Subgroups — C₁₃×#24410 #15710749

Order 3328.

1322 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2884	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2053	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2008	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1910	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1905	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1868	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1794	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
14	C₁₃×#578	—	2	4	no	—
15	C₁₃×#577	—	2	4	no	—
16	C₁₃×#575	—	2	2	no	—
17	C₁₃×#575	C₂²	1	2	yes	—
18	C₂×C₁₃×#137	—	2	2	no	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#568	C₂²	1	1	yes	characteristic
23	C₁₃×#535	C₂²	1	1	yes	characteristic
24	C₁₃×#535	C₂²	1	2	yes	—
25	C₁₃×#519	C₂²	1	2	yes	complemented
26	C₁₃×#464	—	2	4	no	—
27	C₁₃×#460	—	2	4	no	—
28	C₁₃×B(4,𝔽₂)	—	2	4	no	—
29	C₁₃×#449	—	2	2	no	—
30	C₁₃×#448	—	2	2	no	—
31	C₁₃×#424	C₂²	1	2	yes	complemented
32	C₁₃×#421	C₂²	1	2	yes	—
33	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#418	C₂²	1	2	yes	complemented
35	C₁₃×#416	C₂²	1	2	yes	—
36	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#410	—	2	4	no	—
38	C₁₃×#410	C₂²	1	2	yes	—
39	C₁₃×#410	C₂²	1	1	yes	characteristic
40	C₁₃×#410	C₂²	1	1	yes	characteristic
41	C₁₃×#410	C₂²	1	2	yes	complemented
42	C₁₃×#408	C₂²	1	1	yes	characteristic
43	C₁₃×#344	C₂²	1	2	yes	complemented
44	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	C₁₃×2₋¹⁺⁴	—	2	4	no	—
46	C₁₃×2₋¹⁺⁴	—	2	2	no	—
47	C₁₃×2₋¹⁺⁴	—	2	1	no	—
48	C₁₃×2₋¹⁺⁴	—	4	2	no	—
49	C₁₃×H(5,𝔽₂)	—	2	2	no	—
50	C₁₃×H(5,𝔽₂)	—	2	2	no	—
51	C₁₃×H(5,𝔽₂)	—	2	1	no	—
52	C₂×C₁₃×#41	—	2	2	no	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	4	2	no	—
56	C₂×C₁₃×#41	D₄	1	2	yes	complemented
57	C₂×C₁₃×#41	C₂³	1	2	yes	—
58	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	—	2	1	no	—
61	C₂²×Q₈×C₁₃	D₄	1	2	yes	complemented
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#137	—	2	8	no	—
65	C₁₃×#137	—	2	4	no	—
66	C₁₃×#137	—	2	2	no	—
67	C₁₃×#137	—	2	4	no	—
68	C₁₃×#137	—	2	4	no	—
69	C₁₃×#137	—	2	2	no	—
70	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
73	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
74	C₁₃×#135	—	2	8	no	—
75	C₁₃×#135	—	2	4	no	—
76	C₂×C₁₃×Q₁₆	—	2	4	no	—
77	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
78	C₂×C₁₃×SD₁₆	—	2	4	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	4	no	—
82	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
83	C₂×C₁₃×D₈	—	2	1	no	—
84	C₁₃×#131	—	2	4	no	—
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#127	—	2	2	no	—
90	C₁₃×#127	—	2	1	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	1	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	—	4	2	no	—
95	C₁₃×#120	—	2	2	no	—
96	C₁₃×#120	—	2	4	no	—
97	C₄×Q₈×C₁₃	—	2	4	no	—
98	C₄×Q₈×C₁₃	—	4	2	no	—
99	C₁₃×#117	—	2	4	no	—
100	C₁₃×#117	C₂³	1	1	yes	characteristic
101	C₁₃×#117	C₂³	1	2	yes	—
102	C₁₃×#117	C₂³	1	2	yes	—
103	C₁₃×C₄⋊C₈	—	2	4	no	—
104	C₁₃×#104	—	4	2	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#103	—	2	1	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	1	no	—
110	C₁₃×#102	—	2	4	no	—
111	C₁₃×#99	—	2	2	no	—
112	C₁₃×#99	—	2	4	no	—
113	C₁₃×#99	—	2	4	no	—
114	C₁₃×#99	D₄	1	4	yes	—
115	C₁₃×C₂²⋊C₈	—	2	2	no	—
