Subgroups — C₁₃×#61007 #15747346

Order 3328.

1704 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3263	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3262	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3233	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3199	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#3183	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3121	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3118	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	—	2	4	no	—
15	C₁₃×#556	—	2	4	no	—
16	C₁₃×#551	—	2	4	no	—
17	C₁₃×#551	—	2	4	no	—
18	C₁₃×#542	C₂²	1	4	yes	—
19	C₁₃×#542	C₂²	1	4	yes	complemented
20	C₁₃×#536	C₂²	1	2	yes	—
21	C₁₃×#535	C₂²	1	2	yes	—
22	C₁₃×#533	C₂²	1	2	yes	complemented
23	C₁₃×#529	C₂²	1	4	yes	—
24	C₁₃×#529	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
26	C₁₃×#519	C₂²	1	2	yes	complemented
27	C₁₃×#518	C₂²	1	2	yes	complemented
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#499	C₂²	1	2	yes	complemented
30	C₁₃×#499	C₂²	1	2	yes	complemented
31	C₁₃×#495	C₂²	1	2	yes	—
32	C₁₃×#495	C₂²	1	2	yes	—
33	C₁₃×#488	C₂²	1	4	yes	complemented
34	C₁₃×#488	C₂²	1	4	yes	complemented
35	C₁₃×#485	C₂²	1	4	yes	complemented
36	C₁₃×#485	C₂²	1	4	yes	complemented
37	C₁₃×#482	C₂²	1	4	yes	—
38	C₁₃×#482	C₂²	1	4	yes	—
39	C₁₃×#477	C₂²	1	4	yes	complemented
40	C₁₃×#476	C₂²	1	4	yes	complemented
41	C₁₃×#475	C₂²	1	4	yes	complemented
42	C₁₃×#474	C₂²	1	4	yes	complemented
43	C₁₃×#470	C₂²	1	2	yes	complemented
44	C₁₃×#469	C₂²	1	2	yes	—
45	C₁₃×#468	C₂²	1	4	yes	complemented
46	C₁₃×#467	C₂²	1	2	yes	complemented
47	C₁₃×#466	C₂²	1	2	yes	—
48	C₁₃×#465	C₂²	1	4	yes	complemented
49	C₁₃×#464	C₂²	1	4	yes	complemented
50	C₁₃×#464	C₂²	1	4	yes	complemented
51	C₁₃×#463	C₂²	1	4	yes	—
52	C₁₃×#463	C₂²	1	4	yes	—
53	C₁₃×#451	C₂²	1	4	yes	complemented
54	C₁₃×#450	C₂²	1	4	yes	complemented
55	C₁₃×#448	C₂²	1	4	yes	—
56	C₁₃×#447	C₂²	1	4	yes	—
57	C₁₃×#442	C₂²	1	2	yes	—
58	C₁₃×#441	C₂²	1	2	yes	complemented
59	C₁₃×#440	C₂²	1	4	yes	complemented
60	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
61	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
62	C₄×C₁₃×D₈	C₂²	1	2	yes	—
63	C₁₃×#433	C₂²	1	4	yes	complemented
64	C₁₃×#431	C₂²	1	4	yes	complemented
65	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#408	C₂²	1	1	yes	characteristic
68	C₁₃×#408	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×D₈	C₂³	1	2	yes	—
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#126	—	2	4	no	—
88	C₁₃×#126	—	2	4	no	—
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#126	—	2	4	no	—
91	C₁₃×#125	C₂³	1	4	yes	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	—	2	4	no	—
95	C₁₃×#124	—	2	4	no	—
96	C₁₃×#124	—	2	4	no	—
97	C₁₃×#124	C₂³	1	4	yes	—
98	C₁₃×#124	C₂³	1	4	yes	—
