Subgroups — C₁₃×#61370 #15747709

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3389	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3384	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3380	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3380	C₂	1	4	yes	maximal, complemented
6	Q₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3164	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3081	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2948	C₂	1	2	yes	maximal
13	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#554	—	2	2	no	—
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	4	yes	complemented
18	C₁₃×#554	C₂²	1	8	yes	complemented
19	D₄×Q₈×C₁₃	—	2	2	no	—
20	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
21	C₁₃×#544	C₂²	1	4	yes	—
22	C₁₃×#543	—	2	4	no	—
23	C₁₃×#533	C₂²	1	2	yes	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	—	2	4	no	—
26	C₁₃×#518	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#501	C₂²	1	8	yes	complemented
29	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#500	C₂²	1	4	yes	complemented
31	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#499	C₂²	1	2	yes	complemented
33	C₁₃×#499	C₂²	1	4	yes	complemented
34	C₁₃×#499	C₂²	1	2	yes	complemented
35	C₁₃×#498	C₂²	1	2	yes	complemented
36	C₁₃×#478	C₂²	1	8	yes	complemented
37	C₁₃×#478	C₂²	1	8	yes	complemented
38	C₁₃×#478	C₂²	1	8	yes	complemented
39	C₁₃×#476	C₂²	1	4	yes	complemented
40	C₁₃×#476	C₂²	1	8	yes	complemented
41	C₁₃×#474	C₂²	1	4	yes	complemented
42	C₁₃×#474	C₂²	1	8	yes	complemented
43	C₁₃×#446	C₂²	1	2	yes	complemented
44	C₁₃×#446	C₂²	1	2	yes	complemented
45	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
47	C₁₃×#442	C₂²	1	8	yes	—
48	C₄×C₁₃×D₈	C₂²	1	2	yes	—
49	C₄×C₁₃×D₈	C₂²	1	4	yes	—
50	C₄×C₁₃×D₈	C₂²	1	2	yes	—
51	C₄×C₁₃×D₈	C₂²	1	4	yes	—
52	C₄×C₁₃×D₈	C₂²	1	2	yes	—
53	C₄×C₁₃×D₈	C₂²	1	2	yes	—
54	C₁₃×#428	C₂²	1	4	yes	—
55	C₁₃×#427	C₂²	1	2	yes	—
56	C₁₃×#427	C₂²	1	2	yes	—
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₁₃×#424	C₂²	1	2	yes	—
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#418	C₂²	1	4	yes	—
61	C₂×C₁₃×#102	C₂²	1	2	yes	—
62	C₁₃×#405	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	—	2	4	no	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	—	2	2	no	—
67	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
68	C₂×C₁₃×D₈	C₂³	1	2	yes	—
69	C₂×C₁₃×D₈	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	—	2	4	no	—
74	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₃×#125	—	2	4	no	—
80	C₁₃×#125	D₄	1	2	yes	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#125	C₂³	1	8	yes	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	—	2	8	no	—
90	C₁₃×C₂²⋊Q₈	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₁₃×C₂²⋊Q₈	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
94	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	C₂³	1	4	yes	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	C₂³	1	8	yes	—
106	C₄×D₄×C₁₃	C₂³	1	8	yes	—
107	C₁₃×#117	C₂³	1	4	yes	—
108	C₁₃×#117	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#107	C₂³	1	2	yes	—
116	C₁₃×#107	C₂³	1	2	yes	—
117	C₁₃×#107	C₂³	1	2	yes	—
118	C₁₃×#107	C₂³	1	2	yes	—
119	C₁₃×#107	C₂³	1	2	yes	—
120	C₁₃×#107	C₂³	1	2	yes	—
121	C₁₃×#107	C₂³	1	8	yes	—
122	C₁₃×#106	C₂³	1	4	yes	—
123	C₁₃×#106	C₂³	1	4	yes	—
124	C₁₃×#106	C₂³	1	8	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
129	C₁₃×#102	C₂³	1	4	yes	—
130	C₁₃×#102	C₂³	1	4	yes	—
131	C₁₃×#102	C₂³	1	8	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×#97	C₂³	1	4	yes	—
