Subgroups — C₁₃×#60883 #15747222

Order 3328.

1742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3241	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3235	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3234	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3096	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3081	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#559	—	2	2	no	—
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#554	—	2	4	no	—
16	C₁₃×#554	—	2	2	no	—
17	C₁₃×#550	—	2	2	no	—
18	C₁₃×#546	—	2	4	no	—
19	C₁₃×#544	C₂²	1	2	yes	—
20	C₁₃×#544	C₂²	1	4	yes	complemented
21	C₁₃×#540	C₂²	1	4	yes	—
22	C₁₃×#535	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#533	C₂²	1	2	yes	complemented
26	C₁₃×#532	C₂²	1	4	yes	—
27	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
30	C₁₃×#520	C₂²	1	2	yes	—
31	C₁₃×#518	C₂²	1	2	yes	—
32	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
33	C₁₃×#501	C₂²	1	2	yes	complemented
34	C₁₃×#501	C₂²	1	2	yes	complemented
35	C₁₃×#501	C₂²	1	4	yes	complemented
36	C₁₃×#501	C₂²	1	4	yes	complemented
37	C₁₃×#499	C₂²	1	4	yes	complemented
38	C₁₃×#490	C₂²	1	4	yes	—
39	C₁₃×#490	C₂²	1	4	yes	—
40	C₁₃×#490	C₂²	1	2	yes	—
41	C₁₃×#490	C₂²	1	2	yes	—
42	C₁₃×#486	C₂²	1	4	yes	—
43	C₁₃×#482	C₂²	1	8	yes	complemented
44	C₁₃×#482	C₂²	1	8	yes	complemented
45	C₁₃×#481	C₂²	1	8	yes	complemented
46	C₁₃×#480	C₂²	1	8	yes	complemented
47	C₁₃×#478	C₂²	1	8	yes	complemented
48	C₁₃×#478	C₂²	1	8	yes	complemented
49	C₁₃×#476	C₂²	1	8	yes	complemented
50	C₁₃×#474	C₂²	1	8	yes	complemented
51	C₁₃×#433	C₂²	1	4	yes	complemented
52	C₁₃×#432	C₂²	1	4	yes	complemented
53	C₁₃×#428	C₂²	1	4	yes	—
54	C₁₃×#427	C₂²	1	4	yes	—
55	C₁₃×#424	C₂²	1	2	yes	—
56	C₁₃×#418	C₂²	1	4	yes	—
57	C₂×C₁₃×#102	C₂²	1	4	yes	—
58	C₁₃×#408	C₂²	1	2	yes	—
59	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	—	2	4	no	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	—	2	4	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×#127	—	2	2	no	—
73	C₁₃×#127	—	2	2	no	—
74	C₁₃×#127	C₂³	1	2	yes	—
75	C₁₃×#127	C₂³	1	2	yes	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	—	2	4	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	—	2	4	no	—
80	C₁₃×#125	C₂³	1	4	yes	—
81	C₁₃×#125	C₂³	1	2	yes	—
82	C₁₃×#125	C₂³	1	2	yes	—
83	C₁₃×#125	C₂³	1	1	yes	characteristic
84	C₁₃×#125	C₂³	1	1	yes	characteristic
85	C₁₃×#125	C₂³	1	2	yes	—
86	C₁₃×#124	—	2	2	no	—
87	C₁₃×#124	—	2	4	no	—
88	C₁₃×#123	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	4	no	—
92	C₁₃×C₂²⋊Q₈	—	2	4	no	—
93	C₁₃×C₂²⋊Q₈	—	2	4	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×#121	—	2	4	no	—
96	C₁₃×#121	—	2	8	no	—
97	C₁₃×#121	C₂³	1	8	yes	—
98	C₁₃×#120	—	2	4	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	4	no	—
103	C₄×Q₈×C₁₃	D₄	1	2	yes	—
104	C₄×D₄×C₁₃	—	2	4	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	D₄	1	4	yes	—
109	C₄×D₄×C₁₃	D₄	1	2	yes	—
110	C₄×D₄×C₁₃	C₂³	1	8	yes	—
111	C₁₃×#117	C₂³	1	2	yes	—
112	C₁₃×#117	C₂³	1	2	yes	—