99	C₁₃×#123	—	2	2	no	—
100	C₁₃×#123	—	2	2	no	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×#123	—	2	4	no	—
103	C₁₃×#123	—	2	4	no	—
104	C₁₃×#123	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	—	2	4	no	—
107	C₁₃×C₂²⋊Q₈	—	2	4	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×#121	C₂³	1	4	yes	—
111	C₁₃×#121	C₂³	1	4	yes	—
112	C₁₃×#120	—	2	2	no	—
113	C₁₃×#120	—	2	2	no	—
114	C₄×Q₈×C₁₃	—	2	4	no	—
115	C₄×Q₈×C₁₃	—	2	4	no	—
116	C₄×Q₈×C₁₃	D₄	1	2	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
119	C₄×D₄×C₁₃	—	2	4	no	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₄×D₄×C₁₃	—	2	4	no	—
122	C₄×D₄×C₁₃	D₄	1	2	yes	—
123	C₄×D₄×C₁₃	D₄	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₄×D₄×C₁₃	C₂³	1	4	yes	—
126	C₁₃×#117	—	2	4	no	—
127	C₁₃×#117	—	2	4	no	—
128	C₁₃×#117	—	2	4	no	—
129	C₁₃×#117	C₂³	1	2	yes	—
130	C₁₃×#117	C₂³	1	2	yes	—
131	C₁₃×#117	C₂³	1	1	yes	characteristic
132	C₁₃×#117	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₁₃×#107	C₂³	1	2	yes	—
138	C₁₃×#107	C₂³	1	2	yes	—
139	C₁₃×#107	C₂³	1	4	yes	—
140	C₁₃×#106	C₂³	1	4	yes	—
141	C₁₃×#106	C₂³	1	2	yes	—
142	C₁₃×#106	C₂³	1	2	yes	—
143	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
144	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
145	C₁₃×#103	C₂³	1	4	yes	—
146	C₁₃×#103	C₂³	1	4	yes	—
147	C₁₃×#103	C₂³	1	4	yes	—
148	C₁₃×#103	C₂³	1	4	yes	—
149	C₁₃×#102	C₂³	1	4	yes	—
150	C₁₃×#102	C₂³	1	4	yes	—
151	C₁₃×#102	C₂³	1	4	yes	—
152	C₁₃×#102	C₂³	1	4	yes	—
153	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
154	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₁₃×#97	C₂³	1	2	yes	—
156	C₄×C₈×C₁₃	C₂³	1	2	yes	—
157	C₄×C₈×C₁₃	C₂³	1	2	yes	—
158	C₄×C₈×C₁₃	C₂³	1	2	yes	—
159	#61007	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₃	—	2	2	no	—
161	C₁₃×#41	—	4	1	no	—
162	C₁₃×#41	—	4	1	no	—
163	C₂×Q₈×C₁₃	—	2	2	no	—
164	C₂×Q₈×C₁₃	—	2	4	no	—
165	C₂×Q₈×C₁₃	—	4	2	no	—
166	C₂×Q₈×C₁₃	—	4	2	no	—
167	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	2	no	—
172	C₂×D₄×C₁₃	—	4	2	no	—
173	C₂×D₄×C₁₃	—	4	2	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×Q₁₆	—	4	2	no	—
185	C₁₃×Q₁₆	—	4	2	no	—
186	C₁₃×SD₁₆	—	4	4	no	—
187	C₁₃×SD₁₆	—	4	4	no	—
188	C₁₃×D₈	—	4	2	no	—
189	C₁₃×D₈	—	4	2	no	—
190	C₁₃×M₁₆	—	4	1	no	—
191	C₁₃×M₁₆	—	4	1	no	—
192	C₂×C₈×C₁₃	—	4	1	no	—
193	C₂×C₈×C₁₃	—	4	1	no	—
194	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
196	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
197	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
209	C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
222	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	—	2	4	no	—
225	C₄²×C₁₃	—	2	2	no	—
226	C₄²×C₁₃	—	2	2	no	—
227	C₄²×C₁₃	C₂×D₄	1	2	yes	—
228	C₄²×C₁₃	C₂×D₄	1	4	yes	—
