Subgroups — C₁₃×#22453 #15708792

Order 3328.

1362 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2880	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1974	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1876	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1789	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₁₃×#575	—	2	4	no	—
14	C₁₃×#575	—	2	4	no	—
15	C₂×C₁₃×#137	C₄	1	2	yes	complemented
16	C₂×C₁₃×#137	C₄	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×#444	—	2	4	no	—
26	C₁₃×#443	—	2	4	no	—
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
33	C₁₃×#408	—	2	2	no	—
34	C₁₃×#408	—	2	2	no	—
35	C₁₃×#408	C₂²	1	2	yes	complemented
36	C₁₃×#408	C₂²	1	2	yes	complemented
37	C₁₃×#407	—	2	2	no	—
38	C₁₃×#407	C₂²	1	2	yes	—
39	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
40	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₃×#341	C₂²	1	2	yes	complemented
45	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	4	no	—
50	C₂×C₁₃×#41	—	2	4	no	—
51	C₂×C₁₃×#41	—	4	2	no	—
52	C₂×C₁₃×#41	—	4	2	no	—
53	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#137	—	2	8	no	—
63	C₁₃×#137	—	2	8	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
65	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
66	C₁₃×#135	—	2	4	no	—
67	C₁₃×#135	—	2	4	no	—
68	C₁₃×#135	—	2	2	no	—
69	C₁₃×#135	—	2	2	no	—
70	C₁₃×#135	D₄	1	4	yes	—
71	C₁₃×#135	D₄	1	4	yes	—
72	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
76	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
77	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
78	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
79	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
80	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#131	—	2	4	no	—
83	C₁₃×#131	—	2	4	no	—
84	C₁₃×#131	—	4	2	no	—
85	C₁₃×#131	—	4	2	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	—	2	2	no	—
88	C₂×C₁₃×M₁₆	—	2	2	no	—
89	C₂×C₁₃×M₁₆	—	2	2	no	—
90	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
91	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	—	2	2	no	—
95	C₂²×C₈×C₁₃	—	2	2	no	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#108	—	2	2	no	—
104	C₁₃×#108	—	2	2	no	—
105	C₁₃×#104	—	2	4	no	—
106	C₁₃×#104	—	2	4	no	—
107	C₁₃×#104	—	4	2	no	—
108	C₁₃×#104	—	4	2	no	—
109	C₁₃×C₂²⋊C₈	—	2	2	no	—
110	C₁₃×C₂²⋊C₈	—	2	2	no	—
111	C₁₃×C₂²⋊C₈	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
116	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
117	C₁₃×#97	—	2	2	no	—
118	C₄×C₈×C₁₃	—	2	2	no	—
119	C₁₃×#95	—	2	1	no	—
120	#22453	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	2	no	—
122	C₂⁴×C₁₃	#41	1	1	yes	characteristic
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	4	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	—	2	2	no	—
130	C₁₃×#41	—	2	2	no	—
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	4	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	4	no	—
136	C₁₃×#41	—	4	4	no	—
137	C₁₃×#41	C₂×D₄	1	4	yes	—
138	C₁₃×#41	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	4	2	no	—
142	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	4	no	—
167	C₂²×C₄×C₁₃	—	4	4	no	—
168	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×Q₁₆	—	2	4	no	—
173	C₁₃×Q₁₆	—	2	2	no	—
174	C₁₃×Q₁₆	C₂²⋊C₄	1	4	yes	complemented
175	C₁₃×SD₁₆	—	2	4	no	—
176	C₁₃×SD₁₆	—	2	4	no	—
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×SD₁₆	C₂²⋊C₄	1	8	yes	complemented
179	C₁₃×D₈	—	2	4	no	—
180	C₁₃×D₈	—	2	2	no	—
181	C₁₃×D₈	C₂²⋊C₄	1	4	yes	complemented
182	C₁₃×M₁₆	—	2	4	no	—
183	C₁₃×M₁₆	—	2	4	no	—
184	C₁₃×M₁₆	—	2	2	no	—
185	C₁₃×M₁₆	—	2	2	no	—
186	C₁₃×M₁₆	—	2	2	no	—
187	C₁₃×M₁₆	—	2	2	no	—
188	C₁₃×M₁₆	—	4	4	no	—
189	C₁₃×M₁₆	—	4	4	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
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	2	no	—
197	C₂×C₈×C₁₃	—	2	2	no	—
198	C₂×C₈×C₁₃	—	4	4	no	—
199	C₂×C₈×C₁₃	—	4	4	no	—
200	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
201	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₂×#575	C₂×C₁₃	1	1	yes	characteristic
214	C₂×#444	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#443	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2880	C₂×C₁₃	1	2	yes	complemented
217	#1975	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1974	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1876	C₂×C₁₃	1	2	yes	complemented
220	#1876	C₂×C₁₃	1	2	yes	complemented
