Subgroups — C₁₃×#33538 #15719877

Order 3328.

1088 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3414	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2195	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2194	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2193	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2192	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2148	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#359	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#350	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	—	2	1	no	—
13	C₁₃×#578	—	2	1	no	—
14	C₁₃×#578	C₂²	1	2	yes	—
15	C₁₃×#577	—	2	2	no	—
16	C₁₃×#577	—	2	2	no	—
17	C₁₃×#576	—	2	1	no	—
18	C₁₃×#576	C₂²	1	2	yes	—
19	C₁₃×#575	—	2	2	no	—
20	C₁₃×#575	—	2	1	no	—
21	C₁₃×#575	—	2	1	no	—
22	C₂×C₁₃×#135	—	2	2	no	—
23	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
27	C₁₃×#510	—	2	1	no	—
28	C₁₃×#510	C₂²	1	2	yes	complemented
29	C₁₃×#509	—	2	1	no	—
30	C₁₃×#509	C₂²	1	2	yes	complemented
31	C₁₃×#508	—	2	2	no	—
32	C₁₃×#508	—	2	2	no	—
33	C₁₃×#508	—	2	2	no	—
34	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#473	C₂²	1	2	yes	complemented
41	C₁₃×#472	C₂²	1	2	yes	complemented
42	C₁₃×#471	—	2	2	no	—
43	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#413	—	2	1	no	—
45	C₁₃×#362	C₂²	1	2	yes	complemented
46	C₁₃×#361	C₂²	1	2	yes	complemented
47	C₁₃×#359	C₂²	1	2	yes	complemented
48	C₁₃×#359	C₂²	1	2	yes	complemented
49	C₁₃×#350	C₂²	1	2	yes	complemented
50	C₁₃×#350	C₂²	1	2	yes	complemented
51	C₁₃×2₋¹⁺⁴	—	2	2	no	—
52	C₁₃×2₋¹⁺⁴	—	2	2	no	—
53	C₁₃×2₋¹⁺⁴	—	4	1	no	—
54	C₁₃×H(5,𝔽₂)	—	2	2	no	—
55	C₁₃×H(5,𝔽₂)	—	2	2	no	—
56	C₁₃×H(5,𝔽₂)	—	4	2	no	—
57	C₁₃×H(5,𝔽₂)	—	4	1	no	—
58	C₂×C₁₃×#41	—	2	4	no	—
59	C₂×C₁₃×#41	—	2	1	no	—
60	C₂×C₁₃×#41	—	2	1	no	—
61	C₂×C₁₃×#41	—	2	1	no	—
62	C₂×C₁₃×#41	—	4	2	no	—
63	C₂×C₁₃×#41	—	4	2	no	—
64	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
65	C₁₃×#137	—	2	2	no	—
66	C₁₃×#137	—	2	4	no	—
67	C₁₃×#137	—	2	4	no	—
68	C₁₃×#137	—	2	2	no	—
69	C₁₃×#137	—	2	2	no	—
70	C₁₃×#137	—	4	1	no	—
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
73	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
76	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
77	C₁₃×#135	—	2	4	no	—
78	C₁₃×#135	—	2	4	no	—
79	C₁₃×#135	—	2	2	no	—
80	C₁₃×#135	—	2	2	no	—
81	C₁₃×#135	—	2	1	no	—
82	C₁₃×#135	—	2	1	no	—
83	C₁₃×#135	—	2	1	no	—
84	C₁₃×#135	—	2	1	no	—
85	C₁₃×#135	—	2	1	no	—
86	C₁₃×#135	—	2	1	no	—
87	C₁₃×#135	—	2	1	no	—
88	C₁₃×#135	—	2	1	no	—
89	C₁₃×#135	—	4	2	no	—
90	C₁₃×#135	D₄	1	2	yes	—
91	C₁₃×#135	D₄	1	2	yes	—
92	C₁₃×#135	D₄	1	2	yes	—
93	C₁₃×#135	C₂³	1	2	yes	—
94	C₂×C₁₃×Q₁₆	—	2	2	no	—
95	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
96	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×SD₁₆	—	2	4	no	—
99	C₂×C₁₃×SD₁₆	—	2	1	no	—
100	C₂×C₁₃×SD₁₆	—	2	1	no	—