134	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	4	yes	—
139	#61370	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	2	no	—
143	C₂×Q₈×C₁₃	—	2	8	no	—
144	C₂×Q₈×C₁₃	—	8	8	no	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	complemented
150	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	8	no	—
154	C₂²×C₄×C₁₃	—	2	8	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	8	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×D₈	C₂×Q₈	1	8	yes	complemented
161	C₁₃×D₈	C₂×Q₈	1	8	yes	complemented
162	C₁₃×M₁₆	—	2	4	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
165	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
193	C₄²×C₁₃	—	2	4	no	—
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₄²×C₁₃	C₂⁴	1	4	yes	—
199	#3501	C₂×C₁₃	1	2	yes	complemented
200	#3389	C₂×C₁₃	1	4	yes	complemented
201	#3384	C₂×C₁₃	1	4	yes	complemented
202	#3380	C₂×C₁₃	1	2	yes	complemented
203	#3380	C₂×C₁₃	1	4	yes	complemented
204	Q₈×D₈	C₂×C₁₃	1	2	yes	complemented
205	#3164	C₂×C₁₃	1	2	yes	complemented
206	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3081	C₂×C₁₃	1	4	yes	complemented
208	#3077	C₂×C₁₃	1	2	yes	complemented
209	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2948	C₂×C₁₃	1	2	yes	—
211	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	8	2	no	—
215	C₂³×C₁₃	—	8	2	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	4	2	no	—
219	Q₈×C₁₃	—	4	4	no	—
220	Q₈×C₁₃	—	8	2	no	—
221	Q₈×C₁₃	—	8	8	no	—
222	D₄×C₁₃	—	2	8	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	C₂²×Q₈	1	8	yes	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	8	no	—
231	C₂×C₄×C₁₃	—	8	8	no	—
232	C₂×C₄×C₁₃	—	8	4	no	—
233	C₂×C₄×C₁₃	—	8	8	no	—
234	C₂×C₄×C₁₃	—	8	2	no	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
243	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
245	C₈×C₁₃	—	2	1	no	—
246	C₈×C₁₃	—	2	1	no	—
247	C₈×C₁₃	—	2	4	no	—
248	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
249	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
250	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
251	#554	—	2	2	no	—
252	#554	—	2	4	no	—
253	#554	C₂²×C₁₃	1	4	yes	complemented
254	#554	C₂²×C₁₃	1	8	yes	complemented
255	D₄×Q₈	—	2	2	no	—
256	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
257	#544	C₂²×C₁₃	1	4	yes	—
258	#543	—	2	4	no	—
259	#533	C₂²×C₁₃	1	2	yes	—
260	#533	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊Q₈	—	2	4	no	—
262	#518	C₂²×C₁₃	1	4	yes	—
263	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
264	#501	C₂²×C₁₃	1	8	yes	complemented
265	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#500	C₂²×C₁₃	1	4	yes	complemented
267	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
268	#499	C₂²×C₁₃	1	2	yes	complemented
269	#499	C₂²×C₁₃	1	4	yes	complemented
270	#499	C₂²×C₁₃	1	2	yes	complemented
271	#498	C₂²×C₁₃	1	2	yes	complemented
272	#478	C₂²×C₁₃	1	8	yes	complemented
273	#478	C₂²×C₁₃	1	8	yes	complemented
274	#478	C₂²×C₁₃	1	8	yes	complemented
275	#476	C₂²×C₁₃	1	4	yes	complemented
276	#476	C₂²×C₁₃	1	8	yes	complemented
277	#474	C₂²×C₁₃	1	4	yes	complemented
278	#474	C₂²×C₁₃	1	8	yes	complemented
279	#446	C₂²×C₁₃	1	2	yes	complemented
280	#446	C₂²×C₁₃	1	2	yes	complemented
281	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
282	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
283	#442	C₂²×C₁₃	1	8	yes	—
284	C₄×D₈	C₂²×C₁₃	1	2	yes	—
285	C₄×D₈	C₂²×C₁₃	1	4	yes	—
286	C₄×D₈	C₂²×C₁₃	1	2	yes	—
287	C₄×D₈	C₂²×C₁₃	1	4	yes	—
288	C₄×D₈	C₂²×C₁₃	1	2	yes	—
289	C₄×D₈	C₂²×C₁₃	1	2	yes	—
