Subgroups — C₁₃×#62150 #15748489

Order 3328.

1996 conjugacy classes of subgroups.

The subgroup lattice has 512 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×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3354	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3332	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3253	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3227	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	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#555	—	2	3	no	—
15	C₁₃×#555	C₂²	1	3	yes	—
16	C₁₃×#550	—	2	1	no	—
17	C₁₃×#550	C₂²	1	3	yes	—
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	—	2	1	no	—
20	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#547	—	2	3	no	—
22	C₁₃×#547	C₂²	1	6	yes	—
23	C₁₃×#536	—	2	3	no	—
24	C₁₃×#532	—	2	3	no	—
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
28	C₄×C₁₃×#41	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	3	yes	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₁₃×#498	C₂²	1	6	yes	—
32	C₁₃×#486	C₂²	1	6	yes	—
33	C₁₃×#482	C₂²	1	6	yes	—
34	C₁₃×#481	C₂²	1	12	yes	—
35	C₁₃×#477	C₂²	1	3	yes	—
36	C₁₃×#476	C₂²	1	6	yes	—
37	C₁₃×#476	C₂²	1	6	yes	—
38	C₁₃×#476	C₂²	1	3	yes	—
39	C₁₃×#475	C₂²	1	6	yes	—
40	C₁₃×#474	C₂²	1	6	yes	—
41	C₁₃×#469	C₂²	1	12	yes	—
42	C₁₃×#460	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	6	yes	—
44	C₁₃×#459	C₂²	1	3	yes	—
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	1	no	—
56	C₂×C₁₃×#41	—	2	6	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	—	2	3	no	—
59	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
60	C₂×C₁₃×#41	C₂³	1	3	yes	—
61	C₂²×Q₈×C₁₃	—	2	2	no	—
62	C₂²×Q₈×C₁₃	—	2	3	no	—
63	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×D₈	C₂³	1	6	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	—	2	3	no	—
68	C₁₃×C₄⋊Q₈	—	2	3	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
72	C₁₃×#127	—	2	3	no	—
73	C₁₃×#127	C₂³	1	1	yes	characteristic
74	C₁₃×#127	C₂³	1	3	yes	—
75	C₁₃×#124	—	2	6	no	—
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#124	—	2	3	no	—
78	C₁₃×#123	—	2	12	no	—
79	C₁₃×C₂²⋊Q₈	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	—	2	6	no	—
81	C₁₃×#121	—	2	3	no	—
82	C₁₃×#121	—	2	3	no	—
83	C₁₃×#121	—	2	3	no	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	6	no	—
86	C₁₃×#121	C₂³	1	6	yes	—
87	C₁₃×#121	C₂³	1	6	yes	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	—	2	3	no	—
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	—	2	3	no	—
98	C₄×D₄×C₁₃	D₄	1	3	yes	—
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	6	yes	—
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	—	2	3	no	—
105	C₁₃×#117	D₄	1	3	yes	—
106	C₁₃×#117	C₂³	1	3	yes	—
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	6	yes	—
112	C₁₃×#106	C₂³	1	12	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	6	yes	—
118	C₁₃×#102	C₂³	1	12	yes	—
119	C₁₃×#102	C₂³	1	2	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62150	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	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	8	6	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	—	2	3	no	—
134	C₂×Q₈×C₁₃	—	2	3	no	—
135	C₂×Q₈×C₁₃	—	4	12	no	—
136	C₂×Q₈×C₁₃	—	4	8	no	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	3	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	3	no	—
146	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	—	2	6	no	—
150	C₂²×C₄×C₁₃	—	2	3	no	—
151	C₂²×C₄×C₁₃	—	2	3	no	—
152	C₂²×C₄×C₁₃	—	2	3	no	—
153	C₂²×C₄×C₁₃	—	2	6	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
