Subgroups — C₁₃×#17691 #15704030

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 592 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	1	yes	maximal, characteristic
2	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1527	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1524	C₂	1	2	yes	maximal, complemented
12	C₁₃×#559	—	2	1	no	—
13	C₁₃×#559	—	2	1	no	—
14	C₁₃×#556	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#551	—	2	2	no	—
17	C₁₃×#551	—	2	2	no	—
18	C₁₃×#542	C₄	1	2	yes	—
19	C₁₃×#542	C₄	1	2	yes	—
20	C₁₃×#536	C₄	1	1	yes	characteristic
21	C₁₃×#535	C₄	1	1	yes	characteristic
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#529	C₂²	1	2	yes	—
24	C₁₃×#529	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₁₃×#519	C₄	1	1	yes	characteristic
27	C₁₃×#518	C₄	1	1	yes	characteristic
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#446	—	2	1	no	—
30	C₈×Q₈×C₁₃	—	2	1	no	—
31	C₁₃×#436	—	2	1	no	—
32	C₁₃×#436	—	2	2	no	—
33	C₁₃×#435	—	2	2	no	—
34	C₈×D₄×C₁₃	—	2	1	no	—
35	C₁₃×#432	C₂²	1	1	yes	characteristic
36	C₁₃×#432	C₂²	1	1	yes	characteristic
37	C₁₃×#432	C₂²	1	2	yes	complemented
38	C₁₃×#432	C₂²	1	2	yes	complemented
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
43	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#330	C₂²	1	2	yes	complemented
45	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#330	C₂²	1	2	yes	complemented
49	C₁₃×#329	C₂²	1	2	yes	—
50	C₁₃×#329	C₂²	1	2	yes	—
51	C₁₃×#329	C₂²	1	2	yes	—
52	C₁₃×#329	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#127	—	2	1	no	—
64	C₁₃×#126	—	2	2	no	—
65	C₁₃×#126	—	2	2	no	—
66	C₁₃×#126	—	2	2	no	—
67	C₁₃×#126	—	2	2	no	—
68	C₁₃×#125	C₂³	1	1	yes	characteristic
69	C₁₃×#125	C₂³	1	1	yes	characteristic
70	C₁₃×#124	—	2	1	no	—
71	C₁₃×#124	—	2	1	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	2	no	—
74	C₁₃×#124	—	2	1	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#124	C₂×C₄	1	2	yes	—
77	C₁₃×#124	C₂³	1	2	yes	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×#123	—	2	2	no	—
81	C₁₃×#123	—	2	2	no	—
82	C₁₃×#123	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
88	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
89	C₁₃×#121	C₂×C₄	1	2	yes	—
90	C₁₃×#121	C₂×C₄	1	2	yes	—
91	C₁₃×#120	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
105	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₃	D₄	1	2	yes	—
108	C₄×D₄×C₁₃	D₄	1	2	yes	—
109	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
110	C₁₃×#117	—	2	2	no	—
111	C₁₃×#117	—	2	2	no	—
112	C₁₃×#117	—	2	2	no	—
113	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#117	C₂×C₄	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₈	—	2	1	no	—
123	C₁₃×C₄⋊C₈	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	2	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×#97	—	2	2	no	—
131	C₁₃×#97	C₂³	1	1	yes	characteristic
132	C₁₃×#97	C₂³	1	2	yes	—
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	1	yes	characteristic
135	C₁₃×#97	C₂³	1	1	yes	characteristic
136	C₁₃×#97	C₂³	1	2	yes	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	2	no	—
140	#17691	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₁₃×#41	—	4	2	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	4	2	no	—
147	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₁₃×M₁₆	—	4	2	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₁₃×M₁₆	—	4	4	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	4	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
188	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
189	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
206	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
207	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
208	C₄²×C₁₃	—	2	2	no	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
213	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
219	#3510	C₂×C₁₃	1	1	yes	characteristic
220	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1537	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1535	C₂×C₁₃	1	2	yes	complemented
224	#1532	C₂×C₁₃	1	2	yes	complemented
225	#1529	C₂×C₁₃	1	2	yes	complemented
226	#1527	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1527	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1526	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1524	C₂×C₁₃	1	2	yes	complemented
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	—	8	1	no	—
233	C₂³×C₁₃	—	8	1	no	—
234	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	4	2	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	Q₈×C₁₃	—	8	1	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	8	2	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	2	no	—
276	#559	—	2	1	no	—
277	#559	—	2	1	no	—
278	#556	—	2	1	no	—
279	#556	—	2	1	no	—
280	#551	—	2	2	no	—
281	#551	—	2	2	no	—
282	#542	C₄×C₁₃	1	2	yes	—
283	#542	C₄×C₁₃	1	2	yes	—
284	#536	C₄×C₁₃	1	1	yes	characteristic
285	#535	C₄×C₁₃	1	1	yes	characteristic
286	#533	C₂²×C₁₃	1	1	yes	characteristic
287	#529	C₂²×C₁₃	1	2	yes	—
288	#529	C₂²×C₁₃	1	2	yes	—
289	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
290	#519	C₄×C₁₃	1	1	yes	characteristic
291	#518	C₄×C₁₃	1	1	yes	characteristic
292	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
293	#446	—	2	1	no	—
294	C₈×Q₈	—	2	1	no	—
295	#436	—	2	1	no	—
296	#436	—	2	2	no	—
297	#435	—	2	2	no	—
298	C₈×D₄	—	2	1	no	—
299	#432	C₂²×C₁₃	1	1	yes	characteristic
300	#432	C₂²×C₁₃	1	1	yes	characteristic
301	#432	C₂²×C₁₃	1	2	yes	complemented
302	#432	C₂²×C₁₃	1	2	yes	complemented
303	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
304	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
306	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
307	#330	C₂²×C₁₃	1	2	yes	complemented
308	#330	C₂²×C₁₃	1	2	yes	complemented