113	C₁₃×#117	C₂³	1	4	yes	—
114	C₁₃×#117	C₂³	1	1	yes	characteristic
115	C₁₃×#117	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#107	C₂³	1	4	yes	—
125	C₁₃×#107	C₂³	1	8	yes	—
126	C₁₃×#106	C₂³	1	4	yes	—
127	C₁₃×#106	C₂³	1	4	yes	—
128	C₁₃×#106	C₂³	1	8	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
130	C₁₃×#102	C₂³	1	8	yes	—
131	C₁₃×#102	C₂³	1	8	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×#102	C₂³	1	8	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₁₃×#97	C₂³	1	2	yes	—
136	C₁₃×#97	C₂³	1	2	yes	—
137	C₁₃×#97	C₂³	1	2	yes	—
138	C₄×C₈×C₁₃	C₂³	1	2	yes	—
139	#60883	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₁₃×#41	—	2	4	no	—
142	C₁₃×#41	—	8	8	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	8	no	—
152	C₂×D₄×C₁₃	—	8	4	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×M₁₆	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
192	C₄²×C₁₃	—	2	2	no	—
193	C₄²×C₁₃	—	2	4	no	—
194	C₄²×C₁₃	—	2	2	no	—
195	C₄²×C₁₃	C₂×D₄	1	4	yes	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₄²×C₁₃	C₂⁴	1	2	yes	—
200	#3508	C₂×C₁₃	1	1	yes	characteristic
201	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#3241	C₂×C₁₃	1	8	yes	complemented
203	#3235	C₂×C₁₃	1	4	yes	complemented
204	#3234	C₂×C₁₃	1	4	yes	complemented
205	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3096	C₂×C₁₃	1	4	yes	complemented
210	#3081	C₂×C₁₃	1	4	yes	complemented
211	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	—	8	4	no	—
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	8	4	no	—
220	Q₈×C₁₃	—	8	2	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	2	2	no	—
223	D₄×C₁₃	—	2	8	no	—
224	D₄×C₁₃	—	4	8	no	—
225	D₄×C₁₃	—	4	4	no	—
226	D₄×C₁₃	—	8	4	no	—
227	D₄×C₁₃	—	8	8	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	8	8	no	—
236	C₂×C₄×C₁₃	—	8	2	no	—
237	C₂×C₄×C₁₃	—	8	4	no	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
245	C₈×C₁₃	—	2	4	no	—
246	C₈×C₁₃	—	2	4	no	—
247	#559	—	2	2	no	—
248	#557	—	2	2	no	—
249	#554	—	2	4	no	—
250	#554	—	2	2	no	—
251	#550	—	2	2	no	—
252	#546	—	2	4	no	—
253	#544	C₂²×C₁₃	1	2	yes	—
254	#544	C₂²×C₁₃	1	4	yes	complemented
255	#540	C₂²×C₁₃	1	4	yes	—
256	#535	C₂²×C₁₃	1	2	yes	—
257	#533	C₂²×C₁₃	1	1	yes	characteristic
258	#533	C₂²×C₁₃	1	1	yes	characteristic
259	#533	C₂²×C₁₃	1	2	yes	complemented
260	#532	C₂²×C₁₃	1	4	yes	—
261	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
264	#520	C₂²×C₁₃	1	2	yes	—
265	#518	C₂²×C₁₃	1	2	yes	—
266	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
267	#501	C₂²×C₁₃	1	2	yes	complemented
268	#501	C₂²×C₁₃	1	2	yes	complemented
269	#501	C₂²×C₁₃	1	4	yes	complemented
270	#501	C₂²×C₁₃	1	4	yes	complemented
271	#499	C₂²×C₁₃	1	4	yes	complemented
272	#490	C₂²×C₁₃	1	4	yes	—
273	#490	C₂²×C₁₃	1	4	yes	—
274	#490	C₂²×C₁₃	1	2	yes	—
275	#490	C₂²×C₁₃	1	2	yes	—
276	#486	C₂²×C₁₃	1	4	yes	—
277	#482	C₂²×C₁₃	1	8	yes	complemented
278	#482	C₂²×C₁₃	1	8	yes	complemented
279	#481	C₂²×C₁₃	1	8	yes	complemented
280	#480	C₂²×C₁₃	1	8	yes	complemented
