Subgroups — C₁₃×#60939 #15747278

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 698 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, complemented
2	C₁₃×#3263	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3261	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3256	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3255	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3252	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#554	—	2	2	no	—
23	C₁₃×#552	—	2	4	no	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#551	—	2	4	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#542	C₂²	1	4	yes	—
29	C₁₃×#541	C₂²	1	4	yes	—
30	C₁₃×#536	C₂²	1	2	yes	—
31	C₁₃×#533	C₂²	1	4	yes	—
32	C₁₃×#529	C₂²	1	4	yes	—
33	C₁₃×#525	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#519	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₁₃×#479	C₂²	1	4	yes	complemented
39	C₁₃×#479	C₂²	1	4	yes	complemented
40	C₁₃×#479	C₂²	1	4	yes	complemented
41	C₁₃×#478	C₂²	1	4	yes	complemented
42	C₁₃×#477	C₂²	1	4	yes	complemented
43	C₁₃×#476	C₂²	1	4	yes	complemented
44	C₁₃×#475	C₂²	1	4	yes	complemented
45	C₁₃×#475	C₂²	1	4	yes	complemented
46	C₁₃×#470	C₂²	1	2	yes	—
47	C₁₃×#470	C₂²	1	2	yes	—
48	C₁₃×#470	C₂²	1	2	yes	—
49	C₁₃×#470	C₂²	1	2	yes	—
50	C₁₃×#470	C₂²	1	1	yes	characteristic
51	C₁₃×#470	C₂²	1	1	yes	characteristic
52	C₁₃×#470	C₂²	1	4	yes	—
53	C₁₃×#469	C₂²	1	1	yes	characteristic
54	C₁₃×#469	C₂²	1	1	yes	characteristic
55	C₁₃×#468	C₂²	1	2	yes	—
56	C₁₃×#468	C₂²	1	2	yes	—
57	C₁₃×#468	C₂²	1	4	yes	—
58	C₁₃×#467	C₂²	1	4	yes	—
59	C₁₃×#465	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#462	C₂²	1	4	yes	complemented
65	C₁₃×#462	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#428	C₂²	1	2	yes	—
69	C₁₃×#427	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
71	C₁₃×#424	C₂²	1	2	yes	—
72	C₁₃×#424	C₂²	1	2	yes	—
73	C₁₃×#424	C₂²	1	2	yes	—
74	C₁₃×#424	C₂²	1	2	yes	—
75	C₁₃×#423	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	2	yes	—
77	C₁₃×#419	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₂×C₁₃×#103	C₂²	1	2	yes	—
81	C₂×C₁₃×#41	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#137	—	4	4	no	—
85	C₁₃×#135	—	4	2	no	—
86	C₂×C₁₃×Q₁₆	—	4	2	no	—
87	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
90	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
91	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×M₁₆	—	4	2	no	—
95	C₂×C₁₃×M₁₆	—	4	2	no	—
96	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#125	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	—	2	4	no	—
116	C₁₃×#125	C₂³	1	4	yes	—
117	C₁₃×#124	—	2	4	no	—
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×#121	C₂³	1	2	yes	—
135	C₁₃×#121	C₂³	1	2	yes	—
136	C₁₃×#120	—	2	2	no	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	4	no	—
140	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
141	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	2	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	C₂³	1	4	yes	—
148	C₁₃×#117	—	2	4	no	—
149	C₁₃×#117	—	2	2	no	—
150	C₁₃×#117	—	2	4	no	—
151	C₁₃×#117	—	2	4	no	—
152	C₁₃×#117	D₄	1	1	yes	characteristic
153	C₁₃×#117	D₄	1	2	yes	—
154	C₁₃×#117	D₄	1	1	yes	characteristic
155	C₁₃×#117	C₂³	1	2	yes	—
156	C₁₃×#117	C₂³	1	2	yes	—
