Subgroups — C₁₃×#61020 #15747359

Order 3328.

1668 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3261	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3260	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3236	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3120	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#553	—	2	2	no	—
19	C₁₃×#553	—	2	2	no	—
20	C₁₃×#553	—	2	2	no	—
21	C₁₃×#552	—	2	2	no	—
22	C₁₃×#552	—	2	2	no	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#541	C₂²	1	2	yes	—
25	C₁₃×#541	C₂²	1	1	yes	characteristic
26	C₁₃×#541	C₂²	1	2	yes	—
27	C₁₃×#541	C₂²	1	1	yes	characteristic
28	C₁₃×#540	C₂²	1	1	yes	characteristic
29	C₁₃×#540	C₂²	1	1	yes	characteristic
30	C₁₃×#537	C₂²	1	2	yes	—
31	C₁₃×#536	C₂²	1	2	yes	—
32	C₁₃×#533	C₂²	1	2	yes	—
33	C₁₃×#533	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
40	C₁₃×#520	C₂²	1	2	yes	—
41	C₁₃×#519	C₂²	1	2	yes	—
42	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	—
44	C₁₃×#501	C₂²	1	2	yes	—
45	C₁₃×#497	C₂²	1	2	yes	—
46	C₁₃×#497	C₂²	1	2	yes	—
47	C₁₃×#491	C₂²	1	2	yes	—
48	C₁₃×#491	C₂²	1	2	yes	—
49	C₁₃×#489	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	2	yes	—
51	C₁₃×#485	C₂²	1	4	yes	—
52	C₁₃×#484	C₂²	1	4	yes	—
53	C₁₃×#483	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#470	C₂²	1	4	yes	—
60	C₁₃×#468	C₂²	1	4	yes	—
61	C₁₃×#467	C₂²	1	4	yes	—
62	C₁₃×#465	C₂²	1	4	yes	—
63	C₁₃×#462	C₂²	1	4	yes	—
64	C₁₃×#462	C₂²	1	4	yes	—
65	C₁₃×#461	C₂²	1	4	yes	—
66	C₁₃×#460	C₂²	1	4	yes	—
67	C₁₃×#452	C₂²	1	4	yes	—
68	C₁₃×#452	C₂²	1	4	yes	—
69	C₁₃×#451	C₂²	1	4	yes	—
70	C₁₃×#448	C₂²	1	4	yes	—
71	C₁₃×#441	C₂²	1	4	yes	—
72	C₁₃×#440	C₂²	1	4	yes	—
73	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
74	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
75	C₁₃×#433	C₂²	1	2	yes	—
76	C₁₃×#433	C₂²	1	2	yes	—
77	C₁₃×#432	C₂²	1	2	yes	—
78	C₁₃×#432	C₂²	1	2	yes	—
79	C₁₃×#424	C₂²	1	2	yes	—
80	C₁₃×#408	C₂²	1	2	yes	—
81	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
83	C₂×C₁₃×#41	C₂³	1	2	yes	—
84	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
91	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	—	2	2	no	—
93	C₁₃×C₄⋊Q₈	—	2	2	no	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×#127	C₂³	1	1	yes	characteristic
99	C₁₃×#126	—	2	4	no	—
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#126	—	2	2	no	—
102	C₁₃×#126	—	2	2	no	—
103	C₁₃×#126	—	2	2	no	—
104	C₁₃×#126	—	2	2	no	—
105	C₁₃×#125	—	2	2	no	—
106	C₁₃×#125	—	2	2	no	—
107	C₁₃×#125	—	2	4	no	—
108	C₁₃×#125	—	2	4	no	—
109	C₁₃×#125	—	2	2	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	C₂³	1	2	yes	—
113	C₁₃×#125	C₂³	1	1	yes	characteristic
114	C₁₃×#125	C₂³	1	1	yes	characteristic
115	C₁₃×#125	C₂³	1	2	yes	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	2	no	—
122	C₁₃×#123	—	2	2	no	—
123	C₁₃×#123	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	2	yes	—
140	C₄×Q₈×C₁₃	—	2	4	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	D₄	1	2	yes	—
145	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	D₄	1	2	yes	—
155	C₄×D₄×C₁₃	D₄	1	2	yes	—
156	C₄×D₄×C₁₃	D₄	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	C₂³	1	2	yes	—
159	C₁₃×#117	—	2	2	no	—
160	C₁₃×#117	—	2	2	no	—
161	C₁₃×#117	—	2	2	no	—
162	C₁₃×#117	—	2	4	no	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₁₃×#117	C₂³	1	1	yes	characteristic
167	C₁₃×#117	C₂³	1	1	yes	characteristic
168	C₁₃×#117	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₁₃×#107	C₂³	1	4	yes	—
177	C₁₃×#107	C₂³	1	4	yes	—
178	C₁₃×#106	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	4	yes	—