281	#478	C₂²×C₁₃	1	8	yes	complemented
282	#478	C₂²×C₁₃	1	8	yes	complemented
283	#476	C₂²×C₁₃	1	8	yes	complemented
284	#474	C₂²×C₁₃	1	8	yes	complemented
285	#433	C₂²×C₁₃	1	4	yes	complemented
286	#432	C₂²×C₁₃	1	4	yes	complemented
287	#428	C₂²×C₁₃	1	4	yes	—
288	#427	C₂²×C₁₃	1	4	yes	—
289	#424	C₂²×C₁₃	1	2	yes	—
290	#418	C₂²×C₁₃	1	4	yes	—
291	C₂×#102	C₂²×C₁₃	1	4	yes	—
292	#408	C₂²×C₁₃	1	2	yes	—
293	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	8	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	16	4	no	—
301	C₂²×C₁₃	#536	1	2	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	4	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	4	4	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	#536	1	2	yes	—
312	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
317	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
323	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
324	#127	—	2	2	no	—
325	#127	—	2	2	no	—
326	#127	C₂³×C₁₃	1	2	yes	—
327	#127	C₂³×C₁₃	1	2	yes	—
328	#125	—	2	2	no	—
329	#125	—	2	4	no	—
330	#125	—	2	2	no	—
331	#125	—	2	4	no	—
332	#125	C₂³×C₁₃	1	2	yes	—
333	#125	C₂³×C₁₃	1	2	yes	—
334	#125	C₂³×C₁₃	1	1	yes	characteristic
335	#125	C₂³×C₁₃	1	4	yes	—
336	#125	C₂³×C₁₃	1	1	yes	characteristic
337	#125	C₂³×C₁₃	1	2	yes	—
338	#124	—	2	2	no	—
339	#124	—	2	4	no	—
340	#123	—	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	4	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	4	no	—
347	#121	—	2	4	no	—
348	#121	—	2	8	no	—
349	#121	C₂³×C₁₃	1	8	yes	—
350	#120	—	2	4	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	D₄×C₁₃	1	2	yes	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	4	no	—
360	C₄×D₄	D₄×C₁₃	1	4	yes	—
361	C₄×D₄	D₄×C₁₃	1	2	yes	—
362	C₄×D₄	C₂³×C₁₃	1	8	yes	—
363	#117	C₂³×C₁₃	1	2	yes	—
364	#117	C₂³×C₁₃	1	2	yes	—
365	#117	C₂³×C₁₃	1	4	yes	—
366	#117	C₂³×C₁₃	1	1	yes	characteristic
367	#117	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
375	#107	C₂³×C₁₃	1	4	yes	—
376	#107	C₂³×C₁₃	1	4	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	8	yes	—
382	#102	C₂³×C₁₃	1	8	yes	—
383	#102	C₂³×C₁₃	1	8	yes	—
384	#102	C₂³×C₁₃	1	8	yes	—
385	#102	C₂³×C₁₃	1	8	yes	—
386	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
387	#97	C₂³×C₁₃	1	2	yes	—
388	#97	C₂³×C₁₃	1	2	yes	—
389	#97	C₂³×C₁₃	1	2	yes	—
390	C₄×C₈	C₂³×C₁₃	1	2	yes	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	4	2	no	—
393	C₂×C₁₃	—	8	4	no	—
394	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
395	C₂×C₁₃	#3585	1	2	yes	—
396	C₂⁴	—	2	2	no	—
397	#41	—	2	4	no	—
398	#41	—	8	8	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	8	4	no	—
409	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	M₁₆	—	2	4	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
422	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
437	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
438	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
