Subgroups — C₁₃×#24815 #15711154

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1802	C₂	1	2	yes	maximal
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
18	C₁₃×#476	—	2	4	no	—
19	C₄×C₁₃×SD₁₆	—	2	4	no	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#389	—	2	1	no	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#385	—	2	2	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#384	C₂²	1	2	yes	—
37	C₁₃×#380	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₄×D₄×C₁₃	D₄	1	4	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	—	2	4	no	—
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×C₄⋊C₈	—	4	2	no	—
85	C₁₃×#103	—	2	2	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	D₄	1	2	yes	—
94	#24815	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	4	2	no	—
102	C₂×Q₈×C₁₃	—	8	1	no	—
103	C₂×Q₈×C₁₃	—	8	1	no	—
104	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
110	C₂×D₄×C₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	—	8	2	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×SD₁₆	—	2	8	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	4	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	8	2	no	—
150	C₁₃×C₄⋊C₄	—	8	1	no	—
151	C₁₃×C₄⋊C₄	—	8	2	no	—
152	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	4	no	—
155	C₁₃×C₂²⋊C₄	—	4	4	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	4	2	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	#41	1	2	yes	—
161	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
162	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
163	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
164	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
165	#2084	C₂×C₁₃	1	2	yes	complemented
166	#2066	C₂×C₁₃	1	2	yes	complemented
167	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1877	C₂×C₁₃	1	2	yes	—
170	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1802	C₂×C₁₃	1	2	yes	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	4	1	no	—
183	Q₈×C₁₃	—	4	1	no	—
184	Q₈×C₁₃	—	8	4	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	8	8	no	—
213	C₂×C₄×C₁₃	#121	1	2	yes	—
214	C₂×C₄×C₁₃	#121	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
216	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₃	#137	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₃	—	2	2	no	—
225	C₈×C₁₃	—	4	1	no	—
226	C₈×C₁₃	—	4	2	no	—
227	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	—	2	1	no	—
233	#476	—	2	4	no	—
234	C₄×SD₁₆	—	2	4	no	—
235	C₂×#106	C₂²×C₁₃	1	2	yes	—
236	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
239	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#103	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#102	C₂²×C₁₃	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	#395	—	2	2	no	—
245	#391	C₂²×C₁₃	1	2	yes	—
246	#389	—	2	1	no	—
247	#389	—	2	1	no	—
248	#389	C₂²×C₁₃	1	2	yes	—
249	#385	—	2	2	no	—
250	#384	C₂²×C₁₃	1	2	yes	—
251	#384	C₂²×C₁₃	1	1	yes	characteristic
252	#380	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
254	#340	C₂²×C₁₃	1	2	yes	—
255	#340	C₂²×C₁₃	1	2	yes	—
256	#340	C₂²×C₁₃	1	2	yes	—
257	#336	C₂²×C₁₃	1	2	yes	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
266	C₂²×C₁₃	#546	1	1	yes	characteristic
267	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
268	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
270	C₂²×C₁₃	#576	1	1	yes	characteristic
271	C₂²×C₁₃	#577	1	1	yes	characteristic
272	C₄×C₁₃	—	2	4	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	—	8	1	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	#461	1	4	yes	—
281	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
282	C₄×C₁₃	#537	1	1	yes	characteristic
283	C₄×C₁₃	#552	1	1	yes	characteristic
284	C₄×C₁₃	#554	1	1	yes	characteristic
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
293	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	4	2	no	—
303	C₄×D₄	D₄×C₁₃	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	4	4	no	—
312	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	#106	—	2	2	no	—
324	#106	—	2	4	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	4	2	no	—
327	#103	—	2	2	no	—
328	#103	—	4	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	4	no	—
331	C₄×C₈	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	D₄×C₁₃	1	2	yes	—
336	C₂×C₁₃	—	4	4	no	—
337	C₂×C₁₃	#2417	1	1	yes	characteristic
338	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
339	C₂×C₁₃	#3045	1	1	yes	characteristic
340	C₂×C₁₃	#3295	1	1	yes	characteristic
341	C₂×C₁₃	#3331	1	1	yes	characteristic
342	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
343	C₂×C₁₃	#3385	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	8	1	no	—
352	C₂×Q₈	—	8	1	no	—
353	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
359	C₂×D₄	C₁₃×#41	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	8	2	no	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
376	SD₁₆	—	2	8	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	4	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	8	2	no	—
399	C₄⋊C₄	—	8	1	no	—
400	C₄⋊C₄	—	8	2	no	—
401	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
402	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	C₂×D₄×C₁₃	1	2	yes	—
409	C₄²	C₁₃×#41	1	2	yes	—
410	C₁₃	#24815	1	1	yes	characteristic, direct product factor, Sylow
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	1	no	—
423	Q₈	—	8	4	no	—
424	D₄	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	C₁₃×#121	1	2	yes	—
453	C₂×C₄	C₁₃×#121	1	2	yes	—
454	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
455	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
456	C₂×C₄	C₁₃×#137	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
460	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
461	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
474	C₂²	C₁₃×#546	1	1	yes	characteristic
475	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
476	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
477	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
478	C₂²	C₁₃×#576	1	1	yes	characteristic
479	C₂²	C₁₃×#577	1	1	yes	characteristic
480	C₄	—	2	4	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	2	no	—
488	C₄	C₁₃×#461	1	4	yes	—
489	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
490	C₄	C₁₃×#537	1	1	yes	characteristic
491	C₄	C₁₃×#552	1	1	yes	characteristic
492	C₄	C₁₃×#554	1	1	yes	characteristic
493	C₂	—	4	4	no	—
494	C₂	C₁₃×#2417	1	1	yes	characteristic
495	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
496	C₂	C₁₃×#3045	1	1	yes	characteristic
497	C₂	C₁₃×#3295	1	1	yes	characteristic
498	C₂	C₁₃×#3331	1	1	yes	characteristic
499	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
500	C₂	C₁₃×#3385	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1803	C₂	semidirect
50. C₂×C₁₃×SD₁₆	Q₈	semidirect
94. #24815	C₁₃	direct (N × H)
152. C₁₃×C₄⋊C₄	SD₁₆	semidirect
163. #2567	C₂×C₁₃	semidirect
165. #2084	C₂×C₁₃	semidirect
166. #2066	C₂×C₁₃	semidirect
167. #1990	C₂×C₁₃	semidirect
168. #1939	C₂×C₁₃	semidirect
170. #1803	C₂×C₁₃	semidirect
292. C₂×SD₁₆	Q₈×C₁₃	semidirect
401. C₄⋊C₄	C₁₃×SD₁₆	semidirect
410. C₁₃	#24815	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×#476	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2567	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2084	2
C₁₃×#2066	2
C₁₃×#1990	2
C₁₃×#1939	2
C₁₃×#1877	2
C₁₃×#1803	2
C₁₃×#1802	2
#24815	13

Subgroups — C13×#24815 #15711154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24815 #15711154