Subgroups — C₁₃×#62148 #15748487

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3353	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3330	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3254	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3230	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3106	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3079	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
13	C₁₃×#557	C₂²	1	1	yes	characteristic
14	C₁₃×#556	C₂²	1	3	yes	—
15	C₁₃×#552	—	2	3	no	—
16	D₄×Q₈×C₁₃	—	2	1	no	—
17	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#548	—	2	1	no	—
20	C₁₃×#547	—	2	3	no	—
21	C₁₃×#547	C₂²	1	3	yes	—
22	C₁₃×#547	C₂²	1	6	yes	—
23	C₁₃×#536	—	2	3	no	—
24	C₁₃×#533	C₂²	1	3	yes	—
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₁₃×#529	—	2	3	no	—
28	C₄×C₁₃×#41	C₂²	1	3	yes	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
31	C₁₃×#500	C₂²	1	6	yes	—
32	C₁₃×#487	C₂²	1	6	yes	—
33	C₁₃×#484	C₂²	1	12	yes	—
34	C₁₃×#482	C₂²	1	6	yes	—
35	C₁₃×#477	C₂²	1	6	yes	—
36	C₁₃×#477	C₂²	1	3	yes	—
37	C₁₃×#476	C₂²	1	3	yes	—
38	C₁₃×#475	C₂²	1	6	yes	—
39	C₁₃×#474	C₂²	1	6	yes	—
40	C₁₃×#474	C₂²	1	6	yes	—
41	C₁₃×#468	C₂²	1	12	yes	—
42	C₁₃×#461	C₂²	1	6	yes	—
43	C₁₃×#460	C₂²	1	3	yes	—
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#449	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
48	C₄×C₁₃×D₈	C₂²	1	6	yes	—
49	C₁₃×#436	C₂²	1	6	yes	—
50	C₁₃×#431	C₂²	1	3	yes	—
51	C₁₃×#428	C₂²	1	6	yes	—
52	C₁₃×#423	C₂²	1	3	yes	—
53	C₁₃×#417	C₂²	1	6	yes	—
54	C₁₃×2₋¹⁺⁴	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	6	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
58	C₂×C₁₃×#41	C₂³	1	3	yes	—
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	—	2	2	no	—
61	C₂²×Q₈×C₁₃	—	2	3	no	—
62	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
63	C₂×C₁₃×D₈	C₂³	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
65	C₁₃×C₄⋊Q₈	—	2	3	no	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₁₃×#127	C₂³	1	1	yes	characteristic
72	C₁₃×#126	—	2	6	no	—
73	C₁₃×#125	—	2	3	no	—
74	C₁₃×#125	—	2	3	no	—
75	C₁₃×#124	—	2	3	no	—
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×#123	—	2	12	no	—
79	C₁₃×C₂²⋊Q₈	—	2	3	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×C₂²⋊Q₈	—	2	6	no	—
82	C₁₃×C₂²⋊Q₈	—	2	6	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	3	no	—
86	C₁₃×#121	C₂³	1	6	yes	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	—	2	3	no	—
90	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₃	—	2	3	no	—
95	C₄×D₄×C₁₃	—	2	3	no	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	D₄	1	3	yes	—
98	C₄×D₄×C₁₃	C₂³	1	3	yes	—
99	C₄×D₄×C₁₃	C₂³	1	6	yes	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#117	—	2	3	no	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	D₄	1	3	yes	—
105	C₁₃×#117	C₂³	1	3	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₄²×C₁₃	—	2	3	no	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#107	C₂³	1	12	yes	—
112	C₁₃×#107	C₂³	1	6	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×#103	C₂³	1	12	yes	—
118	C₁₃×#103	C₂³	1	6	yes	—
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	2	yes	—
122	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62148	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	6	no	—
127	C₁₃×#41	—	4	3	no	—
128	C₁₃×#41	—	4	12	no	—
129	C₁₃×#41	—	4	24	no	—
