Subgroups — C₁₃×#26254 #15712593

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2445	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#123	—	2	2	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#493	—	2	4	no	—
19	C₄×C₁₃×D₈	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#394	—	2	2	no	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#389	C₂²	1	2	yes	—
36	C₁₃×#386	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	4	no	—
47	C₂×C₁₃×D₈	—	2	2	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	4	2	no	—
54	C₂×C₁₃×D₈	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#127	—	2	4	no	—
60	C₁₃×#127	—	4	2	no	—
61	C₁₃×#123	—	4	8	no	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	—	4	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	2	no	—
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	4	2	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₁₃×#102	—	4	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₄×C₈×C₁₃	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	C₁₃×#95	D₄	1	1	yes	characteristic
92	#26254	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	—	8	2	no	—
111	C₂×D₄×C₁₃	—	8	2	no	—
112	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	8	2	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×D₈	—	2	8	no	—
126	C₁₃×D₈	—	4	8	no	—
127	C₁₃×D₈	—	4	4	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	1	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₃	#41	1	2	yes	—
138	C₂×C₈×C₁₃	#41	1	2	yes	—
139	C₂×C₈×C₁₃	#41	1	2	yes	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	D₈	1	4	yes	complemented
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	8	2	no	—
152	C₁₃×C₂²⋊C₄	—	8	2	no	—
153	C₁₃×C₂²⋊C₄	—	8	2	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₂×#493	C₂×C₁₃	1	1	yes	characteristic
161	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2445	C₂×C₁₃	1	2	yes	complemented
163	#2054	C₂×C₁₃	1	2	yes	complemented
164	#2041	C₂×C₁₃	1	2	yes	complemented
165	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1879	C₂×C₁₃	1	2	yes	complemented
170	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	D₄×C₁₃	—	2	4	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	8	8	no	—
195	D₄×C₁₃	—	8	8	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	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	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	8	no	—
217	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
220	C₂×C₄×C₁₃	#135	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₈×C₁₃	—	4	1	no	—
230	C₈×C₁₃	#123	1	4	yes	complemented
231	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
233	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#127	C₂²×C₁₃	1	2	yes	—
235	C₂×#123	—	2	2	no	—
236	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
237	#493	—	2	4	no	—
238	C₄×D₈	—	2	4	no	—
239	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#102	C₂²×C₁₃	1	2	yes	—
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	2	yes	—
245	C₂×#102	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
249	#394	—	2	2	no	—
250	#394	—	2	2	no	—
251	#390	C₂²×C₁₃	1	2	yes	—
252	#390	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	2	yes	—
254	#389	C₂²×C₁₃	1	2	yes	—
255	#386	—	2	2	no	—
256	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	#340	C₂²×C₁₃	1	2	yes	—
258	#336	C₂²×C₁₃	1	1	yes	characteristic
259	#336	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	8	2	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	—	8	2	no	—
270	C₂²×C₁₃	—	8	2	no	—
271	C₂²×C₁₃	—	8	2	no	—
272	C₂²×C₁₃	—	8	2	no	—
273	C₂²×C₁₃	—	8	2	no	—
274	C₂²×C₁₃	#532	1	1	yes	characteristic
275	C₂²×C₁₃	D₄²	1	1	yes	characteristic
276	C₂²×C₁₃	#550	1	1	yes	characteristic
277	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
279	C₂²×C₁₃	#576	1	1	yes	characteristic
280	C₂²×C₁₃	#576	1	1	yes	characteristic
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	8	2	no	—
288	C₄×C₁₃	—	8	2	no	—
289	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
290	C₄×C₁₃	#540	1	1	yes	characteristic
291	C₄×C₁₃	#546	1	1	yes	characteristic
292	C₄×C₁₃	#559	1	1	yes	characteristic
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
296	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
297	C₂³×C₄	—	2	2	no	—