180	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#103	C₂³	1	4	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₁₃×#97	C₂³	1	2	yes	—
194	C₁₃×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₁₃	C₂³	1	2	yes	—
196	#61020	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₃×#41	—	4	2	no	—
198	C₁₃×#41	—	4	4	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	—	4	4	no	—
202	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
204	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₁₃×Q₁₆	—	4	4	no	—
225	C₁₃×Q₁₆	—	4	4	no	—
226	C₁₃×SD₁₆	—	4	4	no	—
227	C₁₃×SD₁₆	—	4	4	no	—
228	C₁₃×M₁₆	—	4	2	no	—
229	C₂×C₈×C₁₃	—	4	2	no	—
230	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
231	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
252	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
254	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
269	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
270	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
271	C₄²×C₁₃	—	2	2	no	—
272	C₄²×C₁₃	—	2	2	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	C₂×D₄	1	2	yes	—
277	C₄²×C₁₃	C₂×D₄	1	2	yes	—
278	C₄²×C₁₃	C₂×D₄	1	2	yes	—
279	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
283	#3512	C₂×C₁₃	1	1	yes	characteristic
284	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#3261	C₂×C₁₃	1	2	yes	complemented
286	#3260	C₂×C₁₃	1	2	yes	complemented
287	#3240	C₂×C₁₃	1	2	yes	complemented
288	#3236	C₂×C₁₃	1	2	yes	complemented
289	#3218	C₂×C₁₃	1	2	yes	complemented
290	#3216	C₂×C₁₃	1	2	yes	complemented
291	#3201	C₂×C₁₃	1	4	yes	complemented
292	#3181	C₂×C₁₃	1	2	yes	complemented
293	#3172	C₂×C₁₃	1	2	yes	complemented
294	#3127	C₂×C₁₃	1	2	yes	complemented
295	#3126	C₂×C₁₃	1	2	yes	complemented
296	#3120	C₂×C₁₃	1	4	yes	complemented
297	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₁₃	—	2	4	no	—
303	Q₈×C₁₃	—	2	4	no	—
304	Q₈×C₁₃	—	2	4	no	—
305	Q₈×C₁₃	—	4	1	no	—
306	Q₈×C₁₃	—	4	4	no	—
307	Q₈×C₁₃	—	4	4	no	—
308	D₄×C₁₃	—	2	4	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	4	no	—
313	D₄×C₁₃	—	8	2	no	—
314	D₄×C₁₃	—	8	2	no	—
315	D₄×C₁₃	—	8	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	4	2	no	—
325	C₂×C₄×C₁₃	—	4	2	no	—
326	C₂×C₄×C₁₃	—	4	2	no	—
327	C₂×C₄×C₁₃	—	4	4	no	—
328	C₂×C₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	8	2	no	—
330	C₂×C₄×C₁₃	—	8	2	no	—
331	C₂×C₄×C₁₃	—	8	2	no	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
340	C₈×C₁₃	—	2	4	no	—
341	C₈×C₁₃	—	2	4	no	—
342	#557	—	2	2	no	—
343	#556	—	2	2	no	—
344	#553	—	2	2	no	—
345	#553	—	2	2	no	—
346	#553	—	2	2	no	—
347	#552	—	2	2	no	—
348	#552	—	2	2	no	—
349	#552	—	2	2	no	—
350	#541	C₂²×C₁₃	1	2	yes	—
351	#541	C₂²×C₁₃	1	1	yes	characteristic
352	#541	C₂²×C₁₃	1	2	yes	—
353	#541	C₂²×C₁₃	1	1	yes	characteristic
354	#540	C₂²×C₁₃	1	1	yes	characteristic
355	#540	C₂²×C₁₃	1	1	yes	characteristic
356	#537	C₂²×C₁₃	1	2	yes	—
357	#536	C₂²×C₁₃	1	2	yes	—
358	#533	C₂²×C₁₃	1	2	yes	—
359	#533	C₂²×C₁₃	1	2	yes	—
360	#533	C₂²×C₁₃	1	1	yes	characteristic
361	#532	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
363	#529	C₂²×C₁₃	1	2	yes	—
364	#529	C₂²×C₁₃	1	2	yes	—
365	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
366	#520	C₂²×C₁₃	1	2	yes	—
367	#519	C₂²×C₁₃	1	2	yes	—
368	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
369	#501	C₂²×C₁₃	1	2	yes	—
370	#501	C₂²×C₁₃	1	2	yes	—
371	#497	C₂²×C₁₃	1	2	yes	—
372	#497	C₂²×C₁₃	1	2	yes	—
373	#491	C₂²×C₁₃	1	2	yes	—
374	#491	C₂²×C₁₃	1	2	yes	—
375	#489	C₂²×C₁₃	1	2	yes	—
376	#489	C₂²×C₁₃	1	2	yes	—
377	#485	C₂²×C₁₃	1	4	yes	—
378	#484	C₂²×C₁₃	1	4	yes	—
379	#483	C₂²×C₁₃	1	4	yes	—
380	#482	C₂²×C₁₃	1	4	yes	—
381	#479	C₂²×C₁₃	1	4	yes	—
382	#479	C₂²×C₁₃	1	4	yes	—
383	#479	C₂²×C₁₃	1	4	yes	—