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₁₃×#107	C₂³	1	2	yes	—
166	C₁₃×#107	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	2	yes	—
168	C₁₃×#106	C₂³	1	2	yes	—
169	C₁₃×#106	C₂³	1	1	yes	characteristic
170	C₁₃×#106	C₂³	1	1	yes	characteristic
171	C₁₃×#106	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	2	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	2	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	#60939	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₁₃×#41	—	2	4	no	—
189	C₁₃×#41	—	2	4	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	4	no	—
192	C₂×Q₈×C₁₃	—	2	4	no	—
193	C₂×Q₈×C₁₃	—	2	4	no	—
194	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
195	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×Q₁₆	—	4	2	no	—
214	C₁₃×Q₁₆	—	4	2	no	—
215	C₁₃×Q₁₆	—	4	1	no	—
216	C₁₃×Q₁₆	—	4	4	no	—
217	C₁₃×SD₁₆	—	4	2	no	—
218	C₁₃×SD₁₆	—	4	4	no	—
219	C₁₃×D₈	—	4	1	no	—
220	C₁₃×M₁₆	—	2	4	no	—
221	C₁₃×M₁₆	—	4	1	no	—
222	C₁₃×M₁₆	—	4	1	no	—
223	C₁₃×M₁₆	—	4	1	no	—
224	C₁₃×M₁₆	—	4	1	no	—
225	C₁₃×M₁₆	—	4	2	no	—
226	C₂×C₈×C₁₃	—	2	2	no	—
227	C₂×C₈×C₁₃	—	2	2	no	—
228	C₂×C₈×C₁₃	—	4	2	no	—
229	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
232	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
248	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
250	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
251	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
252	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	2	no	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
265	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
266	C₄²×C₁₃	—	2	4	no	—
267	C₄²×C₁₃	—	2	4	no	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	2	no	—
270	C₄²×C₁₃	C₂×D₄	1	2	yes	—
271	C₄²×C₁₃	C₂×D₄	1	2	yes	—
272	C₄²×C₁₃	C₂⁴	1	4	yes	—
273	#3495	C₂×C₁₃	1	2	yes	complemented
274	#3263	C₂×C₁₃	1	2	yes	complemented
275	#3261	C₂×C₁₃	1	2	yes	complemented
276	#3258	C₂×C₁₃	1	4	yes	complemented
277	#3256	C₂×C₁₃	1	2	yes	complemented
278	#3255	C₂×C₁₃	1	2	yes	complemented
279	#3252	C₂×C₁₃	1	4	yes	complemented
280	#3084	C₂×C₁₃	1	2	yes	complemented
281	#3082	C₂×C₁₃	1	2	yes	complemented
282	#3056	C₂×C₁₃	1	2	yes	complemented
283	#3054	C₂×C₁₃	1	1	yes	characteristic
284	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#3046	C₂×C₁₃	1	2	yes	complemented
286	#3044	C₂×C₁₃	1	2	yes	complemented
287	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	4	2	no	—
291	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₁₃	—	2	4	no	—
295	Q₈×C₁₃	—	2	2	no	—
296	Q₈×C₁₃	—	2	4	no	—
297	Q₈×C₁₃	—	2	2	no	—
298	Q₈×C₁₃	—	4	4	no	—
299	Q₈×C₁₃	—	8	4	no	—
300	D₄×C₁₃	—	2	2	no	—
301	D₄×C₁₃	—	2	2	no	—
302	D₄×C₁₃	—	4	4	no	—
303	D₄×C₁₃	—	4	4	no	—
304	D₄×C₁₃	—	8	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	4	no	—
320	C₂×C₄×C₁₃	—	8	4	no	—
321	C₂×C₄×C₁₃	—	8	2	no	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
330	C₈×C₁₃	—	2	1	no	—
331	C₈×C₁₃	—	2	1	no	—
332	C₈×C₁₃	—	2	1	no	—
333	C₈×C₁₃	—	2	1	no	—
334	C₈×C₁₃	—	2	4	no	—
335	C₂×#137	C₂²×C₁₃	1	2	yes	—
336	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
338	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	#556	—	2	2	no	—
341	#554	—	2	2	no	—
342	#552	—	2	4	no	—
343	#552	—	2	2	no	—
344	#552	—	2	2	no	—
345	#551	—	2	4	no	—
