Subgroups — C₁₃×#60391 #15746730

Order 3328.

4666 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3586	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3022	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3020	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3018	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#456	C₂	1	6	yes	maximal, complemented
8	C₁₃×#2901	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2889	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#585	—	2	8	no	—
11	C₁₃×#585	—	2	6	no	—
12	C₁₃×#585	C₂²	1	6	yes	—
13	C₁₃×#585	C₂²	1	2	yes	—
14	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
15	C₂×C₁₃×2₋¹⁺⁴	—	2	2	no	—
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	6	yes	—
17	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#578	—	2	8	no	—
20	C₁₃×#577	—	2	8	no	—
21	C₁₃×#575	C₂²	1	12	yes	complemented
22	C₂×C₁₃×#137	C₂²	1	12	yes	complemented
23	C₁₃×#568	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₁₃	—	2	2	no	—
25	C₁₃×#547	—	2	6	no	—
26	C₁₃×#536	C₂²	1	3	yes	complemented
27	C₁₃×#536	C₂²	1	3	yes	complemented
28	C₁₃×#532	C₂²	1	3	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#456	C₂²	1	12	yes	complemented
32	C₁₃×#456	C₂²	1	24	yes	complemented
33	C₁₃×#455	C₂²	1	12	yes	complemented
34	C₁₃×#454	C₂²	1	12	yes	complemented
35	C₁₃×#453	C₂²	1	4	yes	complemented
36	C₁₃×#421	C₂²	1	12	yes	complemented
37	C₂×C₁₃×#104	C₂²	1	12	yes	complemented
38	C₁₃×#413	C₂²	1	6	yes	complemented
39	C₂×C₁₃×#101	C₂²	1	6	yes	complemented
40	C₁₃×2₋¹⁺⁴	—	2	24	no	—
41	C₁₃×2₋¹⁺⁴	—	2	16	no	—
42	C₁₃×2₋¹⁺⁴	—	2	24	no	—
43	C₁₃×2₋¹⁺⁴	—	2	8	no	—
44	C₁₃×2₋¹⁺⁴	—	2	12	no	—
45	C₁₃×2₋¹⁺⁴	—	2	2	no	—
46	C₁₃×2₋¹⁺⁴	—	2	12	no	—
47	C₁₃×2₋¹⁺⁴	—	2	8	no	—
48	C₁₃×2₋¹⁺⁴	D₄	1	8	yes	complemented
49	C₁₃×2₋¹⁺⁴	C₂³	1	12	yes	—
50	C₁₃×H(5,𝔽₂)	—	2	24	no	—
51	C₁₃×H(5,𝔽₂)	—	2	12	no	—
52	C₁₃×H(5,𝔽₂)	—	2	12	no	—
53	C₁₃×H(5,𝔽₂)	—	2	6	no	—
54	C₁₃×H(5,𝔽₂)	D₄	1	8	yes	complemented
55	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
56	C₂×C₁₃×#41	—	2	8	no	—
57	C₂×C₁₃×#41	—	2	48	no	—
58	C₂×C₁₃×#41	—	2	24	no	—
59	C₂×C₁₃×#41	—	2	8	no	—
60	C₂×C₁₃×#41	—	2	12	no	—
61	C₂×C₁₃×#41	—	2	3	no	—
62	C₂×C₁₃×#41	—	2	12	no	—
63	C₂×C₁₃×#41	—	2	12	no	—
64	C₂×C₁₃×#41	D₄	1	6	yes	—
65	C₂×C₁₃×#41	C₂³	1	12	yes	—
66	C₂×C₁₃×#41	C₂³	1	3	yes	—
67	C₂×C₁₃×#41	C₂³	1	3	yes	—
68	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	—	2	8	no	—
70	C₂²×Q₈×C₁₃	—	2	12	no	—
71	C₂²×Q₈×C₁₃	—	2	1	no	—
72	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
75	C₁₃×#137	—	2	24	no	—
76	C₁₃×#137	—	2	12	no	—
77	C₁₃×#137	C₂³	1	24	yes	—
78	C₁₃×AGL(1,ℤ/8)	—	2	12	no	—
79	C₁₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
