Subgroups — C₁₃×#21061 #15707400

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1928	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1927	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#428	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₁₃×#419	—	2	4	no	—
21	C₁₃×#419	C₄	1	8	yes	complemented
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	4	yes	—
25	C₁₃×#391	—	2	1	no	—
26	C₁₃×#391	—	2	1	no	—
27	C₁₃×#391	C₂²	1	4	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
31	C₁₃×#376	—	2	1	no	—
32	C₂×C₁₃×#95	—	2	2	no	—
33	C₄³×C₁₃	—	2	1	no	—
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#336	C₂²	1	4	yes	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	D₄	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	C₂×C₄	1	4	yes	—
59	C₁₃×#117	D₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	C₂×C₄	1	16	yes	complemented
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	4	no	—
86	C₁₃×#95	—	2	4	no	—
87	#21061	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	—	2	4	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	8	no	—
92	C₂×Q₈×C₁₃	—	2	8	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	4	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	#41	1	2	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	#41	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×M₁₆	—	2	8	no	—
126	C₁₃×M₁₆	—	4	4	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₄²×C₁₃	—	2	4	no	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	4	4	no	—
151	C₄²×C₁₃	—	4	4	no	—
152	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
153	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
154	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
156	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
157	#1928	C₂×C₁₃	1	4	yes	complemented
158	#1927	C₂×C₁₃	1	4	yes	complemented
159	#1736	C₂×C₁₃	1	1	yes	characteristic
160	#1728	C₂×C₁₃	1	1	yes	characteristic
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	C₄×D₄	1	2	yes	—
164	C₂³×C₁₃	#121	1	2	yes	—
165	C₂³×C₁₃	#123	1	2	yes	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	4	no	—
168	Q₈×C₁₃	—	2	4	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	8	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	#117	1	4	yes	—
193	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	#121	1	2	yes	—
196	C₂×C₄×C₁₃	#123	1	2	yes	—
197	C₂×C₄×C₁₃	#124	1	4	yes	—
198	C₂×C₄×C₁₃	#126	1	4	yes	—
199	C₂×C₄×C₁₃	#137	1	4	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃	—	2	4	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
215	#428	—	2	4	no	—
216	C₂×#107	C₂²×C₁₃	1	2	yes	—
217	C₂×#106	C₂²×C₁₃	1	2	yes	—
218	#419	—	2	4	no	—
219	#419	C₄×C₁₃	1	8	yes	complemented
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	4	yes	—
223	#391	—	2	1	no	—
224	#391	—	2	1	no	—
225	#391	C₂²×C₁₃	1	4	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	#376	—	2	1	no	—
230	C₂×#95	—	2	2	no	—
231	C₄³	—	2	1	no	—
232	#340	C₂²×C₁₃	1	4	yes	—
233	#336	C₂²×C₁₃	1	4	yes	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	#388	1	4	yes	—
239	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
241	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#137	1	2	yes	—
243	C₂²×C₁₃	#575	1	2	yes	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	#388	1	4	yes	—
252	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
253	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	2	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
263	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	D₄×C₁₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	#117	C₂×C₄×C₁₃	1	4	yes	—
279	#117	D₄×C₁₃	1	4	yes	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	#107	—	2	4	no	—
299	#106	—	2	4	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	C₂×C₄×C₁₃	1	16	yes	complemented
303	#95	—	2	4	no	—
304	#95	—	2	4	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	C₂×C₁₃	—	2	4	no	—
308	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
309	C₂×C₁₃	C₄×#137	1	2	yes	—
310	C₂×C₁₃	#3039	1	1	yes	characteristic
311	C₂×C₁₃	#3040	1	1	yes	characteristic
312	C₂×C₁₃	#3095	1	2	yes	—
313	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	8	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
345	C₂²×C₄	C₁₃×#41	1	2	yes	—
346	C₂²×C₄	C₁₃×#41	1	2	yes	—
347	C₂²×C₄	C₁₃×#41	1	2	yes	—
348	C₂²×C₄	C₁₃×#41	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	M₁₆	—	2	8	no	—
351	M₁₆	—	4	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
365	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
366	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₄²	—	2	4	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	4	no	—
376	C₄²	—	4	4	no	—
377	C₁₃	#21061	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	C₄×D₄×C₁₃	1	2	yes	—
381	C₂³	C₁₃×#121	1	2	yes	—
382	C₂³	C₁₃×#123	1	2	yes	—
383	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	8	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	C₁₃×#117	1	4	yes	—
410	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
412	C₂×C₄	C₁₃×#121	1	2	yes	—
413	C₂×C₄	C₁₃×#123	1	2	yes	—
414	C₂×C₄	C₁₃×#124	1	4	yes	—
415	C₂×C₄	C₁₃×#126	1	4	yes	—
416	C₂×C₄	C₁₃×#137	1	4	yes	—
417	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	C₁₃×#388	1	4	yes	—
430	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
432	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
433	C₂²	C₂×C₁₃×#137	1	2	yes	—
434	C₂²	C₁₃×#575	1	2	yes	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	4	no	—
441	C₄	—	8	2	no	—
442	C₄	C₁₃×#388	1	4	yes	—
443	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
444	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
445	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
446	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
447	C₂	—	2	4	no	—
448	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
449	C₂	C₄×C₁₃×#137	1	2	yes	—
450	C₂	C₁₃×#3039	1	1	yes	characteristic
451	C₂	C₁₃×#3040	1	1	yes	characteristic
452	C₂	C₁₃×#3095	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₃×#1928	C₂	semidirect
7. C₁₃×#1927	C₂	semidirect
21. C₁₃×#419	C₄	semidirect
82. C₁₃×#103	C₂×C₄	semidirect
87. #21061	C₁₃	direct (N × H)
157. #1928	C₂×C₁₃	semidirect
158. #1927	C₂×C₁₃	semidirect
219. #419	C₄×C₁₃	semidirect
302. #103	C₂×C₄×C₁₃	semidirect
377. C₁₃	#21061	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#428	2
C₂×C₁₃×#419	2
C₂×C₁₃×#391	2
C₄×C₁₃×#117	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1736	2
C₁₃×#1728	2
#21061	13

Subgroups — C13×#21061 #15707400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21061 #15707400