Subgroups — C₁₃×#17682 #15704021

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1534	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1531	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1528	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#557	C₄	1	1	yes	characteristic
13	C₁₃×#554	C₄	1	1	yes	characteristic
14	C₁₃×#554	C₄	1	1	yes	characteristic
15	C₁₃×#553	C₄	1	2	yes	—
16	C₁₃×#552	—	2	2	no	—
17	C₁₃×#552	—	2	1	no	—
18	C₁₃×#552	C₄	1	2	yes	—
19	C₁₃×#547	—	2	1	no	—
20	C₁₃×#547	C₄	1	1	yes	characteristic
21	C₁₃×#541	—	2	1	no	—
22	C₁₃×#539	—	2	2	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₁₃×#529	C₂²	1	2	yes	—
26	C₂×C₁₃×#125	C₂²	1	2	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₁₃	—	2	1	no	—
30	C₁₃×#436	—	2	1	no	—
31	C₁₃×#436	—	2	2	no	—
32	C₁₃×#433	—	2	2	no	—
33	C₁₃×#432	C₂²	1	2	yes	—
34	C₁₃×#432	C₂²	1	1	yes	characteristic
35	C₁₃×#432	C₂²	1	2	yes	—
36	C₁₃×#432	C₂²	1	2	yes	—
37	C₁₃×#424	—	2	1	no	—
38	C₁₃×#408	—	2	1	no	—
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	—
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
43	C₁₃×#330	C₂²	1	1	yes	characteristic
44	C₁₃×#330	C₂²	1	1	yes	characteristic
45	C₁₃×#330	C₂²	1	2	yes	—
46	C₁₃×#330	C₂²	1	2	yes	—
47	C₁₃×#330	C₂²	1	2	yes	—
48	C₁₃×#330	C₂²	1	2	yes	—
49	C₁₃×#330	C₂²	1	2	yes	—
50	C₁₃×#329	C₂²	1	1	yes	characteristic
51	C₁₃×#329	C₂²	1	1	yes	characteristic
52	C₁₃×#329	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#126	—	2	2	no	—
63	C₁₃×#126	—	2	2	no	—
64	C₁₃×#126	—	2	2	no	—
65	C₁₃×#126	—	2	1	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	C₂×C₄	1	2	yes	—
72	C₁₃×#125	C₂×C₄	1	2	yes	—
73	C₁₃×#125	C₂³	1	1	yes	characteristic
74	C₁₃×#125	C₂³	1	2	yes	—
75	C₁₃×#124	C₂³	1	1	yes	characteristic
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	1	no	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×#123	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	C₂×C₄	1	2	yes	—
91	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
105	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₄×D₄×C₁₃	D₄	1	2	yes	—
109	C₁₃×#117	—	2	2	no	—
110	C₁₃×#117	—	2	1	no	—
111	C₁₃×#117	—	2	2	no	—
112	C₁₃×#117	C₂×C₄	1	2	yes	—
113	C₁₃×#117	D₄	1	1	yes	characteristic
114	C₁₃×#117	D₄	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	C₂³	1	1	yes	characteristic
132	C₁₃×#97	C₂³	1	1	yes	characteristic
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	1	yes	characteristic
135	C₁₃×#97	C₂³	1	2	yes	—
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	#17682	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	4	2	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
151	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₁₃×M₁₆	—	4	4	no	—
163	C₁₃×M₁₆	—	4	2	no	—
164	C₁₃×M₁₆	—	4	2	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	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	C₂²×C₄	1	2	yes	—
212	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	#3515	C₂×C₁₃	1	1	yes	characteristic
219	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1535	C₂×C₁₃	1	2	yes	complemented
222	#1534	C₂×C₁₃	1	2	yes	complemented
223	#1531	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1529	C₂×C₁₃	1	2	yes	complemented
226	#1528	C₂×C₁₃	1	2	yes	complemented
227	#1526	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	2	no	—
235	Q₈×C₁₃	—	8	1	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	8	1	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	8	2	no	—
255	C₂×C₄×C₁₃	—	8	2	no	—
256	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₈×C₁₃	—	2	2	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	2	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	2	no	—
271	#557	C₄×C₁₃	1	1	yes	characteristic
272	#554	C₄×C₁₃	1	1	yes	characteristic
273	#554	C₄×C₁₃	1	1	yes	characteristic
274	#553	C₄×C₁₃	1	2	yes	—
275	#552	—	2	2	no	—
276	#552	—	2	1	no	—
277	#552	C₄×C₁₃	1	2	yes	—
278	#547	—	2	1	no	—
279	#547	C₄×C₁₃	1	1	yes	characteristic
280	#541	—	2	1	no	—
281	#539	—	2	2	no	—
282	#533	C₂²×C₁₃	1	1	yes	characteristic
283	#529	C₂²×C₁₃	1	1	yes	characteristic
284	#529	C₂²×C₁₃	1	2	yes	—
285	C₂×#125	C₂²×C₁₃	1	2	yes	—
286	#520	—	2	1	no	—
287	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
288	C₈×Q₈	—	2	1	no	—
289	#436	—	2	1	no	—
290	#436	—	2	2	no	—
291	#433	—	2	2	no	—
292	#432	C₂²×C₁₃	1	2	yes	—
293	#432	C₂²×C₁₃	1	2	yes	—
294	#432	C₂²×C₁₃	1	1	yes	characteristic
295	#432	C₂²×C₁₃	1	2	yes	—
296	#424	—	2	1	no	—
297	#408	—	2	1	no	—
298	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
299	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
301	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
302	#330	C₂²×C₁₃	1	1	yes	characteristic
303	#330	C₂²×C₁₃	1	1	yes	characteristic
304	#330	C₂²×C₁₃	1	2	yes	—
305	#330	C₂²×C₁₃	1	2	yes	—
306	#330	C₂²×C₁₃	1	2	yes	—
307	#330	C₂²×C₁₃	1	2	yes	—
308	#330	C₂²×C₁₃	1	2	yes	—
309	#329	C₂²×C₁₃	1	1	yes	characteristic
