Subgroups — C₁₃×#24860 #15711199

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#479	—	2	1	no	—
25	C₁₃×#479	—	2	1	no	—
26	C₁₃×#479	—	2	1	no	—
27	C₁₃×#479	—	2	1	no	—
28	C₁₃×#478	—	2	1	no	—
29	C₁₃×#478	—	2	1	no	—
30	C₁₃×#441	—	2	1	no	—
31	C₁₃×#440	—	2	1	no	—
32	C₄×C₁₃×Q₁₆	—	2	1	no	—
33	C₄×C₁₃×SD₁₆	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
41	C₁₃×#424	—	2	1	no	—
42	C₁₃×#424	—	2	1	no	—
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₁₃×#424	C₂²	1	1	yes	characteristic
45	C₁₃×#423	—	2	1	no	—
46	C₁₃×#423	C₂²	1	1	yes	characteristic
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#419	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₁₃×#417	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#343	C₂²	1	1	yes	characteristic
65	C₁₃×#341	C₂²	1	1	yes	characteristic
66	C₁₃×#341	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#137	—	2	2	no	—
70	C₁₃×#137	Q₈	1	4	yes	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₁₃×#131	—	2	2	no	—
74	C₁₃×#131	—	2	2	no	—
75	C₁₃×#131	—	4	1	no	—
76	C₁₃×#131	—	4	1	no	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	—	2	1	no	—
86	C₂²×C₈×C₁₃	—	2	1	no	—
87	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#125	—	2	1	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₁₃×#117	—	2	1	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#108	—	4	1	no	—
115	C₁₃×#108	—	4	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×C₄⋊C₈	—	2	1	no	—
130	C₁₃×C₄⋊C₈	—	2	1	no	—
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×C₄⋊C₈	—	2	1	no	—
133	C₁₃×C₄⋊C₈	—	2	1	no	—
134	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#103	—	2	1	no	—
142	C₁₃×#103	—	2	1	no	—
143	C₁₃×#103	—	2	1	no	—
144	C₁₃×#103	—	2	1	no	—
145	C₁₃×#103	—	2	1	no	—
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	—	2	1	no	—
150	C₁₃×#101	—	4	1	no	—
151	C₁₃×#101	—	4	1	no	—
152	C₁₃×#97	—	2	1	no	—
153	C₄×C₈×C₁₃	—	2	1	no	—
154	#24860	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	C₂×Q₈	1	2	yes	—
158	C₁₃×#41	#41	1	2	yes	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×Q₁₆	—	2	4	no	—
179	C₁₃×SD₁₆	—	2	4	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	—	2	1	no	—
191	C₁₃×M₁₆	—	4	2	no	—
192	C₁₃×M₁₆	—	4	2	no	—
193	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	4	2	no	—
205	C₂×C₈×C₁₃	—	4	2	no	—
206	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	4	1	no	—
219	C₁₃×C₄⋊C₄	—	4	1	no	—
220	C₁₃×C₄⋊C₄	—	4	1	no	—
221	C₁₃×C₄⋊C₄	—	4	1	no	—
222	C₁₃×C₄⋊C₄	—	4	1	no	—
223	C₁₃×C₄⋊C₄	—	4	1	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₁₃×C₂²⋊C₄	—	2	1	no	—
227	C₁₃×C₂²⋊C₄	—	2	1	no	—
228	C₁₃×C₂²⋊C₄	—	2	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	4	1	no	—
233	C₄²×C₁₃	—	4	1	no	—
234	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
238	#3080	C₂×C₁₃	1	1	yes	characteristic
239	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
241	#2906	C₂×C₁₃	1	1	yes	characteristic
242	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1908	C₂×C₁₃	1	1	yes	characteristic
249	#1908	C₂×C₁₃	1	1	yes	characteristic
250	#1816	C₂×C₁₃	1	1	yes	characteristic
251	#1815	C₂×C₁₃	1	1	yes	characteristic
252	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	1	no	—
256	Q₈×C₁₃	—	2	2	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	Q₈×C₁₃	—	4	1	no	—
260	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	2	no	—
263	D₄×C₁₃	—	2	1	no	—
264	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	8	1	no	—
280	C₂×C₄×C₁₃	—	8	1	no	—
281	C₂×C₄×C₁₃	—	8	1	no	—
282	C₂×C₄×C₁₃	—	8	1	no	—
283	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
284	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
285	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
286	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	—	2	1	no	—
296	C₈×C₁₃	—	2	1	no	—
297	C₈×C₁₃	—	2	1	no	—
298	C₈×C₁₃	—	4	1	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₈×C₁₃	—	4	1	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	#479	—	2	1	no	—
310	#479	—	2	1	no	—
311	#479	—	2	1	no	—
312	#479	—	2	1	no	—
313	#479	—	2	1	no	—
314	#479	—	2	1	no	—
315	#478	—	2	1	no	—
316	#478	—	2	1	no	—
317	#441	—	2	1	no	—
318	#440	—	2	1	no	—
319	C₄×Q₁₆	—	2	1	no	—
320	C₄×SD₁₆	—	2	1	no	—
321	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
323	#428	C₂²×C₁₃	1	1	yes	characteristic
324	#428	C₂²×C₁₃	1	1	yes	characteristic
325	#428	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
328	#424	—	2	1	no	—
329	#424	—	2	1	no	—
330	#424	C₂²×C₁₃	1	1	yes	characteristic
331	#424	C₂²×C₁₃	1	1	yes	characteristic
332	#423	—	2	1	no	—
333	#423	C₂²×C₁₃	1	1	yes	characteristic
334	#423	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₈	—	2	1	no	—
336	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
337	#419	C₂²×C₁₃	1	1	yes	characteristic