157	C₁₃×SD₁₆	—	2	4	no	—
158	C₁₃×D₈	—	4	6	no	—
159	C₁₃×M₁₆	—	4	6	no	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	6	no	—
164	C₁₃×C₄⋊C₄	—	2	6	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	6	no	—
175	C₁₃×C₂²⋊C₄	—	2	3	no	—
176	C₁₃×C₂²⋊C₄	—	2	3	no	—
177	C₁₃×C₂²⋊C₄	—	2	6	no	—
178	C₁₃×C₂²⋊C₄	—	2	6	no	—
179	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	3	no	—
182	C₄²×C₁₃	—	2	3	no	—
183	C₄²×C₁₃	C₂×D₄	1	3	yes	—
184	C₄²×C₁₃	C₂×D₄	1	3	yes	—
185	C₄²×C₁₃	C₂⁴	1	3	yes	—
186	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
187	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
189	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
190	#3358	C₂×C₁₃	1	2	yes	complemented
191	#3354	C₂×C₁₃	1	6	yes	complemented
192	#3332	C₂×C₁₃	1	6	yes	complemented
193	#3253	C₂×C₁₃	1	3	yes	complemented
194	#3227	C₂×C₁₃	1	3	yes	complemented
195	#3106	C₂×C₁₃	1	3	yes	complemented
196	#3079	C₂×C₁₃	1	3	yes	complemented
197	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	3	no	—
200	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	4	6	no	—
203	Q₈×C₁₃	—	4	12	no	—
204	Q₈×C₁₃	—	8	3	no	—
205	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
206	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
207	D₄×C₁₃	—	2	6	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	3	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	3	no	—
212	D₄×C₁₃	—	4	6	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	4	12	no	—
215	D₄×C₁₃	—	4	6	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	8	3	no	—
218	D₄×C₁₃	—	8	6	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	6	no	—
221	C₂×C₄×C₁₃	—	2	6	no	—
222	C₂×C₄×C₁₃	—	2	3	no	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	3	no	—
226	C₂×C₄×C₁₃	—	2	6	no	—
227	C₂×C₄×C₁₃	—	4	6	no	—
228	C₂×C₄×C₁₃	—	4	12	no	—
229	C₂×C₄×C₁₃	—	4	12	no	—
230	C₂×C₄×C₁₃	—	4	6	no	—
231	C₂×C₄×C₁₃	—	4	6	no	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	2	6	no	—
240	C₂×2₋¹⁺⁴	—	2	1	no	—
241	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
242	#555	—	2	3	no	—
243	#555	C₂²×C₁₃	1	3	yes	—
244	#550	—	2	1	no	—
245	#550	C₂²×C₁₃	1	3	yes	—
246	#550	C₂²×C₁₃	1	1	yes	characteristic
247	D₄×Q₈	—	2	1	no	—
248	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
249	#547	—	2	3	no	—
250	#547	C₂²×C₁₃	1	6	yes	—
251	#536	—	2	3	no	—
252	#532	—	2	3	no	—
253	#532	C₂²×C₁₃	1	3	yes	—
254	#532	C₂²×C₁₃	1	3	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
256	C₄×#41	—	2	1	no	—
257	C₄×#41	C₂²×C₁₃	1	3	yes	—
258	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
259	#498	C₂²×C₁₃	1	6	yes	—
260	#486	C₂²×C₁₃	1	6	yes	—
261	#482	C₂²×C₁₃	1	6	yes	—
262	#481	C₂²×C₁₃	1	12	yes	—
263	#477	C₂²×C₁₃	1	3	yes	—
264	#476	C₂²×C₁₃	1	6	yes	—
265	#476	C₂²×C₁₃	1	6	yes	—
266	#476	C₂²×C₁₃	1	3	yes	—
267	#475	C₂²×C₁₃	1	6	yes	—
268	#474	C₂²×C₁₃	1	6	yes	—
269	#469	C₂²×C₁₃	1	12	yes	—
270	#460	C₂²×C₁₃	1	1	yes	characteristic
271	#459	C₂²×C₁₃	1	6	yes	—
272	#459	C₂²×C₁₃	1	3	yes	—
273	#449	C₂²×C₁₃	1	6	yes	—
274	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
275	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
276	C₄×D₈	C₂²×C₁₃	1	6	yes	—
277	#436	C₂²×C₁₃	1	6	yes	—
278	#431	C₂²×C₁₃	1	3	yes	—
279	#428	C₂²×C₁₃	1	6	yes	—
280	#423	C₂²×C₁₃	1	3	yes	—
281	#417	C₂²×C₁₃	1	6	yes	—
282	C₂²×C₁₃	—	2	3	no	—
283	C₂²×C₁₃	—	2	3	no	—
284	C₂²×C₁₃	—	2	3	no	—
285	C₂²×C₁₃	—	4	3	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	3	no	—
289	C₂²×C₁₃	—	4	3	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	—	2	3	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	3	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	6	no	—