309	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	#329	C₂²×C₁₃	1	2	yes	—
314	#329	C₂²×C₁₃	1	2	yes	—
315	#329	C₂²×C₁₃	1	2	yes	—
316	#329	C₂²×C₁₃	1	2	yes	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	16	2	no	—
327	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	#413	1	2	yes	—
342	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
343	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
344	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
352	#127	—	2	1	no	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#125	C₂³×C₁₃	1	1	yes	characteristic
358	#125	C₂³×C₁₃	1	1	yes	characteristic
359	#124	—	2	1	no	—
360	#124	—	2	1	no	—
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	—	2	1	no	—
364	#124	—	2	1	no	—
365	#124	C₂×C₄×C₁₃	1	2	yes	—
366	#124	C₂³×C₁₃	1	2	yes	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
377	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
378	#121	C₂×C₄×C₁₃	1	2	yes	—
379	#121	C₂×C₄×C₁₃	1	2	yes	—
380	#120	—	2	2	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
386	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
387	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
394	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
395	C₄×D₄	D₄×C₁₃	1	2	yes	—
396	C₄×D₄	D₄×C₁₃	1	2	yes	—
397	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
398	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
399	#117	—	2	2	no	—
400	#117	—	2	2	no	—
401	#117	—	2	2	no	—
402	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
403	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
404	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
405	#117	C₂×C₄×C₁₃	1	2	yes	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	2	no	—
414	C₄⋊C₈	—	2	2	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	#97	—	2	2	no	—
420	#97	C₂³×C₁₃	1	1	yes	characteristic
421	#97	C₂³×C₁₃	1	2	yes	—
422	#97	C₂³×C₁₃	1	1	yes	characteristic
423	#97	C₂³×C₁₃	1	1	yes	characteristic
424	#97	C₂³×C₁₃	1	1	yes	characteristic
425	#97	C₂³×C₁₃	1	2	yes	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	2	no	—
429	C₂×C₁₃	—	4	2	no	—
430	C₂×C₁₃	—	4	1	no	—
431	C₂×C₁₃	—	8	2	no	—
432	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
433	C₂×C₁₃	#2901	1	1	yes	characteristic
434	C₂×C₁₃	#2901	1	1	yes	characteristic
435	C₂⁴	—	2	1	no	—
436	#41	—	4	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
449	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
459	M₁₆	—	4	2	no	—
460	M₁₆	—	4	2	no	—
461	M₁₆	—	4	4	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	4	4	no	—
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	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
480	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
481	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
482	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
483	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
500	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
501	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
507	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₁₃	1	2	yes	—
509	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₃	1	2	yes	—
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₁₃	#17691	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	8	1	no	—
517	C₂³	—	8	1	no	—
518	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
519	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	8	1	no	—
524	Q₈	—	8	1	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
546	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
547	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
548	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
549	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
550	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
551	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	4	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	2	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	16	2	no	—
570	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	C₁₃×#413	1	2	yes	—
585	C₂	—	4	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
589	C₂	C₁₃×#2901	1	1	yes	characteristic
590	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#535	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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×#2971	C₂	semidirect
3. C₁₃×#2970	C₂	semidirect
4. C₁₃×#1537	C₂	semidirect
5. C₁₃×#1535	C₂	semidirect
6. C₁₃×#1532	C₂	semidirect
7. C₁₃×#1529	C₂	semidirect
8. C₁₃×#1527	C₂	semidirect
9. C₁₃×#1527	C₂	semidirect
10. C₁₃×#1526	C₂	semidirect
11. C₁₃×#1524	C₂	semidirect
37. C₁₃×#432	C₂²	semidirect
38. C₁₃×#432	C₂²	semidirect
41. C₄×C₁₃×M₁₆	C₂²	semidirect
42. C₂×C₁₃×#97	C₂²	semidirect
43. C₁₃×#330	C₂²	semidirect
44. C₁₃×#330	C₂²	semidirect
45. C₁₃×#330	C₂²	semidirect
46. C₁₃×#330	C₂²	semidirect
47. C₁₃×#330	C₂²	semidirect
48. C₁₃×#330	C₂²	semidirect
140. #17691	C₁₃	direct (N × H)
220. #2971	C₂×C₁₃	semidirect
221. #2970	C₂×C₁₃	semidirect
222. #1537	C₂×C₁₃	semidirect
223. #1535	C₂×C₁₃	semidirect
224. #1532	C₂×C₁₃	semidirect
225. #1529	C₂×C₁₃	semidirect
226. #1527	C₂×C₁₃	semidirect
227. #1527	C₂×C₁₃	semidirect
228. #1526	C₂×C₁₃	semidirect
229. #1524	C₂×C₁₃	semidirect
301. #432	C₂²×C₁₃	semidirect
302. #432	C₂²×C₁₃	semidirect
305. C₄×M₁₆	C₂²×C₁₃	semidirect
306. C₂×#97	C₂²×C₁₃	semidirect
307. #330	C₂²×C₁₃	semidirect
308. #330	C₂²×C₁₃	semidirect
309. #330	C₂²×C₁₃	semidirect
310. #330	C₂²×C₁₃	semidirect
311. #330	C₂²×C₁₃	semidirect
312. #330	C₂²×C₁₃	semidirect
513. C₁₃	#17691	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×#2971	2
C₁₃×#2970	2
C₁₃×#1537	2
C₁₃×#1535	2
C₁₃×#1532	2
C₁₃×#1529	2
C₁₃×#1527	2
C₁₃×#1526	2
C₁₃×#1524	2
#17691	13

Subgroups — C13×#17691 #15704030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17691 #15704030