80	C₁₃×#135	—	2	24	no	—
81	C₂×C₁₃×Q₁₆	—	2	12	no	—
82	C₂×C₁₃×SD₁₆	—	2	12	no	—
83	C₁₃×#131	—	2	8	no	—
84	C₂×C₁₃×M₁₆	C₂³	1	12	yes	—
85	C₁₃×C₄⋊Q₈	—	2	6	no	—
86	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
88	C₁₃×#127	C₂³	1	1	yes	characteristic
89	C₁₃×#124	C₂³	1	3	yes	—
90	C₁₃×#124	C₂³	1	3	yes	—
91	C₁₃×#123	—	2	6	no	—
92	C₁₃×#123	—	2	6	no	—
93	C₁₃×C₂²⋊Q₈	—	2	6	no	—
94	C₁₃×C₂²⋊Q₈	—	2	6	no	—
95	C₁₃×#121	—	2	6	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	6	no	—
99	C₁₃×#117	C₂³	1	3	yes	—
100	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
101	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#104	C₂³	1	8	yes	—
103	C₁₃×#104	C₂³	1	24	yes	—
104	C₁₃×#101	C₂³	1	12	yes	—
105	C₁₃×#100	C₂³	1	4	yes	—
106	#60391	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₁₃×#41	—	2	48	no	—
108	C₁₃×#41	—	2	48	no	—
109	C₁₃×#41	—	2	48	no	—
110	C₁₃×#41	—	2	24	no	—
111	C₁₃×#41	—	2	24	no	—
112	C₁₃×#41	—	2	8	no	—
113	C₁₃×#41	—	2	8	no	—
114	C₁₃×#41	—	2	24	no	—
115	C₁₃×#41	—	2	24	no	—
116	C₁₃×#41	—	2	24	no	—
117	C₁₃×#41	—	2	24	no	—
118	C₁₃×#41	—	2	12	no	—
119	C₁₃×#41	—	2	12	no	—
120	C₁₃×#41	—	2	12	no	—
121	C₁₃×#41	—	2	12	no	—
122	C₁₃×#41	—	4	12	no	—
123	C₁₃×#41	C₂×D₄	1	24	yes	—
124	C₁₃×#41	C₂×D₄	1	8	yes	—
125	C₁₃×#41	C₂⁴	1	8	yes	—
126	C₂×Q₈×C₁₃	—	2	48	no	—
127	C₂×Q₈×C₁₃	—	2	12	no	—
128	C₂×Q₈×C₁₃	—	2	12	no	—
129	C₂×Q₈×C₁₃	—	2	8	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	2	24	no	—
132	C₂×Q₈×C₁₃	—	2	12	no	—
133	C₂×Q₈×C₁₃	—	2	3	no	—
134	C₂×Q₈×C₁₃	—	2	12	no	—
135	C₂×Q₈×C₁₃	—	4	4	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	12	yes	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	6	yes	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
141	C₂×D₄×C₁₃	—	2	48	no	—
142	C₂×D₄×C₁₃	—	2	12	no	—
143	C₂×D₄×C₁₃	—	2	12	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	12	no	—
146	C₂×D₄×C₁₃	—	2	24	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	3	no	—
150	C₂×D₄×C₁₃	C₂×D₄	1	6	yes	—
151	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
152	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	—	2	24	no	—
156	C₂²×C₄×C₁₃	—	2	24	no	—
157	C₂²×C₄×C₁₃	—	2	12	no	—
158	C₂²×C₄×C₁₃	—	2	3	no	—
159	C₂²×C₄×C₁₃	—	2	3	no	—
160	C₂²×C₄×C₁₃	—	2	3	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
164	C₁₃×Q₁₆	—	2	24	no	—
165	C₁₃×SD₁₆	—	2	8	no	—
166	C₁₃×SD₁₆	—	2	24	no	—
167	C₁₃×D₈	—	2	8	no	—
168	C₁₃×M₁₆	—	2	12	no	—
169	C₁₃×M₁₆	C₂⁴	1	8	yes	—
170	C₂×C₈×C₁₃	—	2	12	no	—
171	C₁₃×C₄⋊C₄	—	2	6	no	—
172	C₁₃×C₄⋊C₄	—	2	12	no	—
173	C₁₃×C₄⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	3	no	—