116	#24410	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	1	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	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	2	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	2	no	—
132	C₁₃×#41	—	4	4	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
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	—	4	4	no	—
143	C₂×Q₈×C₁₃	—	4	2	no	—
144	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	4	4	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	—	4	4	no	—
160	C₂×D₄×C₁₃	—	4	2	no	—
161	C₂×D₄×C₁₃	—	4	2	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×Q₁₆	—	2	4	no	—
175	C₁₃×Q₁₆	—	2	8	no	—
176	C₁₃×SD₁₆	—	2	4	no	—
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×SD₁₆	—	2	8	no	—
179	C₁₃×SD₁₆	—	4	2	no	—
180	C₁₃×SD₁₆	—	4	4	no	—
181	C₁₃×D₈	—	2	4	no	—
182	C₁₃×D₈	—	4	2	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	C₂×C₈×C₁₃	—	2	4	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	2	no	—
191	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	4	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	4	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
201	C₄²×C₁₃	—	2	2	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	2	no	—
204	C₄²×C₁₃	—	4	4	no	—
205	#3586	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3043	C₂×C₁₃	1	2	yes	complemented
207	#3027	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3010	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2884	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2053	C₂×C₁₃	1	2	yes	complemented
211	#2008	C₂×C₁₃	1	2	yes	complemented
212	#1910	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1905	C₂×C₁₃	1	2	yes	complemented
214	#1868	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1794	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	16	1	no	—
222	C₂³×C₁₃	#121	1	2	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	2	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	4	4	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	#120	1	4	yes	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	16	4	no	—
250	D₄×C₁₃	—	16	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	4	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	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	#121	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
272	C₈×C₁₃	—	2	4	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	#585	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
277	#578	—	2	4	no	—
278	#577	—	2	4	no	—
279	#575	—	2	2	no	—
280	#575	C₂²×C₁₃	1	2	yes	—
281	C₂×#137	—	2	2	no	—
282	C₂×#137	C₂²×C₁₃	1	2	yes	—
283	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
284	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
285	#568	C₂²×C₁₃	1	1	yes	characteristic
286	#535	C₂²×C₁₃	1	1	yes	characteristic
287	#535	C₂²×C₁₃	1	2	yes	—
288	#519	C₂²×C₁₃	1	2	yes	complemented
289	#464	—	2	4	no	—
290	#460	—	2	4	no	—
291	B(4,𝔽₂)	—	2	4	no	—
292	#449	—	2	2	no	—
293	#448	—	2	2	no	—
294	#424	C₂²×C₁₃	1	2	yes	complemented
295	#421	C₂²×C₁₃	1	2	yes	—
296	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	#418	C₂²×C₁₃	1	2	yes	complemented
298	#416	C₂²×C₁₃	1	2	yes	—
299	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	#410	—	2	4	no	—