346	#544	C₂²×C₁₃	1	2	yes	—
347	#542	C₂²×C₁₃	1	4	yes	—
348	#541	C₂²×C₁₃	1	4	yes	—
349	#536	C₂²×C₁₃	1	2	yes	—
350	#533	C₂²×C₁₃	1	4	yes	—
351	#529	C₂²×C₁₃	1	4	yes	—
352	#525	C₂²×C₁₃	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
354	#520	C₂²×C₁₃	1	2	yes	—
355	#519	C₂²×C₁₃	1	2	yes	—
356	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
357	#479	C₂²×C₁₃	1	4	yes	complemented
358	#479	C₂²×C₁₃	1	4	yes	complemented
359	#479	C₂²×C₁₃	1	4	yes	complemented
360	#478	C₂²×C₁₃	1	4	yes	complemented
361	#477	C₂²×C₁₃	1	4	yes	complemented
362	#476	C₂²×C₁₃	1	4	yes	complemented
363	#475	C₂²×C₁₃	1	4	yes	complemented
364	#475	C₂²×C₁₃	1	4	yes	complemented
365	#470	C₂²×C₁₃	1	2	yes	—
366	#470	C₂²×C₁₃	1	4	yes	—
367	#470	C₂²×C₁₃	1	1	yes	characteristic
368	#470	C₂²×C₁₃	1	2	yes	—
369	#470	C₂²×C₁₃	1	2	yes	—
370	#470	C₂²×C₁₃	1	1	yes	characteristic
371	#470	C₂²×C₁₃	1	2	yes	—
372	#469	C₂²×C₁₃	1	1	yes	characteristic
373	#469	C₂²×C₁₃	1	1	yes	characteristic
374	#468	C₂²×C₁₃	1	2	yes	—
375	#468	C₂²×C₁₃	1	4	yes	—
376	#468	C₂²×C₁₃	1	2	yes	—
377	#467	C₂²×C₁₃	1	4	yes	—
378	#465	C₂²×C₁₃	1	4	yes	—
379	#464	C₂²×C₁₃	1	4	yes	complemented
380	#464	C₂²×C₁₃	1	4	yes	complemented
381	#464	C₂²×C₁₃	1	4	yes	complemented
382	#463	C₂²×C₁₃	1	4	yes	complemented
383	#462	C₂²×C₁₃	1	4	yes	complemented
384	#462	C₂²×C₁₃	1	4	yes	complemented
385	#462	C₂²×C₁₃	1	4	yes	complemented
386	#461	C₂²×C₁₃	1	4	yes	complemented
387	#428	C₂²×C₁₃	1	2	yes	—
388	#427	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
390	#424	C₂²×C₁₃	1	2	yes	—
391	#424	C₂²×C₁₃	1	2	yes	—
392	#424	C₂²×C₁₃	1	2	yes	—
393	#424	C₂²×C₁₃	1	2	yes	—
394	#423	C₂²×C₁₃	1	2	yes	—
395	#423	C₂²×C₁₃	1	2	yes	—
396	#419	C₂²×C₁₃	1	2	yes	—
397	#417	C₂²×C₁₃	1	2	yes	—
398	#416	C₂²×C₁₃	1	2	yes	—
399	C₂×#103	C₂²×C₁₃	1	2	yes	—
400	C₂²×C₁₃	—	2	2	no	—
401	C₂²×C₁₃	—	2	2	no	—
402	C₂²×C₁₃	—	2	2	no	—
403	C₂²×C₁₃	—	2	1	no	—
404	C₂²×C₁₃	—	2	1	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	2	no	—
407	C₂²×C₁₃	—	4	2	no	—
408	C₂²×C₁₃	—	8	2	no	—
409	C₂²×C₁₃	#537	1	2	yes	—
410	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₁₃	—	2	4	no	—
412	C₄×C₁₃	—	2	4	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	1	no	—
415	C₄×C₁₃	—	4	4	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	—	4	4	no	—
420	C₄×C₁₃	#537	1	2	yes	—
421	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂×#41	C₂³×C₁₃	1	2	yes	—
424	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
425	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	#137	—	4	4	no	—
427	#135	—	4	2	no	—
428	C₂×Q₁₆	—	4	2	no	—
429	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
430	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
431	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
433	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
434	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
435	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×M₁₆	—	4	2	no	—
437	C₂×M₁₆	—	4	2	no	—
438	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
439	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
441	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
450	#126	—	2	4	no	—
451	#126	—	2	4	no	—
452	#126	—	2	4	no	—
453	#126	—	2	4	no	—
454	#125	—	2	4	no	—
455	#125	—	2	4	no	—
456	#125	—	2	2	no	—
457	#125	—	2	4	no	—