130	C₂×Q₈×C₁₃	—	2	3	no	—
131	C₂×Q₈×C₁₃	—	2	6	no	—
132	C₂×Q₈×C₁₃	—	2	3	no	—
133	C₂×Q₈×C₁₃	—	4	12	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	—	4	8	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
138	C₂×D₄×C₁₃	—	2	3	no	—
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	—	2	6	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	3	no	—
148	C₂²×C₄×C₁₃	—	2	3	no	—
149	C₂²×C₄×C₁₃	—	2	6	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₁₃×SD₁₆	—	4	6	no	—
154	C₁₃×D₈	—	2	4	no	—
155	C₁₃×M₁₆	—	4	6	no	—
156	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
158	C₁₃×C₄⋊C₄	—	2	3	no	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	—	2	6	no	—
161	C₁₃×C₄⋊C₄	—	2	6	no	—
162	C₁₃×C₄⋊C₄	—	2	6	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
172	C₁₃×C₂²⋊C₄	—	2	6	no	—
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	3	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	6	no	—
178	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
179	C₄²×C₁₃	—	2	3	no	—
180	C₄²×C₁₃	—	2	3	no	—
181	C₄²×C₁₃	—	2	3	no	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂×D₄	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	3	yes	—
185	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
186	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
188	Q₈×D₈	C₂×C₁₃	1	2	yes	complemented
189	#3359	C₂×C₁₃	1	2	yes	complemented
190	#3353	C₂×C₁₃	1	6	yes	complemented
191	#3330	C₂×C₁₃	1	6	yes	complemented
192	#3254	C₂×C₁₃	1	3	yes	complemented
193	#3230	C₂×C₁₃	1	3	yes	complemented
194	#3106	C₂×C₁₃	1	3	yes	complemented
195	#3079	C₂×C₁₃	1	3	yes	complemented
196	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
200	Q₈×C₁₃	—	2	3	no	—
201	Q₈×C₁₃	—	2	3	no	—
202	Q₈×C₁₃	—	4	6	no	—
203	Q₈×C₁₃	—	4	6	no	—
204	Q₈×C₁₃	—	4	12	no	—
205	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
206	D₄×C₁₃	—	2	6	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	—	4	12	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
215	C₂×C₄×C₁₃	—	2	6	no	—
216	C₂×C₄×C₁₃	—	2	6	no	—
217	C₂×C₄×C₁₃	—	2	3	no	—
218	C₂×C₄×C₁₃	—	2	3	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	3	no	—
221	C₂×C₄×C₁₃	—	2	3	no	—
222	C₂×C₄×C₁₃	—	2	6	no	—
223	C₂×C₄×C₁₃	—	4	6	no	—
224	C₂×C₄×C₁₃	—	4	12	no	—
225	C₂×C₄×C₁₃	—	4	6	no	—
226	C₂×C₄×C₁₃	—	4	12	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	6	no	—
236	C₂×2₋¹⁺⁴	—	2	1	no	—
237	#557	C₂²×C₁₃	1	1	yes	characteristic
238	#556	C₂²×C₁₃	1	3	yes	—
239	#552	—	2	3	no	—
240	D₄×Q₈	—	2	1	no	—
241	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
242	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	#548	—	2	1	no	—
244	#547	—	2	3	no	—
245	#547	C₂²×C₁₃	1	3	yes	—
246	#547	C₂²×C₁₃	1	6	yes	—
247	#536	—	2	3	no	—
248	#533	C₂²×C₁₃	1	3	yes	—
249	#532	C₂²×C₁₃	1	3	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
251	#529	—	2	3	no	—
252	C₄×#41	C₂²×C₁₃	1	3	yes	—
253	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄×Q₈	—	2	1	no	—
255	#500	C₂²×C₁₃	1	6	yes	—
256	#487	C₂²×C₁₃	1	6	yes	—
257	#484	C₂²×C₁₃	1	12	yes	—
258	#482	C₂²×C₁₃	1	6	yes	—
259	#477	C₂²×C₁₃	1	6	yes	—
260	#477	C₂²×C₁₃	1	3	yes	—
261	#476	C₂²×C₁₃	1	3	yes	—
262	#475	C₂²×C₁₃	1	6	yes	—
263	#474	C₂²×C₁₃	1	6	yes	—
264	#474	C₂²×C₁₃	1	6	yes	—
265	#468	C₂²×C₁₃	1	12	yes	—
266	#461	C₂²×C₁₃	1	6	yes	—
267	#460	C₂²×C₁₃	1	3	yes	—
268	#459	C₂²×C₁₃	1	1	yes	characteristic
269	#449	C₂²×C₁₃	1	6	yes	—
