Subgroups — C₁₃×#33541 #15719880

Order 3328.

1104 conjugacy classes of subgroups.

The subgroup lattice has 600 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	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2193	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2192	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2148	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2143	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#585	—	2	1	no	—
11	C₁₃×#578	—	2	1	no	—
12	C₁₃×#578	C₂²	1	2	yes	complemented
13	C₁₃×#577	—	2	2	no	—
14	C₁₃×#577	—	2	2	no	—
15	C₁₃×#576	—	2	1	no	—
16	C₁₃×#576	C₂²	1	2	yes	complemented
17	C₁₃×#575	—	2	2	no	—
18	C₁₃×#575	—	2	1	no	—
19	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
20	C₂×C₁₃×#135	—	2	2	no	—
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
25	C₁₃×#509	—	2	2	no	—
26	C₁₃×#509	—	2	2	no	—
27	C₁₃×#509	—	2	2	no	—
28	C₁₃×#509	C₂²	1	4	yes	complemented
29	C₂×C₁₃×SD₃₂	—	2	1	no	—
30	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
31	C₂×C₁₃×D₁₆	—	2	1	no	—
32	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#472	—	2	2	no	—
36	C₁₃×#472	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#100	—	2	1	no	—
39	C₁₃×#362	C₂²	1	2	yes	complemented
40	C₁₃×#361	C₂²	1	2	yes	complemented
41	C₁₃×#359	C₂²	1	4	yes	complemented
42	C₁₃×#350	C₂²	1	4	yes	complemented
43	C₁₃×2₋¹⁺⁴	—	2	2	no	—
44	C₁₃×2₋¹⁺⁴	—	2	2	no	—
45	C₁₃×2₋¹⁺⁴	—	4	1	no	—
46	C₁₃×H(5,𝔽₂)	—	2	2	no	—
47	C₁₃×H(5,𝔽₂)	—	2	2	no	—
48	C₁₃×H(5,𝔽₂)	—	4	2	no	—
49	C₁₃×H(5,𝔽₂)	—	4	1	no	—
50	C₂×C₁₃×#41	—	2	4	no	—
51	C₂×C₁₃×#41	—	2	1	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂×C₁₃×#41	—	4	2	no	—
54	C₂×C₁₃×#41	—	4	2	no	—
55	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₁₃×#137	—	2	2	no	—
58	C₁₃×#137	—	2	4	no	—
59	C₁₃×#137	—	2	4	no	—
60	C₁₃×#137	—	2	2	no	—
61	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
62	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
63	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
65	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
66	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
67	C₁₃×#135	—	2	4	no	—
68	C₁₃×#135	—	2	4	no	—
69	C₁₃×#135	—	2	2	no	—
70	C₁₃×#135	—	2	2	no	—
71	C₁₃×#135	—	2	1	no	—
72	C₁₃×#135	—	2	1	no	—
73	C₁₃×#135	—	2	1	no	—
74	C₁₃×#135	—	2	1	no	—
75	C₁₃×#135	D₄	1	2	yes	—
76	C₁₃×#135	D₄	1	2	yes	—
77	C₁₃×#135	D₄	1	2	yes	—
78	C₁₃×#135	C₂³	1	2	yes	—
79	C₂×C₁₃×Q₁₆	—	2	2	no	—
80	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
81	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×SD₁₆	—	2	4	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	4	1	no	—
86	C₂×C₁₃×D₈	—	2	2	no	—
87	C₂×C₁₃×D₈	—	2	1	no	—
88	C₂×C₁₃×D₈	—	2	1	no	—
89	C₂×C₁₃×D₈	—	2	1	no	—
90	C₂×C₁₃×D₈	—	2	1	no	—
91	C₂×C₁₃×D₈	—	2	1	no	—
92	C₂×C₁₃×D₈	—	4	1	no	—
93	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
94	C₂×C₁₃×D₈	C₂³	1	2	yes	—
