Subgroups — C₁₃×#23718 #15710057

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2079	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic
13	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#442	—	2	1	no	—
23	C₁₃×#441	—	2	1	no	—
24	C₁₃×#440	—	2	1	no	—
25	C₁₃×#440	—	2	1	no	—
26	C₄×C₁₃×Q₁₆	—	2	1	no	—
27	C₄×C₁₃×SD₁₆	—	2	1	no	—
28	C₄×C₁₃×SD₁₆	—	2	1	no	—
29	C₄×C₁₃×SD₁₆	—	2	2	no	—
30	C₄×C₁₃×SD₁₆	—	2	2	no	—
31	C₄×C₁₃×D₈	—	2	1	no	—
32	C₁₃×#433	—	2	2	no	—
33	C₁₃×#431	—	2	2	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
39	C₁₃×#424	C₂²	1	1	yes	characteristic
40	C₁₃×#424	C₂²	1	1	yes	characteristic
41	C₁₃×#419	C₂²	1	1	yes	characteristic
42	C₁₃×#418	C₂²	1	1	yes	characteristic
43	C₁₃×#417	C₂²	1	1	yes	characteristic
44	C₁₃×#417	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
51	C₁₃×#408	C₂²	1	1	yes	characteristic
52	C₁₃×#408	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#343	C₂²	1	1	yes	characteristic
58	C₁₃×#343	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#341	C₂²	1	1	yes	characteristic
62	C₁₃×#341	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₁₃×#137	—	2	2	no	—
68	C₁₃×#137	—	2	2	no	—
69	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
70	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
100	C₁₃×#117	—	2	1	no	—
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#108	—	2	2	no	—
110	C₁₃×#108	—	2	2	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×#106	—	2	1	no	—
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#102	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#101	—	2	2	no	—
129	C₁₃×#101	—	2	2	no	—
130	C₁₃×#100	—	2	2	no	—
131	C₁₃×#100	—	2	2	no	—
132	C₁₃×C₂²⋊C₈	—	2	2	no	—
133	C₁₃×C₂²⋊C₈	—	2	2	no	—
134	C₁₃×#97	—	2	1	no	—
135	C₁₃×#97	—	2	1	no	—
136	C₁₃×#97	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	D₄	1	2	yes	—
141	C₄×C₈×C₁₃	D₄	1	2	yes	—
142	#23718	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	1	no	—
144	C₁₃×#41	—	2	1	no	—
145	C₁₃×#41	—	2	1	no	—
146	C₁₃×#41	—	2	1	no	—
147	C₁₃×#41	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	#41	1	2	yes	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₃	#41	1	2	yes	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	—	4	1	no	—
171	C₂²×C₄×C₁₃	—	8	2	no	—
172	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×Q₁₆	—	2	4	no	—
176	C₁₃×SD₁₆	—	2	8	no	—
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×SD₁₆	—	2	4	no	—
179	C₁₃×D₈	—	2	4	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	#41	1	2	yes	—
191	C₁₃×M₁₆	#41	1	2	yes	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
203	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₂²⋊C₄	—	2	1	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	2	1	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₁₃×C₂²⋊C₄	—	4	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	4	1	no	—
223	C₄²×C₁₃	—	4	1	no	—
224	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
230	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2079	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2051	C₂×C₁₃	1	1	yes	characteristic
238	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2019	C₂×C₁₃	1	1	yes	characteristic
240	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₄×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₄×#100	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	8	1	no	—
248	C₂³×C₁₃	—	8	1	no	—
249	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
250	Q₈×C₁₃	—	2	2	no	—
251	Q₈×C₁₃	—	2	1	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	2	1	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	2	1	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	1	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	8	2	no	—
279	C₂×C₄×C₁₃	—	8	2	no	—
280	C₂×C₄×C₁₃	—	8	1	no	—
281	C₂×C₄×C₁₃	—	8	1	no	—
282	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
283	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
284	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
285	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₈×C₁₃	—	2	2	no	—
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	2	2	no	—
295	C₈×C₁₃	—	2	2	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₈×C₁₃	—	4	1	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	#442	—	2	1	no	—
307	#441	—	2	1	no	—
308	#440	—	2	1	no	—
309	#440	—	2	1	no	—
310	C₄×Q₁₆	—	2	1	no	—
311	C₄×SD₁₆	—	2	1	no	—
312	C₄×SD₁₆	—	2	1	no	—
313	C₄×SD₁₆	—	2	2	no	—
314	C₄×SD₁₆	—	2	2	no	—
315	C₄×D₈	—	2	1	no	—
316	#433	—	2	2	no	—
317	#431	—	2	2	no	—
318	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
320	#428	C₂²×C₁₃	1	1	yes	characteristic
321	#428	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
323	#424	C₂²×C₁₃	1	1	yes	characteristic
324	#424	C₂²×C₁₃	1	1	yes	characteristic
325	#419	C₂²×C₁₃	1	1	yes	characteristic
326	#418	C₂²×C₁₃	1	1	yes	characteristic
327	#417	C₂²×C₁₃	1	1	yes	characteristic
328	#417	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
335	#408	C₂²×C₁₃	1	1	yes	characteristic
336	#408	C₂²×C₁₃	1	1	yes	characteristic
337	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
