Subgroups — C₁₃×#60944 #15747283

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3250	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3191	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3167	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3102	C₂	1	8	yes	maximal, complemented
12	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#529	—	2	2	no	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	—	2	2	no	—
23	C₁₃×#529	C₂²	1	4	yes	—
24	C₁₃×#529	C₂²	1	4	yes	—
25	C₁₃×#525	—	2	2	no	—
26	C₁₃×#525	—	2	2	no	—
27	C₁₃×#525	C₂²	1	4	yes	—
28	C₄×C₁₃×#41	—	2	2	no	—
29	C₄×C₁₃×#41	—	2	2	no	—
30	C₄×C₁₃×#41	C₂²	1	4	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#498	C₂²	1	2	yes	complemented
35	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#492	C₂²	1	2	yes	complemented
38	C₁₃×#487	C₂²	1	2	yes	complemented
39	C₁₃×#487	C₂²	1	2	yes	complemented
40	C₁₃×#486	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#485	C₂²	1	8	yes	—
43	C₁₃×#482	C₂²	1	8	yes	—
44	C₁₃×#479	C₂²	1	8	yes	complemented
45	C₁₃×#478	C₂²	1	8	yes	complemented
46	C₁₃×#467	C₂²	1	4	yes	—
47	C₁₃×#466	C₂²	1	4	yes	—
48	C₁₃×#465	C₂²	1	8	yes	—
49	C₁₃×#464	C₂²	1	8	yes	complemented
50	C₁₃×#463	C₂²	1	8	yes	complemented
51	C₁₃×#452	C₂²	1	8	yes	—
52	C₁₃×#449	C₂²	1	8	yes	—
53	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
54	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
55	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
56	C₁₃×#431	C₂²	1	4	yes	—
57	C₁₃×#431	C₂²	1	2	yes	—
58	C₁₃×#431	C₂²	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
61	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×D₈	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₃×#127	C₂³	1	2	yes	—
78	C₁₃×#126	—	2	4	no	—
79	C₁₃×#126	—	2	4	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	—	2	2	no	—
82	C₁₃×#125	C₂³	1	4	yes	—
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	—	2	2	no	—
85	C₁₃×#124	C₂³	1	4	yes	—
86	C₁₃×#123	—	2	4	no	—
87	C₁₃×#123	—	2	4	no	—
88	C₁₃×#123	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	—	2	2	no	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	2	no	—
99	C₁₃×#121	C₂³	1	4	yes	—
100	C₁₃×#121	C₂³	1	4	yes	—
101	C₁₃×#120	—	2	4	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	—	2	2	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	C₂³	1	4	yes	—
119	C₄×D₄×C₁₃	C₂³	1	4	yes	—
120	C₁₃×#117	—	2	2	no	—
121	C₁₃×#117	—	2	2	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	—	2	4	no	—
125	C₁₃×#117	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	—	2	4	no	—
127	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	D₄	1	2	yes	—
129	C₂×C₄²×C₁₃	D₄	1	2	yes	—
130	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₁₃×#107	C₂³	1	4	yes	—
136	C₁₃×#107	C₂³	1	4	yes	—
137	C₁₃×#106	C₂³	1	8	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
140	C₁₃×#103	C₂³	1	8	yes	—
141	C₁₃×#103	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	8	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
146	C₄×C₈×C₁₃	C₂³	1	2	yes	—
147	C₄×C₈×C₁₃	C₂³	1	2	yes	—
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×C₈×C₁₃	C₂³	1	2	yes	—
150	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
151	#60944	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₁₃×#41	—	4	8	no	—
154	C₁₃×#41	—	4	8	no	—
155	C₁₃×#41	—	4	8	no	—
156	C₂×Q₈×C₁₃	—	2	2	no	—
157	C₂×Q₈×C₁₃	—	2	2	no	—
158	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×Q₁₆	—	4	4	no	—
184	C₁₃×SD₁₆	—	4	8	no	—
185	C₁₃×D₈	—	4	4	no	—
186	C₂×C₈×C₁₃	—	4	2	no	—
187	C₂×C₈×C₁₃	—	4	2	no	—
188	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
189	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
190	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₃	C₂×D₄	1	2	yes	—
221	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
225	#3444	C₂×C₁₃	1	2	yes	complemented
226	#3250	C₂×C₁₃	1	4	yes	complemented
227	#3231	C₂×C₁₃	1	2	yes	complemented
228	#3228	C₂×C₁₃	1	2	yes	complemented
229	#3210	C₂×C₁₃	1	2	yes	complemented
230	#3207	C₂×C₁₃	1	2	yes	complemented
231	#3191	C₂×C₁₃	1	4	yes	complemented
232	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3167	C₂×C₁₃	1	2	yes	complemented
235	#3102	C₂×C₁₃	1	8	yes	complemented