101	C₂×C₁₃×SD₁₆	—	2	1	no	—
102	C₂×C₁₃×D₈	—	2	2	no	—
103	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
104	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
106	C₁₃×#131	—	2	1	no	—
107	C₁₃×#131	—	2	1	no	—
108	C₁₃×#131	D₄	1	2	yes	—
109	C₁₃×#131	C₂³	1	2	yes	—
110	C₂×C₁₃×M₁₆	—	2	1	no	—
111	C₂×C₁₃×M₁₆	—	2	1	no	—
112	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
113	C₂²×C₈×C₁₃	—	2	1	no	—
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×Q₃₂	—	2	2	no	—
116	C₁₃×Q₃₂	—	2	2	no	—
117	C₁₃×SD₃₂	—	2	2	no	—
118	C₁₃×SD₃₂	—	2	2	no	—
119	C₁₃×SD₃₂	—	2	2	no	—
120	C₁₃×SD₃₂	—	2	2	no	—
121	C₁₃×D₁₆	—	2	2	no	—
122	C₁₃×D₁₆	—	2	2	no	—
123	C₁₃×M₃₂	—	2	1	no	—
124	C₁₃×M₃₂	C₂³	1	2	yes	—
125	C₂×C₁₃×C₁₆	—	2	1	no	—
126	C₂×C₁₃×C₁₆	—	2	1	no	—
127	C₂×C₁₃×C₁₆	—	2	1	no	—
128	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
130	C₁₃×#108	—	2	1	no	—
131	C₁₃×#108	C₂³	1	2	yes	—
132	C₁₃×#101	—	2	2	no	—
133	C₁₃×#100	—	2	2	no	—
134	#33538	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₁₃×#41	—	2	1	no	—
136	C₁₃×#41	—	2	1	no	—
137	C₁₃×#41	—	2	4	no	—
138	C₁₃×#41	—	2	4	no	—
139	C₁₃×#41	—	2	2	no	—
140	C₁₃×#41	—	2	2	no	—
141	C₁₃×#41	—	2	2	no	—
142	C₁₃×#41	—	2	2	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₁₃×#41	—	4	4	no	—
147	C₁₃×#41	—	4	2	no	—
148	C₁₃×#41	—	4	2	no	—
149	C₁₃×#41	—	4	2	no	—
150	C₁₃×#41	—	4	2	no	—
151	C₁₃×#41	—	4	1	no	—
152	C₁₃×#41	—	4	1	no	—
153	C₁₃×#41	—	4	1	no	—
154	C₁₃×#41	—	4	1	no	—
155	C₁₃×#41	—	4	1	no	—
156	C₁₃×#41	—	4	1	no	—
157	C₁₃×#41	—	4	1	no	—
158	C₁₃×#41	—	4	1	no	—
159	C₁₃×#41	D₈	1	2	yes	—
160	C₁₃×#41	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₁₃	—	2	4	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	4	2	no	—
166	C₂×Q₈×C₁₃	—	4	2	no	—
167	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	4	4	no	—
174	C₂×D₄×C₁₃	—	4	4	no	—
175	C₂×D₄×C₁₃	—	4	2	no	—
176	C₂×D₄×C₁₃	—	4	4	no	—
177	C₂×D₄×C₁₃	—	4	1	no	—
178	C₂×D₄×C₁₃	—	4	1	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	—	4	1	no	—
181	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	4	4	no	—
184	C₂²×C₄×C₁₃	—	4	1	no	—
185	C₂²×C₄×C₁₃	—	4	1	no	—
186	C₂²×C₄×C₁₃	—	4	1	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₁₃×Q₁₆	—	2	4	no	—
189	C₁₃×Q₁₆	—	2	1	no	—
190	C₁₃×Q₁₆	—	2	1	no	—
191	C₁₃×Q₁₆	—	2	1	no	—
192	C₁₃×Q₁₆	—	2	1	no	—
193	C₁₃×Q₁₆	—	4	2	no	—
194	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
195	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
196	C₁₃×SD₁₆	—	2	4	no	—
197	C₁₃×SD₁₆	—	2	4	no	—
198	C₁₃×SD₁₆	—	2	2	no	—
199	C₁₃×SD₁₆	—	2	2	no	—
200	C₁₃×SD₁₆	—	2	2	no	—
201	C₁₃×SD₁₆	—	2	2	no	—
202	C₁₃×SD₁₆	—	4	2	no	—
203	C₁₃×SD₁₆	—	4	2	no	—
204	C₁₃×SD₁₆	—	4	1	no	—
205	C₁₃×SD₁₆	—	4	1	no	—
206	C₁₃×D₈	—	2	4	no	—
207	C₁₃×D₈	—	2	1	no	—
208	C₁₃×D₈	—	2	1	no	—
209	C₁₃×D₈	—	2	1	no	—
210	C₁₃×D₈	—	2	1	no	—
211	C₁₃×D₈	—	4	2	no	—
212	C₁₃×D₈	C₂×D₄	1	2	yes	—
213	C₁₃×D₈	C₂×D₄	1	2	yes	—