338	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
339	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
341	#343	C₂²×C₁₃	1	1	yes	characteristic
342	#343	C₂²×C₁₃	1	1	yes	characteristic
343	#343	C₂²×C₁₃	1	1	yes	characteristic
344	#343	C₂²×C₁₃	1	1	yes	characteristic
345	#341	C₂²×C₁₃	1	1	yes	characteristic
346	#341	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₁₃	—	2	1	no	—
348	C₂²×C₁₃	—	2	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	2	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	8	2	no	—
354	C₂²×C₁₃	—	8	2	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	—	8	1	no	—
357	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
358	C₂²×C₁₃	#529	1	1	yes	characteristic
359	C₂²×C₁₃	#529	1	1	yes	characteristic
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	#471	1	2	yes	—
370	C₄×C₁₃	#525	1	1	yes	characteristic
371	C₄×C₁₃	#525	1	1	yes	characteristic
372	C₄×C₁₃	#525	1	1	yes	characteristic
373	C₄×C₁₃	#532	1	1	yes	characteristic
374	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	#137	—	2	2	no	—
379	#137	—	2	2	no	—
380	AGL(1,ℤ/8)	—	2	2	no	—
381	AGL(1,ℤ/8)	—	2	2	no	—
382	C₂×Q₁₆	—	2	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	1	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
402	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
410	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
411	#117	—	2	1	no	—
412	#117	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
420	#108	—	2	2	no	—
421	#108	—	2	2	no	—
422	#107	—	2	1	no	—
423	#107	—	2	1	no	—
424	#106	—	2	2	no	—
425	#106	—	2	1	no	—
426	#106	—	2	1	no	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	2	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#103	—	2	2	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	2	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#101	—	2	2	no	—
440	#101	—	2	2	no	—
441	#100	—	2	2	no	—
442	#100	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	#97	—	2	1	no	—
446	#97	—	2	1	no	—
447	#97	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	C₄×C₈	—	2	1	no	—
451	C₄×C₈	D₄×C₁₃	1	2	yes	—
452	C₄×C₈	D₄×C₁₃	1	2	yes	—
453	C₂×C₁₃	—	2	1	no	—
454	C₂×C₁₃	—	2	1	no	—
455	C₂×C₁₃	—	8	1	no	—
456	C₂×C₁₃	—	8	2	no	—
457	C₂×C₁₃	#2392	1	1	yes	characteristic
458	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
459	C₂×C₁₃	#3067	1	1	yes	characteristic
460	C₂⁴	—	2	1	no	—
461	#41	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂×Q₈	C₁₃×#41	1	2	yes	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂×D₄	C₁₃×#41	1	2	yes	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	8	2	no	—
489	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
490	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
492	Q₁₆	—	2	4	no	—
493	SD₁₆	—	2	8	no	—
494	SD₁₆	—	2	4	no	—
495	SD₁₆	—	2	4	no	—
496	D₈	—	2	4	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	C₁₃×#41	1	2	yes	—
508	M₁₆	C₁₃×#41	1	2	yes	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
520	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	4	1	no	—
540	C₄²	—	4	1	no	—
541	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₁₃	#23718	1	1	yes	characteristic, direct product factor, Sylow
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	8	1	no	—
551	C₂³	—	8	1	no	—
552	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
553	Q₈	—	2	2	no	—
554	Q₈	—	2	1	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
587	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
588	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
594	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
614	C₂²	C₁₃×#529	1	1	yes	characteristic
615	C₂²	C₁₃×#529	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₁₃×#471	1	2	yes	—
626	C₄	C₁₃×#525	1	1	yes	characteristic
627	C₄	C₁₃×#525	1	1	yes	characteristic
628	C₄	C₁₃×#525	1	1	yes	characteristic
629	C₄	C₁₃×#532	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₃×#2392	1	1	yes	characteristic
635	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
636	C₂	C₁₃×#3067	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×#137	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#2922	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2079	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#2052	C₂	semidirect
11. C₁₃×#2046	C₂	semidirect
13. C₄×C₁₃×#108	C₂	semidirect
14. C₄×C₁₃×#101	C₂	semidirect
15. C₄×C₁₃×#100	C₂	semidirect
142. #23718	C₁₃	direct (N × H)
228. C₄×#137	C₂×C₁₃	semidirect
230. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
231. #2922	C₂×C₁₃	semidirect
232. #2090	C₂×C₁₃	semidirect
233. #2079	C₂×C₁₃	semidirect
234. #2064	C₂×C₁₃	semidirect
235. #2063	C₂×C₁₃	semidirect
236. #2052	C₂×C₁₃	semidirect
238. #2046	C₂×C₁₃	semidirect
240. C₄×#108	C₂×C₁₃	semidirect
241. C₄×#101	C₂×C₁₃	semidirect
242. C₄×#100	C₂×C₁₃	semidirect
545. C₁₃	#23718	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2922	2
C₁₃×#2090	2
C₁₃×#2079	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#2046	2
C₁₃×#2019	2
C₄×C₁₃×#108	2
C₄×C₁₃×#101	2
C₄×C₁₃×#100	2
#23718	13

Subgroups — C13×#23718 #15710057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23718 #15710057