Subgroups — C₁₃×#24573 #15710912

Order 3328.

936 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2079	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1907	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1821	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1815	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#481	—	2	1	no	—
20	C₁₃×#481	—	2	1	no	—
21	C₁₃×#481	—	2	2	no	—
22	C₁₃×#449	—	2	1	no	—
23	C₁₃×#449	—	2	1	no	—
24	C₁₃×#448	—	2	1	no	—
25	C₁₃×#447	—	2	1	no	—
26	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
28	C₁₃×#417	—	2	1	no	—
29	C₁₃×#417	—	2	1	no	—
30	C₁₃×#417	C₂²	1	1	yes	characteristic
31	C₁₃×#417	C₂²	1	1	yes	characteristic
32	C₁₃×#417	C₂²	1	2	yes	—
33	C₁₃×#417	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	—	2	1	no	—
35	C₂×C₁₃×#102	—	2	1	no	—
36	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
38	C₁₃×#408	—	2	2	no	—
39	C₁₃×#408	C₂²	1	2	yes	—
40	C₁₃×#407	—	2	1	no	—
41	C₁₃×#407	C₂²	1	1	yes	characteristic
42	C₁₃×#407	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#343	C₂²	1	2	yes	complemented
46	C₁₃×#343	C₂²	1	2	yes	complemented
47	C₁₃×#343	C₂²	1	2	yes	complemented
48	C₁₃×#341	C₂²	1	2	yes	complemented
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	—	2	4	no	—
52	C₂×C₁₃×#41	—	4	2	no	—
53	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
66	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	1	no	—
69	C₂×C₁₃×D₈	—	2	1	no	—
70	C₂×C₁₃×D₈	—	2	1	no	—
71	C₁₃×#131	—	2	4	no	—
72	C₁₃×#131	—	4	2	no	—
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	2	no	—
75	C₂×C₁₃×M₁₆	—	4	2	no	—
76	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	2	no	—
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	—	2	1	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₁₃×#108	—	4	2	no	—
96	C₁₃×#106	—	2	2	no	—
97	C₁₃×#106	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	1	no	—
101	C₁₃×#103	—	2	1	no	—
102	C₁₃×#102	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#100	—	4	2	no	—
109	C₁₃×C₂²⋊C₈	—	2	1	no	—
110	C₁₃×C₂²⋊C₈	—	2	1	no	—
111	C₁₃×C₂²⋊C₈	—	2	1	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₁₃×C₂²⋊C₈	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
116	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
118	#24573	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	1	no	—
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂⁴×C₁₃	#41	1	1	yes	characteristic
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	1	no	—
129	C₁₃×#41	—	4	1	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	#41	1	4	yes	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	4	1	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	4	1	no	—
148	C₂×D₄×C₁₃	—	4	4	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	—	8	2	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	8	2	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×SD₁₆	—	4	2	no	—
174	C₁₃×SD₁₆	—	4	2	no	—
175	C₁₃×D₈	—	4	2	no	—
176	C₁₃×D₈	—	4	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	—	2	2	no	—
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	2	no	—
182	C₁₃×M₁₆	—	2	2	no	—
183	C₁₃×M₁₆	—	4	4	no	—
184	C₁₃×M₁₆	—	4	2	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	2	no	—
191	C₂×C₈×C₁₃	—	4	4	no	—
192	C₂×C₈×C₁₃	—	4	2	no	—
193	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3006	C₂×C₁₃	1	1	yes	characteristic
205	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2079	C₂×C₁₃	1	2	yes	complemented
208	#2051	C₂×C₁₃	1	2	yes	complemented
209	#1907	C₂×C₁₃	1	2	yes	complemented
210	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1821	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1815	C₂×C₁₃	1	2	yes	complemented
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	—	4	2	no	—
223	C₂³×C₁₃	—	8	1	no	—
224	C₂³×C₁₃	—	8	1	no	—
225	C₂³×C₁₃	—	8	1	no	—
226	C₂³×C₁₃	#121	1	1	yes	characteristic
227	C₂³×C₁₃	#121	1	1	yes	characteristic
228	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	#123	1	2	yes	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	2	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	2	no	—
247	D₄×C₁₃	#123	1	2	yes	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	8	2	no	—
266	C₂×C₄×C₁₃	—	8	2	no	—
267	C₂×C₄×C₁₃	—	8	1	no	—
268	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	2	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	2	no	—
280	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#131	C₂²×C₁₃	1	2	yes	—
284	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
287	#481	—	2	1	no	—
288	#481	—	2	1	no	—
289	#481	—	2	2	no	—
290	#449	—	2	1	no	—
291	#449	—	2	1	no	—
292	#448	—	2	1	no	—
293	#447	—	2	1	no	—
294	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
295	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
296	#417	—	2	1	no	—
297	#417	—	2	1	no	—
298	#417	C₂²×C₁₃	1	2	yes	—
299	#417	C₂²×C₁₃	1	1	yes	characteristic
300	#417	C₂²×C₁₃	1	2	yes	—
301	#417	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#103	—	2	1	no	—
303	C₂×#102	—	2	1	no	—
304	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
305	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
306	#408	—	2	2	no	—
307	#408	C₂²×C₁₃	1	2	yes	—
308	#407	—	2	1	no	—
309	#407	C₂²×C₁₃	1	1	yes	characteristic
310	#407	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	—	2	1	no	—
