Subgroups — C₁₃×#60972 #15747311

Order 3328.

1824 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3256	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3197	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3182	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3111	C₂	1	8	yes	maximal, complemented
12	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#529	—	2	2	no	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	—	2	2	no	—
23	C₁₃×#529	C₂²	1	4	yes	—
24	C₁₃×#529	C₂²	1	4	yes	—
25	C₁₃×#525	—	2	2	no	—
26	C₁₃×#525	—	2	2	no	—
27	C₁₃×#525	C₂²	1	4	yes	—
28	C₄×C₁₃×#41	—	2	2	no	—
29	C₄×C₁₃×#41	—	2	2	no	—
30	C₄×C₁₃×#41	C₂²	1	4	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#500	C₂²	1	2	yes	complemented
33	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#492	C₂²	1	2	yes	complemented
38	C₁₃×#487	C₂²	1	2	yes	complemented
39	C₁₃×#487	C₂²	1	2	yes	complemented
40	C₁₃×#486	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#485	C₂²	1	8	yes	—
43	C₁₃×#482	C₂²	1	8	yes	—
44	C₁₃×#479	C₂²	1	8	yes	complemented
45	C₁₃×#478	C₂²	1	8	yes	complemented
46	C₁₃×#470	C₂²	1	4	yes	—
47	C₁₃×#469	C₂²	1	4	yes	—
48	C₁₃×#468	C₂²	1	8	yes	—
49	C₁₃×#464	C₂²	1	8	yes	complemented
50	C₁₃×#463	C₂²	1	8	yes	complemented
51	C₁₃×#452	C₂²	1	8	yes	—
52	C₁₃×#449	C₂²	1	8	yes	—
53	C₁₃×#442	C₂²	1	4	yes	complemented
54	C₁₃×#441	C₂²	1	4	yes	complemented
55	C₁₃×#440	C₂²	1	8	yes	complemented
56	C₁₃×#432	C₂²	1	4	yes	—
57	C₁₃×#431	C₂²	1	2	yes	—
58	C₁₃×#431	C₂²	1	2	yes	—
59	C₁₃×#423	C₂²	1	2	yes	—
60	C₁₃×#407	C₂²	1	2	yes	—
61	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	D₄	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×D₈	C₂³	1	4	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₃×#127	C₂³	1	2	yes	—
77	C₁₃×#126	—	2	4	no	—
78	C₁₃×#126	—	2	4	no	—
79	C₁₃×#125	—	2	2	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	C₂³	1	4	yes	—
85	C₁₃×#123	—	2	4	no	—
86	C₁₃×#123	—	2	4	no	—
87	C₁₃×#123	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	C₂³	1	4	yes	—
99	C₁₃×#121	C₂³	1	4	yes	—
100	C₁₃×#120	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	—	2	2	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	C₂³	1	4	yes	—
118	C₄×D₄×C₁₃	C₂³	1	4	yes	—
119	C₁₃×#117	—	2	2	no	—
120	C₁₃×#117	—	2	2	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	—	2	4	no	—
126	C₂×C₄²×C₁₃	D₄	1	2	yes	—
127	C₂×C₄²×C₁₃	D₄	1	2	yes	—
128	C₂×C₄²×C₁₃	D₄	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₁₃×#107	C₂³	1	8	yes	—
134	C₁₃×#106	C₂³	1	4	yes	—
135	C₁₃×#106	C₂³	1	4	yes	—
136	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
138	C₁₃×#103	C₂³	1	8	yes	—
139	C₁₃×#103	C₂³	1	8	yes	—
140	C₁₃×#102	C₂³	1	8	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×#97	C₂³	1	2	yes	—
145	C₁₃×#97	C₂³	1	2	yes	—
146	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₃	C₂³	1	2	yes	—
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	#60972	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₁₃×#41	—	4	8	no	—
152	C₁₃×#41	—	4	8	no	—
153	C₁₃×#41	—	4	8	no	—
154	C₂×Q₈×C₁₃	—	2	2	no	—
155	C₂×Q₈×C₁₃	—	2	2	no	—
156	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	4	4	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×Q₁₆	—	4	4	no	—
179	C₁₃×SD₁₆	—	4	8	no	—
180	C₁₃×D₈	—	4	4	no	—
181	C₁₃×M₁₆	—	4	2	no	—
182	C₁₃×M₁₆	—	4	2	no	—
183	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	C₂×D₄	1	2	yes	—
211	C₄²×C₁₃	C₂×D₄	1	2	yes	—
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₄²×C₁₃	C₂⁴	1	2	yes	—
220	#3444	C₂×C₁₃	1	2	yes	complemented
221	#3256	C₂×C₁₃	1	4	yes	complemented
222	#3231	C₂×C₁₃	1	2	yes	complemented
223	#3228	C₂×C₁₃	1	2	yes	complemented
224	#3210	C₂×C₁₃	1	2	yes	complemented
225	#3207	C₂×C₁₃	1	2	yes	complemented
226	#3197	C₂×C₁₃	1	4	yes	complemented
227	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#3182	C₂×C₁₃	1	2	yes	complemented