290	#428	C₂²×C₁₃	1	4	yes	—
291	#427	C₂²×C₁₃	1	2	yes	—
292	#427	C₂²×C₁₃	1	2	yes	—
293	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
294	#424	C₂²×C₁₃	1	2	yes	—
295	#423	C₂²×C₁₃	1	1	yes	characteristic
296	#418	C₂²×C₁₃	1	4	yes	—
297	C₂×#102	C₂²×C₁₃	1	2	yes	—
298	#405	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	8	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	8	8	no	—
306	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
307	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	4	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	D₄×Q₈	1	2	yes	—
317	C₄×C₁₃	#576	1	2	yes	—
318	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
319	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂²×Q₈	—	2	4	no	—
321	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
322	C₂³×C₄	—	2	2	no	—
323	C₂×D₈	Q₈×C₁₃	1	8	yes	complemented
324	C₂×D₈	C₂³×C₁₃	1	2	yes	—
325	C₂×D₈	C₂³×C₁₃	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
331	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
333	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
335	#125	—	2	4	no	—
336	#125	D₄×C₁₃	1	2	yes	—
337	#125	C₂³×C₁₃	1	4	yes	—
338	#125	C₂³×C₁₃	1	8	yes	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	8	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	C₂²⋊Q₈	—	2	8	no	—
348	C₂²⋊Q₈	—	2	8	no	—
349	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
350	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
354	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	C₂³×C₁₃	1	4	yes	—
360	C₄×D₄	C₂³×C₁₃	1	4	yes	—
361	C₄×D₄	C₂³×C₁₃	1	8	yes	—
362	C₄×D₄	C₂³×C₁₃	1	8	yes	—
363	#117	C₂³×C₁₃	1	4	yes	—
364	#117	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	—	2	8	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	8	no	—
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	#107	C₂³×C₁₃	1	2	yes	—
372	#107	C₂³×C₁₃	1	2	yes	—
373	#107	C₂³×C₁₃	1	2	yes	—
374	#107	C₂³×C₁₃	1	2	yes	—
375	#107	C₂³×C₁₃	1	2	yes	—
376	#107	C₂³×C₁₃	1	2	yes	—
377	#107	C₂³×C₁₃	1	8	yes	—
378	#106	C₂³×C₁₃	1	4	yes	—
379	#106	C₂³×C₁₃	1	4	yes	—
380	#106	C₂³×C₁₃	1	8	yes	—
381	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
382	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
383	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
384	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
385	#102	C₂³×C₁₃	1	4	yes	—
386	#102	C₂³×C₁₃	1	4	yes	—
387	#102	C₂³×C₁₃	1	8	yes	—
388	#102	C₂³×C₁₃	1	8	yes	—
389	#97	C₂³×C₁₃	1	4	yes	—
390	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₁₃	1	4	yes	—
395	C₂×C₁₃	—	2	2	no	—
396	C₂×C₁₃	—	4	8	no	—
397	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
398	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
399	C₂×C₁₃	#3584	1	1	yes	characteristic
400	C₂⁴	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	8	no	—
404	C₂×Q₈	—	8	8	no	—
405	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
406	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	complemented
410	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	8	4	no	—
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	D₈	C₂×Q₈×C₁₃	1	8	yes	complemented
421	D₈	C₂×Q₈×C₁₃	1	8	yes	complemented
422	M₁₆	—	2	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
425	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
428	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
453	C₄²	—	2	4	no	—
454	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
457	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
458	C₄²	C₂⁴×C₁₃	1	4	yes	—
