Subgroups — C₁₃×#61269 #15747608

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	2	yes	maximal
2	C₁₃×#3356	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3352	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3349	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3095	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₁₃×#556	C₂²	1	4	yes	—
20	C₁₃×#554	C₂²	1	4	yes	—
21	C₁₃×#552	—	2	4	no	—
22	C₁₃×#552	C₂²	1	4	yes	—
23	C₁₃×#552	C₂²	1	4	yes	—
24	C₁₃×#551	—	2	4	no	—
25	C₁₃×#544	C₂²	1	2	yes	—
26	C₁₃×#542	—	2	2	no	—
27	C₁₃×#541	—	2	2	no	—
28	C₁₃×#536	C₂²	1	2	yes	—
29	C₁₃×#533	—	2	2	no	—
30	C₁₃×#529	—	2	2	no	—
31	C₁₃×#525	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₁₃×#520	C₂²	1	2	yes	—
34	C₁₃×#519	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₁₃×#501	C₂²	1	4	yes	complemented
37	C₁₃×#499	C₂²	1	2	yes	complemented
38	C₁₃×#498	C₂²	1	2	yes	complemented
39	C₁₃×#485	C₂²	1	4	yes	—
40	C₁₃×#485	C₂²	1	4	yes	—
41	C₁₃×#485	C₂²	1	4	yes	complemented
42	C₁₃×#485	C₂²	1	4	yes	complemented
43	C₁₃×#484	C₂²	1	4	yes	—
44	C₁₃×#484	C₂²	1	4	yes	complemented
45	C₁₃×#483	C₂²	1	4	yes	—
46	C₁₃×#483	C₂²	1	4	yes	complemented
47	C₁₃×#479	C₂²	1	4	yes	complemented
48	C₁₃×#479	C₂²	1	4	yes	complemented
49	C₁₃×#477	C₂²	1	4	yes	complemented
50	C₁₃×#475	C₂²	1	4	yes	complemented
51	C₁₃×#470	C₂²	1	4	yes	—
52	C₁₃×#470	C₂²	1	4	yes	—
53	C₁₃×#470	C₂²	1	2	yes	complemented
54	C₁₃×#470	C₂²	1	2	yes	complemented
55	C₁₃×#467	C₂²	1	4	yes	complemented
56	C₁₃×#441	C₂²	1	2	yes	complemented
57	C₁₃×#441	C₂²	1	2	yes	complemented
58	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
59	C₁₃×#436	C₂²	1	4	yes	—
60	C₁₃×#435	C₂²	1	4	yes	—
61	C₁₃×#428	C₂²	1	2	yes	—
62	C₁₃×#428	C₂²	1	2	yes	—
63	C₁₃×#428	C₂²	1	2	yes	—
64	C₁₃×#428	C₂²	1	2	yes	—
65	C₁₃×#428	C₂²	1	2	yes	—
66	C₁₃×#428	C₂²	1	2	yes	—
67	C₁₃×#428	C₂²	1	4	yes	complemented
68	C₁₃×#427	C₂²	1	1	yes	characteristic
69	C₁₃×#427	C₂²	1	2	yes	—
70	C₁₃×#427	C₂²	1	1	yes	characteristic
71	C₁₃×#427	C₂²	1	2	yes	complemented
72	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
74	C₁₃×#424	C₂²	1	1	yes	characteristic
75	C₁₃×#419	C₂²	1	2	yes	—
76	C₁₃×#419	C₂²	1	2	yes	—
77	C₂×C₁₃×#103	C₂²	1	2	yes	—
78	C₁₃×#408	C₂²	1	1	yes	characteristic
79	C₁₃×#407	C₂²	1	1	yes	characteristic
80	C₁₃×#405	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×Q₁₆	—	2	4	no	—
85	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
87	C₁₃×#131	—	2	4	no	—
88	C₂×C₁₃×M₁₆	—	2	4	no	—
89	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#126	—	2	4	no	—
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#126	—	2	4	no	—
104	C₁₃×#125	—	2	2	no	—
105	C₁₃×#125	—	2	4	no	—
106	C₁₃×#125	—	2	4	no	—
107	C₁₃×#125	—	2	4	no	—
108	C₁₃×#125	C₂³	1	4	yes	—
109	C₁₃×#124	—	2	2	no	—
110	C₁₃×#124	—	2	4	no	—
111	C₁₃×#123	—	2	4	no	—
112	C₁₃×#123	—	2	4	no	—
113	C₁₃×#123	—	2	4	no	—
114	C₁₃×#123	D₄	1	2	yes	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#121	D₄	1	2	yes	—
126	C₁₃×#120	D₄	1	2	yes	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	4	no	—
131	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
132	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
133	C₄×D₄×C₁₃	—	2	2	no	—
134	C₄×D₄×C₁₃	—	2	4	no	—
135	C₄×D₄×C₁₃	—	2	4	no	—
136	C₄×D₄×C₁₃	C₂³	1	4	yes	—