384	#478	C₂²×C₁₃	1	4	yes	—
385	#470	C₂²×C₁₃	1	4	yes	—
386	#468	C₂²×C₁₃	1	4	yes	—
387	#467	C₂²×C₁₃	1	4	yes	—
388	#465	C₂²×C₁₃	1	4	yes	—
389	#462	C₂²×C₁₃	1	4	yes	—
390	#462	C₂²×C₁₃	1	4	yes	—
391	#461	C₂²×C₁₃	1	4	yes	—
392	#460	C₂²×C₁₃	1	4	yes	—
393	#452	C₂²×C₁₃	1	4	yes	—
394	#452	C₂²×C₁₃	1	4	yes	—
395	#451	C₂²×C₁₃	1	4	yes	—
396	#448	C₂²×C₁₃	1	4	yes	—
397	#441	C₂²×C₁₃	1	4	yes	—
398	#440	C₂²×C₁₃	1	4	yes	—
399	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
400	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
401	#433	C₂²×C₁₃	1	2	yes	—
402	#433	C₂²×C₁₃	1	2	yes	—
403	#432	C₂²×C₁₃	1	2	yes	—
404	#432	C₂²×C₁₃	1	2	yes	—
405	#424	C₂²×C₁₃	1	2	yes	—
406	#408	C₂²×C₁₃	1	2	yes	—
407	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	2	1	no	—
413	C₂²×C₁₃	—	2	1	no	—
414	C₂²×C₁₃	—	2	1	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	2	no	—
422	C₄×C₁₃	—	2	2	no	—
423	C₄×C₁₃	—	2	1	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	4	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	4	no	—
431	C₄×C₁₃	#585	1	2	yes	—
432	C₂×#41	C₂³×C₁₃	1	2	yes	—
433	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
435	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
436	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
438	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
439	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
440	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
444	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
445	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
447	#127	C₂³×C₁₃	1	1	yes	characteristic
448	#126	—	2	4	no	—
449	#126	—	2	4	no	—
450	#126	—	2	2	no	—
451	#126	—	2	2	no	—
452	#126	—	2	2	no	—
453	#126	—	2	2	no	—
454	#125	—	2	2	no	—
455	#125	—	2	2	no	—
456	#125	—	2	4	no	—
457	#125	—	2	4	no	—
458	#125	—	2	2	no	—
459	#125	—	2	2	no	—
460	#125	—	2	2	no	—
461	#125	C₂³×C₁₃	1	2	yes	—
462	#125	C₂³×C₁₃	1	1	yes	characteristic
463	#125	C₂³×C₁₃	1	1	yes	characteristic
464	#125	C₂³×C₁₃	1	2	yes	—
465	#124	—	2	2	no	—
466	#124	C₂³×C₁₃	1	2	yes	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	#123	—	2	2	no	—
470	#123	—	2	2	no	—
471	#123	—	2	2	no	—
472	#123	—	2	2	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
478	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
479	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
480	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
481	#121	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	C₂³×C₁₃	1	2	yes	—
488	#121	C₂³×C₁₃	1	2	yes	—
489	C₄×Q₈	—	2	4	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	D₄×C₁₃	1	2	yes	—
494	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
495	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
496	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	D₄×C₁₃	1	2	yes	—
504	C₄×D₄	D₄×C₁₃	1	2	yes	—
505	C₄×D₄	D₄×C₁₃	1	2	yes	—
506	C₄×D₄	C₂³×C₁₃	1	2	yes	—
507	C₄×D₄	C₂³×C₁₃	1	2	yes	—
508	#117	—	2	2	no	—
509	#117	—	2	2	no	—
510	#117	—	2	2	no	—
511	#117	—	2	4	no	—
512	#117	—	2	2	no	—
513	#117	—	2	2	no	—
514	#117	C₂³×C₁₃	1	2	yes	—
515	#117	C₂³×C₁₃	1	1	yes	characteristic
516	#117	C₂³×C₁₃	1	1	yes	characteristic
517	#117	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
525	#107	C₂³×C₁₃	1	4	yes	—
526	#107	C₂³×C₁₃	1	4	yes	—
527	#106	C₂³×C₁₃	1	4	yes	—
528	#106	C₂³×C₁₃	1	4	yes	—
529	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
530	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
531	#103	C₂³×C₁₃	1	4	yes	—
532	#103	C₂³×C₁₃	1	4	yes	—
533	#103	C₂³×C₁₃	1	4	yes	—
534	#103	C₂³×C₁₃	1	4	yes	—
535	#103	C₂³×C₁₃	1	4	yes	—
536	#103	C₂³×C₁₃	1	4	yes	—
537	#102	C₂³×C₁₃	1	4	yes	—
538	#102	C₂³×C₁₃	1	4	yes	—