221	#1811	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1789	C₂×C₁₃	1	2	yes	complemented
223	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	4	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	8	2	no	—
233	C₂³×C₁₃	C₄×D₄	1	2	yes	—
234	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	4	no	—
239	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	4	4	no	—
247	D₄×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	2	1	no	—
283	C₈×C₁₃	—	4	2	no	—
284	C₈×C₁₃	—	4	2	no	—
285	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
286	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂²×#41	C₂²×C₁₃	1	2	yes	—
288	#575	—	2	4	no	—
289	#575	—	2	4	no	—
290	C₂×#137	C₄×C₁₃	1	2	yes	complemented
291	C₂×#137	C₄×C₁₃	1	2	yes	complemented
292	C₂×AGL(1,ℤ/8)	C₄×C₁₃	1	2	yes	complemented
293	C₂×AGL(1,ℤ/8)	C₄×C₁₃	1	2	yes	complemented
294	C₂×#135	C₂²×C₁₃	1	2	yes	—
295	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
299	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	#444	—	2	4	no	—
301	#443	—	2	4	no	—
302	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
305	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
306	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
307	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
308	#408	—	2	2	no	—
309	#408	—	2	2	no	—
310	#408	C₂²×C₁₃	1	2	yes	complemented
311	#408	C₂²×C₁₃	1	2	yes	complemented
312	#407	—	2	2	no	—
313	#407	C₂²×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₈	—	2	2	no	—
315	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
319	#341	C₂²×C₁₃	1	2	yes	complemented
320	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	4	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	8	1	no	—
335	C₂²×C₁₃	—	8	8	no	—
336	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₂²×C₁₃	#546	1	1	yes	characteristic
338	C₂²×C₁₃	#546	1	1	yes	characteristic
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	4	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
345	C₄×C₁₃	#518	1	1	yes	characteristic
346	C₄×C₁₃	D₄²	1	1	yes	characteristic
347	C₄×C₁₃	D₄²	1	1	yes	characteristic
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	4	no	—
351	C₂×#41	—	2	4	no	—
352	C₂×#41	—	4	2	no	—
353	C₂×#41	—	4	2	no	—
354	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
355	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
356	C₂×#41	C₂³×C₁₃	1	2	yes	—
357	C₂×#41	C₂³×C₁₃	1	2	yes	—
358	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	#137	—	2	8	no	—
364	#137	—	2	8	no	—
365	AGL(1,ℤ/8)	—	2	8	no	—
366	AGL(1,ℤ/8)	—	2	8	no	—
367	#135	—	2	4	no	—
368	#135	—	2	4	no	—
369	#135	—	2	2	no	—
370	#135	—	2	2	no	—
371	#135	D₄×C₁₃	1	4	yes	—
372	#135	D₄×C₁₃	1	4	yes	—
373	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
374	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
375	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
376	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
377	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
378	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
379	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
380	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
381	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
382	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#131	—	2	4	no	—
384	#131	—	2	4	no	—
385	#131	—	4	2	no	—
386	#131	—	4	2	no	—
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
392	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
393	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
394	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
395	C₂²×C₈	—	2	2	no	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
404	#108	—	2	2	no	—
405	#108	—	2	2	no	—
406	#104	—	2	4	no	—
407	#104	—	2	4	no	—
408	#104	—	4	2	no	—
409	#104	—	4	2	no	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
417	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
418	#97	—	2	2	no	—
419	C₄×C₈	—	2	2	no	—
420	#95	—	2	1	no	—
421	C₂×C₁₃	—	2	1	no	—
422	C₂×C₁₃	—	2	1	no	—
423	C₂×C₁₃	—	4	2	no	—
424	C₂×C₁₃	—	4	4	no	—
425	C₂×C₁₃	—	8	2	no	—
426	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
427	C₂×C₁₃	#2955	1	1	yes	characteristic
428	C₂×C₁₃	#2956	1	1	yes	characteristic
429	C₂⁴	—	2	2	no	—
430	C₂⁴	C₁₃×#41	1	1	yes	characteristic
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	4	no	—
434	#41	—	2	4	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	—	4	4	no	—
440	#41	—	4	4	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	4	no	—