175	C₁₃×C₂²⋊C₄	—	2	6	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₄²×C₁₃	—	2	3	no	—
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	3	yes	—
180	2₋¹⁺⁶	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#3586	C₂×C₁₃	1	2	yes	complemented
182	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3022	C₂×C₁₃	1	6	yes	complemented
184	#3020	C₂×C₁₃	1	6	yes	complemented
185	#3018	C₂×C₁₃	1	6	yes	complemented
186	C₂×#456	C₂×C₁₃	1	6	yes	complemented
187	#2901	C₂×C₁₃	1	2	yes	complemented
188	#2889	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	12	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
194	Q₈×C₁₃	—	2	24	no	—
195	Q₈×C₁₃	—	2	12	no	—
196	Q₈×C₁₃	—	2	12	no	—
197	Q₈×C₁₃	—	2	6	no	—
198	Q₈×C₁₃	—	2	6	no	—
199	Q₈×C₁₃	—	4	6	no	—
200	Q₈×C₁₃	#120	1	4	yes	—
201	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
202	D₄×C₁₃	—	2	16	no	—
203	D₄×C₁₃	—	2	24	no	—
204	D₄×C₁₃	—	2	24	no	—
205	D₄×C₁₃	—	2	12	no	—
206	D₄×C₁₃	—	2	8	no	—
207	D₄×C₁₃	—	2	12	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	4	4	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	#120	1	12	yes	—
213	D₄×C₁₃	C₂²×D₄	1	8	yes	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	48	no	—
216	C₂×C₄×C₁₃	—	2	12	no	—
217	C₂×C₄×C₁₃	—	2	12	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	24	no	—
220	C₂×C₄×C₁₃	—	2	12	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	3	no	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	4	6	no	—
225	C₂×C₄×C₁₃	—	4	6	no	—
226	C₂×C₄×C₁₃	—	4	6	no	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	8	no	—
232	#585	—	2	8	no	—
233	#585	—	2	6	no	—
234	#585	C₂²×C₁₃	1	6	yes	—
235	#585	C₂²×C₁₃	1	2	yes	—
236	C₂×2₋¹⁺⁴	—	2	8	no	—
237	C₂×2₋¹⁺⁴	—	2	2	no	—
238	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	6	yes	—
239	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	#578	—	2	8	no	—
242	#577	—	2	8	no	—
243	#575	C₂²×C₁₃	1	12	yes	complemented
244	C₂×#137	C₂²×C₁₃	1	12	yes	complemented
245	#568	C₂²×C₁₃	1	2	yes	complemented
246	D₄×Q₈	—	2	2	no	—
247	#547	—	2	6	no	—
248	#536	C₂²×C₁₃	1	3	yes	complemented
249	#536	C₂²×C₁₃	1	3	yes	complemented
250	#532	C₂²×C₁₃	1	3	yes	complemented
251	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
252	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
253	#456	C₂²×C₁₃	1	12	yes	complemented
254	#456	C₂²×C₁₃	1	24	yes	complemented
255	#455	C₂²×C₁₃	1	12	yes	complemented
256	#454	C₂²×C₁₃	1	12	yes	complemented
257	#453	C₂²×C₁₃	1	4	yes	complemented
258	#421	C₂²×C₁₃	1	12	yes	complemented
259	C₂×#104	C₂²×C₁₃	1	12	yes	complemented
260	#413	C₂²×C₁₃	1	6	yes	complemented
261	C₂×#101	C₂²×C₁₃	1	6	yes	complemented
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	8	no	—