229	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₄²×C₁₃	C₂⁴	1	2	yes	—
232	#3510	C₂×C₁₃	1	2	yes	complemented
233	#3263	C₂×C₁₃	1	2	yes	complemented
234	#3262	C₂×C₁₃	1	2	yes	complemented
235	#3233	C₂×C₁₃	1	4	yes	complemented
236	#3211	C₂×C₁₃	1	4	yes	complemented
237	#3202	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3200	C₂×C₁₃	1	2	yes	complemented
239	#3199	C₂×C₁₃	1	1	yes	characteristic
240	#3183	C₂×C₁₃	1	2	yes	complemented
241	#3168	C₂×C₁₃	1	2	yes	complemented
242	#3121	C₂×C₁₃	1	4	yes	complemented
243	#3118	C₂×C₁₃	1	4	yes	complemented
244	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	4	no	—
246	C₂³×C₁₃	—	4	4	no	—
247	C₂³×C₁₃	—	8	4	no	—
248	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	Q₈×C₁₃	—	2	4	no	—
251	Q₈×C₁₃	—	2	4	no	—
252	Q₈×C₁₃	—	4	1	no	—
253	Q₈×C₁₃	—	4	4	no	—
254	Q₈×C₁₃	—	8	4	no	—
255	D₄×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	2	4	no	—
257	D₄×C₁₃	—	4	2	no	—
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	8	4	no	—
261	D₄×C₁₃	—	8	4	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	8	4	no	—
273	C₂×C₄×C₁₃	—	8	4	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
280	C₈×C₁₃	—	2	2	no	—
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	2	2	no	—
284	#559	—	2	4	no	—
285	#556	—	2	4	no	—
286	#551	—	2	4	no	—
287	#551	—	2	4	no	—
288	#542	C₂²×C₁₃	1	4	yes	—
289	#542	C₂²×C₁₃	1	4	yes	complemented
290	#536	C₂²×C₁₃	1	2	yes	—
291	#535	C₂²×C₁₃	1	2	yes	—
292	#533	C₂²×C₁₃	1	2	yes	complemented
293	#529	C₂²×C₁₃	1	4	yes	—
294	#529	C₂²×C₁₃	1	4	yes	complemented
295	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
296	#519	C₂²×C₁₃	1	2	yes	complemented
297	#518	C₂²×C₁₃	1	2	yes	complemented
298	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
299	#499	C₂²×C₁₃	1	2	yes	complemented
300	#499	C₂²×C₁₃	1	2	yes	complemented
301	#495	C₂²×C₁₃	1	2	yes	—
302	#495	C₂²×C₁₃	1	2	yes	—
303	#488	C₂²×C₁₃	1	4	yes	complemented
304	#488	C₂²×C₁₃	1	4	yes	complemented
305	#485	C₂²×C₁₃	1	4	yes	complemented
306	#485	C₂²×C₁₃	1	4	yes	complemented
307	#482	C₂²×C₁₃	1	4	yes	—
308	#482	C₂²×C₁₃	1	4	yes	—
309	#477	C₂²×C₁₃	1	4	yes	complemented
310	#476	C₂²×C₁₃	1	4	yes	complemented
311	#475	C₂²×C₁₃	1	4	yes	complemented
312	#474	C₂²×C₁₃	1	4	yes	complemented
313	#470	C₂²×C₁₃	1	2	yes	complemented
314	#469	C₂²×C₁₃	1	2	yes	—
315	#468	C₂²×C₁₃	1	4	yes	complemented
316	#467	C₂²×C₁₃	1	2	yes	complemented
317	#466	C₂²×C₁₃	1	2	yes	—
318	#465	C₂²×C₁₃	1	4	yes	complemented
319	#464	C₂²×C₁₃	1	4	yes	complemented
320	#464	C₂²×C₁₃	1	4	yes	complemented
321	#463	C₂²×C₁₃	1	4	yes	—
322	#463	C₂²×C₁₃	1	4	yes	—
323	#451	C₂²×C₁₃	1	4	yes	complemented
324	#450	C₂²×C₁₃	1	4	yes	complemented
325	#448	C₂²×C₁₃	1	4	yes	—
326	#447	C₂²×C₁₃	1	4	yes	—
327	#442	C₂²×C₁₃	1	2	yes	—
328	#441	C₂²×C₁₃	1	2	yes	complemented
