Subgroups — C₁₃×#24626 #15710965

Order 3328.

1110 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2011	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1982	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	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	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	—	2	1	no	—
21	C₁₃×#459	—	2	4	no	—
22	C₄×C₁₃×D₈	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#392	—	2	2	no	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#388	—	2	2	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#380	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂×C₁₃×D₈	—	2	4	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	4	2	no	—
57	C₂×C₁₃×D₈	—	4	2	no	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#127	—	2	4	no	—
62	C₁₃×#127	—	2	2	no	—
63	C₁₃×#127	—	2	2	no	—
64	C₁₃×#127	—	4	2	no	—
65	C₁₃×#121	—	4	4	no	—
66	C₁₃×#121	—	4	4	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
71	C₁₃×#117	—	4	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₄²×C₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	2	2	no	—
89	C₁₃×C₄⋊C₈	—	2	2	no	—
90	C₁₃×C₄⋊C₈	—	4	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#102	—	4	2	no	—
96	C₁₃×#102	—	4	2	no	—
97	C₄×C₈×C₁₃	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	D₄	1	2	yes	—
100	#24626	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	1	no	—
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	1	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	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	8	1	no	—
129	C₂×D₄×C₁₃	—	8	2	no	—
130	C₂×D₄×C₁₃	—	8	1	no	—
131	C₂×D₄×C₁₃	—	8	2	no	—
132	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₁₃	#41	1	2	yes	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×D₈	—	2	8	no	—
149	C₁₃×D₈	—	4	8	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	#41	1	2	yes	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	—	8	1	no	—
167	C₁₃×C₄⋊C₄	D₈	1	4	yes	complemented
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	—	8	2	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	4	4	no	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	#41	1	2	yes	—
180	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2541	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#2054	C₂×C₁₃	1	2	yes	complemented
185	#2011	C₂×C₁₃	1	2	yes	complemented
186	#1982	C₂×C₁₃	1	2	yes	complemented
187	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1925	C₂×C₁₃	1	2	yes	complemented
190	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	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	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	—	4	2	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	4	1	no	—
219	D₄×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	4	1	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	8	8	no	—
226	D₄×C₁₃	—	8	4	no	—
227	D₄×C₁₃	—	8	8	no	—
228	D₄×C₁₃	—	8	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	8	4	no	—
247	C₂×C₄×C₁₃	#121	1	2	yes	—
248	C₂×C₄×C₁₃	#121	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
250	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
251	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₁₃	—	2	2	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₈×C₁₃	—	4	2	no	—
261	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
263	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#127	C₂²×C₁₃	1	2	yes	—
265	C₂×#121	—	2	1	no	—
266	C₂×#121	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#117	—	2	1	no	—
270	#459	—	2	4	no	—
271	C₄×D₈	—	2	4	no	—
272	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
275	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#102	C₂²×C₁₃	1	2	yes	—
278	C₂×#102	C₂²×C₁₃	1	2	yes	—
279	C₂×#102	C₂²×C₁₃	1	2	yes	—
280	C₂×#102	C₂²×C₁₃	1	2	yes	—
281	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
282	#392	—	2	2	no	—
283	#390	C₂²×C₁₃	1	2	yes	—
284	#390	C₂²×C₁₃	1	2	yes	—
285	#388	—	2	2	no	—
286	#384	C₂²×C₁₃	1	1	yes	characteristic
287	#380	—	2	1	no	—
288	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	#340	C₂²×C₁₃	1	2	yes	—
291	#336	C₂²×C₁₃	1	2	yes	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	8	1	no	—
299	C₂²×C₁₃	—	8	1	no	—
300	C₂²×C₁₃	—	8	1	no	—
301	C₂²×C₁₃	—	8	1	no	—
302	C₂²×C₁₃	—	8	1	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	8	1	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	—	8	2	no	—
308	C₂²×C₁₃	—	8	2	no	—
309	C₂²×C₁₃	—	8	2	no	—
310	C₂²×C₁₃	—	8	2	no	—
311	C₂²×C₁₃	—	8	2	no	—
312	C₂²×C₁₃	—	8	2	no	—
313	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
314	C₂²×C₁₃	#546	1	1	yes	characteristic
315	C₂²×C₁₃	#550	1	1	yes	characteristic
316	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²×C₁₃	#576	1	1	yes	characteristic
319	C₂²×C₁₃	#577	1	1	yes	characteristic
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	—	8	2	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	#459	1	4	yes	—