338	#417	C₂²×C₁₃	1	1	yes	characteristic
339	#417	C₂²×C₁₃	1	1	yes	characteristic
340	#417	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
345	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
346	#343	C₂²×C₁₃	1	1	yes	characteristic
347	#343	C₂²×C₁₃	1	1	yes	characteristic
348	#343	C₂²×C₁₃	1	1	yes	characteristic
349	#343	C₂²×C₁₃	1	1	yes	characteristic
350	#343	C₂²×C₁₃	1	1	yes	characteristic
351	#343	C₂²×C₁₃	1	1	yes	characteristic
352	#341	C₂²×C₁₃	1	1	yes	characteristic
353	#341	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×C₁₃	—	2	1	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
360	C₂²×C₁₃	#552	1	1	yes	characteristic
361	C₂²×C₁₃	#554	1	1	yes	characteristic
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	2	1	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
374	C₄×C₁₃	#537	1	1	yes	characteristic
375	C₄×C₁₃	#546	1	1	yes	characteristic
376	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
377	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	#137	—	2	2	no	—
380	#137	Q₈×C₁₃	1	4	yes	—
381	C₂×Q₁₆	—	2	1	no	—
382	C₂×SD₁₆	—	2	1	no	—
383	#131	—	2	2	no	—
384	#131	—	2	2	no	—
385	#131	—	4	1	no	—
386	#131	—	4	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	#125	—	2	1	no	—
400	#125	—	2	1	no	—
401	#125	—	2	1	no	—
402	#125	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
408	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
412	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
413	#117	—	2	1	no	—
414	#117	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	#108	—	4	1	no	—
425	#108	—	4	1	no	—
426	#107	—	2	1	no	—
427	#107	—	2	1	no	—
428	#107	—	2	1	no	—
429	#107	—	2	1	no	—
430	#107	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	#106	—	2	1	no	—
435	#106	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
445	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
446	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
447	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
448	#103	—	2	1	no	—
449	#103	—	2	1	no	—
450	#103	—	2	1	no	—
451	#103	—	2	1	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	—	2	1	no	—
455	#103	—	2	1	no	—
456	#103	—	2	1	no	—
457	#102	—	2	1	no	—
458	#102	—	2	1	no	—
459	#102	—	2	1	no	—
460	#101	—	4	1	no	—
461	#101	—	4	1	no	—
462	#97	—	2	1	no	—
463	C₄×C₈	—	2	1	no	—
464	C₂×C₁₃	—	2	1	no	—
465	C₂×C₁₃	—	2	1	no	—
466	C₂×C₁₃	—	4	2	no	—
467	C₂×C₁₃	#2417	1	1	yes	characteristic
468	C₂×C₁₃	#3067	1	1	yes	characteristic
469	C₂×C₁₃	#3069	1	1	yes	characteristic
470	#41	—	2	1	no	—
471	#41	—	2	1	no	—
472	#41	C₂×Q₈×C₁₃	1	2	yes	—
473	#41	C₁₃×#41	1	2	yes	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
491	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	Q₁₆	—	2	4	no	—
494	SD₁₆	—	2	4	no	—
495	M₁₆	—	2	1	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	4	2	no	—
507	M₁₆	—	4	2	no	—
508	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	4	2	no	—
520	C₂×C₈	—	4	2	no	—
521	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	4	1	no	—
548	C₄²	—	4	1	no	—
549	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₁₃	#24860	1	1	yes	characteristic, direct product factor, Sylow
554	C₂³	—	2	1	no	—
555	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
556	Q₈	—	2	1	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	1	no	—
565	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	1	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
585	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
587	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
592	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
610	C₂²	C₁₃×#552	1	1	yes	characteristic
611	C₂²	C₁₃×#554	1	1	yes	characteristic
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
624	C₄	C₁₃×#537	1	1	yes	characteristic
625	C₄	C₁₃×#546	1	1	yes	characteristic
626	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	4	2	no	—
630	C₂	C₁₃×#2417	1	1	yes	characteristic
631	C₂	C₁₃×#3067	1	1	yes	characteristic
632	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#479	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2064	C₂	semidirect
9. C₁₃×#1998	C₂	semidirect
10. C₁₃×#1950	C₂	semidirect
15. C₁₃×#1801	C₂	semidirect
154. #24860	C₁₃	direct (N × H)
239. C₂×#479	C₂×C₁₃	semidirect
242. #2090	C₂×C₁₃	semidirect
243. #2089	C₂×C₁₃	semidirect
244. #2064	C₂×C₁₃	semidirect
245. #2064	C₂×C₁₃	semidirect
246. #1998	C₂×C₁₃	semidirect
247. #1950	C₂×C₁₃	semidirect
252. #1801	C₂×C₁₃	semidirect
553. C₁₃	#24860	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×#3080	2
C₂×C₁₃×#479	2
C₄×C₁₃×#137	2
C₁₃×#2906	2
C₁₃×#2090	2
C₁₃×#2089	2
C₁₃×#2064	2
C₁₃×#1998	2
C₁₃×#1950	2
C₁₃×#1908	2
C₁₃×#1816	2
C₁₃×#1815	2
C₁₃×#1801	2
#24860	13

Subgroups — C13×#24860 #15711199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24860 #15711199