329	#440	C₂²×C₁₃	1	4	yes	complemented
330	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
331	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
332	C₄×D₈	C₂²×C₁₃	1	2	yes	—
333	#433	C₂²×C₁₃	1	4	yes	complemented
334	#431	C₂²×C₁₃	1	4	yes	complemented
335	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	#408	C₂²×C₁₃	1	1	yes	characteristic
338	#408	C₂²×C₁₃	1	1	yes	characteristic
339	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	—	2	1	no	—
345	C₂²×C₁₃	—	4	4	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	16	4	no	—
349	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	4	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	—	4	4	no	—
357	C₄×C₁₃	—	4	4	no	—
358	C₄×C₁₃	#585	1	1	yes	characteristic
359	C₄×C₁₃	#585	1	1	yes	characteristic
360	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
363	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
364	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
365	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
366	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
367	C₂×D₈	C₂³×C₁₃	1	2	yes	—
368	C₂×D₈	C₂³×C₁₃	1	2	yes	—
369	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
375	#127	—	2	2	no	—
376	#126	—	2	4	no	—
377	#126	—	2	4	no	—
378	#126	—	2	4	no	—
379	#126	—	2	4	no	—
380	#125	C₂³×C₁₃	1	4	yes	—
381	#124	—	2	2	no	—
382	#124	—	2	2	no	—
383	#124	—	2	4	no	—
384	#124	—	2	4	no	—
385	#124	—	2	4	no	—
386	#124	C₂³×C₁₃	1	4	yes	—
387	#124	C₂³×C₁₃	1	4	yes	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	4	no	—
391	#123	—	2	4	no	—
392	#123	—	2	4	no	—
393	#123	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	4	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
398	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
399	#121	C₂³×C₁₃	1	4	yes	—
400	#121	C₂³×C₁₃	1	4	yes	—
401	#120	—	2	2	no	—
402	#120	—	2	2	no	—
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	2	4	no	—
405	C₄×Q₈	D₄×C₁₃	1	2	yes	—
406	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
407	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	—	2	4	no	—
410	C₄×D₄	—	2	4	no	—
411	C₄×D₄	D₄×C₁₃	1	2	yes	—
412	C₄×D₄	D₄×C₁₃	1	4	yes	—
413	C₄×D₄	C₂³×C₁₃	1	4	yes	—
414	C₄×D₄	C₂³×C₁₃	1	4	yes	—
415	#117	—	2	4	no	—
416	#117	—	2	4	no	—
417	#117	—	2	4	no	—
418	#117	C₂³×C₁₃	1	2	yes	—
419	#117	C₂³×C₁₃	1	2	yes	—
420	#117	C₂³×C₁₃	1	2	yes	—
421	#117	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	4	no	—
423	C₂×C₂²⋊C₄	—	2	4	no	—
424	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	#107	C₂³×C₁₃	1	2	yes	—
427	#107	C₂³×C₁₃	1	2	yes	—
428	#107	C₂³×C₁₃	1	4	yes	—
429	#106	C₂³×C₁₃	1	4	yes	—
430	#106	C₂³×C₁₃	1	2	yes	—
431	#106	C₂³×C₁₃	1	2	yes	—
432	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
433	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
