Subgroups — C₁₃×#24856 #15711195

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1907	C₂	1	2	yes	maximal
10	C₁₃×#1815	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#477	—	2	1	no	—
18	C₁₃×#476	—	2	1	no	—
19	C₁₃×#476	—	2	1	no	—
20	C₁₃×#476	—	2	1	no	—
21	C₁₃×#476	—	2	2	no	—
22	C₁₃×#475	—	2	1	no	—
23	C₁₃×#474	—	2	1	no	—
24	C₁₃×#442	—	2	1	no	—
25	C₁₃×#440	—	2	1	no	—
26	C₄×C₁₃×SD₁₆	—	2	1	no	—
27	C₄×C₁₃×D₈	—	2	1	no	—
28	C₂×C₁₃×#108	C₂²	1	2	yes	—
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#428	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	C₂²	1	2	yes	—
32	C₁₃×#424	—	2	2	no	—
33	C₁₃×#424	C₂²	1	2	yes	—
34	C₁₃×#423	—	2	1	no	—
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#418	C₂²	1	1	yes	characteristic
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₁₃×#417	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	2	yes	—
43	C₂×C₁₃×#100	C₂²	1	2	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
45	C₁₃×#343	C₂²	1	2	yes	—
46	C₁₃×#343	C₂²	1	2	yes	—
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#341	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
54	C₁₃×AGL(1,ℤ/8)	Q₈	1	4	yes	complemented
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₁₃×#131	—	2	4	no	—
58	C₁₃×#131	—	4	2	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	—	2	2	no	—
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	—	2	1	no	—
70	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
71	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	—	2	1	no	—
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₄×D₄×C₁₃	—	2	1	no	—
77	C₄×D₄×C₁₃	—	2	1	no	—
78	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
79	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
80	C₁₃×#117	—	2	1	no	—
81	C₁₃×#117	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	1	no	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#108	—	4	2	no	—
89	C₁₃×#107	—	2	1	no	—
90	C₁₃×#107	—	2	2	no	—
91	C₁₃×#106	—	2	2	no	—
92	C₁₃×#106	—	2	2	no	—
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×#106	—	2	2	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×C₄⋊C₈	—	2	2	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	—	2	1	no	—
100	C₁₃×C₄⋊C₈	—	2	1	no	—
101	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
104	C₁₃×#103	—	2	1	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#102	—	2	1	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	2	1	no	—
111	C₁₃×#102	—	2	1	no	—
112	C₁₃×#100	—	4	2	no	—
113	C₁₃×#97	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	#24856	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₁₃×#41	C₂×Q₈	1	2	yes	—
120	C₁₃×#41	#41	1	2	yes	—
121	C₂×Q₈×C₁₃	—	4	1	no	—
122	C₂×Q₈×C₁₃	—	4	1	no	—
123	C₂×Q₈×C₁₃	—	8	2	no	—
124	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	—	8	2	no	—
141	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₁₃×SD₁₆	—	2	4	no	—
145	C₁₃×D₈	—	2	4	no	—
146	C₁₃×M₁₆	—	2	1	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	2	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	2	1	no	—
151	C₁₃×M₁₆	—	2	1	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	4	4	no	—
154	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	4	4	no	—
162	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₄⋊C₄	—	4	1	no	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₁₃×C₂²⋊C₄	—	4	1	no	—
178	C₁₃×C₂²⋊C₄	—	4	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
186	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
189	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#2090	C₂×C₁₃	1	2	yes	complemented
191	#2063	C₂×C₁₃	1	2	yes	complemented
192	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1907	C₂×C₁₃	1	2	yes	—
195	#1815	C₂×C₁₃	1	2	yes	complemented
196	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	8	1	no	—
202	C₂³×C₁₃	—	8	1	no	—
203	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	1	no	—
205	Q₈×C₁₃	—	8	2	no	—
206	Q₈×C₁₃	—	8	2	no	—
207	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	1	no	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	8	1	no	—
227	C₂×C₄×C₁₃	—	8	2	no	—
228	C₂×C₄×C₁₃	—	8	2	no	—
229	C₂×C₄×C₁₃	—	8	1	no	—
230	C₂×C₄×C₁₃	—	8	2	no	—
231	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₁₃	—	2	2	no	—
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	4	1	no	—
245	C₈×C₁₃	—	4	2	no	—
246	C₈×C₁₃	—	4	2	no	—
247	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#131	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
252	#477	—	2	1	no	—
253	#476	—	2	1	no	—
254	#476	—	2	1	no	—
255	#476	—	2	1	no	—
256	#476	—	2	2	no	—
257	#475	—	2	1	no	—
258	#474	—	2	1	no	—
259	#442	—	2	1	no	—
260	#440	—	2	1	no	—
261	C₄×SD₁₆	—	2	1	no	—
262	C₄×D₈	—	2	1	no	—
263	C₂×#108	C₂²×C₁₃	1	2	yes	—
264	#428	C₂²×C₁₃	1	2	yes	—
265	#428	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#106	C₂²×C₁₃	1	2	yes	—
267	#424	—	2	2	no	—
268	#424	C₂²×C₁₃	1	2	yes	—
269	#423	—	2	1	no	—
270	#423	C₂²×C₁₃	1	1	yes	characteristic
271	#423	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	2	1	no	—