298	C₂×D₈	—	2	4	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	2	no	—
301	C₂×D₈	—	2	2	no	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	2	2	no	—
305	C₂×D₈	—	4	2	no	—
306	C₂×D₈	D₄×C₁₃	1	4	yes	—
307	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
311	#127	—	2	4	no	—
312	#127	—	4	2	no	—
313	#123	—	4	8	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	4	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	#107	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	4	2	no	—
336	#102	—	4	2	no	—
337	#102	—	4	2	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	D₄×C₁₃	1	1	yes	characteristic
343	#95	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₁₃	—	8	4	no	—
345	C₂×C₁₃	—	16	2	no	—
346	C₂×C₁₃	#2445	1	1	yes	characteristic
347	C₂×C₁₃	#3169	1	1	yes	characteristic
348	C₂×C₁₃	#3176	1	1	yes	characteristic
349	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
350	C₂×C₁₃	#3280	1	1	yes	characteristic
351	C₂×C₁₃	#3391	1	1	yes	characteristic
352	C₂×C₁₃	#3396	1	1	yes	characteristic
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	4	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	8	2	no	—
371	C₂×D₄	—	8	2	no	—
372	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	8	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	D₈	—	2	8	no	—
386	D₈	—	4	8	no	—
387	D₈	—	4	4	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
397	C₂×C₈	C₁₃×#41	1	2	yes	—
398	C₂×C₈	C₁₃×#41	1	2	yes	—
399	C₂×C₈	C₁₃×#41	1	2	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	C₁₃×D₈	1	4	yes	complemented
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	8	2	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₁₃	#26254	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	—	2	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	8	8	no	—
445	D₄	—	8	8	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	8	8	no	—
467	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
468	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
469	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
470	C₂×C₄	C₁₃×#135	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
475	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	1	no	—
480	C₈	C₁₃×#123	1	4	yes	complemented
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	C₁₃×#532	1	1	yes	characteristic
496	C₂²	D₄²×C₁₃	1	1	yes	characteristic
497	C₂²	C₁₃×#550	1	1	yes	characteristic
498	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
499	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
500	C₂²	C₁₃×#576	1	1	yes	characteristic
501	C₂²	C₁₃×#576	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	2	no	—
510	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
511	C₄	C₁₃×#540	1	1	yes	characteristic
512	C₄	C₁₃×#546	1	1	yes	characteristic
513	C₄	C₁₃×#559	1	1	yes	characteristic
514	C₂	—	8	4	no	—
515	C₂	—	16	2	no	—
516	C₂	C₁₃×#2445	1	1	yes	characteristic
517	C₂	C₁₃×#3169	1	1	yes	characteristic
518	C₂	C₁₃×#3176	1	1	yes	characteristic
519	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
520	C₂	C₁₃×#3280	1	1	yes	characteristic
521	C₂	C₁₃×#3391	1	1	yes	characteristic
522	C₂	C₁₃×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#493	C₂
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
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2445	C₂	semidirect
4. C₁₃×#2054	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#1970	C₂	semidirect
7. C₁₃×#1970	C₂	semidirect
8. C₁₃×#1970	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
92. #26254	C₁₃	direct (N × H)
146. C₁₃×C₄⋊C₄	D₈	semidirect
161. C₂×C₄×D₈	C₂×C₁₃	semidirect
162. #2445	C₂×C₁₃	semidirect
163. #2054	C₂×C₁₃	semidirect
164. #2041	C₂×C₁₃	semidirect
165. #1970	C₂×C₁₃	semidirect
166. #1970	C₂×C₁₃	semidirect
167. #1970	C₂×C₁₃	semidirect
168. #1942	C₂×C₁₃	semidirect
169. #1879	C₂×C₁₃	semidirect
170. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
230. C₈×C₁₃	#123	semidirect
406. C₄⋊C₄	C₁₃×D₈	semidirect
420. C₁₃	#26254	direct (N × H)
480. C₈	C₁₃×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#493	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2445	2
C₁₃×#2054	2
C₁₃×#2041	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1879	2
C₈×C₁₃×C₄⋊C₄	2
#26254	13

Subgroups — C13×#26254 #15712593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26254 #15712593