439	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	C₂×D₄×C₁₃	1	4	yes	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
455	C₄²	C₂⁴×C₁₃	1	2	yes	—
456	C₁₃	#60883	1	1	yes	characteristic, direct product factor, Sylow
457	C₂³	—	2	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	8	4	no	—
460	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
461	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	8	4	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	8	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	4	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
489	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	2	4	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	16	4	no	—
498	C₂²	C₁₃×#536	1	2	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	C₁₃×#536	1	2	yes	—
509	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	4	no	—
513	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
514	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3241	C₂	semidirect
4. C₁₃×#3235	C₂	semidirect
5. C₁₃×#3234	C₂	semidirect
6. C₁₃×#3166	C₂	semidirect
7. C₁₃×#3162	C₂	semidirect
8. C₁₃×#3138	C₂	semidirect
9. C₂×C₁₃×#490	C₂	semidirect
10. C₁₃×#3096	C₂	semidirect
11. C₁₃×#3081	C₂	semidirect
12. C₁₃×#2923	C₂	semidirect
20. C₁₃×#544	C₂²	semidirect
25. C₁₃×#533	C₂²	semidirect
29. C₂×C₁₃×#125	C₂²	semidirect
33. C₁₃×#501	C₂²	semidirect
34. C₁₃×#501	C₂²	semidirect
35. C₁₃×#501	C₂²	semidirect
36. C₁₃×#501	C₂²	semidirect
37. C₁₃×#499	C₂²	semidirect
43. C₁₃×#482	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#481	C₂²	semidirect
46. C₁₃×#480	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#478	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#474	C₂²	semidirect
51. C₁₃×#433	C₂²	semidirect
52. C₁₃×#432	C₂²	semidirect
139. #60883	C₁₃	direct (N × H)
201. #3504	C₂×C₁₃	semidirect
202. #3241	C₂×C₁₃	semidirect
203. #3235	C₂×C₁₃	semidirect
204. #3234	C₂×C₁₃	semidirect
205. #3166	C₂×C₁₃	semidirect
206. #3162	C₂×C₁₃	semidirect
207. #3138	C₂×C₁₃	semidirect
208. C₂×#490	C₂×C₁₃	semidirect
209. #3096	C₂×C₁₃	semidirect
210. #3081	C₂×C₁₃	semidirect
211. #2923	C₂×C₁₃	semidirect
254. #544	C₂²×C₁₃	semidirect
259. #533	C₂²×C₁₃	semidirect
263. C₂×#125	C₂²×C₁₃	semidirect
267. #501	C₂²×C₁₃	semidirect
268. #501	C₂²×C₁₃	semidirect
269. #501	C₂²×C₁₃	semidirect
270. #501	C₂²×C₁₃	semidirect
271. #499	C₂²×C₁₃	semidirect
277. #482	C₂²×C₁₃	semidirect
278. #482	C₂²×C₁₃	semidirect
279. #481	C₂²×C₁₃	semidirect
280. #480	C₂²×C₁₃	semidirect
281. #478	C₂²×C₁₃	semidirect
282. #478	C₂²×C₁₃	semidirect
283. #476	C₂²×C₁₃	semidirect
284. #474	C₂²×C₁₃	semidirect
285. #433	C₂²×C₁₃	semidirect
286. #432	C₂²×C₁₃	semidirect
456. C₁₃	#60883	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×#3508	2
C₁₃×#3504	2
C₁₃×#3241	2
C₁₃×#3235	2
C₁₃×#3234	2
C₁₃×#3166	2
C₁₃×#3162	2
C₁₃×#3138	2
C₂×C₁₃×#490	2
C₁₃×#3096	2
C₁₃×#3081	2
C₁₃×#2923	2
#60883	13

Subgroups — C13×#60883 #15747222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60883 #15747222