539	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
540	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
541	#97	C₂³×C₁₃	1	2	yes	—
542	#97	C₂³×C₁₃	1	2	yes	—
543	#97	C₂³×C₁₃	1	2	yes	—
544	C₄×C₈	C₂³×C₁₃	1	2	yes	—
545	C₂×C₁₃	—	4	1	no	—
546	C₂×C₁₃	—	4	1	no	—
547	C₂×C₁₃	—	4	1	no	—
548	C₂×C₁₃	—	8	2	no	—
549	C₂×C₁₃	#3449	1	1	yes	characteristic
550	C₂×C₁₃	#3586	1	2	yes	—
551	#41	—	4	2	no	—
552	#41	—	4	4	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	4	4	no	—
556	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
558	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
573	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
574	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
578	Q₁₆	—	4	4	no	—
579	Q₁₆	—	4	4	no	—
580	SD₁₆	—	4	4	no	—
581	SD₁₆	—	4	4	no	—
582	M₁₆	—	4	2	no	—
583	C₂×C₈	—	4	2	no	—
584	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
585	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
606	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
607	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
608	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
609	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
610	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
623	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	C₂×D₄×C₁₃	1	2	yes	—
631	C₄²	C₂×D₄×C₁₃	1	2	yes	—
632	C₄²	C₂×D₄×C₁₃	1	2	yes	—
633	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
636	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₁₃	#61020	1	1	yes	characteristic, direct product factor, Sylow
638	C₂³	—	2	2	no	—
639	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
641	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
642	Q₈	—	2	4	no	—
643	Q₈	—	2	4	no	—
644	Q₈	—	2	4	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	4	no	—
647	Q₈	—	4	4	no	—
648	D₄	—	2	4	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	4	no	—
653	D₄	—	8	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	8	2	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
680	C₈	—	2	4	no	—
681	C₈	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	4	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	4	no	—
704	C₄	C₁₃×#585	1	2	yes	—
705	C₂	—	4	1	no	—
706	C₂	—	4	1	no	—
707	C₂	—	4	1	no	—
708	C₂	—	8	2	no	—
709	C₂	C₁₃×#3449	1	1	yes	characteristic
710	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×#3512	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×#3509	C₂	semidirect
3. C₁₃×#3261	C₂	semidirect
4. C₁₃×#3260	C₂	semidirect
5. C₁₃×#3240	C₂	semidirect
6. C₁₃×#3236	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3216	C₂	semidirect
9. C₁₃×#3201	C₂	semidirect
10. C₁₃×#3181	C₂	semidirect
11. C₁₃×#3172	C₂	semidirect
12. C₁₃×#3127	C₂	semidirect
13. C₁₃×#3126	C₂	semidirect
14. C₁₃×#3120	C₂	semidirect
15. C₁₃×#2923	C₂	semidirect
196. #61020	C₁₃	direct (N × H)
284. #3509	C₂×C₁₃	semidirect
285. #3261	C₂×C₁₃	semidirect
286. #3260	C₂×C₁₃	semidirect
287. #3240	C₂×C₁₃	semidirect
288. #3236	C₂×C₁₃	semidirect
289. #3218	C₂×C₁₃	semidirect
290. #3216	C₂×C₁₃	semidirect
291. #3201	C₂×C₁₃	semidirect
292. #3181	C₂×C₁₃	semidirect
293. #3172	C₂×C₁₃	semidirect
294. #3127	C₂×C₁₃	semidirect
295. #3126	C₂×C₁₃	semidirect
296. #3120	C₂×C₁₃	semidirect
297. #2923	C₂×C₁₃	semidirect
637. C₁₃	#61020	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×#3512	2
C₁₃×#3509	2
C₁₃×#3261	2
C₁₃×#3260	2
C₁₃×#3240	2
C₁₃×#3236	2
C₁₃×#3218	2
C₁₃×#3216	2
C₁₃×#3201	2
C₁₃×#3181	2
C₁₃×#3172	2
C₁₃×#3127	2
C₁₃×#3126	2
C₁₃×#3120	2
C₁₃×#2923	2
#61020	13

Subgroups — C13×#61020 #15747359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61020 #15747359