273	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
274	#418	C₂²×C₁₃	1	1	yes	characteristic
275	#417	C₂²×C₁₃	1	2	yes	—
276	#417	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#102	C₂²×C₁₃	1	2	yes	—
278	C₂×#100	C₂²×C₁₃	1	2	yes	—
279	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
280	#343	C₂²×C₁₃	1	2	yes	—
281	#343	C₂²×C₁₃	1	2	yes	—
282	#343	C₂²×C₁₃	1	2	yes	—
283	#341	C₂²×C₁₃	1	2	yes	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	—	8	2	no	—
292	C₂²×C₁₃	—	8	1	no	—
293	C₂²×C₁₃	—	8	1	no	—
294	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
295	C₂²×C₁₃	#552	1	1	yes	characteristic
296	C₂²×C₁₃	#554	1	1	yes	characteristic
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	4	1	no	—
302	C₄×C₁₃	—	4	1	no	—
303	C₄×C₁₃	—	8	1	no	—
304	C₄×C₁₃	—	8	2	no	—
305	C₄×C₁₃	#471	1	2	yes	—
306	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
307	C₄×C₁₃	#537	1	1	yes	characteristic
308	C₄×C₁₃	#546	1	1	yes	characteristic
309	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
310	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	AGL(1,ℤ/8)	—	2	2	no	—
315	AGL(1,ℤ/8)	Q₈×C₁₃	1	4	yes	complemented
316	C₂×SD₁₆	—	2	1	no	—
317	C₂×D₈	—	2	1	no	—
318	#131	—	2	4	no	—
319	#131	—	4	2	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
322	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
323	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
340	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
341	#117	—	2	1	no	—
342	#117	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	#108	—	4	2	no	—
350	#107	—	2	1	no	—
351	#107	—	2	2	no	—
352	#106	—	2	2	no	—
353	#106	—	2	2	no	—
354	#106	—	2	1	no	—
355	#106	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
363	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
364	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
365	#103	—	2	1	no	—
366	#103	—	2	2	no	—
367	#102	—	2	1	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	2	1	no	—
372	#102	—	2	1	no	—
373	#100	—	4	2	no	—
374	#97	—	2	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	2	1	no	—
378	C₂×C₁₃	—	4	2	no	—
379	C₂×C₁₃	—	8	2	no	—
380	C₂×C₁₃	#2417	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
382	C₂×C₁₃	#3068	1	1	yes	characteristic
383	C₂⁴	—	2	1	no	—
384	#41	—	2	1	no	—
385	#41	—	2	1	no	—
386	#41	C₂×Q₈×C₁₃	1	2	yes	—
387	#41	C₁₃×#41	1	2	yes	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	8	2	no	—
391	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	8	2	no	—
408	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
409	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
411	SD₁₆	—	2	4	no	—
412	D₈	—	2	4	no	—
413	M₁₆	—	2	1	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	4	4	no	—
421	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
430	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	4	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₁₃	#24856	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	8	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
461	Q₈	—	2	1	no	—
462	Q₈	—	8	2	no	—
463	Q₈	—	8	2	no	—
464	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	8	1	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
489	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
490	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
491	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
496	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	2	2	no	—
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
515	C₂²	C₁₃×#552	1	1	yes	characteristic
516	C₂²	C₁₃×#554	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	2	no	—
525	C₄	C₁₃×#471	1	2	yes	—
526	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
527	C₄	C₁₃×#537	1	1	yes	characteristic
528	C₄	C₁₃×#546	1	1	yes	characteristic
529	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
530	C₂	—	2	1	no	—
531	C₂	—	2	1	no	—
532	C₂	—	4	2	no	—
533	C₂	—	8	2	no	—
534	C₂	C₁₃×#2417	1	1	yes	characteristic
535	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
536	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3079	C₂	semidirect
2. C₂×C₁₃×#476	C₂	semidirect
4. C₁₃×#2906	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1815	C₂	semidirect
11. C₁₃×#1800	C₂	semidirect
54. C₁₃×AGL(1,ℤ/8)	Q₈	semidirect
115. #24856	C₁₃	direct (N × H)
186. #3079	C₂×C₁₃	semidirect
187. C₂×#476	C₂×C₁₃	semidirect
189. #2906	C₂×C₁₃	semidirect
190. #2090	C₂×C₁₃	semidirect
191. #2063	C₂×C₁₃	semidirect
192. #1997	C₂×C₁₃	semidirect
193. #1950	C₂×C₁₃	semidirect
195. #1815	C₂×C₁₃	semidirect
196. #1800	C₂×C₁₃	semidirect
315. AGL(1,ℤ/8)	Q₈×C₁₃	semidirect
453. C₁₃	#24856	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3079	2
C₂×C₁₃×#476	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2906	2
C₁₃×#2090	2
C₁₃×#2063	2
C₁₃×#1997	2
C₁₃×#1950	2
C₁₃×#1907	2
C₁₃×#1815	2
C₁₃×#1800	2
#24856	13

Subgroups — C13×#24856 #15711195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24856 #15711195