264	C₂²×C₁₃	—	4	3	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	—	8	12	no	—
269	C₂²×C₁₃	—	8	8	no	—
270	C₂²×C₁₃	C₂×#120	1	6	yes	—
271	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	8	no	—
274	C₄×C₁₃	—	2	6	no	—
275	C₄×C₁₃	—	4	3	no	—
276	C₄×C₁₃	—	4	3	no	—
277	C₄×C₁₃	C₂×#120	1	6	yes	—
278	C₄×C₁₃	C₂³×D₄	1	2	yes	—
279	2₋¹⁺⁴	—	2	24	no	—
280	2₋¹⁺⁴	—	2	16	no	—
281	2₋¹⁺⁴	—	2	24	no	—
282	2₋¹⁺⁴	—	2	8	no	—
283	2₋¹⁺⁴	—	2	12	no	—
284	2₋¹⁺⁴	—	2	2	no	—
285	2₋¹⁺⁴	—	2	12	no	—
286	2₋¹⁺⁴	—	2	8	no	—
287	2₋¹⁺⁴	D₄×C₁₃	1	8	yes	complemented
288	2₋¹⁺⁴	C₂³×C₁₃	1	12	yes	—
289	H(5,𝔽₂)	—	2	24	no	—
290	H(5,𝔽₂)	—	2	12	no	—
291	H(5,𝔽₂)	—	2	12	no	—
292	H(5,𝔽₂)	—	2	6	no	—
293	H(5,𝔽₂)	D₄×C₁₃	1	8	yes	complemented
294	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
295	C₂×#41	—	2	8	no	—
296	C₂×#41	—	2	48	no	—
297	C₂×#41	—	2	24	no	—
298	C₂×#41	—	2	8	no	—
299	C₂×#41	—	2	12	no	—
300	C₂×#41	—	2	3	no	—
301	C₂×#41	—	2	12	no	—
302	C₂×#41	—	2	12	no	—
303	C₂×#41	D₄×C₁₃	1	6	yes	—
304	C₂×#41	C₂³×C₁₃	1	12	yes	—
305	C₂×#41	C₂³×C₁₃	1	3	yes	—
306	C₂×#41	C₂³×C₁₃	1	3	yes	—
307	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×Q₈	—	2	8	no	—
309	C₂²×Q₈	—	2	12	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
312	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
313	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
314	#137	—	2	24	no	—
315	#137	—	2	12	no	—
316	#137	C₂³×C₁₃	1	24	yes	—
317	AGL(1,ℤ/8)	—	2	12	no	—
318	AGL(1,ℤ/8)	C₂³×C₁₃	1	8	yes	—
319	#135	—	2	24	no	—
320	C₂×Q₁₆	—	2	12	no	—
321	C₂×SD₁₆	—	2	12	no	—
322	#131	—	2	8	no	—
323	C₂×M₁₆	C₂³×C₁₃	1	12	yes	—
324	C₄⋊Q₈	—	2	6	no	—
325	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
326	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
327	#127	C₂³×C₁₃	1	1	yes	characteristic
328	#124	C₂³×C₁₃	1	3	yes	—
329	#124	C₂³×C₁₃	1	3	yes	—
330	#123	—	2	6	no	—
331	#123	—	2	6	no	—
332	C₂²⋊Q₈	—	2	6	no	—
333	C₂²⋊Q₈	—	2	6	no	—
334	#121	—	2	6	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×D₄	—	2	3	no	—
337	C₄×D₄	—	2	6	no	—
338	#117	C₂³×C₁₃	1	3	yes	—
339	C₂×C₄⋊C₄	—	2	6	no	—
340	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
341	#104	C₂³×C₁₃	1	8	yes	—
342	#104	C₂³×C₁₃	1	24	yes	—
343	#101	C₂³×C₁₃	1	12	yes	—
344	#100	C₂³×C₁₃	1	4	yes	—
345	C₂×C₁₃	—	2	1	no	—
346	C₂×C₁₃	—	2	6	no	—
347	C₂×C₁₃	—	4	2	no	—
348	C₂×C₁₃	—	4	8	no	—
349	C₂×C₁₃	—	8	1	no	—
350	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
351	#41	—	2	48	no	—
352	#41	—	2	48	no	—
353	#41	—	2	48	no	—
354	#41	—	2	24	no	—
355	#41	—	2	24	no	—
356	#41	—	2	8	no	—
357	#41	—	2	8	no	—
358	#41	—	2	24	no	—
359	#41	—	2	24	no	—
360	#41	—	2	24	no	—
