Subgroups — C₁₃×#24781 #15711120

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2417	C₂	1	2	yes	maximal
6	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₁₃×#467	—	2	4	no	—
20	C₁₃×#467	—	2	4	no	—
21	C₈×D₄×C₁₃	—	2	4	no	—
22	C₂×C₁₃×#107	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#398	—	2	2	no	—
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#386	—	2	2	no	—
39	C₁₃×#380	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₃	D₄	1	4	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₂²⋊Q₈	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	4	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×#107	—	2	4	no	—
86	C₁₃×#107	D₄	1	4	yes	complemented
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₄×C₈×C₁₃	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	#24781	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	Q₁₆	1	4	yes	complemented
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	—	8	2	no	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	4	4	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	8	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	4	4	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₃	#41	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	4	4	no	—
156	C₁₃×C₄⋊C₄	—	4	4	no	—
157	C₁₃×C₄⋊C₄	—	4	4	no	—
158	C₁₃×C₄⋊C₄	—	8	2	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
160	C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	4	4	no	—
164	C₁₃×C₂²⋊C₄	—	8	2	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
170	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2417	C₂×C₁₃	1	2	yes	—
172	#2068	C₂×C₁₃	1	2	yes	complemented
173	#2036	C₂×C₁₃	1	2	yes	complemented
174	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1872	C₂×C₁₃	1	2	yes	complemented
177	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	#121	1	2	yes	—
189	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
190	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
191	C₂³×C₁₃	#135	1	2	yes	—
192	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₃	—	4	2	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	Q₈×C₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	8	8	no	—
229	C₂×C₄×C₁₃	#121	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	4	1	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	#121	1	4	yes	—
241	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
245	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
248	#467	—	2	4	no	—
249	#467	—	2	4	no	—
250	C₈×D₄	—	2	4	no	—
251	C₂×#107	—	2	4	no	—
252	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#107	C₂²×C₁₃	1	2	yes	—
255	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₃	1	2	yes	—
258	C₂×#103	C₂²×C₁₃	1	2	yes	—
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
263	#398	—	2	2	no	—
264	#396	—	2	2	no	—
265	#391	C₂²×C₁₃	1	2	yes	—
266	#389	C₂²×C₁₃	1	2	yes	—
267	#386	—	2	2	no	—
268	#380	—	2	2	no	—
269	#380	C₂²×C₁₃	1	2	yes	—
270	#340	C₂²×C₁₃	1	2	yes	—
271	#340	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	4	1	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	#467	1	4	yes	complemented
286	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
287	C₂²×C₁₃	D₄²	1	1	yes	characteristic
288	C₂²×C₁₃	#547	1	1	yes	characteristic
289	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
290	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
291	C₂²×C₁₃	#576	1	1	yes	characteristic
292	C₂²×C₁₃	#578	1	1	yes	characteristic
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	4	1	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	8	2	no	—
299	C₄×C₁₃	—	8	2	no	—
300	C₄×C₁₃	—	8	2	no	—
301	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
302	C₄×C₁₃	#537	1	1	yes	characteristic
303	C₄×C₁₃	#548	1	1	yes	characteristic
304	C₄×C₁₃	#553	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
306	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	D₄×C₁₃	1	4	yes	—
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	4	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	4	2	no	—
335	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	#107	—	2	2	no	—
346	#107	—	2	2	no	—
347	#107	—	2	4	no	—
348	#107	D₄×C₁₃	1	4	yes	complemented
349	C₄⋊C₈	—	2	2	no	—
350	#103	—	2	4	no	—
351	#103	—	2	4	no	—
352	#103	—	4	2	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₄×C₈	—	2	2	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	—	2	2	no	—
360	C₂×C₁₃	—	2	4	no	—
361	C₂×C₁₃	—	4	2	no	—
362	C₂×C₁₃	#2416	1	1	yes	characteristic
363	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
364	C₂×C₁₃	#3061	1	1	yes	characteristic
365	C₂×C₁₃	#3280	1	1	yes	characteristic
366	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
367	C₂×C₁₃	#3336	1	1	yes	characteristic
368	C₂×C₁₃	#3338	1	1	yes	characteristic
369	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	C₁₃×Q₁₆	1	4	yes	complemented
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	8	2	no	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₁₃×#41	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	Q₁₆	—	4	4	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	8	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	4	4	no	—
415	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
416	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
417	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
418	C₂×C₈	C₁₃×#41	1	2	yes	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	4	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	8	2	no	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	8	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₁₃	#24781	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	C₁₃×#121	1	2	yes	—
449	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
450	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
451	C₂³	C₁₃×#135	1	2	yes	—
452	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	D₄	—	2	8	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	8	no	—
489	C₂×C₄	C₁₃×#121	1	2	yes	—
490	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	1	no	—
500	C₈	C₁₃×#121	1	4	yes	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	C₁₃×#467	1	4	yes	complemented
515	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
516	C₂²	D₄²×C₁₃	1	1	yes	characteristic
517	C₂²	C₁₃×#547	1	1	yes	characteristic
518	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
519	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
520	C₂²	C₁₃×#576	1	1	yes	characteristic
521	C₂²	C₁₃×#578	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	—	8	2	no	—
530	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
531	C₄	C₁₃×#537	1	1	yes	characteristic
532	C₄	C₁₃×#548	1	1	yes	characteristic
533	C₄	C₁₃×#553	1	1	yes	characteristic
534	C₂	—	2	4	no	—
535	C₂	—	4	2	no	—
536	C₂	C₁₃×#2416	1	1	yes	characteristic
537	C₂	C₂×C₁₃×#467	1	1	yes	characteristic
538	C₂	C₁₃×#3061	1	1	yes	characteristic
539	C₂	C₁₃×#3280	1	1	yes	characteristic
540	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
541	C₂	C₁₃×#3336	1	1	yes	characteristic
542	C₂	C₁₃×#3338	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#467	C₂	semidirect
2. C₂×C₁₃×#467	C₂	semidirect
4. C₂²×C₁₃×#107	C₂	semidirect
6. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#1969	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1872	C₂	semidirect
11. C₁₃×#1808	C₂	semidirect
86. C₁₃×#107	D₄	semidirect
98. #24781	C₁₃	direct (N × H)
109. C₂×D₄×C₁₃	Q₁₆	semidirect
167. C₂×#467	C₂×C₁₃	semidirect
168. C₂×#467	C₂×C₁₃	semidirect
170. C₂²×#107	C₂×C₁₃	semidirect
172. #2068	C₂×C₁₃	semidirect
173. #2036	C₂×C₁₃	semidirect
174. #1969	C₂×C₁₃	semidirect
175. #1942	C₂×C₁₃	semidirect
176. #1872	C₂×C₁₃	semidirect
177. #1808	C₂×C₁₃	semidirect
285. C₂²×C₁₃	#467	semidirect
348. #107	D₄×C₁₃	semidirect
379. C₂×D₄	C₁₃×Q₁₆	semidirect
437. C₁₃	#24781	direct (N × H)
514. C₂²	C₁₃×#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#467	2
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#107	2
C₁₃×#2417	2
C₁₃×#2068	2
C₁₃×#2036	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1872	2
C₁₃×#1808	2
#24781	13

Subgroups — C13×#24781 #15711120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24781 #15711120