
417	C₂×C₁₃	—	8	4	no	—
418	C₂×C₁₃	#3449	1	1	yes	characteristic
419	C₂×C₁₃	C₂×#575	1	2	yes	—
420	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
421	#41	—	4	4	no	—
422	#41	—	4	4	no	—
423	#41	—	4	8	no	—
424	#41	—	4	8	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
450	Q₁₆	—	4	4	no	—
451	SD₁₆	—	4	8	no	—
452	D₈	—	4	4	no	—
453	M₁₆	—	4	2	no	—
454	M₁₆	—	4	2	no	—
455	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
456	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
468	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	4	no	—
481	C₄²	C₂×D₄×C₁₃	1	2	yes	—
482	C₄²	C₂×D₄×C₁₃	1	2	yes	—
483	C₄²	C₂×D₄×C₁₃	1	2	yes	—
484	C₄²	C₂×D₄×C₁₃	1	2	yes	—
485	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₃	1	2	yes	—
487	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
490	C₄²	C₂⁴×C₁₃	1	2	yes	—
491	C₁₃	#60967	1	1	yes	characteristic, direct product factor, Sylow
492	C₂³	—	2	4	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	4	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
532	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
533	C₈	—	2	4	no	—
534	C₈	—	2	4	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	C₁₃×#575	1	4	yes	—
554	C₄	C₁₃×#585	1	1	yes	characteristic
555	C₄	C₁₃×#585	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	4	2	no	—
558	C₂	—	8	4	no	—
559	C₂	C₁₃×#3449	1	1	yes	characteristic
560	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3255	C₂	semidirect
3. C₁₃×#3254	C₂	semidirect
4. C₁₃×#3253	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3212	C₂	semidirect
7. C₁₃×#3197	C₂	semidirect
8. C₁₃×#3183	C₂	semidirect
9. C₁₃×#3116	C₂	semidirect
10. C₁₃×#3115	C₂	semidirect
11. C₁₃×#2920	C₂	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
36. C₁₃×#477	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#475	C₂²	semidirect
39. C₁₃×#474	C₂²	semidirect
43. C₁₃×#462	C₂²	semidirect
44. C₁₃×#461	C₂²	semidirect
45. C₁₃×#460	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
49. C₁₃×#442	C₂²	semidirect
50. C₁₃×#441	C₂²	semidirect
51. C₁₃×#440	C₂²	semidirect
140. #60967	C₁₃	direct (N × H)
212. #3444	C₂×C₁₃	semidirect
213. #3255	C₂×C₁₃	semidirect
214. #3254	C₂×C₁₃	semidirect
215. #3253	C₂×C₁₃	semidirect
216. #3233	C₂×C₁₃	semidirect
217. #3212	C₂×C₁₃	semidirect
218. #3197	C₂×C₁₃	semidirect
219. #3183	C₂×C₁₃	semidirect
220. #3116	C₂×C₁₃	semidirect
221. #3115	C₂×C₁₃	semidirect
222. #2920	C₂×C₁₃	semidirect
285. #499	C₂²×C₁₃	semidirect
286. #495	C₂²×C₁₃	semidirect
287. #488	C₂²×C₁₃	semidirect
290. #477	C₂²×C₁₃	semidirect
291. #476	C₂²×C₁₃	semidirect
292. #475	C₂²×C₁₃	semidirect
293. #474	C₂²×C₁₃	semidirect
297. #462	C₂²×C₁₃	semidirect
298. #461	C₂²×C₁₃	semidirect
299. #460	C₂²×C₁₃	semidirect
300. #459	C₂²×C₁₃	semidirect
303. #442	C₂²×C₁₃	semidirect
304. #441	C₂²×C₁₃	semidirect
305. #440	C₂²×C₁₃	semidirect
491. C₁₃	#60967	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×#3444	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3253	2
C₁₃×#3233	2
C₁₃×#3212	2
C₁₃×#3197	2
C₁₃×#3183	2
C₁₃×#3116	2
C₁₃×#3115	2
C₁₃×#2920	2
#60967	13

Subgroups — C13×#60967 #15747306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60967 #15747306