361	#41	—	2	24	no	—
362	#41	—	2	12	no	—
363	#41	—	2	12	no	—
364	#41	—	2	12	no	—
365	#41	—	2	12	no	—
366	#41	—	4	12	no	—
367	#41	C₂×D₄×C₁₃	1	24	yes	—
368	#41	C₂×D₄×C₁₃	1	8	yes	—
369	#41	C₂⁴×C₁₃	1	8	yes	—
370	C₂×Q₈	—	2	48	no	—
371	C₂×Q₈	—	2	12	no	—
372	C₂×Q₈	—	2	12	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	24	no	—
376	C₂×Q₈	—	2	12	no	—
377	C₂×Q₈	—	2	3	no	—
378	C₂×Q₈	—	2	12	no	—
379	C₂×Q₈	—	4	4	no	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	12	yes	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	6	yes	—
382	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
384	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
385	C₂×D₄	—	2	48	no	—
386	C₂×D₄	—	2	12	no	—
387	C₂×D₄	—	2	12	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	12	no	—
390	C₂×D₄	—	2	24	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	3	no	—
394	C₂×D₄	C₂×D₄×C₁₃	1	6	yes	—
395	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
396	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
397	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	—	2	24	no	—
400	C₂²×C₄	—	2	24	no	—
401	C₂²×C₄	—	2	12	no	—
402	C₂²×C₄	—	2	3	no	—
403	C₂²×C₄	—	2	3	no	—
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
408	Q₁₆	—	2	24	no	—
409	SD₁₆	—	2	8	no	—
410	SD₁₆	—	2	24	no	—
411	D₈	—	2	8	no	—
412	M₁₆	—	2	12	no	—
413	M₁₆	C₂⁴×C₁₃	1	8	yes	—
414	C₂×C₈	—	2	12	no	—
415	C₄⋊C₄	—	2	6	no	—
416	C₄⋊C₄	—	2	12	no	—
417	C₄⋊C₄	—	2	3	no	—
418	C₂²⋊C₄	—	2	3	no	—
419	C₂²⋊C₄	—	2	6	no	—
420	C₂²⋊C₄	—	2	6	no	—
421	C₄²	—	2	3	no	—
422	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₄²	C₂⁴×C₁₃	1	3	yes	—
424	C₁₃	#60391	1	1	yes	characteristic, direct product factor, Sylow
425	C₂³	—	2	8	no	—
426	C₂³	—	2	12	no	—
427	C₂³	—	2	1	no	—
428	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
429	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
430	Q₈	—	2	24	no	—
431	Q₈	—	2	12	no	—
432	Q₈	—	2	12	no	—
433	Q₈	—	2	6	no	—
434	Q₈	—	2	6	no	—
435	Q₈	—	4	6	no	—
436	Q₈	C₁₃×#120	1	4	yes	—
437	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
438	D₄	—	2	16	no	—
439	D₄	—	2	24	no	—
440	D₄	—	2	24	no	—
441	D₄	—	2	12	no	—
442	D₄	—	2	8	no	—
443	D₄	—	2	12	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	6	no	—
448	D₄	C₁₃×#120	1	12	yes	—
449	D₄	C₂²×D₄×C₁₃	1	8	yes	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	48	no	—
452	C₂×C₄	—	2	12	no	—
453	C₂×C₄	—	2	12	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	24	no	—
456	C₂×C₄	—	2	12	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	4	6	no	—
461	C₂×C₄	—	4	6	no	—
462	C₂×C₄	—	4	6	no	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