312	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
313	#343	C₂²×C₁₃	1	2	yes	complemented
314	#343	C₂²×C₁₃	1	2	yes	complemented
315	#343	C₂²×C₁₃	1	2	yes	complemented
316	#341	C₂²×C₁₃	1	2	yes	complemented
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	8	4	no	—
332	C₂²×C₁₃	—	8	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	8	1	no	—
335	C₂²×C₁₃	—	16	2	no	—
336	C₂²×C₁₃	#471	1	2	yes	—
337	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
338	C₂²×C₁₃	#551	1	2	yes	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	2	no	—
345	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
346	C₄×C₁₃	#534	1	1	yes	characteristic
347	C₄×C₁₃	#546	1	2	yes	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	4	no	—
351	C₂×#41	—	4	2	no	—
352	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
353	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
354	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	AGL(1,ℤ/8)	—	2	4	no	—
365	AGL(1,ℤ/8)	—	4	2	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×D₈	—	2	1	no	—
369	C₂×D₈	—	2	1	no	—
370	#131	—	2	4	no	—
371	#131	—	4	2	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	—	4	2	no	—
375	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
376	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
377	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	#108	—	4	2	no	—
395	#106	—	2	2	no	—
396	#106	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#100	—	4	2	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
415	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
417	C₂×C₁₃	—	2	2	no	—
418	C₂×C₁₃	—	2	2	no	—
419	C₂×C₁₃	—	4	1	no	—
420	C₂×C₁₃	—	4	2	no	—
421	C₂×C₁₃	—	8	1	no	—
422	C₂×C₁₃	—	16	1	no	—
423	C₂×C₁₃	#2412	1	1	yes	characteristic
424	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
425	C₂×C₁₃	#3068	1	1	yes	characteristic
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	2	1	no	—
428	C₂⁴	C₁₃×#41	1	1	yes	characteristic
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	4	4	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	4	no	—
438	#41	C₁₃×#41	1	4	yes	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	8	2	no	—
459	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	8	2	no	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
480	SD₁₆	—	4	2	no	—
481	SD₁₆	—	4	2	no	—
482	D₈	—	4	2	no	—
483	D₈	—	4	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	4	4	no	—
491	M₁₆	—	4	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	4	4	no	—
499	C₂×C₈	—	4	2	no	—
500	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
501	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₁₃	#24573	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³	—	2	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	8	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	1	no	—
523	C₂³	C₁₃×#121	1	1	yes	characteristic
524	C₂³	C₁₃×#121	1	1	yes	characteristic
525	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	C₁₃×#123	1	2	yes	—
531	D₄	—	2	4	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	C₁₃×#123	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
566	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
570	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	4	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	16	2	no	—
596	C₂²	C₁₃×#471	1	2	yes	—
597	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
598	C₂²	C₁₃×#551	1	2	yes	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	2	no	—
605	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
606	C₄	C₁₃×#534	1	1	yes	characteristic
607	C₄	C₁₃×#546	1	2	yes	—
608	C₂	—	2	2	no	—
609	C₂	—	2	2	no	—
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₁₃×#2412	1	1	yes	characteristic
615	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
616	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#481	C₂	semidirect
3. C₂×C₁₃×#417	C₂	semidirect
4. C₁₃×#2880	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2051	C₂	semidirect
7. C₁₃×#1907	C₂	semidirect
8. C₁₃×#1900	C₂	semidirect
9. C₁₃×#1855	C₂	semidirect
10. C₁₃×#1821	C₂	semidirect
11. C₁₃×#1815	C₂	semidirect
26. C₂×C₁₃×#108	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
37. C₂×C₁₃×#100	C₂²	semidirect
45. C₁₃×#343	C₂²	semidirect
46. C₁₃×#343	C₂²	semidirect
47. C₁₃×#343	C₂²	semidirect
48. C₁₃×#341	C₂²	semidirect
118. #24573	C₁₃	direct (N × H)
203. C₂×#481	C₂×C₁₃	semidirect
205. C₂×#417	C₂×C₁₃	semidirect
206. #2880	C₂×C₁₃	semidirect
207. #2079	C₂×C₁₃	semidirect
208. #2051	C₂×C₁₃	semidirect
209. #1907	C₂×C₁₃	semidirect
210. #1900	C₂×C₁₃	semidirect
211. #1855	C₂×C₁₃	semidirect
212. #1821	C₂×C₁₃	semidirect
213. #1815	C₂×C₁₃	semidirect
294. C₂×#108	C₂²×C₁₃	semidirect
295. C₂×#106	C₂²×C₁₃	semidirect
304. C₂×#102	C₂²×C₁₃	semidirect
305. C₂×#100	C₂²×C₁₃	semidirect
313. #343	C₂²×C₁₃	semidirect
314. #343	C₂²×C₁₃	semidirect
315. #343	C₂²×C₁₃	semidirect
316. #341	C₂²×C₁₃	semidirect
510. C₁₃	#24573	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#481	2
C₁₃×#3006	2
C₂×C₁₃×#417	2
C₁₃×#2880	2
C₁₃×#2079	2
C₁₃×#2051	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1821	2
C₁₃×#1815	2
#24573	13

Subgroups — C13×#24573 #15710912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24573 #15710912