214	C₁₃×M₁₆	—	2	1	no	—
215	C₁₃×M₁₆	—	2	2	no	—
216	C₁₃×M₁₆	—	2	2	no	—
217	C₁₃×M₁₆	—	2	2	no	—
218	C₁₃×M₁₆	—	4	1	no	—
219	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	2	no	—
222	C₂×C₈×C₁₃	—	2	2	no	—
223	C₂×C₈×C₁₃	—	4	1	no	—
224	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₁₃×C₁₆	—	2	1	no	—
231	C₁₃×C₁₆	—	2	1	no	—
232	C₁₃×C₁₆	—	2	2	no	—
233	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3414	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#3067	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2195	C₂×C₁₃	1	2	yes	complemented
238	#2194	C₂×C₁₃	1	2	yes	complemented
239	#2193	C₂×C₁₃	1	2	yes	complemented
240	#2192	C₂×C₁₃	1	2	yes	complemented
241	#2148	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₂×#359	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂×#350	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	4	4	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
250	Q₈×C₁₃	—	2	1	no	—
251	Q₈×C₁₃	—	2	2	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	4	4	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	4	1	no	—
256	Q₈×C₁₃	—	4	1	no	—
257	Q₈×C₁₃	—	4	1	no	—
258	Q₈×C₁₃	C₂×D₈	1	2	yes	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	2	no	—
263	D₄×C₁₃	—	2	1	no	—
264	D₄×C₁₃	—	4	4	no	—
265	D₄×C₁₃	—	4	4	no	—
266	D₄×C₁₃	—	4	4	no	—
267	D₄×C₁₃	—	4	2	no	—
268	D₄×C₁₃	—	4	2	no	—
269	D₄×C₁₃	—	4	2	no	—
270	D₄×C₁₃	—	4	2	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	8	1	no	—
276	D₄×C₁₃	—	8	1	no	—
277	D₄×C₁₃	C₂×D₈	1	2	yes	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	4	4	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	2	no	—
287	C₂×C₄×C₁₃	—	4	2	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	2	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	8	1	no	—
292	C₂×C₄×C₁₃	—	8	1	no	—
293	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
294	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
297	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₈×C₁₃	—	2	2	no	—
300	C₈×C₁₃	—	4	2	no	—
301	C₈×C₁₃	#120	1	1	yes	characteristic
302	C₈×C₁₃	#120	1	1	yes	characteristic
303	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	#585	—	2	1	no	—
306	#578	—	2	1	no	—
307	#578	C₂²×C₁₃	1	2	yes	—
308	#577	—	2	2	no	—
309	#577	—	2	2	no	—
310	#576	—	2	1	no	—
311	#576	C₂²×C₁₃	1	2	yes	—
312	#575	—	2	2	no	—
313	#575	—	2	1	no	—
314	#575	—	2	1	no	—
315	C₂×#135	—	2	2	no	—
316	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
320	#510	—	2	1	no	—
321	#510	C₂²×C₁₃	1	2	yes	complemented
322	#509	—	2	1	no	—
323	#509	C₂²×C₁₃	1	2	yes	complemented
324	#508	—	2	2	no	—
325	#508	—	2	2	no	—
326	#508	—	2	2	no	—
327	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	#473	C₂²×C₁₃	1	2	yes	complemented
334	#472	C₂²×C₁₃	1	2	yes	complemented
335	#471	—	2	2	no	—
336	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	#413	—	2	1	no	—