466	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
467	C₈	—	2	8	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	8	no	—
470	C₂²	—	4	3	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	12	no	—
475	C₂²	—	8	8	no	—
476	C₂²	C₂×C₁₃×#120	1	6	yes	—
477	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	8	no	—
480	C₄	—	2	6	no	—
481	C₄	—	4	3	no	—
482	C₄	—	4	3	no	—
483	C₄	C₂×C₁₃×#120	1	6	yes	—
484	C₄	C₂³×D₄×C₁₃	1	2	yes	—
485	C₂	—	2	1	no	—
486	C₂	—	2	6	no	—
487	C₂	—	4	2	no	—
488	C₂	—	4	8	no	—
489	C₂	—	8	1	no	—
490	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×2₋¹⁺⁶	C₂	semidirect
2. C₁₃×#3586	C₂	semidirect
3. C₁₃×#3499	C₂	semidirect
4. C₁₃×#3022	C₂	semidirect
5. C₁₃×#3020	C₂	semidirect
6. C₁₃×#3018	C₂	semidirect
7. C₂×C₁₃×#456	C₂	semidirect
8. C₁₃×#2901	C₂	semidirect
9. C₁₃×#2889	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
21. C₁₃×#575	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₁₃×#568	C₂²	semidirect
26. C₁₃×#536	C₂²	semidirect
27. C₁₃×#536	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₄×C₁₃×#41	C₂²	semidirect
31. C₁₃×#456	C₂²	semidirect
32. C₁₃×#456	C₂²	semidirect
33. C₁₃×#455	C₂²	semidirect
34. C₁₃×#454	C₂²	semidirect
35. C₁₃×#453	C₂²	semidirect
36. C₁₃×#421	C₂²	semidirect
37. C₂×C₁₃×#104	C₂²	semidirect
38. C₁₃×#413	C₂²	semidirect
39. C₂×C₁₃×#101	C₂²	semidirect
48. C₁₃×2₋¹⁺⁴	D₄	semidirect
54. C₁₃×H(5,𝔽₂)	D₄	semidirect
106. #60391	C₁₃	direct (N × H)
180. 2₋¹⁺⁶	C₂×C₁₃	semidirect
181. #3586	C₂×C₁₃	semidirect
182. #3499	C₂×C₁₃	semidirect
183. #3022	C₂×C₁₃	semidirect
184. #3020	C₂×C₁₃	semidirect
185. #3018	C₂×C₁₃	semidirect
186. C₂×#456	C₂×C₁₃	semidirect
187. #2901	C₂×C₁₃	semidirect
188. #2889	C₂×C₁₃	semidirect
240. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
243. #575	C₂²×C₁₃	semidirect
244. C₂×#137	C₂²×C₁₃	semidirect
245. #568	C₂²×C₁₃	semidirect
248. #536	C₂²×C₁₃	semidirect
249. #536	C₂²×C₁₃	semidirect
250. #532	C₂²×C₁₃	semidirect
251. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
252. C₄×#41	C₂²×C₁₃	semidirect
253. #456	C₂²×C₁₃	semidirect
254. #456	C₂²×C₁₃	semidirect
255. #455	C₂²×C₁₃	semidirect
256. #454	C₂²×C₁₃	semidirect
257. #453	C₂²×C₁₃	semidirect
258. #421	C₂²×C₁₃	semidirect
259. C₂×#104	C₂²×C₁₃	semidirect
260. #413	C₂²×C₁₃	semidirect
261. C₂×#101	C₂²×C₁₃	semidirect
287. 2₋¹⁺⁴	D₄×C₁₃	semidirect
293. H(5,𝔽₂)	D₄×C₁₃	semidirect
424. C₁₃	#60391	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×2₋¹⁺⁶	2
C₁₃×#3586	2
C₁₃×#3499	2
C₁₃×#3022	2
C₁₃×#3020	2
C₁₃×#3018	2
C₂×C₁₃×#456	2
C₁₃×#2901	2
C₁₃×#2889	2
#60391	13

Subgroups — C13×#60391 #15746730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60391 #15746730