Subgroups — C₁₃×#24543 #15710882

Order 3328.

980 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2503	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1878	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1805	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#452	—	2	4	no	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₃×#417	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#400	—	2	1	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	—	2	2	no	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#381	—	2	2	no	—
35	C₁₃×#380	—	2	1	no	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	4	2	no	—
46	C₂×C₁₃×#41	D₄	1	4	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	4	2	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	4	2	no	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	4	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	—	4	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	4	2	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	D₄	1	1	yes	characteristic
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	#24543	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₁₃×#41	—	2	8	no	—
100	C₁₃×#41	—	4	4	no	—
101	C₁₃×#41	—	4	8	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₃	#41	1	4	yes	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	#41	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	4	4	no	—
134	C₁₃×SD₁₆	—	4	4	no	—
135	C₁₃×M₁₆	—	4	4	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	8	2	no	—
156	C₁₃×C₂²⋊C₄	—	8	1	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	4	4	no	—
160	C₂×#452	C₂×C₁₃	1	1	yes	characteristic
161	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
162	#2503	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2341	C₂×C₁₃	1	1	yes	characteristic
164	#2073	C₂×C₁₃	1	2	yes	complemented
165	#2055	C₂×C₁₃	1	2	yes	complemented
166	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1878	C₂×C₁₃	1	2	yes	complemented
168	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1824	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1805	C₂×C₁₃	1	2	yes	complemented
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	#121	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	4	1	no	—
185	Q₈×C₁₃	—	4	1	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	#123	1	4	yes	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	4	8	no	—
191	D₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	#121	1	2	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₁₃	—	4	1	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	1	no	—
224	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
231	#452	—	2	4	no	—
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
233	#417	—	2	4	no	—
234	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#102	C₂²×C₁₃	1	2	yes	—
238	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
240	#400	—	2	1	no	—
241	#400	—	2	1	no	—
242	#391	C₂²×C₁₃	1	2	yes	—
243	#390	—	2	2	no	—
244	#390	C₂²×C₁₃	1	2	yes	—
245	#382	C₂²×C₁₃	1	2	yes	—
246	#381	—	2	2	no	—
247	#380	—	2	1	no	—
248	#380	C₂²×C₁₃	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	—	2	1	no	—
250	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
251	#340	C₂²×C₁₃	1	2	yes	—
252	#340	C₂²×C₁₃	1	2	yes	—
253	#340	C₂²×C₁₃	1	2	yes	—
254	#336	C₂²×C₁₃	1	2	yes	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
266	C₂²×C₁₃	#546	1	2	yes	—
267	C₂²×C₁₃	#575	1	2	yes	—
268	C₂²×C₁₃	#577	1	1	yes	characteristic
269	C₂²×C₁₃	#578	1	1	yes	characteristic
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	4	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	8	1	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
279	C₄×C₁₃	#534	1	1	yes	characteristic
280	C₄×C₁₃	#551	1	2	yes	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	4	2	no	—
284	C₂×#41	D₄×C₁₃	1	4	yes	—
285	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	4	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	4	2	no	—
298	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
320	C₄⋊C₈	—	4	2	no	—
321	#103	—	2	4	no	—
322	#103	—	2	2	no	—
323	#103	—	4	2	no	—
324	#102	—	2	4	no	—
325	#102	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	D₄×C₁₃	1	1	yes	characteristic
333	#95	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₁₃	—	4	2	no	—
335	C₂×C₁₃	—	8	2	no	—
336	C₂×C₁₃	#2412	1	1	yes	characteristic
337	C₂×C₁₃	#3040	1	1	yes	characteristic
338	C₂×C₁₃	#3046	1	1	yes	characteristic
339	C₂×C₁₃	#3317	1	2	yes	—
340	C₂×C₁₃	#3327	1	2	yes	—
341	C₂⁴	—	2	1	no	—
342	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
343	#41	—	2	8	no	—
344	#41	—	4	4	no	—
345	#41	—	4	8	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
353	C₂×Q₈	C₁₃×#41	1	4	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₁₃×#41	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	SD₁₆	—	4	4	no	—
379	M₁₆	—	4	4	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	8	2	no	—
400	C₂²⋊C₄	—	8	1	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	4	4	no	—
404	C₁₃	#24543	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	C₁₃×#121	1	2	yes	—
415	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	2	no	—
421	Q₈	C₁₃×#123	1	4	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	C₁₃×#121	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
453	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
454	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
455	C₈	—	4	1	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
469	C₂²	C₁₃×#546	1	2	yes	—
470	C₂²	C₁₃×#575	1	2	yes	—
471	C₂²	C₁₃×#577	1	1	yes	characteristic
472	C₂²	C₁₃×#578	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
482	C₄	C₁₃×#534	1	1	yes	characteristic
483	C₄	C₁₃×#551	1	2	yes	—
484	C₂	—	4	2	no	—
485	C₂	—	8	2	no	—
486	C₂	C₁₃×#2412	1	1	yes	characteristic
487	C₂	C₁₃×#3040	1	1	yes	characteristic
488	C₂	C₁₃×#3046	1	1	yes	characteristic
489	C₂	C₁₃×#3317	1	2	yes	—
490	C₂	C₁₃×#3327	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2503	C₂	semidirect
5. C₁₃×#2073	C₂	semidirect
6. C₁₃×#2055	C₂	semidirect
7. C₁₃×#1894	C₂	semidirect
8. C₁₃×#1878	C₂	semidirect
9. C₁₃×#1851	C₂	semidirect
10. C₁₃×#1824	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
96. #24543	C₁₃	direct (N × H)
162. #2503	C₂×C₁₃	semidirect
164. #2073	C₂×C₁₃	semidirect
165. #2055	C₂×C₁₃	semidirect
166. #1894	C₂×C₁₃	semidirect
167. #1878	C₂×C₁₃	semidirect
168. #1851	C₂×C₁₃	semidirect
169. #1824	C₂×C₁₃	semidirect
170. #1805	C₂×C₁₃	semidirect
404. C₁₃	#24543	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×#452	2
C₂×C₁₃×#417	2
C₁₃×#2503	2
C₁₃×#2341	2
C₁₃×#2073	2
C₁₃×#2055	2
C₁₃×#1894	2
C₁₃×#1878	2
C₁₃×#1851	2
C₁₃×#1824	2
C₁₃×#1805	2
#24543	13

Subgroups — C13×#24543 #15710882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24543 #15710882