338	#362	C₂²×C₁₃	1	2	yes	complemented
339	#361	C₂²×C₁₃	1	2	yes	complemented
340	#359	C₂²×C₁₃	1	2	yes	complemented
341	#359	C₂²×C₁₃	1	2	yes	complemented
342	#350	C₂²×C₁₃	1	2	yes	complemented
343	#350	C₂²×C₁₃	1	2	yes	complemented
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	8	1	no	—
350	C₂²×C₁₃	—	16	1	no	—
351	C₂²×C₁₃	—	16	1	no	—
352	C₂²×C₁₃	—	16	1	no	—
353	C₂²×C₁₃	—	16	4	no	—
354	C₂²×C₁₃	#447	1	1	yes	characteristic
355	C₂²×C₁₃	#447	1	1	yes	characteristic
356	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	#447	1	1	yes	characteristic
362	C₄×C₁₃	#447	1	1	yes	characteristic
363	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
364	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
365	2₋¹⁺⁴	—	2	2	no	—
366	2₋¹⁺⁴	—	2	2	no	—
367	2₋¹⁺⁴	—	4	1	no	—
368	H(5,𝔽₂)	—	2	2	no	—
369	H(5,𝔽₂)	—	2	2	no	—
370	H(5,𝔽₂)	—	4	2	no	—
371	H(5,𝔽₂)	—	4	1	no	—
372	C₂×#41	—	2	4	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	4	2	no	—
377	C₂×#41	—	4	2	no	—
378	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
379	#137	—	2	2	no	—
380	#137	—	2	4	no	—
381	#137	—	2	4	no	—
382	#137	—	2	2	no	—
383	#137	—	2	2	no	—
384	#137	—	4	1	no	—
385	AGL(1,ℤ/8)	—	2	2	no	—
386	AGL(1,ℤ/8)	—	2	4	no	—
387	AGL(1,ℤ/8)	—	2	4	no	—
388	AGL(1,ℤ/8)	—	2	2	no	—
389	AGL(1,ℤ/8)	—	2	2	no	—
390	AGL(1,ℤ/8)	—	4	1	no	—
391	#135	—	2	4	no	—
392	#135	—	2	4	no	—
393	#135	—	2	2	no	—
394	#135	—	2	2	no	—
395	#135	—	2	1	no	—
396	#135	—	2	1	no	—
397	#135	—	2	1	no	—
398	#135	—	2	1	no	—
399	#135	—	2	1	no	—
400	#135	—	2	1	no	—
401	#135	—	2	1	no	—
402	#135	—	2	1	no	—
403	#135	—	4	2	no	—
404	#135	D₄×C₁₃	1	2	yes	—
405	#135	D₄×C₁₃	1	2	yes	—
406	#135	D₄×C₁₃	1	2	yes	—
407	#135	C₂³×C₁₃	1	2	yes	—
408	C₂×Q₁₆	—	2	2	no	—
409	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
410	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×SD₁₆	—	2	4	no	—
413	C₂×SD₁₆	—	2	1	no	—
414	C₂×SD₁₆	—	2	1	no	—
415	C₂×SD₁₆	—	2	1	no	—
416	C₂×D₈	—	2	2	no	—
417	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
418	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
420	#131	—	2	1	no	—
421	#131	—	2	1	no	—
422	#131	D₄×C₁₃	1	2	yes	—
423	#131	C₂³×C₁₃	1	2	yes	—
424	C₂×M₁₆	—	2	1	no	—
425	C₂×M₁₆	—	2	1	no	—
426	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₈	—	2	1	no	—
428	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	Q₃₂	—	2	2	no	—
430	Q₃₂	—	2	2	no	—
431	SD₃₂	—	2	2	no	—
432	SD₃₂	—	2	2	no	—
433	SD₃₂	—	2	2	no	—
434	SD₃₂	—	2	2	no	—
435	D₁₆	—	2	2	no	—
436	D₁₆	—	2	2	no	—
437	M₃₂	—	2	1	no	—
438	M₃₂	C₂³×C₁₃	1	2	yes	—
439	C₂×C₁₆	—	2	1	no	—
440	C₂×C₁₆	—	2	1	no	—
441	C₂×C₁₆	—	2	1	no	—
442	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
444	#108	—	2	1	no	—
445	#108	C₂³×C₁₃	1	2	yes	—
446	#101	—	2	2	no	—
447	#100	—	2	2	no	—
448	C₂×C₁₃	—	2	1	no	—
449	C₂×C₁₃	—	2	1	no	—
450	C₂×C₁₃	—	2	1	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	8	2	no	—
