Subgroups — C₁₃×#24721 #15711060

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 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×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2079	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2051	C₂	1	2	yes	maximal
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1951	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1931	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#477	—	2	1	no	—
17	C₁₃×#476	—	2	1	no	—
18	C₁₃×#476	—	2	1	no	—
19	C₁₃×#476	—	2	1	no	—
20	C₁₃×#476	—	2	2	no	—
21	C₁₃×#475	—	2	1	no	—
22	C₁₃×#474	—	2	1	no	—
23	C₁₃×#442	—	2	1	no	—
24	C₁₃×#440	—	2	1	no	—
25	C₄×C₁₃×SD₁₆	—	2	1	no	—
26	C₄×C₁₃×D₈	—	2	1	no	—
27	C₁₃×#433	—	2	2	no	—
28	C₁₃×#432	—	2	1	no	—
29	C₁₃×#431	—	2	1	no	—
30	C₂×C₁₃×#108	C₂²	1	2	yes	—
31	C₁₃×#428	C₂²	1	2	yes	—
32	C₁₃×#428	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	2	yes	—
34	C₁₃×#423	C₂²	1	1	yes	characteristic
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#418	C₂²	1	1	yes	characteristic
38	C₁₃×#417	C₂²	1	2	yes	—
39	C₁₃×#417	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	2	yes	—
41	C₂×C₁₃×#100	C₂²	1	2	yes	—
42	C₁₃×#408	C₂²	1	2	yes	—
43	C₁₃×#405	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)	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
68	C₄×D₄×C₁₃	—	2	1	no	—
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#108	—	2	4	no	—
85	C₁₃×#107	—	2	1	no	—
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×#106	—	2	2	no	—
88	C₁₃×#106	—	2	2	no	—
89	C₁₃×#106	—	2	1	no	—
90	C₁₃×#106	—	2	2	no	—
91	C₁₃×C₄⋊C₈	—	2	1	no	—
92	C₁₃×C₄⋊C₈	—	2	1	no	—
93	C₁₃×C₄⋊C₈	—	2	1	no	—
94	C₁₃×C₄⋊C₈	—	2	1	no	—
95	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
98	C₁₃×#103	—	2	1	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#102	—	2	1	no	—
101	C₁₃×#102	—	2	2	no	—
102	C₁₃×#102	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	C₁₃×#100	—	2	4	no	—
107	C₁₃×C₂²⋊C₈	—	2	2	no	—
108	C₁₃×C₂²⋊C₈	—	2	2	no	—
109	C₁₃×#97	—	2	2	no	—
110	C₁₃×#97	—	2	1	no	—
111	C₄×C₈×C₁₃	—	2	2	no	—
112	C₄×C₈×C₁₃	—	2	1	no	—
113	#24721	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	4	1	no	—
120	C₂×Q₈×C₁₃	—	4	1	no	—
121	C₂×Q₈×C₁₃	—	8	2	no	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	#41	1	2	yes	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	4	1	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	—	8	2	no	—
139	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×D₈	—	2	4	no	—
144	C₁₃×M₁₆	—	2	1	no	—
145	C₁₃×M₁₆	—	2	2	no	—
146	C₁₃×M₁₆	—	2	2	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	2	1	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	#41	1	2	yes	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₁₃×C₂²⋊C₄	—	4	1	no	—
174	C₁₃×C₂²⋊C₄	—	4	1	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
185	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#2079	C₂×C₁₃	1	2	yes	complemented
187	#2051	C₂×C₁₃	1	2	yes	—
188	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1951	C₂×C₁₃	1	2	yes	complemented
190	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1931	C₂×C₁₃	1	2	yes	complemented
192	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	8	1	no	—
198	C₂³×C₁₃	—	8	1	no	—
199	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	1	no	—
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	8	2	no	—
203	Q₈×C₁₃	—	8	2	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	1	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	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	1	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	8	1	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	—	8	2	no	—
225	C₂×C₄×C₁₃	—	8	1	no	—
226	C₂×C₄×C₁₃	—	8	2	no	—
227	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
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	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₈×C₁₃	—	4	1	no	—
242	C₈×C₁₃	—	4	2	no	—
243	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	#477	—	2	1	no	—
248	#476	—	2	1	no	—
249	#476	—	2	1	no	—
250	#476	—	2	1	no	—
251	#476	—	2	2	no	—
252	#475	—	2	1	no	—
253	#474	—	2	1	no	—
254	#442	—	2	1	no	—
255	#440	—	2	1	no	—
256	C₄×SD₁₆	—	2	1	no	—
257	C₄×D₈	—	2	1	no	—
258	#433	—	2	2	no	—
259	#432	—	2	1	no	—
260	#431	—	2	1	no	—
261	C₂×#108	C₂²×C₁₃	1	2	yes	—
262	#428	C₂²×C₁₃	1	2	yes	—
263	#428	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#106	C₂²×C₁₃	1	2	yes	—
265	#423	C₂²×C₁₃	1	1	yes	characteristic
266	#423	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
268	#418	C₂²×C₁₃	1	1	yes	characteristic
269	#417	C₂²×C₁₃	1	2	yes	—