298	C₄×C₁₃	—	4	3	no	—
299	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
300	C₄×C₁₃	#577	1	2	yes	—
301	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₄×C₁₃	#585	1	1	yes	characteristic
303	2₋¹⁺⁴	—	4	8	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	6	no	—
306	C₂×#41	—	2	3	no	—
307	C₂×#41	—	2	3	no	—
308	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
309	C₂×#41	C₂³×C₁₃	1	3	yes	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	3	no	—
312	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
313	C₂×D₈	C₂³×C₁₃	1	6	yes	—
314	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
315	C₄⋊Q₈	—	2	3	no	—
316	C₄⋊Q₈	—	2	3	no	—
317	C₄⋊Q₈	—	2	3	no	—
318	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
319	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
320	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
321	#127	—	2	3	no	—
322	#127	C₂³×C₁₃	1	1	yes	characteristic
323	#127	C₂³×C₁₃	1	3	yes	—
324	#124	—	2	6	no	—
325	#124	—	2	3	no	—
326	#124	—	2	3	no	—
327	#123	—	2	12	no	—
328	C₂²⋊Q₈	—	2	6	no	—
329	C₂²⋊Q₈	—	2	6	no	—
330	#121	—	2	3	no	—
331	#121	—	2	3	no	—
332	#121	—	2	3	no	—
333	#121	—	2	3	no	—
334	#121	—	2	6	no	—
335	#121	C₂³×C₁₃	1	6	yes	—
336	#121	C₂³×C₁₃	1	6	yes	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
339	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
341	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₄×D₄	—	2	3	no	—
343	C₄×D₄	—	2	3	no	—
344	C₄×D₄	—	2	3	no	—
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	D₄×C₁₃	1	3	yes	—
348	C₄×D₄	C₂³×C₁₃	1	3	yes	—
349	C₄×D₄	C₂³×C₁₃	1	3	yes	—
350	C₄×D₄	C₂³×C₁₃	1	6	yes	—
351	C₄×D₄	C₂³×C₁₃	1	3	yes	—
352	#117	—	2	3	no	—
353	#117	—	2	3	no	—
354	#117	D₄×C₁₃	1	3	yes	—
355	#117	C₂³×C₁₃	1	3	yes	—
356	C₂×C₄⋊C₄	—	2	3	no	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
358	C₂×C₄²	—	2	3	no	—
359	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
360	#107	C₂³×C₁₃	1	6	yes	—
361	#106	C₂³×C₁₃	1	12	yes	—
362	#106	C₂³×C₁₃	1	6	yes	—
363	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
364	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
365	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
366	#103	C₂³×C₁₃	1	6	yes	—
367	#102	C₂³×C₁₃	1	12	yes	—
368	#102	C₂³×C₁₃	1	2	yes	—
369	#102	C₂³×C₁₃	1	6	yes	—
370	#102	C₂³×C₁₃	1	6	yes	—
371	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
372	C₄×C₈	C₂³×C₁₃	1	6	yes	—
373	C₂×C₁₃	—	4	3	no	—
374	C₂×C₁₃	—	8	3	no	—
375	C₂×C₁₃	—	8	2	no	—
376	C₂×C₁₃	#3489	1	1	yes	characteristic
377	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	2	6	no	—
381	#41	—	4	3	no	—
382	#41	—	4	12	no	—
383	#41	—	4	24	no	—
384	#41	—	4	4	no	—
385	#41	—	8	6	no	—
386	C₂×Q₈	—	2	6	no	—
387	C₂×Q₈	—	2	3	no	—
388	C₂×Q₈	—	2	3	no	—
389	C₂×Q₈	—	4	12	no	—
390	C₂×Q₈	—	4	8	no	—
391	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂×D₄	—	2	3	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	3	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	3	no	—
400	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
401	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
402	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
403	C₂²×C₄	—	2	6	no	—
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	—	2	3	no	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	—	2	6	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
411	SD₁₆	—	2	4	no	—
412	D₈	—	4	6	no	—
413	M₁₆	—	4	6	no	—
414	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