458	#125	C₂³×C₁₃	1	4	yes	—
459	#124	—	2	4	no	—
460	#124	C₂³×C₁₃	1	4	yes	—
461	#123	—	2	2	no	—
462	#123	—	2	4	no	—
463	#123	—	2	4	no	—
464	#123	—	2	4	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	4	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
473	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
474	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
475	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
476	#121	C₂³×C₁₃	1	2	yes	—
477	#121	C₂³×C₁₃	1	2	yes	—
478	#120	—	2	2	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	—	2	4	no	—
482	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
483	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
484	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	4	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	C₂³×C₁₃	1	4	yes	—
490	#117	—	2	4	no	—
491	#117	—	2	2	no	—
492	#117	—	2	4	no	—
493	#117	—	2	4	no	—
494	#117	D₄×C₁₃	1	1	yes	characteristic
495	#117	D₄×C₁₃	1	2	yes	—
496	#117	D₄×C₁₃	1	1	yes	characteristic
497	#117	C₂³×C₁₃	1	2	yes	—
498	#117	C₂³×C₁₃	1	2	yes	—
499	#117	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₂²⋊C₄	—	2	2	no	—
505	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
507	#107	C₂³×C₁₃	1	2	yes	—
508	#107	C₂³×C₁₃	1	4	yes	—
509	#106	C₂³×C₁₃	1	2	yes	—
510	#106	C₂³×C₁₃	1	2	yes	—
511	#106	C₂³×C₁₃	1	1	yes	characteristic
512	#106	C₂³×C₁₃	1	1	yes	characteristic
513	#106	C₂³×C₁₃	1	4	yes	—
514	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
515	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
516	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
517	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
518	#103	C₂³×C₁₃	1	4	yes	—
519	#103	C₂³×C₁₃	1	4	yes	—
520	#103	C₂³×C₁₃	1	2	yes	—
521	#103	C₂³×C₁₃	1	2	yes	—
522	#103	C₂³×C₁₃	1	4	yes	—
523	#103	C₂³×C₁₃	1	4	yes	—
524	#103	C₂³×C₁₃	1	4	yes	—
525	#102	C₂³×C₁₃	1	2	yes	—
526	#102	C₂³×C₁₃	1	2	yes	—
527	#102	C₂³×C₁₃	1	4	yes	—
528	C₂×C₁₃	—	2	2	no	—
529	C₂×C₁₃	—	4	1	no	—
530	C₂×C₁₃	—	4	1	no	—
531	C₂×C₁₃	—	8	2	no	—
532	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
533	C₂×C₁₃	#3586	1	2	yes	—
534	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
535	#41	—	2	4	no	—
536	#41	—	2	4	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	4	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
542	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
560	Q₁₆	—	4	2	no	—
561	Q₁₆	—	4	2	no	—
562	Q₁₆	—	4	1	no	—
563	Q₁₆	—	4	4	no	—
564	SD₁₆	—	4	2	no	—
565	SD₁₆	—	4	4	no	—
566	D₈	—	4	1	no	—
567	M₁₆	—	2	4	no	—
568	M₁₆	—	4	1	no	—
569	M₁₆	—	4	1	no	—
570	M₁₆	—	4	1	no	—
571	M₁₆	—	4	1	no	—
572	M₁₆	—	4	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	4	2	no	—
576	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
579	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
580	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
597	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
598	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
611	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
612	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	2	no	—
617	C₄²	C₂×D₄×C₁₃	1	2	yes	—
618	C₄²	C₂×D₄×C₁₃	1	2	yes	—
619	C₄²	C₂⁴×C₁₃	1	4	yes	—
620	C₁₃	#60939	1	1	yes	characteristic, direct product factor, Sylow
