Subgroups — C₁₃×#24835 #15711174

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2086	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1893	C₂	1	2	yes	maximal
10	C₁₃×#1808	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#474	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₁₃×#391	—	2	1	no	—
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#388	—	2	1	no	—
34	C₁₃×#386	—	2	1	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₁₃×#380	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	—	2	4	no	—
53	C₂²×C₈×C₁₃	—	2	4	no	—
54	C₂²×C₈×C₁₃	—	4	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	4	4	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	Q₈	1	4	yes	complemented
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	4	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#107	—	4	2	no	—
90	C₁₃×C₄⋊C₈	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
93	C₁₃×#102	—	2	4	no	—
94	C₁₃×#102	—	4	2	no	—
95	C₁₃×#95	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	#24835	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	1	no	—
102	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	4	1	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	D₈	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₁₃	#41	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	4	8	no	—
147	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	4	2	no	—
158	C₁₃×C₄⋊C₄	—	4	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	4	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	4	2	no	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	#41	1	2	yes	—
176	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
180	#2086	C₂×C₁₃	1	2	yes	complemented
181	#2067	C₂×C₁₃	1	2	yes	complemented
182	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1893	C₂×C₁₃	1	2	yes	—
185	#1808	C₂×C₁₃	1	2	yes	complemented
186	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
199	C₂³×C₁₃	C₂×D₈	1	2	yes	—
200	C₂³×C₁₃	#137	1	2	yes	—
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₃	—	8	4	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	—	4	8	no	—
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	8	4	no	—
239	C₂×C₄×C₁₃	#121	1	2	yes	—
240	C₂×C₄×C₁₃	#121	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
242	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
243	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
244	C₂×C₄×C₁₃	#135	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₁₃	—	2	4	no	—
252	C₈×C₁₃	—	4	2	no	—
253	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	—	2	1	no	—
256	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	—	2	1	no	—
258	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
260	#474	—	2	4	no	—
261	C₂×#107	C₂²×C₁₃	1	2	yes	—
262	C₂×#107	C₂²×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₈	—	2	4	no	—
264	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#102	C₂²×C₁₃	1	2	yes	—
268	C₂×#102	C₂²×C₁₃	1	2	yes	—
269	#391	—	2	1	no	—
270	#390	C₂²×C₁₃	1	1	yes	characteristic
271	#389	—	2	1	no	—
272	#389	C₂²×C₁₃	1	2	yes	—
273	#389	C₂²×C₁₃	1	1	yes	characteristic
274	#388	—	2	1	no	—
275	#386	—	2	1	no	—
276	#384	C₂²×C₁₃	1	1	yes	characteristic
277	#380	—	2	1	no	—
278	#380	C₂²×C₁₃	1	1	yes	characteristic
279	#380	C₂²×C₁₃	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	—	2	1	no	—
282	#340	C₂²×C₁₃	1	2	yes	—
283	#340	C₂²×C₁₃	1	2	yes	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	#340	C₂²×C₁₃	1	2	yes	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	8	1	no	—
296	C₂²×C₁₃	—	8	1	no	—
297	C₂²×C₁₃	—	8	1	no	—
298	C₂²×C₁₃	—	8	1	no	—
299	C₂²×C₁₃	#474	1	4	yes	complemented
300	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
302	C₂²×C₁₃	#537	1	1	yes	characteristic
303	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
304	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
305	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
306	C₂²×C₁₃	#575	1	1	yes	characteristic
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	4	1	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	8	1	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	—	8	1	no	—
315	C₄×C₁₃	—	8	2	no	—
316	C₄×C₁₃	#466	1	4	yes	—
317	C₄×C₁₃	#546	1	1	yes	characteristic
318	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
319	C₄×C₁₃	#552	1	1	yes	characteristic
320	C₄×C₁₃	#554	1	1	yes	characteristic
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×C₈	—	2	4	no	—
329	C₂²×C₈	—	2	4	no	—
330	C₂²×C₈	—	4	2	no	—
331	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	4	4	no	—
336	#121	—	2	2	no	—
337	#121	Q₈×C₁₃	1	4	yes	complemented
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	4	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	#107	—	2	4	no	—
365	#107	—	4	2	no	—
366	C₄⋊C₈	—	2	4	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
369	#102	—	2	4	no	—
370	#102	—	4	2	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	C₂×C₁₃	—	2	4	no	—
377	C₂×C₁₃	—	8	2	no	—
378	C₂×C₁₃	#2417	1	1	yes	characteristic
379	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
380	C₂×C₁₃	#3056	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
382	C₂×C₁₃	#3076	1	1	yes	characteristic
383	C₂×C₁₃	#3245	1	1	yes	characteristic
384	C₂×C₁₃	#3248	1	1	yes	characteristic
385	C₂⁴	—	2	1	no	—
386	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	C₁₃×D₈	1	4	yes	—
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
423	C₂²×C₄	C₁₃×#41	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	8	no	—
431	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	4	2	no	—
458	C₄²	C₂×D₄×C₁₃	1	2	yes	—
459	C₄²	C₁₃×#41	1	2	yes	—
460	C₁₃	#24835	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
473	C₂³	C₂×C₁₃×D₈	1	2	yes	—
474	C₂³	C₁₃×#137	1	2	yes	—
475	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	Q₈	—	8	4	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	C₁₃×#121	1	2	yes	—
514	C₂×C₄	C₁₃×#121	1	2	yes	—
515	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
516	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
517	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
518	C₂×C₄	C₁₃×#135	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
523	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₁₃×#474	1	4	yes	complemented
541	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
542	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂²	C₁₃×#537	1	1	yes	characteristic
544	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
545	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
546	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
547	C₂²	C₁₃×#575	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	2	no	—
557	C₄	C₁₃×#466	1	4	yes	—
558	C₄	C₁₃×#546	1	1	yes	characteristic
559	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
560	C₄	C₁₃×#552	1	1	yes	characteristic
561	C₄	C₁₃×#554	1	1	yes	characteristic
562	C₂	—	2	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₁₃×#2417	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
566	C₂	C₁₃×#3056	1	1	yes	characteristic
567	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
568	C₂	C₁₃×#3076	1	1	yes	characteristic
569	C₂	C₁₃×#3245	1	1	yes	characteristic
570	C₂	C₁₃×#3248	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#474	C₂	semidirect
2. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
3. C₁₃×#2857	C₂	semidirect
5. C₁₃×#2086	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1808	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
61. C₁₃×#121	Q₈	semidirect
92. C₁₃×C₄⋊C₈	D₄	semidirect
100. #24835	C₁₃	direct (N × H)
176. C₂×#474	C₂×C₁₃	semidirect
177. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
178. #2857	C₂×C₁₃	semidirect
180. #2086	C₂×C₁₃	semidirect
181. #2067	C₂×C₁₃	semidirect
182. #1988	C₂×C₁₃	semidirect
183. #1947	C₂×C₁₃	semidirect
185. #1808	C₂×C₁₃	semidirect
186. #1802	C₂×C₁₃	semidirect
299. C₂²×C₁₃	#474	semidirect
337. #121	Q₈×C₁₃	semidirect
368. C₄⋊C₈	D₄×C₁₃	semidirect
460. C₁₃	#24835	direct (N × H)
540. C₂²	C₁₃×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#474	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#2857	2
C₄×C₁₃×#121	2
C₁₃×#2086	2
C₁₃×#2067	2
C₁₃×#1988	2
C₁₃×#1947	2
C₁₃×#1893	2
C₁₃×#1808	2
C₁₃×#1802	2
#24835	13

Subgroups — C13×#24835 #15711174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24835 #15711174