434	#103	C₂³×C₁₃	1	4	yes	—
435	#103	C₂³×C₁₃	1	4	yes	—
436	#103	C₂³×C₁₃	1	4	yes	—
437	#103	C₂³×C₁₃	1	4	yes	—
438	#102	C₂³×C₁₃	1	4	yes	—
439	#102	C₂³×C₁₃	1	4	yes	—
440	#102	C₂³×C₁₃	1	4	yes	—
441	#102	C₂³×C₁₃	1	4	yes	—
442	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
443	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
444	#97	C₂³×C₁₃	1	2	yes	—
445	C₄×C₈	C₂³×C₁₃	1	2	yes	—
446	C₄×C₈	C₂³×C₁₃	1	2	yes	—
447	C₄×C₈	C₂³×C₁₃	1	2	yes	—
448	C₂×C₁₃	—	4	1	no	—
449	C₂×C₁₃	—	4	2	no	—
450	C₂×C₁₃	—	8	4	no	—
451	C₂×C₁₃	#3449	1	1	yes	characteristic
452	C₂×C₁₃	#3584	1	2	yes	—
453	C₂⁴	—	2	2	no	—
454	#41	—	4	1	no	—
455	#41	—	4	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
477	Q₁₆	—	4	2	no	—
478	Q₁₆	—	4	2	no	—
479	SD₁₆	—	4	4	no	—
480	SD₁₆	—	4	4	no	—
481	D₈	—	4	2	no	—
482	D₈	—	4	2	no	—
483	M₁₆	—	4	1	no	—
484	M₁₆	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
488	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
489	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
490	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
491	C₄⋊C₄	—	2	4	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	C₂×D₄×C₁₃	1	4	yes	—
499	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
515	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂×D₄×C₁₃	1	2	yes	—
521	C₄²	C₂×D₄×C₁₃	1	4	yes	—
522	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₄²	C₂⁴×C₁₃	1	2	yes	—
525	C₁₃	#61007	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	4	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	8	4	no	—
529	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
530	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	Q₈	—	2	4	no	—
532	Q₈	—	2	4	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	4	no	—
535	Q₈	—	8	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	4	no	—
541	D₄	—	8	4	no	—
542	D₄	—	8	4	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
558	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	16	4	no	—
573	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	4	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	C₁₃×#585	1	1	yes	characteristic
583	C₄	C₁₃×#585	1	1	yes	characteristic
584	C₂	—	4	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	8	4	no	—
587	C₂	C₁₃×#3449	1	1	yes	characteristic
588	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3199	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
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3263	C₂	semidirect
3. C₁₃×#3262	C₂	semidirect
4. C₁₃×#3233	C₂	semidirect
5. C₁₃×#3211	C₂	semidirect
6. C₁₃×#3202	C₂	semidirect
7. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3183	C₂	semidirect
10. C₁₃×#3168	C₂	semidirect
11. C₁₃×#3121	C₂	semidirect
12. C₁₃×#3118	C₂	semidirect