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
626	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	Q₈	—	2	4	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	4	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	8	4	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	2	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	8	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	—	8	2	no	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
657	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
660	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
661	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
662	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
663	C₈	—	2	1	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	4	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	8	2	no	—
677	C₂²	C₁₃×#537	1	2	yes	—
678	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
679	C₄	—	2	4	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	4	no	—
688	C₄	C₁₃×#537	1	2	yes	—
689	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
690	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	8	2	no	—
695	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
696	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×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3495	C₂	semidirect
2. C₁₃×#3263	C₂	semidirect
3. C₁₃×#3261	C₂	semidirect
4. C₁₃×#3258	C₂	semidirect
5. C₁₃×#3256	C₂	semidirect
6. C₁₃×#3255	C₂	semidirect
7. C₁₃×#3252	C₂	semidirect
8. C₁₃×#3084	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
10. C₁₃×#3056	C₂	semidirect
12. C₂×C₁₃×#470	C₂	semidirect
13. C₁₃×#3046	C₂	semidirect
14. C₁₃×#3044	C₂	semidirect
15. C₁₃×#2905	C₂	semidirect
38. C₁₃×#479	C₂²	semidirect
39. C₁₃×#479	C₂²	semidirect
40. C₁₃×#479	C₂²	semidirect
41. C₁₃×#478	C₂²	semidirect
42. C₁₃×#477	C₂²	semidirect
43. C₁₃×#476	C₂²	semidirect
44. C₁₃×#475	C₂²	semidirect
45. C₁₃×#475	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
186. #60939	C₁₃	direct (N × H)
273. #3495	C₂×C₁₃	semidirect
274. #3263	C₂×C₁₃	semidirect
275. #3261	C₂×C₁₃	semidirect
276. #3258	C₂×C₁₃	semidirect
277. #3256	C₂×C₁₃	semidirect
278. #3255	C₂×C₁₃	semidirect
279. #3252	C₂×C₁₃	semidirect
280. #3084	C₂×C₁₃	semidirect
281. #3082	C₂×C₁₃	semidirect
282. #3056	C₂×C₁₃	semidirect
284. C₂×#470	C₂×C₁₃	semidirect
285. #3046	C₂×C₁₃	semidirect
286. #3044	C₂×C₁₃	semidirect
287. #2905	C₂×C₁₃	semidirect
357. #479	C₂²×C₁₃	semidirect
358. #479	C₂²×C₁₃	semidirect
359. #479	C₂²×C₁₃	semidirect
360. #478	C₂²×C₁₃	semidirect
361. #477	C₂²×C₁₃	semidirect
362. #476	C₂²×C₁₃	semidirect
363. #475	C₂²×C₁₃	semidirect
364. #475	C₂²×C₁₃	semidirect
379. #464	C₂²×C₁₃	semidirect
380. #464	C₂²×C₁₃	semidirect
381. #464	C₂²×C₁₃	semidirect
382. #463	C₂²×C₁₃	semidirect
383. #462	C₂²×C₁₃	semidirect
384. #462	C₂²×C₁₃	semidirect
385. #462	C₂²×C₁₃	semidirect
386. #461	C₂²×C₁₃	semidirect
620. C₁₃	#60939	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×#3263	2
C₁₃×#3261	2
C₁₃×#3258	2
C₁₃×#3256	2
C₁₃×#3255	2
C₁₃×#3252	2
C₁₃×#3084	2
C₁₃×#3082	2
C₁₃×#3056	2
C₁₃×#3054	2
C₂×C₁₃×#470	2
C₁₃×#3046	2
C₁₃×#3044	2
C₁₃×#2905	2
#60939	13

Subgroups — C13×#60939 #15747278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60939 #15747278