270	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
271	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
272	C₄×D₈	C₂²×C₁₃	1	6	yes	—
273	#436	C₂²×C₁₃	1	6	yes	—
274	#431	C₂²×C₁₃	1	3	yes	—
275	#428	C₂²×C₁₃	1	6	yes	—
276	#423	C₂²×C₁₃	1	3	yes	—
277	#417	C₂²×C₁₃	1	6	yes	—
278	C₂²×C₁₃	—	2	3	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	3	no	—
281	C₂²×C₁₃	—	2	3	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	3	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	3	no	—
291	C₄×C₁₃	—	4	3	no	—
292	C₄×C₁₃	—	4	6	no	—
293	C₄×C₁₃	—	4	3	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
296	C₄×C₁₃	#578	1	2	yes	—
297	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
298	C₄×C₁₃	#585	1	1	yes	characteristic
299	2₋¹⁺⁴	—	4	8	no	—
300	C₂×#41	—	2	6	no	—
301	C₂×#41	—	2	3	no	—
302	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
303	C₂×#41	C₂³×C₁₃	1	3	yes	—
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	2	3	no	—
307	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
308	C₂×D₈	C₂³×C₁₃	1	2	yes	—
309	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
310	C₄⋊Q₈	—	2	3	no	—
311	C₄⋊Q₈	—	2	3	no	—
312	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
316	#127	C₂³×C₁₃	1	1	yes	characteristic
317	#126	—	2	6	no	—
318	#125	—	2	3	no	—
319	#125	—	2	3	no	—
320	#124	—	2	3	no	—
321	#124	—	2	3	no	—
322	#123	—	2	6	no	—
323	#123	—	2	12	no	—
324	C₂²⋊Q₈	—	2	3	no	—
325	C₂²⋊Q₈	—	2	3	no	—
326	C₂²⋊Q₈	—	2	6	no	—
327	C₂²⋊Q₈	—	2	6	no	—
328	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
329	#121	—	2	3	no	—
330	#121	—	2	3	no	—
331	#121	C₂³×C₁₃	1	6	yes	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	—	2	3	no	—
334	C₄×Q₈	—	2	3	no	—
335	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
336	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
337	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
338	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	D₄×C₁₃	1	3	yes	—
343	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₄×D₄	C₂³×C₁₃	1	3	yes	—
345	C₄×D₄	C₂³×C₁₃	1	6	yes	—
346	C₄×D₄	C₂³×C₁₃	1	3	yes	—
347	#117	—	2	3	no	—
348	#117	—	2	3	no	—
349	#117	D₄×C₁₃	1	3	yes	—
350	#117	C₂³×C₁₃	1	3	yes	—
351	C₂×C₄⋊C₄	—	2	3	no	—
352	C₂×C₄⋊C₄	—	2	3	no	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
354	C₂×C₄²	—	2	3	no	—
355	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
356	#107	C₂³×C₁₃	1	12	yes	—
357	#107	C₂³×C₁₃	1	6	yes	—
358	#106	C₂³×C₁₃	1	6	yes	—
359	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
360	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
361	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
362	#103	C₂³×C₁₃	1	12	yes	—
363	#103	C₂³×C₁₃	1	6	yes	—
364	#102	C₂³×C₁₃	1	6	yes	—
365	#102	C₂³×C₁₃	1	6	yes	—
366	#102	C₂³×C₁₃	1	2	yes	—
367	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
368	C₄×C₈	C₂³×C₁₃	1	6	yes	—
369	C₂×C₁₃	—	4	3	no	—
370	C₂×C₁₃	—	4	2	no	—
371	C₂×C₁₃	—	8	2	no	—
372	C₂×C₁₃	#3489	1	1	yes	characteristic
373	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
375	#41	—	2	4	no	—
376	#41	—	2	6	no	—
377	#41	—	4	3	no	—
378	#41	—	4	12	no	—
379	#41	—	4	24	no	—
380	C₂×Q₈	—	2	3	no	—
381	C₂×Q₈	—	2	6	no	—
382	C₂×Q₈	—	2	3	no	—
383	C₂×Q₈	—	4	12	no	—
384	C₂×Q₈	—	4	8	no	—
385	C₂×Q₈	—	4	4	no	—
386	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
388	C₂×D₄	—	2	3	no	—
389	C₂×D₄	—	2	6	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