236	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	4	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₃	—	2	8	no	—
244	Q₈×C₁₃	—	4	4	no	—
245	Q₈×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	2	8	no	—
247	D₄×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	8	no	—
250	D₄×C₁₃	—	4	4	no	—
251	D₄×C₁₃	—	4	4	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	8	no	—
267	C₂×C₄×C₁₃	—	4	8	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	#135	1	4	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	—	2	4	no	—
281	C₈×C₁₃	—	2	2	no	—
282	#533	C₂²×C₁₃	1	2	yes	—
283	#533	C₂²×C₁₃	1	2	yes	—
284	#533	C₂²×C₁₃	1	2	yes	—
285	#532	C₂²×C₁₃	1	2	yes	—
286	#532	C₂²×C₁₃	1	2	yes	—
287	#532	C₂²×C₁₃	1	2	yes	—
288	#529	—	2	2	no	—
289	#529	—	2	2	no	—
290	#529	—	2	2	no	—
291	#529	—	2	2	no	—
292	#529	C₂²×C₁₃	1	4	yes	—
293	#529	C₂²×C₁₃	1	4	yes	—
294	#525	—	2	2	no	—
295	#525	—	2	2	no	—
296	#525	C₂²×C₁₃	1	4	yes	—
297	C₄×#41	—	2	2	no	—
298	C₄×#41	—	2	2	no	—
299	C₄×#41	C₂²×C₁₃	1	4	yes	—
300	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
301	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	#498	C₂²×C₁₃	1	2	yes	complemented
304	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	#492	C₂²×C₁₃	1	2	yes	complemented
307	#487	C₂²×C₁₃	1	2	yes	complemented
308	#487	C₂²×C₁₃	1	2	yes	complemented
309	#486	C₂²×C₁₃	1	2	yes	complemented
310	#486	C₂²×C₁₃	1	2	yes	complemented
311	#485	C₂²×C₁₃	1	8	yes	—
312	#482	C₂²×C₁₃	1	8	yes	—
313	#479	C₂²×C₁₃	1	8	yes	complemented
314	#478	C₂²×C₁₃	1	8	yes	complemented
315	#467	C₂²×C₁₃	1	4	yes	—
316	#466	C₂²×C₁₃	1	4	yes	—
317	#465	C₂²×C₁₃	1	8	yes	—
318	#464	C₂²×C₁₃	1	8	yes	complemented
319	#463	C₂²×C₁₃	1	8	yes	complemented
320	#452	C₂²×C₁₃	1	8	yes	—
321	#449	C₂²×C₁₃	1	8	yes	—
322	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
323	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
324	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
325	#431	C₂²×C₁₃	1	4	yes	—
326	#431	C₂²×C₁₃	1	2	yes	—
327	#431	C₂²×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
329	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
330	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	C₂×#135	1	2	yes	—
342	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	4	4	no	—
349	C₄×C₁₃	—	4	4	no	—
350	C₄×C₁₃	—	4	4	no	—
351	C₄×C₁₃	C₂×#135	1	2	yes	—
352	C₄×C₁₃	C₂×#135	1	2	yes	—
353	C₄×C₁₃	#575	1	2	yes	—
354	C₄×C₁₃	#585	1	2	yes	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	C₂³×C₁₃	1	4	yes	—
358	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
362	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
363	C₂×D₈	C₂³×C₁₃	1	4	yes	—
364	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
365	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
366	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
367	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
368	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
369	#127	C₂³×C₁₃	1	2	yes	—
370	#126	—	2	4	no	—
371	#126	—	2	4	no	—
372	#125	—	2	2	no	—
373	#125	—	2	2	no	—
374	#125	C₂³×C₁₃	1	4	yes	—
375	#124	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	C₂³×C₁₃	1	4	yes	—
378	#123	—	2	4	no	—
379	#123	—	2	4	no	—
380	#123	—	2	4	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
386	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	C₂³×C₁₃	1	4	yes	—
392	#121	C₂³×C₁₃	1	4	yes	—
393	#120	—	2	4	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
399	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	C₂³×C₁₃	1	4	yes	—
411	C₄×D₄	C₂³×C₁₃	1	4	yes	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	—	2	4	no	—
415	#117	—	2	4	no	—
416	#117	—	2	4	no	—
417	#117	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄²	D₄×C₁₃	1	2	yes	—
421	C₂×C₄²	D₄×C₁₃	1	2	yes	—
422	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
427	#107	C₂³×C₁₃	1	4	yes	—
428	#107	C₂³×C₁₃	1	4	yes	—
429	#106	C₂³×C₁₃	1	8	yes	—
430	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
431	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
432	#103	C₂³×C₁₃	1	8	yes	—
433	#103	C₂³×C₁₃	1	8	yes	—
434	#102	C₂³×C₁₃	1	8	yes	—
435	#102	C₂³×C₁₃	1	8	yes	—
436	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