453	C₂×C₁₃	—	8	2	no	—
454	C₂×C₁₃	—	16	1	no	—
455	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
456	#41	—	2	1	no	—
457	#41	—	2	1	no	—
458	#41	—	2	4	no	—
459	#41	—	2	4	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	—	4	4	no	—
465	#41	—	4	4	no	—
466	#41	—	4	4	no	—
467	#41	—	4	4	no	—
468	#41	—	4	2	no	—
469	#41	—	4	2	no	—
470	#41	—	4	2	no	—
471	#41	—	4	2	no	—
472	#41	—	4	1	no	—
473	#41	—	4	1	no	—
474	#41	—	4	1	no	—
475	#41	—	4	1	no	—
476	#41	—	4	1	no	—
477	#41	—	4	1	no	—
478	#41	—	4	1	no	—
479	#41	—	4	1	no	—
480	#41	C₁₃×D₈	1	2	yes	—
481	#41	C₂×D₄×C₁₃	1	2	yes	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	4	2	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	4	4	no	—
495	C₂×D₄	—	4	4	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	1	no	—
499	C₂×D₄	—	4	1	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	4	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	Q₁₆	—	2	4	no	—
510	Q₁₆	—	2	1	no	—
511	Q₁₆	—	2	1	no	—
512	Q₁₆	—	2	1	no	—
513	Q₁₆	—	2	1	no	—
514	Q₁₆	—	4	2	no	—
515	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
516	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
517	SD₁₆	—	2	4	no	—
518	SD₁₆	—	2	4	no	—
519	SD₁₆	—	2	2	no	—
520	SD₁₆	—	2	2	no	—
521	SD₁₆	—	2	2	no	—
522	SD₁₆	—	2	2	no	—
523	SD₁₆	—	4	2	no	—
524	SD₁₆	—	4	2	no	—
525	SD₁₆	—	4	1	no	—
526	SD₁₆	—	4	1	no	—
527	D₈	—	2	4	no	—
528	D₈	—	2	1	no	—
529	D₈	—	2	1	no	—
530	D₈	—	2	1	no	—
531	D₈	—	2	1	no	—
532	D₈	—	4	2	no	—
533	D₈	C₂×D₄×C₁₃	1	2	yes	—
534	D₈	C₂×D₄×C₁₃	1	2	yes	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	2	no	—
537	M₁₆	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	M₁₆	—	4	1	no	—
540	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	4	1	no	—
545	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₁₆	—	2	1	no	—
552	C₁₆	—	2	1	no	—
553	C₁₆	—	2	2	no	—
554	C₁₃	#33538	1	1	yes	characteristic, direct product factor, Sylow
555	C₂³	—	2	1	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
561	Q₈	—	2	1	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	4	4	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	C₂×C₁₃×D₈	1	2	yes	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	4	no	—
576	D₄	—	4	4	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	8	1	no	—
587	D₄	—	8	1	no	—
588	D₄	C₂×C₁₃×D₈	1	2	yes	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	8	1	no	—
603	C₂×C₄	—	8	1	no	—
604	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
605	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
607	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
608	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
610	C₈	—	2	2	no	—
611	C₈	—	4	2	no	—
612	C₈	C₁₃×#120	1	1	yes	characteristic
613	C₈	C₁₃×#120	1	1	yes	characteristic
614	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