415	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	6	no	—
418	C₄⋊C₄	—	2	6	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
423	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
424	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
425	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
426	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₂²⋊C₄	—	2	3	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	3	no	—
430	C₂²⋊C₄	—	2	3	no	—
431	C₂²⋊C₄	—	2	6	no	—
432	C₂²⋊C₄	—	2	6	no	—
433	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	3	no	—
436	C₄²	—	2	3	no	—
437	C₄²	C₂×D₄×C₁₃	1	3	yes	—
438	C₄²	C₂×D₄×C₁₃	1	3	yes	—
439	C₄²	C₂⁴×C₁₃	1	3	yes	—
440	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₁₃	#62150	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	2	no	—
443	C₂³	—	2	3	no	—
444	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
445	Q₈	—	2	1	no	—
446	Q₈	—	4	6	no	—
447	Q₈	—	4	12	no	—
448	Q₈	—	8	3	no	—
449	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
450	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
451	D₄	—	2	6	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	3	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	3	no	—
456	D₄	—	4	6	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	12	no	—
459	D₄	—	4	6	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	3	no	—
462	D₄	—	8	6	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	6	no	—
465	C₂×C₄	—	2	6	no	—
466	C₂×C₄	—	2	3	no	—
467	C₂×C₄	—	2	3	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	3	no	—
470	C₂×C₄	—	2	6	no	—
471	C₂×C₄	—	4	6	no	—
472	C₂×C₄	—	4	12	no	—
473	C₂×C₄	—	4	12	no	—
474	C₂×C₄	—	4	6	no	—
475	C₂×C₄	—	4	6	no	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	6	no	—
484	C₂²	—	2	3	no	—
485	C₂²	—	2	3	no	—
486	C₂²	—	2	3	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	3	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	3	no	—
492	C₂²	—	4	2	no	—
493	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
494	C₄	—	2	1	no	—
495	C₄	—	2	3	no	—
496	C₄	—	2	3	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	6	no	—
500	C₄	—	4	3	no	—
501	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
502	C₄	C₁₃×#577	1	2	yes	—
503	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
504	C₄	C₁₃×#585	1	1	yes	characteristic
505	C₂	—	4	3	no	—
506	C₂	—	8	2	no	—
507	C₂	—	8	3	no	—
508	C₂	C₁₃×#3489	1	1	yes	characteristic
509	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
510	C₂	C₂×C₁₃×#577	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×#3483	C₂	semidirect
3. Q₈×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3354	C₂	semidirect
6. C₁₃×#3332	C₂	semidirect
7. C₁₃×#3253	C₂	semidirect
8. C₁₃×#3227	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
124. #62150	C₁₃	direct (N × H)
187. #3499	C₂×C₁₃	semidirect
188. #3483	C₂×C₁₃	semidirect
189. Q₈×SD₁₆	C₂×C₁₃	semidirect
190. #3358	C₂×C₁₃	semidirect
191. #3354	C₂×C₁₃	semidirect
192. #3332	C₂×C₁₃	semidirect
193. #3253	C₂×C₁₃	semidirect
194. #3227	C₂×C₁₃	semidirect
195. #3106	C₂×C₁₃	semidirect
196. #3079	C₂×C₁₃	semidirect
197. #2991	C₂×C₁₃	semidirect
206. Q₈×C₁₃	2₋¹⁺⁴	semidirect
441. C₁₃	#62150	direct (N × H)
450. Q₈	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×#3483	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3358	2
C₁₃×#3354	2
C₁₃×#3332	2
C₁₃×#3253	2
C₁₃×#3227	2
C₁₃×#3106	2
C₁₃×#3079	2
C₁₃×#2991	2
#62150	13

Subgroups — C13×#62150 #15748489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62150 #15748489