301	#410	C₂²×C₁₃	1	1	yes	characteristic
302	#410	C₂²×C₁₃	1	2	yes	—
303	#410	C₂²×C₁₃	1	1	yes	characteristic
304	#410	C₂²×C₁₃	1	2	yes	complemented
305	#408	C₂²×C₁₃	1	1	yes	characteristic
306	#344	C₂²×C₁₃	1	2	yes	complemented
307	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	complemented
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	1	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	8	2	no	—
314	C₂²×C₁₃	—	8	1	no	—
315	C₂²×C₁₃	—	8	4	no	—
316	C₂²×C₁₃	—	8	2	no	—
317	C₂²×C₁₃	—	8	1	no	—
318	C₂²×C₁₃	—	16	2	no	—
319	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
320	C₂²×C₁₃	D₄²	1	2	yes	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	1	no	—
326	C₄×C₁₃	—	8	2	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
329	C₄×C₁₃	#534	1	1	yes	characteristic
330	C₄×C₁₃	#546	1	2	yes	—
331	2₋¹⁺⁴	—	2	4	no	—
332	2₋¹⁺⁴	—	2	2	no	—
333	2₋¹⁺⁴	—	2	1	no	—
334	2₋¹⁺⁴	—	4	2	no	—
335	H(5,𝔽₂)	—	2	2	no	—
336	H(5,𝔽₂)	—	2	2	no	—
337	H(5,𝔽₂)	—	2	1	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	4	2	no	—
342	C₂×#41	D₄×C₁₃	1	2	yes	complemented
343	C₂×#41	C₂³×C₁₃	1	2	yes	—
344	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	D₄×C₁₃	1	2	yes	complemented
348	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
350	#137	—	2	8	no	—
351	#137	—	2	4	no	—
352	#137	—	2	2	no	—
353	#137	—	2	4	no	—
354	#137	—	2	4	no	—
355	#137	—	2	2	no	—
356	AGL(1,ℤ/8)	—	2	4	no	—
357	AGL(1,ℤ/8)	—	2	2	no	—
358	AGL(1,ℤ/8)	—	2	2	no	—
359	AGL(1,ℤ/8)	—	4	2	no	—
360	#135	—	2	8	no	—
361	#135	—	2	4	no	—
362	C₂×Q₁₆	—	2	4	no	—
363	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	2	no	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
369	C₂×D₈	—	2	1	no	—
370	#131	—	2	4	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
374	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
375	#127	—	2	2	no	—
376	#127	—	2	1	no	—
377	#124	—	2	2	no	—
378	#124	—	2	1	no	—
379	#121	—	2	2	no	—
380	#121	—	4	2	no	—
381	#120	—	2	2	no	—
382	#120	—	2	4	no	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×Q₈	—	4	2	no	—
385	#117	—	2	4	no	—
386	#117	C₂³×C₁₃	1	2	yes	—
387	#117	C₂³×C₁₃	1	1	yes	characteristic
388	#117	C₂³×C₁₃	1	2	yes	—
389	C₄⋊C₈	—	2	4	no	—
390	#104	—	4	2	no	—
391	#103	—	2	2	no	—
392	#103	—	2	1	no	—
393	#103	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	1	no	—
396	#102	—	2	4	no	—
397	#99	—	2	2	no	—
398	#99	—	2	4	no	—
399	#99	—	2	4	no	—
400	#99	D₄×C₁₃	1	4	yes	—
401	C₂²⋊C₈	—	2	2	no	—
402	C₂×C₁₃	—	2	2	no	—
403	C₂×C₁₃	—	2	1	no	—
404	C₂×C₁₃	—	4	2	no	—
405	C₂×C₁₃	—	8	1	no	—
406	C₂×C₁₃	—	8	2	no	—
407	C₂×C₁₃	—	16	1	no	—
408	C₂×C₁₃	#2410	1	1	yes	characteristic
409	C₂⁴	—	2	1	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	4	2	no	—
421	#41	—	4	8	no	—
422	#41	—	4	4	no	—
423	#41	—	4	2	no	—
424	#41	—	4	4	no	—
425	#41	—	4	2	no	—
426	#41	—	4	2	no	—
427	#41	—	4	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×Q₈	—	4	4	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
437	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
439	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
440	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
456	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
466	Q₁₆	—	2	4	no	—
467	Q₁₆	—	2	8	no	—
468	SD₁₆	—	2	4	no	—
469	SD₁₆	—	2	4	no	—
470	SD₁₆	—	2	8	no	—