327	C₄×C₁₃	#525	1	1	yes	characteristic
328	C₄×C₁₃	#535	1	1	yes	characteristic
329	C₄×C₁₃	#553	1	1	yes	characteristic
330	C₄×C₁₃	#555	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂×D₈	—	2	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂×D₈	—	2	4	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	4	2	no	—
345	C₂×D₈	—	4	2	no	—
346	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	#127	—	2	4	no	—
350	#127	—	2	2	no	—
351	#127	—	2	2	no	—
352	#127	—	4	2	no	—
353	#121	—	4	4	no	—
354	#121	—	4	4	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
359	#117	—	4	4	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#107	—	2	2	no	—
377	C₄⋊C₈	—	2	2	no	—
378	C₄⋊C₈	—	4	2	no	—
379	#102	—	2	2	no	—
380	#102	—	2	4	no	—
381	#102	—	2	2	no	—
382	#102	—	2	4	no	—
383	#102	—	4	2	no	—
384	#102	—	4	2	no	—
385	C₄×C₈	—	2	2	no	—
386	#95	—	2	2	no	—
387	#95	D₄×C₁₃	1	2	yes	—
388	C₂×C₁₃	—	8	2	no	—
389	C₂×C₁₃	—	8	2	no	—
390	C₂×C₁₃	—	16	2	no	—
391	C₂×C₁₃	#2414	1	1	yes	characteristic
392	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
393	C₂×C₁₃	#3045	1	1	yes	characteristic
394	C₂×C₁₃	#3294	1	1	yes	characteristic
395	C₂×C₁₃	#3325	1	1	yes	characteristic
396	C₂×C₁₃	#3391	1	1	yes	characteristic
397	C₂×C₁₃	#3397	1	1	yes	characteristic
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	8	1	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	—	8	1	no	—
428	C₂×D₄	—	8	2	no	—
429	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂×D₄	C₁₃×#41	1	2	yes	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	D₈	—	2	8	no	—
446	D₈	—	4	8	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	C₁₃×#41	1	2	yes	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	8	1	no	—
464	C₄⋊C₄	C₁₃×D₈	1	4	yes	complemented
465	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	2	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	8	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	4	4	no	—
475	C₄²	C₂×D₄×C₁₃	1	2	yes	—
476	C₄²	C₁₃×#41	1	2	yes	—
477	C₁₃	#24626	1	1	yes	characteristic, direct product factor, Sylow
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	8	no	—
513	D₄	—	8	4	no	—
514	D₄	—	8	8	no	—
515	D₄	—	8	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₁₃×#121	1	2	yes	—
535	C₂×C₄	C₁₃×#121	1	2	yes	—
536	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
537	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
538	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
542	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
543	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
545	C₈	—	2	2	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	2	no	—
569	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
570	C₂²	C₁₃×#546	1	1	yes	characteristic
571	C₂²	C₁₃×#550	1	1	yes	characteristic
572	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
573	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₂²	C₁₃×#576	1	1	yes	characteristic
575	C₂²	C₁₃×#577	1	1	yes	characteristic
576	C₄	—	2	4	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	2	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	2	no	—
582	C₄	C₁₃×#459	1	4	yes	—
583	C₄	C₁₃×#525	1	1	yes	characteristic
584	C₄	C₁₃×#535	1	1	yes	characteristic
585	C₄	C₁₃×#553	1	1	yes	characteristic
586	C₄	C₁₃×#555	1	1	yes	characteristic
587	C₂	—	8	2	no	—
588	C₂	—	8	2	no	—
589	C₂	—	16	2	no	—
590	C₂	C₁₃×#2414	1	1	yes	characteristic
591	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
592	C₂	C₁₃×#3045	1	1	yes	characteristic
593	C₂	C₁₃×#3294	1	1	yes	characteristic
594	C₂	C₁₃×#3325	1	1	yes	characteristic
595	C₂	C₁₃×#3391	1	1	yes	characteristic
596	C₂	C₁₃×#3397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₂×C₁₃×#459	C₂	semidirect
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2541	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2054	C₂	semidirect
6. C₁₃×#2011	C₂	semidirect
7. C₁₃×#1982	C₂	semidirect
8. C₁₃×#1957	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
70. C₄×D₄×C₁₃	D₄	semidirect
100. #24626	C₁₃	direct (N × H)
167. C₁₃×C₄⋊C₄	D₈	semidirect
180. C₂×#459	C₂×C₁₃	semidirect
181. C₂×C₄×D₈	C₂×C₁₃	semidirect
182. #2541	C₂×C₁₃	semidirect
183. #2354	C₂×C₁₃	semidirect
184. #2054	C₂×C₁₃	semidirect
185. #2011	C₂×C₁₃	semidirect
186. #1982	C₂×C₁₃	semidirect
187. #1957	C₂×C₁₃	semidirect
188. #1939	C₂×C₁₃	semidirect
189. #1925	C₂×C₁₃	semidirect
190. #1802	C₂×C₁₃	semidirect
358. C₄×D₄	D₄×C₁₃	semidirect
464. C₄⋊C₄	C₁₃×D₈	semidirect
477. C₁₃	#24626	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×#459	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2541	2
C₁₃×#2354	2
C₁₃×#2054	2
C₁₃×#2011	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1939	2
C₁₃×#1925	2
C₁₃×#1802	2
#24626	13

Subgroups — C13×#24626 #15710965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24626 #15710965