95	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
96	C₁₃×#131	—	2	1	no	—
97	C₁₃×#131	—	2	1	no	—
98	C₁₃×#131	D₄	1	2	yes	—
99	C₁₃×#131	C₂³	1	2	yes	—
100	C₂×C₁₃×M₁₆	—	2	1	no	—
101	C₂×C₁₃×M₁₆	—	2	1	no	—
102	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	—	2	1	no	—
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×SD₃₂	—	2	4	no	—
106	C₁₃×SD₃₂	—	2	4	no	—
107	C₁₃×D₁₆	—	2	4	no	—
108	C₁₃×D₁₆	—	2	4	no	—
109	C₁₃×M₃₂	—	2	1	no	—
110	C₁₃×M₃₂	—	2	1	no	—
111	C₁₃×M₃₂	—	2	1	no	—
112	C₁₃×M₃₂	C₂³	1	2	yes	—
113	C₂×C₁₃×C₁₆	—	2	1	no	—
114	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
115	C₁₃×#108	—	2	1	no	—
116	C₁₃×#108	C₂³	1	2	yes	—
117	C₁₃×#100	—	2	4	no	—
118	#33541	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	4	1	no	—
120	C₁₃×#41	—	2	1	no	—
121	C₁₃×#41	—	2	1	no	—
122	C₁₃×#41	—	2	4	no	—
123	C₁₃×#41	—	2	4	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	4	4	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	2	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	—	4	1	no	—
137	C₁₃×#41	—	4	1	no	—
138	C₁₃×#41	—	4	1	no	—
139	C₁₃×#41	—	4	1	no	—
140	C₁₃×#41	D₈	1	2	yes	—
141	C₁₃×#41	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	4	2	no	—
146	C₂×Q₈×C₁₃	—	4	2	no	—
147	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	4	4	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	2	no	—
156	C₂×D₄×C₁₃	—	4	4	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	—	4	2	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	—	4	1	no	—
163	C₂×D₄×C₁₃	—	4	1	no	—
164	C₂×D₄×C₁₃	—	4	1	no	—
165	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	4	4	no	—
168	C₂²×C₄×C₁₃	—	4	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₁₃×Q₁₆	—	2	4	no	—
172	C₁₃×Q₁₆	—	2	1	no	—
173	C₁₃×Q₁₆	—	2	1	no	—
174	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
175	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
176	C₁₃×SD₁₆	—	2	4	no	—
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×SD₁₆	—	2	2	no	—
179	C₁₃×SD₁₆	—	2	2	no	—
180	C₁₃×SD₁₆	—	2	2	no	—
181	C₁₃×SD₁₆	—	2	2	no	—
182	C₁₃×SD₁₆	—	4	4	no	—
183	C₁₃×D₈	—	2	4	no	—
184	C₁₃×D₈	—	2	1	no	—
185	C₁₃×D₈	—	2	1	no	—
186	C₁₃×D₈	—	2	2	no	—
187	C₁₃×D₈	—	2	2	no	—
188	C₁₃×D₈	—	4	4	no	—
189	C₁₃×D₈	—	4	1	no	—
190	C₁₃×D₈	—	4	1	no	—
191	C₁₃×D₈	C₂×D₄	1	2	yes	—
192	C₁₃×D₈	C₂×D₄	1	2	yes	—
193	C₁₃×M₁₆	—	2	1	no	—
194	C₁₃×M₁₆	—	2	2	no	—
195	C₁₃×M₁₆	—	2	2	no	—
196	C₁₃×M₁₆	—	2	2	no	—
197	C₁₃×M₁₆	—	4	1	no	—
198	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	2	no	—
201	C₂×C₈×C₁₃	—	2	2	no	—
202	C₂×C₈×C₁₃	—	4	1	no	—
203	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₁₃×C₁₆	—	2	2	no	—
210	C₁₃×C₁₆	—	2	2	no	—
211	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2193	C₂×C₁₃	1	4	yes	complemented
216	#2192	C₂×C₁₃	1	4	yes	complemented
217	#2148	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2143	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2117	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	1	no	—