471	SD₁₆	—	4	2	no	—
472	SD₁₆	—	4	4	no	—
473	D₈	—	2	4	no	—
474	D₈	—	4	2	no	—
475	M₁₆	—	2	4	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	C₂×C₈	—	2	4	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	4	4	no	—
497	C₁₃	#24410	1	1	yes	characteristic, direct product factor, Sylow
498	C₂³	—	2	1	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	16	1	no	—
504	C₂³	C₁₃×#121	1	2	yes	—
505	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	4	4	no	—
514	Q₈	—	4	2	no	—
515	Q₈	C₁₃×#120	1	4	yes	—
516	D₄	—	2	4	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	4	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	16	4	no	—
532	D₄	—	16	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	C₁₃×#121	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
553	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
554	C₈	—	2	4	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	16	2	no	—
568	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
569	C₂²	D₄²×C₁₃	1	2	yes	—
570	C₄	—	2	4	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	2	no	—
576	C₄	—	8	1	no	—
577	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
578	C₄	C₁₃×#534	1	1	yes	characteristic
579	C₄	C₁₃×#546	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	2	1	no	—
582	C₂	—	4	2	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	1	no	—
585	C₂	—	16	1	no	—
586	C₂	C₁₃×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3586	C₂	semidirect
2. C₁₃×#3043	C₂	semidirect
3. C₁₃×#3027	C₂	semidirect
4. C₁₃×#3010	C₂	semidirect
5. C₁₃×#2884	C₂	semidirect
6. C₁₃×#2053	C₂	semidirect
7. C₁₃×#2008	C₂	semidirect
8. C₁₃×#1910	C₂	semidirect
9. C₁₃×#1905	C₂	semidirect
10. C₁₃×#1868	C₂	semidirect
11. C₁₃×#1794	C₂	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×C₁₃×SD₁₆	C₂²	semidirect
25. C₁₃×#519	C₂²	semidirect
31. C₁₃×#424	C₂²	semidirect
33. C₁₃×#419	C₂²	semidirect
34. C₁₃×#418	C₂²	semidirect
36. C₁₃×#416	C₂²	semidirect
41. C₁₃×#410	C₂²	semidirect
43. C₁₃×#344	C₂²	semidirect
44. C₁₃×H(3,ℤ/4)	C₂²	semidirect
56. C₂×C₁₃×#41	D₄	semidirect
61. C₂²×Q₈×C₁₃	D₄	semidirect
77. C₂×C₁₃×Q₁₆	D₄	semidirect
82. C₂×C₁₃×SD₁₆	D₄	semidirect
116. #24410	C₁₃	direct (N × H)
205. #3586	C₂×C₁₃	semidirect
206. #3043	C₂×C₁₃	semidirect
207. #3027	C₂×C₁₃	semidirect
208. #3010	C₂×C₁₃	semidirect
209. #2884	C₂×C₁₃	semidirect
210. #2053	C₂×C₁₃	semidirect
211. #2008	C₂×C₁₃	semidirect
212. #1910	C₂×C₁₃	semidirect
213. #1905	C₂×C₁₃	semidirect
214. #1868	C₂×C₁₃	semidirect
215. #1794	C₂×C₁₃	semidirect
283. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
284. C₂²×SD₁₆	C₂²×C₁₃	semidirect
288. #519	C₂²×C₁₃	semidirect
294. #424	C₂²×C₁₃	semidirect
296. #419	C₂²×C₁₃	semidirect
297. #418	C₂²×C₁₃	semidirect
299. #416	C₂²×C₁₃	semidirect
304. #410	C₂²×C₁₃	semidirect
306. #344	C₂²×C₁₃	semidirect
307. H(3,ℤ/4)	C₂²×C₁₃	semidirect
342. C₂×#41	D₄×C₁₃	semidirect
347. C₂²×Q₈	D₄×C₁₃	semidirect
363. C₂×Q₁₆	D₄×C₁₃	semidirect
368. C₂×SD₁₆	D₄×C₁₃	semidirect
497. C₁₃	#24410	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×#3586	2
C₁₃×#3043	2
C₁₃×#3027	2
C₁₃×#3010	2
C₁₃×#2884	2
C₁₃×#2053	2
C₁₃×#2008	2
C₁₃×#1910	2
C₁₃×#1905	2
C₁₃×#1868	2
C₁₃×#1794	2
#24410	13

Subgroups — C13×#24410 #15710749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24410 #15710749