615	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
616	C₂²	—	2	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	16	1	no	—
623	C₂²	—	16	1	no	—
624	C₂²	—	16	1	no	—
625	C₂²	—	16	4	no	—
626	C₂²	C₁₃×#447	1	1	yes	characteristic
627	C₂²	C₁₃×#447	1	1	yes	characteristic
628	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
629	C₄	—	2	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	8	1	no	—
633	C₄	C₁₃×#447	1	1	yes	characteristic
634	C₄	C₁₃×#447	1	1	yes	characteristic
635	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
636	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	4	2	no	—
641	C₂	—	8	2	no	—
642	C₂	—	8	2	no	—
643	C₂	—	16	1	no	—
644	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#447
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3584	C₂	semidirect
2. C₁₃×#3414	C₂	semidirect
3. C₂×C₁₃×#508	C₂	semidirect
4. C₁₃×#3067	C₂	semidirect
5. C₁₃×#2195	C₂	semidirect
6. C₁₃×#2194	C₂	semidirect
7. C₁₃×#2193	C₂	semidirect
8. C₁₃×#2192	C₂	semidirect
9. C₁₃×#2148	C₂	semidirect
10. C₂×C₁₃×#359	C₂	semidirect
11. C₂×C₁₃×#350	C₂	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
28. C₁₃×#510	C₂²	semidirect
30. C₁₃×#509	C₂²	semidirect
34. C₂×C₁₃×Q₃₂	C₂²	semidirect
35. C₂×C₁₃×SD₃₂	C₂²	semidirect
36. C₂×C₁₃×SD₃₂	C₂²	semidirect
37. C₂×C₁₃×D₁₆	C₂²	semidirect
38. C₂×C₁₃×M₃₂	C₂²	semidirect
39. C₂²×C₁₃×C₁₆	C₂²	semidirect
40. C₁₃×#473	C₂²	semidirect
41. C₁₃×#472	C₂²	semidirect
43. C₂×C₁₃×#108	C₂²	semidirect
45. C₁₃×#362	C₂²	semidirect
46. C₁₃×#361	C₂²	semidirect
47. C₁₃×#359	C₂²	semidirect
48. C₁₃×#359	C₂²	semidirect
49. C₁₃×#350	C₂²	semidirect
50. C₁₃×#350	C₂²	semidirect
134. #33538	C₁₃	direct (N × H)
233. #3584	C₂×C₁₃	semidirect
234. #3414	C₂×C₁₃	semidirect
235. C₂×#508	C₂×C₁₃	semidirect
236. #3067	C₂×C₁₃	semidirect
237. #2195	C₂×C₁₃	semidirect
238. #2194	C₂×C₁₃	semidirect
239. #2193	C₂×C₁₃	semidirect
240. #2192	C₂×C₁₃	semidirect
241. #2148	C₂×C₁₃	semidirect
242. C₂×#359	C₂×C₁₃	semidirect
243. C₂×#350	C₂×C₁₃	semidirect
318. C₂×#135	C₂²×C₁₃	semidirect
321. #510	C₂²×C₁₃	semidirect
323. #509	C₂²×C₁₃	semidirect
327. C₂×Q₃₂	C₂²×C₁₃	semidirect
328. C₂×SD₃₂	C₂²×C₁₃	semidirect
329. C₂×SD₃₂	C₂²×C₁₃	semidirect
330. C₂×D₁₆	C₂²×C₁₃	semidirect
331. C₂×M₃₂	C₂²×C₁₃	semidirect
332. C₂²×C₁₆	C₂²×C₁₃	semidirect
333. #473	C₂²×C₁₃	semidirect
334. #472	C₂²×C₁₃	semidirect
336. C₂×#108	C₂²×C₁₃	semidirect
338. #362	C₂²×C₁₃	semidirect
339. #361	C₂²×C₁₃	semidirect
340. #359	C₂²×C₁₃	semidirect
341. #359	C₂²×C₁₃	semidirect
342. #350	C₂²×C₁₃	semidirect
343. #350	C₂²×C₁₃	semidirect
554. C₁₃	#33538	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×#3584	2
C₁₃×#3414	2
C₂×C₁₃×#508	2
C₁₃×#3067	2
C₁₃×#2195	2
C₁₃×#2194	2
C₁₃×#2193	2
C₁₃×#2192	2
C₁₃×#2148	2
C₂×C₁₃×#359	2
C₂×C₁₃×#350	2
#33538	13

Subgroups — C13×#33538 #15719877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33538 #15719877