310	#329	C₂²×C₁₃	1	1	yes	characteristic
311	#329	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	#421	1	2	yes	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
344	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
345	#126	—	2	2	no	—
346	#126	—	2	2	no	—
347	#126	—	2	2	no	—
348	#126	—	2	1	no	—
349	#125	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	—	2	1	no	—
352	#125	—	2	2	no	—
353	#125	—	2	2	no	—
354	#125	C₂×C₄×C₁₃	1	2	yes	—
355	#125	C₂×C₄×C₁₃	1	2	yes	—
356	#125	C₂³×C₁₃	1	1	yes	characteristic
357	#125	C₂³×C₁₃	1	2	yes	—
358	#124	C₂³×C₁₃	1	1	yes	characteristic
359	#123	—	2	2	no	—
360	#123	—	2	1	no	—
361	#123	—	2	2	no	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
372	#121	—	2	2	no	—
373	#121	C₂×C₄×C₁₃	1	2	yes	—
374	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
379	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
380	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
381	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
387	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
388	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
389	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
390	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
391	C₄×D₄	D₄×C₁₃	1	2	yes	—
392	#117	—	2	2	no	—
393	#117	—	2	1	no	—
394	#117	—	2	2	no	—
395	#117	C₂×C₄×C₁₃	1	2	yes	—
396	#117	D₄×C₁₃	1	1	yes	characteristic
397	#117	D₄×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	2	no	—
409	C₂²⋊C₈	—	2	2	no	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	#97	—	2	1	no	—
414	#97	C₂³×C₁₃	1	1	yes	characteristic
415	#97	C₂³×C₁₃	1	1	yes	characteristic
416	#97	C₂³×C₁₃	1	1	yes	characteristic
417	#97	C₂³×C₁₃	1	1	yes	characteristic
418	#97	C₂³×C₁₃	1	2	yes	—
419	#97	C₂³×C₁₃	1	2	yes	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	2	no	—
423	C₂×C₁₃	—	4	1	no	—
424	C₂×C₁₃	—	4	2	no	—
425	C₂×C₁₃	—	8	1	no	—
426	C₂×C₁₃	#2889	1	1	yes	characteristic
427	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
428	C₂×C₁₃	#2901	1	1	yes	characteristic
429	#41	—	4	2	no	—
430	#41	—	4	4	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
438	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
439	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	M₁₆	—	4	4	no	—
451	M₁₆	—	4	2	no	—
452	M₁₆	—	4	2	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	4	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
479	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
480	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
483	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
494	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
495	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
500	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
501	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₁₃	1	2	yes	—
504	C₄²	C₂×D₄×C₁₃	1	2	yes	—
505	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₁₃	#17682	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	1	no	—
508	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
509	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
510	Q₈	—	2	2	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	8	1	no	—
514	D₄	—	2	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	4	no	—
518	D₄	—	8	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
535	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
536	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
537	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
538	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
539	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	2	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	2	no	—
572	C₄	C₁₃×#421	1	2	yes	—
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	C₁₃×#2889	1	1	yes	characteristic
577	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
578	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×#3515	C₂
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×#2923	C₂	semidirect
4. C₁₃×#1535	C₂	semidirect
5. C₁₃×#1534	C₂	semidirect
6. C₁₃×#1531	C₂	semidirect
7. C₁₃×#1529	C₂	semidirect
8. C₁₃×#1529	C₂	semidirect
9. C₁₃×#1528	C₂	semidirect
10. C₁₃×#1526	C₂	semidirect
11. C₁₃×#1524	C₂	semidirect
140. #17682	C₁₃	direct (N × H)
219. #2971	C₂×C₁₃	semidirect
220. #2923	C₂×C₁₃	semidirect
221. #1535	C₂×C₁₃	semidirect
222. #1534	C₂×C₁₃	semidirect
223. #1531	C₂×C₁₃	semidirect
224. #1529	C₂×C₁₃	semidirect
225. #1529	C₂×C₁₃	semidirect
226. #1528	C₂×C₁₃	semidirect
227. #1526	C₂×C₁₃	semidirect
228. #1524	C₂×C₁₃	semidirect
506. C₁₃	#17682	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×#3515	2
C₁₃×#2971	2
C₁₃×#2923	2
C₁₃×#1535	2
C₁₃×#1534	2
C₁₃×#1531	2
C₁₃×#1529	2
C₁₃×#1528	2
C₁₃×#1526	2
C₁₃×#1524	2
#17682	13

Subgroups — C13×#17682 #15704021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17682 #15704021