223	C₂³×C₁₃	—	4	1	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	8	1	no	—
226	C₂³×C₁₃	—	8	1	no	—
227	C₂³×C₁₃	—	16	2	no	—
228	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	2	2	no	—
232	Q₈×C₁₃	—	4	4	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	C₂×D₈	1	2	yes	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	4	4	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	8	1	no	—
253	D₄×C₁₃	—	8	1	no	—
254	D₄×C₁₃	C₂×D₈	1	2	yes	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
271	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₁₃	—	2	2	no	—
274	C₈×C₁₃	—	4	2	no	—
275	C₈×C₁₃	#120	1	1	yes	characteristic
276	C₈×C₁₃	#120	1	1	yes	characteristic
277	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	#585	—	2	1	no	—
280	#578	—	2	1	no	—
281	#578	C₂²×C₁₃	1	2	yes	complemented
282	#577	—	2	2	no	—
283	#577	—	2	2	no	—
284	#576	—	2	1	no	—
285	#576	C₂²×C₁₃	1	2	yes	complemented
286	#575	—	2	2	no	—
287	#575	—	2	1	no	—
288	C₂×AGL(1,ℤ/8)	—	2	1	no	—
289	C₂×#135	—	2	2	no	—
290	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
294	#509	—	2	2	no	—
295	#509	—	2	2	no	—
296	#509	—	2	2	no	—
297	#509	C₂²×C₁₃	1	4	yes	complemented
298	C₂×SD₃₂	—	2	1	no	—
299	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
300	C₂×D₁₆	—	2	1	no	—
301	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
302	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	#472	—	2	2	no	—
305	#472	C₂²×C₁₃	1	4	yes	complemented
306	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#100	—	2	1	no	—
308	#362	C₂²×C₁₃	1	2	yes	complemented
309	#361	C₂²×C₁₃	1	2	yes	complemented
310	#359	C₂²×C₁₃	1	4	yes	complemented
311	#350	C₂²×C₁₃	1	4	yes	complemented
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	4	1	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	8	1	no	—
317	C₂²×C₁₃	—	8	2	no	—
318	C₂²×C₁₃	—	16	1	no	—
319	C₂²×C₁₃	—	16	1	no	—
320	C₂²×C₁₃	—	16	2	no	—
321	C₂²×C₁₃	—	16	2	no	—
322	C₂²×C₁₃	—	16	2	no	—
323	C₂²×C₁₃	—	16	4	no	—
324	C₂²×C₁₃	#447	1	1	yes	characteristic
325	C₂²×C₁₃	#447	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	4	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	#447	1	1	yes	characteristic
331	C₄×C₁₃	#447	1	1	yes	characteristic
332	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
333	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
334	2₋¹⁺⁴	—	2	2	no	—
335	2₋¹⁺⁴	—	2	2	no	—
336	2₋¹⁺⁴	—	4	1	no	—
337	H(5,𝔽₂)	—	2	2	no	—
338	H(5,𝔽₂)	—	2	2	no	—
339	H(5,𝔽₂)	—	4	2	no	—
340	H(5,𝔽₂)	—	4	1	no	—
341	C₂×#41	—	2	4	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	4	2	no	—
345	C₂×#41	—	4	2	no	—
346	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
347	C₂²×D₄	—	2	1	no	—
348	#137	—	2	2	no	—
349	#137	—	2	4	no	—
350	#137	—	2	4	no	—
351	#137	—	2	2	no	—
352	AGL(1,ℤ/8)	—	2	2	no	—
353	AGL(1,ℤ/8)	—	2	4	no	—
354	AGL(1,ℤ/8)	—	2	4	no	—
355	AGL(1,ℤ/8)	—	2	4	no	—