137	C₁₃×#117	—	2	2	no	—
138	C₁₃×#117	—	2	2	no	—
139	C₁₃×#117	—	2	4	no	—
140	C₁₃×#117	—	2	4	no	—
141	C₁₃×#117	—	2	4	no	—
142	C₁₃×#117	C₂³	1	2	yes	—
143	C₁₃×#117	C₂³	1	2	yes	—
144	C₁₃×#117	C₂³	1	4	yes	—
145	C₁₃×#117	C₂³	1	2	yes	—
146	C₁₃×#117	C₂³	1	2	yes	—
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₂×C₄²×C₁₃	—	2	2	no	—
156	C₁₃×#107	C₂³	1	2	yes	—
157	C₁₃×#107	C₂³	1	2	yes	—
158	C₁₃×#107	C₂³	1	2	yes	—
159	C₁₃×#107	C₂³	1	2	yes	—
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#106	C₂³	1	2	yes	—
163	C₁₃×#106	C₂³	1	2	yes	—
164	C₁₃×#106	C₂³	1	1	yes	characteristic
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	1	yes	characteristic
167	C₁₃×#106	C₂³	1	1	yes	characteristic
168	C₁₃×#106	C₂³	1	1	yes	characteristic
169	C₁₃×#106	C₂³	1	2	yes	—
170	C₁₃×#106	C₂³	1	2	yes	—
171	C₁₃×#106	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#97	C₂³	1	2	yes	—
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	#61269	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	2	2	no	—
186	C₁₃×#41	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	4	no	—
190	C₂×Q₈×C₁₃	—	2	4	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₁₃×Q₁₆	—	2	4	no	—
209	C₁₃×Q₁₆	—	2	4	no	—
210	C₁₃×M₁₆	—	2	2	no	—
211	C₁₃×M₁₆	—	2	2	no	—
212	C₁₃×M₁₆	—	2	4	no	—
213	C₁₃×M₁₆	—	2	4	no	—
214	C₁₃×M₁₆	—	2	4	no	—
215	C₂×C₈×C₁₃	—	2	2	no	—
216	C₂×C₈×C₁₃	—	2	4	no	—
217	C₂×C₈×C₁₃	#41	1	4	yes	—
218	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
219	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
220	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
221	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×C₄⋊C₄	—	2	4	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
238	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
243	C₁₃×C₂²⋊C₄	—	2	2	no	—
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
245	C₁₃×C₂²⋊C₄	—	2	2	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
254	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	—	2	2	no	—
257	C₄²×C₁₃	—	2	2	no	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	—	2	4	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	C₂⁴	1	2	yes	—
263	#3495	C₂×C₁₃	1	2	yes	—
264	#3356	C₂×C₁₃	1	4	yes	complemented
265	#3352	C₂×C₁₃	1	4	yes	complemented
266	#3349	C₂×C₁₃	1	4	yes	complemented
267	#3344	C₂×C₁₃	1	4	yes	complemented
268	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#3097	C₂×C₁₃	1	2	yes	complemented
270	#3095	C₂×C₁₃	1	2	yes	complemented
271	#3082	C₂×C₁₃	1	2	yes	complemented
272	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2930	C₂×C₁₃	1	1	yes	characteristic
276	#2912	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2911	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	4	2	no	—
280	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₁₃	—	2	2	no	—
284	Q₈×C₁₃	—	2	4	no	—
285	Q₈×C₁₃	—	2	4	no	—
286	Q₈×C₁₃	—	4	4	no	—
287	Q₈×C₁₃	—	8	4	no	—
288	D₄×C₁₃	—	2	4	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	4	4	no	—
305	C₂×C₄×C₁₃	—	8	4	no	—
306	C₂×C₄×C₁₃	—	8	2	no	—
307	C₂×C₄×C₁₃	—	8	2	no	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
314	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	2	2	no	—
317	C₈×C₁₃	—	2	2	no	—
318	C₈×C₁₃	C₂×#41	1	2	yes	—
319	C₈×C₁₃	C₂×#41	1	2	yes	—