393	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
394	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	—	2	6	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	3	no	—
398	C₂²×C₄	—	2	3	no	—
399	C₂²×C₄	—	2	6	no	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
403	SD₁₆	—	4	6	no	—
404	D₈	—	2	4	no	—
405	M₁₆	—	4	6	no	—
406	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
407	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
408	C₄⋊C₄	—	2	3	no	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	6	no	—
411	C₄⋊C₄	—	2	6	no	—
412	C₄⋊C₄	—	2	6	no	—
413	C₄⋊C₄	—	2	3	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
418	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
419	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
421	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	3	no	—
426	C₂²⋊C₄	—	2	6	no	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
429	C₄²	—	2	3	no	—
430	C₄²	—	2	3	no	—
431	C₄²	—	2	3	no	—
432	C₄²	C₂×D₄×C₁₃	1	3	yes	—
433	C₄²	C₂×D₄×C₁₃	1	3	yes	—
434	C₄²	C₂⁴×C₁₃	1	3	yes	—
435	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₁₃	#62148	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
440	Q₈	—	2	3	no	—
441	Q₈	—	2	3	no	—
442	Q₈	—	4	6	no	—
443	Q₈	—	4	12	no	—
444	Q₈	—	4	6	no	—
445	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
446	D₄	—	2	6	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	1	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	6	no	—
452	D₄	—	4	12	no	—
453	D₄	—	4	2	no	—
454	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	2	6	no	—
457	C₂×C₄	—	2	3	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	4	6	no	—
464	C₂×C₄	—	4	12	no	—
465	C₂×C₄	—	4	6	no	—
466	C₂×C₄	—	4	12	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	6	no	—
476	C₂²	—	2	3	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	2	3	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	3	no	—
488	C₄	—	2	3	no	—
489	C₄	—	4	6	no	—
490	C₄	—	4	3	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	3	no	—
493	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
494	C₄	C₁₃×#578	1	2	yes	—
495	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
496	C₄	C₁₃×#585	1	1	yes	characteristic
497	C₂	—	4	3	no	—
498	C₂	—	4	2	no	—
499	C₂	—	8	2	no	—
500	C₂	C₁₃×#3489	1	1	yes	characteristic
501	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3499	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. Q₈×C₁₃×D₈	C₂	semidirect
4. C₁₃×#3359	C₂	semidirect
5. C₁₃×#3353	C₂	semidirect
6. C₁₃×#3330	C₂	semidirect
7. C₁₃×#3254	C₂	semidirect
8. C₁₃×#3230	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
124. #62148	C₁₃	direct (N × H)
186. #3499	C₂×C₁₃	semidirect
187. #3482	C₂×C₁₃	semidirect
188. Q₈×D₈	C₂×C₁₃	semidirect
189. #3359	C₂×C₁₃	semidirect
190. #3353	C₂×C₁₃	semidirect
191. #3330	C₂×C₁₃	semidirect
192. #3254	C₂×C₁₃	semidirect
193. #3230	C₂×C₁₃	semidirect
194. #3106	C₂×C₁₃	semidirect
195. #3079	C₂×C₁₃	semidirect
196. #2991	C₂×C₁₃	semidirect
214. D₄×C₁₃	2₋¹⁺⁴	semidirect
436. C₁₃	#62148	direct (N × H)
454. D₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3499	2
C₁₃×#3482	2
Q₈×C₁₃×D₈	2
C₁₃×#3359	2
C₁₃×#3353	2
C₁₃×#3330	2
C₁₃×#3254	2
C₁₃×#3230	2
C₁₃×#3106	2
C₁₃×#3079	2
C₁₃×#2991	2
#62148	13

Subgroups — C13×#62148 #15748487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62148 #15748487