437	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
438	C₄×C₈	C₂³×C₁₃	1	2	yes	—
439	C₄×C₈	C₂³×C₁₃	1	2	yes	—
440	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₄×C₈	C₂³×C₁₃	1	2	yes	—
442	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₁₃	—	2	2	no	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	8	4	no	—
446	C₂×C₁₃	#3449	1	1	yes	characteristic
447	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
449	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
450	#41	—	4	8	no	—
451	#41	—	4	8	no	—
452	#41	—	4	8	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
480	Q₁₆	—	4	4	no	—
481	SD₁₆	—	4	8	no	—
482	D₈	—	4	4	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
486	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
487	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	2	4	no	—
512	C₄²	C₂×D₄×C₁₃	1	2	yes	—
513	C₄²	C₂×D₄×C₁₃	1	2	yes	—
514	C₄²	C₂×D₄×C₁₃	1	2	yes	—
515	C₄²	C₂×D₄×C₁₃	1	2	yes	—
516	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₁₃	1	2	yes	—
518	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
520	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₄²	C₂⁴×C₁₃	1	2	yes	—
522	C₁₃	#60944	1	1	yes	characteristic, direct product factor, Sylow
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
529	Q₈	—	2	8	no	—
530	Q₈	—	4	4	no	—
531	Q₈	—	4	4	no	—
532	D₄	—	2	8	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	8	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	8	no	—
553	C₂×C₄	—	4	8	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	C₁₃×#135	1	4	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	4	no	—
567	C₈	—	2	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	4	no	—
577	C₂²	C₂×C₁₃×#135	1	2	yes	—
578	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	1	no	—
584	C₄	—	4	4	no	—
585	C₄	—	4	4	no	—
586	C₄	—	4	4	no	—
587	C₄	C₂×C₁₃×#135	1	2	yes	—
588	C₄	C₂×C₁₃×#135	1	2	yes	—
589	C₄	C₁₃×#575	1	2	yes	—
590	C₄	C₁₃×#585	1	2	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	4	2	no	—
593	C₂	—	8	4	no	—
594	C₂	C₁₃×#3449	1	1	yes	characteristic
595	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
596	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3250	C₂	semidirect
3. C₁₃×#3231	C₂	semidirect
4. C₁₃×#3228	C₂	semidirect
5. C₁₃×#3210	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3191	C₂	semidirect
8. C₁₃×#3170	C₂	semidirect
9. C₁₃×#3169	C₂	semidirect
10. C₁₃×#3167	C₂	semidirect
11. C₁₃×#3102	C₂	semidirect
12. C₂×C₁₃×#431	C₂	semidirect
32. C₁₃×#500	C₂²	semidirect
33. C₁₃×#500	C₂²	semidirect
34. C₁₃×#498	C₂²	semidirect
35. C₁₃×#494	C₂²	semidirect
36. C₁₃×#493	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#487	C₂²	semidirect
39. C₁₃×#487	C₂²	semidirect
40. C₁₃×#486	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
44. C₁₃×#479	C₂²	semidirect
45. C₁₃×#478	C₂²	semidirect
49. C₁₃×#464	C₂²	semidirect
50. C₁₃×#463	C₂²	semidirect
53. C₄×C₁₃×Q₁₆	C₂²	semidirect
54. C₄×C₁₃×SD₁₆	C₂²	semidirect
55. C₄×C₁₃×D₈	C₂²	semidirect
151. #60944	C₁₃	direct (N × H)
225. #3444	C₂×C₁₃	semidirect
226. #3250	C₂×C₁₃	semidirect
227. #3231	C₂×C₁₃	semidirect
228. #3228	C₂×C₁₃	semidirect
229. #3210	C₂×C₁₃	semidirect
230. #3207	C₂×C₁₃	semidirect
231. #3191	C₂×C₁₃	semidirect
232. #3170	C₂×C₁₃	semidirect
233. #3169	C₂×C₁₃	semidirect
234. #3167	C₂×C₁₃	semidirect
235. #3102	C₂×C₁₃	semidirect
236. C₂×#431	C₂×C₁₃	semidirect
301. #500	C₂²×C₁₃	semidirect
302. #500	C₂²×C₁₃	semidirect
303. #498	C₂²×C₁₃	semidirect
304. #494	C₂²×C₁₃	semidirect
305. #493	C₂²×C₁₃	semidirect
306. #492	C₂²×C₁₃	semidirect
307. #487	C₂²×C₁₃	semidirect
308. #487	C₂²×C₁₃	semidirect
309. #486	C₂²×C₁₃	semidirect
310. #486	C₂²×C₁₃	semidirect
313. #479	C₂²×C₁₃	semidirect
314. #478	C₂²×C₁₃	semidirect
318. #464	C₂²×C₁₃	semidirect
319. #463	C₂²×C₁₃	semidirect
322. C₄×Q₁₆	C₂²×C₁₃	semidirect
323. C₄×SD₁₆	C₂²×C₁₃	semidirect
324. C₄×D₈	C₂²×C₁₃	semidirect
522. C₁₃	#60944	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×#3444	2
C₁₃×#3250	2
C₁₃×#3231	2
C₁₃×#3228	2
C₁₃×#3210	2
C₁₃×#3207	2
C₁₃×#3191	2
C₁₃×#3170	2
C₁₃×#3169	2
C₁₃×#3167	2
C₁₃×#3102	2
C₂×C₁₃×#431	2
#60944	13

Subgroups — C13×#60944 #15747283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60944 #15747283