320	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
323	#556	C₂²×C₁₃	1	4	yes	—
324	#554	C₂²×C₁₃	1	4	yes	—
325	#552	—	2	4	no	—
326	#552	C₂²×C₁₃	1	4	yes	—
327	#552	C₂²×C₁₃	1	4	yes	—
328	#551	—	2	4	no	—
329	#544	C₂²×C₁₃	1	2	yes	—
330	#542	—	2	2	no	—
331	#541	—	2	2	no	—
332	#536	C₂²×C₁₃	1	2	yes	—
333	#533	—	2	2	no	—
334	#529	—	2	2	no	—
335	#525	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
337	#520	C₂²×C₁₃	1	2	yes	—
338	#519	C₂²×C₁₃	1	2	yes	—
339	C₂×#117	C₂²×C₁₃	1	2	yes	—
340	#501	C₂²×C₁₃	1	4	yes	complemented
341	#499	C₂²×C₁₃	1	2	yes	complemented
342	#498	C₂²×C₁₃	1	2	yes	complemented
343	#485	C₂²×C₁₃	1	4	yes	—
344	#485	C₂²×C₁₃	1	4	yes	—
345	#485	C₂²×C₁₃	1	4	yes	complemented
346	#485	C₂²×C₁₃	1	4	yes	complemented
347	#484	C₂²×C₁₃	1	4	yes	—
348	#484	C₂²×C₁₃	1	4	yes	complemented
349	#483	C₂²×C₁₃	1	4	yes	—
350	#483	C₂²×C₁₃	1	4	yes	complemented
351	#479	C₂²×C₁₃	1	4	yes	complemented
352	#479	C₂²×C₁₃	1	4	yes	complemented
353	#477	C₂²×C₁₃	1	4	yes	complemented
354	#475	C₂²×C₁₃	1	4	yes	complemented
355	#470	C₂²×C₁₃	1	4	yes	—
356	#470	C₂²×C₁₃	1	4	yes	—
357	#470	C₂²×C₁₃	1	2	yes	complemented
358	#470	C₂²×C₁₃	1	2	yes	complemented
359	#467	C₂²×C₁₃	1	4	yes	complemented
360	#441	C₂²×C₁₃	1	2	yes	complemented
361	#441	C₂²×C₁₃	1	2	yes	complemented
362	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
363	#436	C₂²×C₁₃	1	4	yes	—
364	#435	C₂²×C₁₃	1	4	yes	—
365	#428	C₂²×C₁₃	1	2	yes	—
366	#428	C₂²×C₁₃	1	2	yes	—
367	#428	C₂²×C₁₃	1	2	yes	—
368	#428	C₂²×C₁₃	1	2	yes	—
369	#428	C₂²×C₁₃	1	2	yes	—
370	#428	C₂²×C₁₃	1	2	yes	—
371	#428	C₂²×C₁₃	1	4	yes	complemented
372	#427	C₂²×C₁₃	1	2	yes	—
373	#427	C₂²×C₁₃	1	1	yes	characteristic
374	#427	C₂²×C₁₃	1	1	yes	characteristic
375	#427	C₂²×C₁₃	1	2	yes	complemented
376	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
378	#424	C₂²×C₁₃	1	1	yes	characteristic
379	#419	C₂²×C₁₃	1	2	yes	—
380	#419	C₂²×C₁₃	1	2	yes	—
381	C₂×#103	C₂²×C₁₃	1	2	yes	—
382	#408	C₂²×C₁₃	1	1	yes	characteristic
383	#407	C₂²×C₁₃	1	1	yes	characteristic
384	#405	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×C₁₃	—	2	2	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	4	no	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	8	2	no	—
392	C₂²×C₁₃	#547	1	2	yes	—
393	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
394	C₄×C₁₃	—	2	4	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	4	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	4	no	—
403	C₄×C₁₃	#547	1	2	yes	—
404	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
405	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
408	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×Q₁₆	—	2	4	no	—
410	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
411	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
412	#131	—	2	4	no	—
413	C₂×M₁₆	—	2	4	no	—
414	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
415	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
416	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
418	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
421	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	—	2	2	no	—
424	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
425	#126	—	2	4	no	—
426	#126	—	2	4	no	—
427	#126	—	2	4	no	—
428	#126	—	2	4	no	—
429	#125	—	2	2	no	—