356	AGL(1,ℤ/8)	—	2	2	no	—
357	AGL(1,ℤ/8)	—	4	2	no	—
358	#135	—	2	4	no	—
359	#135	—	2	4	no	—
360	#135	—	2	2	no	—
361	#135	—	2	2	no	—
362	#135	—	2	1	no	—
363	#135	—	2	1	no	—
364	#135	—	2	1	no	—
365	#135	—	2	1	no	—
366	#135	D₄×C₁₃	1	2	yes	—
367	#135	D₄×C₁₃	1	2	yes	—
368	#135	D₄×C₁₃	1	2	yes	—
369	#135	C₂³×C₁₃	1	2	yes	—
370	C₂×Q₁₆	—	2	2	no	—
371	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
372	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×SD₁₆	—	2	4	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	4	1	no	—
377	C₂×D₈	—	2	2	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	1	no	—
381	C₂×D₈	—	2	1	no	—
382	C₂×D₈	—	2	1	no	—
383	C₂×D₈	—	4	1	no	—
384	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
385	C₂×D₈	C₂³×C₁₃	1	2	yes	—
386	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
387	#131	—	2	1	no	—
388	#131	—	2	1	no	—
389	#131	D₄×C₁₃	1	2	yes	—
390	#131	C₂³×C₁₃	1	2	yes	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	SD₃₂	—	2	4	no	—
397	SD₃₂	—	2	4	no	—
398	D₁₆	—	2	4	no	—
399	D₁₆	—	2	4	no	—
400	M₃₂	—	2	1	no	—
401	M₃₂	—	2	1	no	—
402	M₃₂	—	2	1	no	—
403	M₃₂	C₂³×C₁₃	1	2	yes	—
404	C₂×C₁₆	—	2	1	no	—
405	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
406	#108	—	2	1	no	—
407	#108	C₂³×C₁₃	1	2	yes	—
408	#100	—	2	4	no	—
409	C₂×C₁₃	—	2	1	no	—
410	C₂×C₁₃	—	2	1	no	—
411	C₂×C₁₃	—	2	1	no	—
412	C₂×C₁₃	—	4	2	no	—
413	C₂×C₁₃	—	8	2	no	—
414	C₂×C₁₃	—	8	2	no	—
415	C₂×C₁₃	—	16	2	no	—
416	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
417	C₂⁴	—	4	1	no	—
418	#41	—	2	1	no	—
419	#41	—	2	1	no	—
420	#41	—	2	4	no	—
421	#41	—	2	4	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	4	4	no	—
427	#41	—	4	4	no	—
428	#41	—	4	4	no	—
429	#41	—	4	4	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	C₁₃×D₈	1	2	yes	—
439	#41	C₂×D₄×C₁₃	1	2	yes	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	—	4	2	no	—
445	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	Q₁₆	—	2	4	no	—
470	Q₁₆	—	2	1	no	—
471	Q₁₆	—	2	1	no	—
472	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
473	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
474	SD₁₆	—	2	4	no	—
475	SD₁₆	—	2	4	no	—
476	SD₁₆	—	2	2	no	—
477	SD₁₆	—	2	2	no	—
478	SD₁₆	—	2	2	no	—
479	SD₁₆	—	2	2	no	—
480	SD₁₆	—	4	4	no	—
481	D₈	—	2	4	no	—
482	D₈	—	2	1	no	—
483	D₈	—	2	1	no	—
484	D₈	—	2	2	no	—
485	D₈	—	2	2	no	—
486	D₈	—	4	4	no	—
487	D₈	—	4	1	no	—
488	D₈	—	4	1	no	—
489	D₈	C₂×D₄×C₁₃	1	2	yes	—
490	D₈	C₂×D₄×C₁₃	1	2	yes	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
507	C₁₆	—	2	2	no	—
508	C₁₆	—	2	2	no	—
509	C₁₃	#33541	1	1	yes	characteristic, direct product factor, Sylow
510	C₂³	—	2	1	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	8	1	no	—
516	C₂³	—	8	1	no	—
517	C₂³	—	16	2	no	—
518	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
519	Q₈	—	2	1	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	4	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	C₂×C₁₃×D₈	1	2	yes	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	1	no	—