444	#41	—	4	4	no	—
445	#41	C₂×D₄×C₁₃	1	4	yes	—
446	#41	C₂×D₄×C₁₃	1	4	yes	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
480	Q₁₆	—	2	4	no	—
481	Q₁₆	—	2	2	no	—
482	Q₁₆	C₁₃×C₂²⋊C₄	1	4	yes	complemented
483	SD₁₆	—	2	4	no	—
484	SD₁₆	—	2	4	no	—
485	SD₁₆	—	2	4	no	—
486	SD₁₆	C₁₃×C₂²⋊C₄	1	8	yes	complemented
487	D₈	—	2	4	no	—
488	D₈	—	2	2	no	—
489	D₈	C₁₃×C₂²⋊C₄	1	4	yes	complemented
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	4	no	—
497	M₁₆	—	4	4	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	4	4	no	—
507	C₂×C₈	—	4	4	no	—
508	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
509	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
510	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
511	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
513	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₁₃	#22453	1	1	yes	characteristic, direct product factor, Sylow
522	C₂³	—	2	2	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	8	2	no	—
531	C₂³	C₄×D₄×C₁₃	1	2	yes	—
532	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	4	no	—
537	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
538	D₄	—	2	4	no	—
539	D₄	—	2	4	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	4	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	2	no	—
580	C₈	—	2	1	no	—
581	C₈	—	4	2	no	—
582	C₈	—	4	2	no	—
583	C₈	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
584	C₈	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	8	no	—
599	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
600	C₂²	C₁₃×#546	1	1	yes	characteristic
601	C₂²	C₁₃×#546	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	4	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	8	1	no	—
607	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
608	C₄	C₁₃×#518	1	1	yes	characteristic
609	C₄	D₄²×C₁₃	1	1	yes	characteristic
610	C₄	D₄²×C₁₃	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	4	2	no	—
614	C₂	—	4	4	no	—
615	C₂	—	8	2	no	—
616	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
617	C₂	C₁₃×#2955	1	1	yes	characteristic
618	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#444	C₂	semidirect
3. C₂×C₁₃×#443	C₂	semidirect
4. C₁₃×#2880	C₂	semidirect
5. C₁₃×#1975	C₂	semidirect
6. C₁₃×#1974	C₂	semidirect
7. C₁₃×#1876	C₂	semidirect
8. C₁₃×#1876	C₂	semidirect
9. C₁₃×#1811	C₂	semidirect
10. C₁₃×#1789	C₂	semidirect
11. C₁₃×#1753	C₂	semidirect
15. C₂×C₁₃×#137	C₄	semidirect
16. C₂×C₁₃×#137	C₄	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
22. C₂×C₁₃×#131	C₂²	semidirect
23. C₂×C₁₃×#131	C₂²	semidirect
27. C₂×C₁₃×#108	C₂²	semidirect
28. C₂×C₁₃×#108	C₂²	semidirect
29. C₂×C₁₃×#104	C₂²	semidirect
30. C₂×C₁₃×#104	C₂²	semidirect
31. C₂×C₁₃×#104	C₂²	semidirect
32. C₂×C₁₃×#104	C₂²	semidirect
35. C₁₃×#408	C₂²	semidirect
36. C₁₃×#408	C₂²	semidirect
41. C₂×C₁₃×#97	C₂²	semidirect
42. C₂×C₄×C₈×C₁₃	C₂²	semidirect
44. C₁₃×#341	C₂²	semidirect
45. C₁₃×#336	C₂²	semidirect
46. C₁₃×#336	C₂²	semidirect
120. #22453	C₁₃	direct (N × H)
174. C₁₃×Q₁₆	C₂²⋊C₄	semidirect
178. C₁₃×SD₁₆	C₂²⋊C₄	semidirect
181. C₁₃×D₈	C₂²⋊C₄	semidirect
214. C₂×#444	C₂×C₁₃	semidirect
215. C₂×#443	C₂×C₁₃	semidirect
216. #2880	C₂×C₁₃	semidirect
217. #1975	C₂×C₁₃	semidirect
218. #1974	C₂×C₁₃	semidirect
219. #1876	C₂×C₁₃	semidirect
220. #1876	C₂×C₁₃	semidirect
221. #1811	C₂×C₁₃	semidirect
222. #1789	C₂×C₁₃	semidirect
223. #1753	C₂×C₁₃	semidirect
290. C₂×#137	C₄×C₁₃	semidirect
291. C₂×#137	C₄×C₁₃	semidirect
292. C₂×AGL(1,ℤ/8)	C₄×C₁₃	semidirect
293. C₂×AGL(1,ℤ/8)	C₄×C₁₃	semidirect
297. C₂×#131	C₂²×C₁₃	semidirect
298. C₂×#131	C₂²×C₁₃	semidirect
302. C₂×#108	C₂²×C₁₃	semidirect
303. C₂×#108	C₂²×C₁₃	semidirect
304. C₂×#104	C₂²×C₁₃	semidirect
305. C₂×#104	C₂²×C₁₃	semidirect
306. C₂×#104	C₂²×C₁₃	semidirect
307. C₂×#104	C₂²×C₁₃	semidirect
310. #408	C₂²×C₁₃	semidirect
311. #408	C₂²×C₁₃	semidirect
316. C₂×#97	C₂²×C₁₃	semidirect
317. C₂×C₄×C₈	C₂²×C₁₃	semidirect
319. #341	C₂²×C₁₃	semidirect
320. #336	C₂²×C₁₃	semidirect
321. #336	C₂²×C₁₃	semidirect
482. Q₁₆	C₁₃×C₂²⋊C₄	semidirect
486. SD₁₆	C₁₃×C₂²⋊C₄	semidirect
489. D₈	C₁₃×C₂²⋊C₄	semidirect
521. C₁₃	#22453	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×#575	2
C₂×C₁₃×#444	2
C₂×C₁₃×#443	2
C₁₃×#2880	2
C₁₃×#1975	2
C₁₃×#1974	2
C₁₃×#1876	2
C₁₃×#1811	2
C₁₃×#1789	2
C₁₃×#1753	2
#22453	13

Subgroups — C13×#22453 #15708792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22453 #15708792