430	#125	—	2	4	no	—
431	#125	—	2	4	no	—
432	#125	—	2	4	no	—
433	#125	C₂³×C₁₃	1	4	yes	—
434	#124	—	2	2	no	—
435	#124	—	2	4	no	—
436	#123	—	2	4	no	—
437	#123	—	2	4	no	—
438	#123	—	2	4	no	—
439	#123	D₄×C₁₃	1	2	yes	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	4	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
446	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
447	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
448	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
450	#121	D₄×C₁₃	1	2	yes	—
451	#120	D₄×C₁₃	1	2	yes	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	—	2	4	no	—
456	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
457	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	4	no	—
460	C₄×D₄	—	2	4	no	—
461	C₄×D₄	C₂³×C₁₃	1	4	yes	—
462	#117	—	2	2	no	—
463	#117	—	2	2	no	—
464	#117	—	2	4	no	—
465	#117	—	2	4	no	—
466	#117	—	2	4	no	—
467	#117	C₂³×C₁₃	1	2	yes	—
468	#117	C₂³×C₁₃	1	2	yes	—
469	#117	C₂³×C₁₃	1	2	yes	—
470	#117	C₂³×C₁₃	1	2	yes	—
471	#117	C₂³×C₁₃	1	4	yes	—
472	#117	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₂²⋊C₄	—	2	2	no	—
479	C₂×C₂²⋊C₄	—	2	2	no	—
480	C₂×C₄²	—	2	2	no	—
481	#107	C₂³×C₁₃	1	2	yes	—
482	#107	C₂³×C₁₃	1	2	yes	—
483	#107	C₂³×C₁₃	1	2	yes	—
484	#107	C₂³×C₁₃	1	2	yes	—
485	#107	C₂³×C₁₃	1	4	yes	—
486	#107	C₂³×C₁₃	1	4	yes	—
487	#106	C₂³×C₁₃	1	2	yes	—
488	#106	C₂³×C₁₃	1	2	yes	—
489	#106	C₂³×C₁₃	1	1	yes	characteristic
490	#106	C₂³×C₁₃	1	4	yes	—
491	#106	C₂³×C₁₃	1	1	yes	characteristic
492	#106	C₂³×C₁₃	1	1	yes	characteristic
493	#106	C₂³×C₁₃	1	1	yes	characteristic
494	#106	C₂³×C₁₃	1	2	yes	—
495	#106	C₂³×C₁₃	1	2	yes	—
496	#106	C₂³×C₁₃	1	4	yes	—
497	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
498	#103	C₂³×C₁₃	1	4	yes	—
499	#103	C₂³×C₁₃	1	4	yes	—
500	#103	C₂³×C₁₃	1	4	yes	—
501	#103	C₂³×C₁₃	1	4	yes	—
502	#103	C₂³×C₁₃	1	4	yes	—
503	#103	C₂³×C₁₃	1	4	yes	—
504	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
505	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
506	#97	C₂³×C₁₃	1	2	yes	—
507	C₄×C₈	C₂³×C₁₃	1	2	yes	—
508	C₂×C₁₃	—	2	2	no	—
509	C₂×C₁₃	—	4	2	no	—
510	C₂×C₁₃	—	4	2	no	—
511	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
512	C₂×C₁₃	#3586	1	2	yes	—
513	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
522	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
523	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	Q₁₆	—	2	4	no	—
538	Q₁₆	—	2	4	no	—
539	M₁₆	—	2	2	no	—
540	M₁₆	—	2	2	no	—
541	M₁₆	—	2	4	no	—
542	M₁₆	—	2	4	no	—
543	M₁₆	—	2	4	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	2	4	no	—
546	C₂×C₈	C₁₃×#41	1	4	yes	—
547	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
548	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
549	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
550	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
566	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
567	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
583	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	C₂⁴×C₁₃	1	2	yes	—
592	C₁₃	#61269	1	1	yes	characteristic, direct product factor, Sylow
593	C₂³	—	2	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	4	no	—
600	Q₈	—	2	4	no	—
601	Q₈	—	4	4	no	—