459	C₁₃	#61370	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	4	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	4	no	—
468	Q₈	—	8	8	no	—
469	Q₈	—	8	2	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	4	no	—
472	D₄	C₂²×Q₈×C₁₃	1	8	yes	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
491	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
492	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	4	no	—
496	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
497	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
505	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	D₄×Q₈×C₁₃	1	2	yes	—
515	C₄	C₁₃×#576	1	2	yes	—
516	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
517	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	4	8	no	—
520	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
521	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
522	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
2. C₁₃×#3389	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3380	C₂	semidirect
5. C₁₃×#3380	C₂	semidirect
6. Q₈×C₁₃×D₈	C₂	semidirect
7. C₁₃×#3164	C₂	semidirect
8. C₁₃×#3160	C₂	semidirect
9. C₁₃×#3081	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
17. C₁₃×#554	C₂²	semidirect
18. C₁₃×#554	C₂²	semidirect
20. D₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#501	C₂²	semidirect
29. C₁₃×#500	C₂²	semidirect
30. C₁₃×#500	C₂²	semidirect
31. C₁₃×#500	C₂²	semidirect
32. C₁₃×#499	C₂²	semidirect
33. C₁₃×#499	C₂²	semidirect
34. C₁₃×#499	C₂²	semidirect
35. C₁₃×#498	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#478	C₂²	semidirect
38. C₁₃×#478	C₂²	semidirect
39. C₁₃×#476	C₂²	semidirect
40. C₁₃×#476	C₂²	semidirect
41. C₁₃×#474	C₂²	semidirect
42. C₁₃×#474	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₁₃×#446	C₂²	semidirect
45. C₈×Q₈×C₁₃	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
67. C₂×C₁₃×D₈	Q₈	semidirect
139. #61370	C₁₃	direct (N × H)
149. C₂×D₄×C₁₃	C₂×Q₈	semidirect
160. C₁₃×D₈	C₂×Q₈	semidirect
161. C₁₃×D₈	C₂×Q₈	semidirect
164. C₂×C₈×C₁₃	C₂×Q₈	semidirect
199. #3501	C₂×C₁₃	semidirect
200. #3389	C₂×C₁₃	semidirect
201. #3384	C₂×C₁₃	semidirect
202. #3380	C₂×C₁₃	semidirect
203. #3380	C₂×C₁₃	semidirect
204. Q₈×D₈	C₂×C₁₃	semidirect
205. #3164	C₂×C₁₃	semidirect
206. #3160	C₂×C₁₃	semidirect
207. #3081	C₂×C₁₃	semidirect
208. #3077	C₂×C₁₃	semidirect
209. #2960	C₂×C₁₃	semidirect
253. #554	C₂²×C₁₃	semidirect
254. #554	C₂²×C₁₃	semidirect
256. D₄×Q₈	C₂²×C₁₃	semidirect
264. #501	C₂²×C₁₃	semidirect
265. #500	C₂²×C₁₃	semidirect
266. #500	C₂²×C₁₃	semidirect
267. #500	C₂²×C₁₃	semidirect
268. #499	C₂²×C₁₃	semidirect
269. #499	C₂²×C₁₃	semidirect
270. #499	C₂²×C₁₃	semidirect
271. #498	C₂²×C₁₃	semidirect
272. #478	C₂²×C₁₃	semidirect
273. #478	C₂²×C₁₃	semidirect
274. #478	C₂²×C₁₃	semidirect
275. #476	C₂²×C₁₃	semidirect
276. #476	C₂²×C₁₃	semidirect
277. #474	C₂²×C₁₃	semidirect
278. #474	C₂²×C₁₃	semidirect
279. #446	C₂²×C₁₃	semidirect
280. #446	C₂²×C₁₃	semidirect
281. C₈×Q₈	C₂²×C₁₃	semidirect
282. C₈×Q₈	C₂²×C₁₃	semidirect
323. C₂×D₈	Q₈×C₁₃	semidirect
409. C₂×D₄	C₂×Q₈×C₁₃	semidirect
420. D₈	C₂×Q₈×C₁₃	semidirect
421. D₈	C₂×Q₈×C₁₃	semidirect
424. C₂×C₈	C₂×Q₈×C₁₃	semidirect
459. C₁₃	#61370	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×#3501	2
C₁₃×#3389	2
C₁₃×#3384	2
C₁₃×#3380	2
Q₈×C₁₃×D₈	2
C₁₃×#3164	2
C₁₃×#3160	2
C₁₃×#3081	2
C₁₃×#3077	2
C₁₃×#2960	2
C₁₃×#2948	2
C₂×C₄×C₁₃×D₈	2
#61370	13

Subgroups — C13×#61370 #15747709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61370 #15747709