544	D₄	C₂×C₁₃×D₈	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
558	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
559	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
560	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
561	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₈	—	2	2	no	—
564	C₈	—	4	2	no	—
565	C₈	C₁₃×#120	1	1	yes	characteristic
566	C₈	C₁₃×#120	1	1	yes	characteristic
567	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₂²	—	2	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	16	1	no	—
576	C₂²	—	16	1	no	—
577	C₂²	—	16	2	no	—
578	C₂²	—	16	2	no	—
579	C₂²	—	16	2	no	—
580	C₂²	—	16	4	no	—
581	C₂²	C₁₃×#447	1	1	yes	characteristic
582	C₂²	C₁₃×#447	1	1	yes	characteristic
583	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	C₁₃×#447	1	1	yes	characteristic
588	C₄	C₁₃×#447	1	1	yes	characteristic
589	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
590	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	4	2	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	2	no	—
597	C₂	—	16	2	no	—
598	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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. C₂×C₁₃×#509	C₂	semidirect
3. C₂×C₁₃×#509	C₂	semidirect
4. C₂×C₁₃×#472	C₂	semidirect
5. C₁₃×#2193	C₂	semidirect
6. C₁₃×#2192	C₂	semidirect
7. C₁₃×#2148	C₂	semidirect
8. C₁₃×#2143	C₂	semidirect
9. C₁₃×#2117	C₂	semidirect
12. C₁₃×#578	C₂²	semidirect
16. C₁₃×#576	C₂²	semidirect
23. C₂²×C₁₃×D₈	C₂²	semidirect
28. C₁₃×#509	C₂²	semidirect
30. C₂×C₁₃×SD₃₂	C₂²	semidirect
32. C₂×C₁₃×D₁₆	C₂²	semidirect
33. C₂×C₁₃×M₃₂	C₂²	semidirect
34. C₂×C₁₃×M₃₂	C₂²	semidirect
36. C₁₃×#472	C₂²	semidirect
37. C₂×C₁₃×#108	C₂²	semidirect
39. C₁₃×#362	C₂²	semidirect
40. C₁₃×#361	C₂²	semidirect
41. C₁₃×#359	C₂²	semidirect
42. C₁₃×#350	C₂²	semidirect
118. #33541	C₁₃	direct (N × H)
211. #3584	C₂×C₁₃	semidirect
212. C₂×#509	C₂×C₁₃	semidirect
213. C₂×#509	C₂×C₁₃	semidirect
214. C₂×#472	C₂×C₁₃	semidirect
215. #2193	C₂×C₁₃	semidirect
216. #2192	C₂×C₁₃	semidirect
217. #2148	C₂×C₁₃	semidirect
218. #2143	C₂×C₁₃	semidirect
219. #2117	C₂×C₁₃	semidirect
281. #578	C₂²×C₁₃	semidirect
285. #576	C₂²×C₁₃	semidirect
292. C₂²×D₈	C₂²×C₁₃	semidirect
297. #509	C₂²×C₁₃	semidirect
299. C₂×SD₃₂	C₂²×C₁₃	semidirect
301. C₂×D₁₆	C₂²×C₁₃	semidirect
302. C₂×M₃₂	C₂²×C₁₃	semidirect
303. C₂×M₃₂	C₂²×C₁₃	semidirect
305. #472	C₂²×C₁₃	semidirect
306. C₂×#108	C₂²×C₁₃	semidirect
308. #362	C₂²×C₁₃	semidirect
309. #361	C₂²×C₁₃	semidirect
310. #359	C₂²×C₁₃	semidirect
311. #350	C₂²×C₁₃	semidirect
509. C₁₃	#33541	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
C₂×C₁₃×#509	2
C₂×C₁₃×#472	2
C₁₃×#2193	2
C₁₃×#2192	2
C₁₃×#2148	2
C₁₃×#2143	2
C₁₃×#2117	2
#33541	13

Subgroups — C13×#33541 #15719880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33541 #15719880