270	#417	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×#100	C₂²×C₁₃	1	2	yes	—
273	#408	C₂²×C₁₃	1	2	yes	—
274	#405	C₂²×C₁₃	1	2	yes	—
275	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
276	#343	C₂²×C₁₃	1	2	yes	—
277	#343	C₂²×C₁₃	1	2	yes	—
278	#343	C₂²×C₁₃	1	2	yes	—
279	#341	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	1	no	—
290	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
291	C₂²×C₁₃	#552	1	1	yes	characteristic
292	C₂²×C₁₃	#556	1	1	yes	characteristic
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	—	8	2	no	—
301	C₄×C₁₃	#471	1	2	yes	—
302	C₄×C₁₃	#525	1	1	yes	characteristic
303	C₄×C₁₃	#536	1	1	yes	characteristic
304	C₄×C₁₃	#547	1	1	yes	characteristic
305	C₄×C₁₃	#548	1	1	yes	characteristic
306	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	AGL(1,ℤ/8)	—	2	2	no	—
311	AGL(1,ℤ/8)	—	2	2	no	—
312	C₂×SD₁₆	—	2	1	no	—
313	C₂×D₈	—	2	1	no	—
314	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
316	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
317	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
324	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
332	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
333	#117	—	2	1	no	—
334	#117	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#108	—	2	4	no	—
342	#107	—	2	1	no	—
343	#107	—	2	2	no	—
344	#106	—	2	2	no	—
345	#106	—	2	2	no	—
346	#106	—	2	1	no	—
347	#106	—	2	2	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
353	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
354	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
355	#103	—	2	1	no	—
356	#103	—	2	2	no	—
357	#102	—	2	1	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#102	—	2	2	no	—
361	#102	—	2	1	no	—
362	#102	—	2	1	no	—
363	#100	—	2	4	no	—
364	C₂²⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	#97	—	2	2	no	—
367	#97	—	2	1	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	1	no	—
370	C₂×C₁₃	—	2	1	no	—
371	C₂×C₁₃	—	2	1	no	—
372	C₂×C₁₃	—	8	1	no	—
373	C₂×C₁₃	—	8	2	no	—
374	C₂×C₁₃	#2415	1	1	yes	characteristic
375	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
376	C₂×C₁₃	#3068	1	1	yes	characteristic
377	C₂⁴	—	2	1	no	—
378	#41	—	2	1	no	—
379	#41	—	2	1	no	—
380	#41	—	2	1	no	—
381	#41	—	2	1	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	8	2	no	—
385	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	C₁₃×#41	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
403	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	SD₁₆	—	2	4	no	—
406	D₈	—	2	4	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	2	1	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	C₁₃×#41	1	2	yes	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
422	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₁₃	#24721	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	8	1	no	—
451	C₂³	—	8	1	no	—
452	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
453	Q₈	—	2	1	no	—
454	Q₈	—	2	1	no	—
455	Q₈	—	8	2	no	—
456	Q₈	—	8	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
481	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
482	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
483	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
488	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	1	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
507	C₂²	C₁₃×#552	1	1	yes	characteristic
508	C₂²	C₁₃×#556	1	1	yes	characteristic
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₄	C₁₃×#471	1	2	yes	—
518	C₄	C₁₃×#525	1	1	yes	characteristic
519	C₄	C₁₃×#536	1	1	yes	characteristic
520	C₄	C₁₃×#547	1	1	yes	characteristic
521	C₄	C₁₃×#548	1	1	yes	characteristic
522	C₂	—	2	1	no	—
523	C₂	—	2	1	no	—
524	C₂	—	8	1	no	—
525	C₂	—	8	2	no	—
526	C₂	C₁₃×#2415	1	1	yes	characteristic
527	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
528	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×#2925	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1951	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1931	C₂	semidirect
11. C₁₃×#1800	C₂	semidirect
113. #24721	C₁₃	direct (N × H)
182. #3079	C₂×C₁₃	semidirect
183. C₂×#476	C₂×C₁₃	semidirect
185. #2925	C₂×C₁₃	semidirect
186. #2079	C₂×C₁₃	semidirect
188. #1997	C₂×C₁₃	semidirect
189. #1951	C₂×C₁₃	semidirect
190. #1950	C₂×C₁₃	semidirect
191. #1931	C₂×C₁₃	semidirect
192. #1800	C₂×C₁₃	semidirect
445. C₁₃	#24721	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×#2925	2
C₁₃×#2079	2
C₁₃×#2051	2
C₁₃×#1997	2
C₁₃×#1951	2
C₁₃×#1950	2
C₁₃×#1931	2
C₁₃×#1800	2
#24721	13

Subgroups — C13×#24721 #15711060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24721 #15711060