230	#3111	C₂×C₁₃	1	8	yes	complemented
231	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	8	no	—
238	Q₈×C₁₃	—	4	4	no	—
239	Q₈×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	2	8	no	—
241	D₄×C₁₃	—	4	8	no	—
242	D₄×C₁₃	—	4	8	no	—
243	D₄×C₁₃	—	4	8	no	—
244	D₄×C₁₃	—	4	4	no	—
245	D₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	—	4	8	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	4	no	—
271	C₈×C₁₃	—	2	2	no	—
272	#533	C₂²×C₁₃	1	2	yes	—
273	#533	C₂²×C₁₃	1	2	yes	—
274	#533	C₂²×C₁₃	1	2	yes	—
275	#532	C₂²×C₁₃	1	2	yes	—
276	#532	C₂²×C₁₃	1	2	yes	—
277	#532	C₂²×C₁₃	1	2	yes	—
278	#529	—	2	2	no	—
279	#529	—	2	2	no	—
280	#529	—	2	2	no	—
281	#529	—	2	2	no	—
282	#529	C₂²×C₁₃	1	4	yes	—
283	#529	C₂²×C₁₃	1	4	yes	—
284	#525	—	2	2	no	—
285	#525	—	2	2	no	—
286	#525	C₂²×C₁₃	1	4	yes	—
287	C₄×#41	—	2	2	no	—
288	C₄×#41	—	2	2	no	—
289	C₄×#41	C₂²×C₁₃	1	4	yes	—
290	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
291	#500	C₂²×C₁₃	1	2	yes	complemented
292	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
296	#492	C₂²×C₁₃	1	2	yes	complemented
297	#487	C₂²×C₁₃	1	2	yes	complemented
298	#487	C₂²×C₁₃	1	2	yes	complemented
299	#486	C₂²×C₁₃	1	2	yes	complemented
300	#486	C₂²×C₁₃	1	2	yes	complemented
301	#485	C₂²×C₁₃	1	8	yes	—
302	#482	C₂²×C₁₃	1	8	yes	—
303	#479	C₂²×C₁₃	1	8	yes	complemented
304	#478	C₂²×C₁₃	1	8	yes	complemented
305	#470	C₂²×C₁₃	1	4	yes	—
306	#469	C₂²×C₁₃	1	4	yes	—
307	#468	C₂²×C₁₃	1	8	yes	—
308	#464	C₂²×C₁₃	1	8	yes	complemented
309	#463	C₂²×C₁₃	1	8	yes	complemented
310	#452	C₂²×C₁₃	1	8	yes	—
311	#449	C₂²×C₁₃	1	8	yes	—
312	#442	C₂²×C₁₃	1	4	yes	complemented
313	#441	C₂²×C₁₃	1	4	yes	complemented
314	#440	C₂²×C₁₃	1	8	yes	complemented
315	#432	C₂²×C₁₃	1	4	yes	—
316	#431	C₂²×C₁₃	1	2	yes	—
317	#431	C₂²×C₁₃	1	2	yes	—
318	#423	C₂²×C₁₃	1	2	yes	—
319	#407	C₂²×C₁₃	1	2	yes	—
320	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	—	4	4	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	4	4	no	—
338	C₄×C₁₃	—	4	4	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	#575	1	4	yes	—
341	C₄×C₁₃	#585	1	2	yes	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	C₂³×C₁₃	1	4	yes	—
345	C₂³×C₄	D₄×C₁₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
348	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
349	C₂×D₈	C₂³×C₁₃	1	4	yes	—
350	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
351	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
352	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
353	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
354	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
355	#127	C₂³×C₁₃	1	2	yes	—
356	#126	—	2	4	no	—
357	#126	—	2	4	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	C₂³×C₁₃	1	4	yes	—
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	C₂³×C₁₃	1	4	yes	—
364	#123	—	2	4	no	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
372	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
373	#121	—	2	2	no	—
374	#121	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	C₂³×C₁₃	1	4	yes	—
378	#121	C₂³×C₁₃	1	4	yes	—
379	#120	—	2	4	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	C₂³×C₁₃	1	4	yes	—
397	C₄×D₄	C₂³×C₁₃	1	4	yes	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	—	2	4	no	—
401	#117	—	2	4	no	—
402	#117	—	2	4	no	—
403	#117	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄²	—	2	4	no	—
405	C₂×C₄²	D₄×C₁₃	1	2	yes	—
406	C₂×C₄²	D₄×C₁₃	1	2	yes	—
407	C₂×C₄²	D₄×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
412	#107	C₂³×C₁₃	1	8	yes	—
413	#106	C₂³×C₁₃	1	4	yes	—
414	#106	C₂³×C₁₃	1	4	yes	—
415	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
416	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
417	#103	C₂³×C₁₃	1	8	yes	—
418	#103	C₂³×C₁₃	1	8	yes	—