13. C₁₃×#2922	C₂	semidirect
19. C₁₃×#542	C₂²	semidirect
22. C₁₃×#533	C₂²	semidirect
24. C₁₃×#529	C₂²	semidirect
25. C₂×C₁₃×#124	C₂²	semidirect
26. C₁₃×#519	C₂²	semidirect
27. C₁₃×#518	C₂²	semidirect
29. C₁₃×#499	C₂²	semidirect
30. C₁₃×#499	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#488	C₂²	semidirect
35. C₁₃×#485	C₂²	semidirect
36. C₁₃×#485	C₂²	semidirect
39. C₁₃×#477	C₂²	semidirect
40. C₁₃×#476	C₂²	semidirect
41. C₁₃×#475	C₂²	semidirect
42. C₁₃×#474	C₂²	semidirect
43. C₁₃×#470	C₂²	semidirect
45. C₁₃×#468	C₂²	semidirect
46. C₁₃×#467	C₂²	semidirect
48. C₁₃×#465	C₂²	semidirect
49. C₁₃×#464	C₂²	semidirect
50. C₁₃×#464	C₂²	semidirect
53. C₁₃×#451	C₂²	semidirect
54. C₁₃×#450	C₂²	semidirect
58. C₁₃×#441	C₂²	semidirect
59. C₁₃×#440	C₂²	semidirect
60. C₄×C₁₃×Q₁₆	C₂²	semidirect
61. C₄×C₁₃×SD₁₆	C₂²	semidirect
63. C₁₃×#433	C₂²	semidirect
64. C₁₃×#431	C₂²	semidirect
65. C₁₃×#424	C₂²	semidirect
66. C₁₃×#424	C₂²	semidirect
69. C₄×C₁₃×M₁₆	C₂²	semidirect
70. C₂×C₄×C₈×C₁₃	C₂²	semidirect
159. #61007	C₁₃	direct (N × H)
232. #3510	C₂×C₁₃	semidirect
233. #3263	C₂×C₁₃	semidirect
234. #3262	C₂×C₁₃	semidirect
235. #3233	C₂×C₁₃	semidirect
236. #3211	C₂×C₁₃	semidirect
237. #3202	C₂×C₁₃	semidirect
238. #3200	C₂×C₁₃	semidirect
240. #3183	C₂×C₁₃	semidirect
241. #3168	C₂×C₁₃	semidirect
242. #3121	C₂×C₁₃	semidirect
243. #3118	C₂×C₁₃	semidirect
244. #2922	C₂×C₁₃	semidirect
289. #542	C₂²×C₁₃	semidirect
292. #533	C₂²×C₁₃	semidirect
294. #529	C₂²×C₁₃	semidirect
295. C₂×#124	C₂²×C₁₃	semidirect
296. #519	C₂²×C₁₃	semidirect
297. #518	C₂²×C₁₃	semidirect
299. #499	C₂²×C₁₃	semidirect
300. #499	C₂²×C₁₃	semidirect
303. #488	C₂²×C₁₃	semidirect
304. #488	C₂²×C₁₃	semidirect
305. #485	C₂²×C₁₃	semidirect
306. #485	C₂²×C₁₃	semidirect
309. #477	C₂²×C₁₃	semidirect
310. #476	C₂²×C₁₃	semidirect
311. #475	C₂²×C₁₃	semidirect
312. #474	C₂²×C₁₃	semidirect
313. #470	C₂²×C₁₃	semidirect
315. #468	C₂²×C₁₃	semidirect
316. #467	C₂²×C₁₃	semidirect
318. #465	C₂²×C₁₃	semidirect
319. #464	C₂²×C₁₃	semidirect
320. #464	C₂²×C₁₃	semidirect
323. #451	C₂²×C₁₃	semidirect
324. #450	C₂²×C₁₃	semidirect
328. #441	C₂²×C₁₃	semidirect
329. #440	C₂²×C₁₃	semidirect
330. C₄×Q₁₆	C₂²×C₁₃	semidirect
331. C₄×SD₁₆	C₂²×C₁₃	semidirect
333. #433	C₂²×C₁₃	semidirect
334. #431	C₂²×C₁₃	semidirect
335. #424	C₂²×C₁₃	semidirect
336. #424	C₂²×C₁₃	semidirect
339. C₄×M₁₆	C₂²×C₁₃	semidirect
340. C₂×C₄×C₈	C₂²×C₁₃	semidirect
525. C₁₃	#61007	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×#3510	2
C₁₃×#3263	2
C₁₃×#3262	2
C₁₃×#3233	2
C₁₃×#3211	2
C₁₃×#3202	2
C₁₃×#3200	2
C₁₃×#3199	2
C₁₃×#3183	2
C₁₃×#3168	2
C₁₃×#3121	2
C₁₃×#3118	2
C₁₃×#2922	2
#61007	13

Subgroups — C13×#61007 #15747346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61007 #15747346