602	Q₈	—	8	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	8	4	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	2	no	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
628	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
629	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
630	C₈	—	2	2	no	—
631	C₈	—	2	2	no	—
632	C₈	—	2	2	no	—
633	C₈	C₂×C₁₃×#41	1	2	yes	—
634	C₈	C₂×C₁₃×#41	1	2	yes	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	8	2	no	—
642	C₂²	C₁₃×#547	1	2	yes	—
643	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
644	C₄	—	2	4	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	4	no	—
653	C₄	C₁₃×#547	1	2	yes	—
654	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
655	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
656	C₂	—	2	2	no	—
657	C₂	—	4	2	no	—
658	C₂	—	4	2	no	—
659	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
660	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3356	C₂	semidirect
3. C₁₃×#3352	C₂	semidirect
4. C₁₃×#3349	C₂	semidirect
5. C₁₃×#3344	C₂	semidirect
6. C₁₃×#3163	C₂	semidirect
7. C₁₃×#3097	C₂	semidirect
8. C₁₃×#3095	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
10. C₁₃×#3059	C₂	semidirect
11. C₂×C₁₃×#470	C₂	semidirect
12. C₁₃×#2950	C₂	semidirect
14. C₁₃×#2912	C₂	semidirect
15. C₁₃×#2911	C₂	semidirect
36. C₁₃×#501	C₂²	semidirect
37. C₁₃×#499	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
41. C₁₃×#485	C₂²	semidirect
42. C₁₃×#485	C₂²	semidirect
44. C₁₃×#484	C₂²	semidirect
46. C₁₃×#483	C₂²	semidirect
47. C₁₃×#479	C₂²	semidirect
48. C₁₃×#479	C₂²	semidirect
49. C₁₃×#477	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
53. C₁₃×#470	C₂²	semidirect
54. C₁₃×#470	C₂²	semidirect
55. C₁₃×#467	C₂²	semidirect
56. C₁₃×#441	C₂²	semidirect
57. C₁₃×#441	C₂²	semidirect
58. C₄×C₁₃×Q₁₆	C₂²	semidirect
67. C₁₃×#428	C₂²	semidirect
71. C₁₃×#427	C₂²	semidirect
73. C₂×C₁₃×#106	C₂²	semidirect
183. #61269	C₁₃	direct (N × H)
264. #3356	C₂×C₁₃	semidirect
265. #3352	C₂×C₁₃	semidirect
266. #3349	C₂×C₁₃	semidirect
267. #3344	C₂×C₁₃	semidirect
268. #3163	C₂×C₁₃	semidirect
269. #3097	C₂×C₁₃	semidirect
270. #3095	C₂×C₁₃	semidirect
271. #3082	C₂×C₁₃	semidirect
272. #3059	C₂×C₁₃	semidirect
273. C₂×#470	C₂×C₁₃	semidirect
274. #2950	C₂×C₁₃	semidirect
276. #2912	C₂×C₁₃	semidirect
277. #2911	C₂×C₁₃	semidirect
340. #501	C₂²×C₁₃	semidirect
341. #499	C₂²×C₁₃	semidirect
342. #498	C₂²×C₁₃	semidirect
345. #485	C₂²×C₁₃	semidirect
346. #485	C₂²×C₁₃	semidirect
348. #484	C₂²×C₁₃	semidirect
350. #483	C₂²×C₁₃	semidirect
351. #479	C₂²×C₁₃	semidirect
352. #479	C₂²×C₁₃	semidirect
353. #477	C₂²×C₁₃	semidirect
354. #475	C₂²×C₁₃	semidirect
357. #470	C₂²×C₁₃	semidirect
358. #470	C₂²×C₁₃	semidirect
359. #467	C₂²×C₁₃	semidirect
360. #441	C₂²×C₁₃	semidirect
361. #441	C₂²×C₁₃	semidirect
362. C₄×Q₁₆	C₂²×C₁₃	semidirect
371. #428	C₂²×C₁₃	semidirect
375. #427	C₂²×C₁₃	semidirect
377. C₂×#106	C₂²×C₁₃	semidirect
592. C₁₃	#61269	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×#3495	2
C₁₃×#3356	2
C₁₃×#3352	2
C₁₃×#3349	2
C₁₃×#3344	2
C₁₃×#3163	2
C₁₃×#3097	2
C₁₃×#3095	2
C₁₃×#3082	2
C₁₃×#3059	2
C₂×C₁₃×#470	2
C₁₃×#2950	2
C₁₃×#2930	2
C₁₃×#2912	2
C₁₃×#2911	2
#61269	13

Subgroups — C13×#61269 #15747608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61269 #15747608