419	#102	C₂³×C₁₃	1	8	yes	—
420	#102	C₂³×C₁₃	1	8	yes	—
421	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
422	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
423	#97	C₂³×C₁₃	1	2	yes	—
424	#97	C₂³×C₁₃	1	2	yes	—
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₃	1	2	yes	—
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₁₃	—	4	2	no	—
429	C₂×C₁₃	—	4	1	no	—
430	C₂×C₁₃	—	8	4	no	—
431	C₂×C₁₃	#3449	1	1	yes	characteristic
432	C₂×C₁₃	C₂×#575	1	2	yes	—
433	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
434	#41	—	4	8	no	—
435	#41	—	4	8	no	—
436	#41	—	4	8	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
461	Q₁₆	—	4	4	no	—
462	SD₁₆	—	4	8	no	—
463	D₈	—	4	4	no	—
464	M₁₆	—	4	2	no	—
465	M₁₆	—	4	2	no	—
466	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
467	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
468	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	C₂×D₄×C₁₃	1	2	yes	—
494	C₄²	C₂×D₄×C₁₃	1	2	yes	—
495	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₃	1	2	yes	—
497	C₄²	C₂×D₄×C₁₃	1	2	yes	—
498	C₄²	C₂×D₄×C₁₃	1	2	yes	—
499	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
502	C₄²	C₂⁴×C₁₃	1	2	yes	—
503	C₁₃	#60972	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
509	Q₈	—	2	8	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	4	4	no	—
512	D₄	—	2	8	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	8	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
540	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	2	4	no	—
543	C₈	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	4	no	—
562	C₄	C₁₃×#575	1	4	yes	—
563	C₄	C₁₃×#585	1	2	yes	—
564	C₂	—	4	1	no	—
565	C₂	—	4	2	no	—
566	C₂	—	8	4	no	—
567	C₂	C₁₃×#3449	1	1	yes	characteristic
568	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3256	C₂	semidirect
3. C₁₃×#3231	C₂	semidirect
4. C₁₃×#3228	C₂	semidirect
5. C₁₃×#3210	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3197	C₂	semidirect
8. C₁₃×#3185	C₂	semidirect
9. C₁₃×#3184	C₂	semidirect
10. C₁₃×#3182	C₂	semidirect
11. C₁₃×#3111	C₂	semidirect
12. C₁₃×#2920	C₂	semidirect
32. C₁₃×#500	C₂²	semidirect
33. C₁₃×#498	C₂²	semidirect
34. C₁₃×#498	C₂²	semidirect
35. C₁₃×#494	C₂²	semidirect
36. C₁₃×#493	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#487	C₂²	semidirect
39. C₁₃×#487	C₂²	semidirect
40. C₁₃×#486	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
44. C₁₃×#479	C₂²	semidirect
45. C₁₃×#478	C₂²	semidirect
49. C₁₃×#464	C₂²	semidirect
50. C₁₃×#463	C₂²	semidirect
53. C₁₃×#442	C₂²	semidirect
54. C₁₃×#441	C₂²	semidirect
55. C₁₃×#440	C₂²	semidirect
149. #60972	C₁₃	direct (N × H)
220. #3444	C₂×C₁₃	semidirect
221. #3256	C₂×C₁₃	semidirect
222. #3231	C₂×C₁₃	semidirect
223. #3228	C₂×C₁₃	semidirect
224. #3210	C₂×C₁₃	semidirect
225. #3207	C₂×C₁₃	semidirect
226. #3197	C₂×C₁₃	semidirect
227. #3185	C₂×C₁₃	semidirect
228. #3184	C₂×C₁₃	semidirect
229. #3182	C₂×C₁₃	semidirect
230. #3111	C₂×C₁₃	semidirect
231. #2920	C₂×C₁₃	semidirect
291. #500	C₂²×C₁₃	semidirect
292. #498	C₂²×C₁₃	semidirect
293. #498	C₂²×C₁₃	semidirect
294. #494	C₂²×C₁₃	semidirect
295. #493	C₂²×C₁₃	semidirect
296. #492	C₂²×C₁₃	semidirect
297. #487	C₂²×C₁₃	semidirect
298. #487	C₂²×C₁₃	semidirect
299. #486	C₂²×C₁₃	semidirect
300. #486	C₂²×C₁₃	semidirect
303. #479	C₂²×C₁₃	semidirect
304. #478	C₂²×C₁₃	semidirect
308. #464	C₂²×C₁₃	semidirect
309. #463	C₂²×C₁₃	semidirect
312. #442	C₂²×C₁₃	semidirect
313. #441	C₂²×C₁₃	semidirect
314. #440	C₂²×C₁₃	semidirect
503. C₁₃	#60972	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×#3444	2
C₁₃×#3256	2
C₁₃×#3231	2
C₁₃×#3228	2
C₁₃×#3210	2
C₁₃×#3207	2
C₁₃×#3197	2
C₁₃×#3185	2
C₁₃×#3184	2
C₁₃×#3182	2
C₁₃×#3111	2
C₁₃×#2920	2
#60972	13

Subgroups — C13×#60972 #15747311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60972 #15747311