Subgroups — C₁₃×#24827 #15711166

Order 3328.

880 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2083	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#477	—	2	4	no	—
19	C₁₃×#440	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
29	C₁₃×#399	—	2	1	no	—
30	C₁₃×#399	—	2	1	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	—	2	2	no	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#382	—	2	1	no	—
36	C₁₃×#382	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₄⋊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	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	8	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	4	2	no	—
59	C₄×Q₈×C₁₃	D₄	1	4	yes	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#107	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	4	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×#102	—	4	2	no	—
88	C₁₃×#97	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	D₄	1	1	yes	characteristic
93	C₁₃×#95	D₄	1	1	yes	characteristic
94	#24827	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	4	4	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂×Q₈×C₁₃	#41	1	2	yes	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
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	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×SD₁₆	—	2	8	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₄²×C₁₃	—	2	4	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	4	4	no	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₄²×C₁₃	#41	1	2	yes	—
156	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
158	#2542	C₂×C₁₃	1	1	yes	characteristic
159	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2083	C₂×C₁₃	1	2	yes	complemented
161	#2067	C₂×C₁₃	1	2	yes	—
162	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1880	C₂×C₁₃	1	2	yes	—
165	#1804	C₂×C₁₃	1	1	yes	characteristic
166	#1803	C₂×C₁₃	1	2	yes	complemented
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	8	4	no	—
177	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	4	1	no	—
181	D₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	#121	1	2	yes	—
204	C₂×C₄×C₁₃	#121	1	2	yes	—
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₈×C₁₃	—	4	2	no	—
215	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	—	2	2	no	—
218	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
221	#477	—	2	4	no	—
222	#440	—	2	4	no	—
223	C₂×#107	C₂²×C₁₃	1	2	yes	—
224	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
232	#399	—	2	1	no	—
233	#399	—	2	1	no	—
234	#390	C₂²×C₁₃	1	2	yes	—
235	#389	—	2	2	no	—
236	#389	C₂²×C₁₃	1	2	yes	—
237	#384	C₂²×C₁₃	1	2	yes	—
238	#382	—	2	1	no	—
239	#382	C₂²×C₁₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	#340	C₂²×C₁₃	1	2	yes	—
243	#340	C₂²×C₁₃	1	2	yes	—
244	#340	C₂²×C₁₃	1	2	yes	—
245	#336	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
252	C₂²×C₁₃	#546	1	1	yes	characteristic
253	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
255	C₂²×C₁₃	#578	1	2	yes	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
266	C₄×C₁₃	#537	1	1	yes	characteristic
267	C₄×C₁₃	#552	1	1	yes	characteristic
268	C₄×C₁₃	#554	1	1	yes	characteristic
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
276	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₂²⋊Q₈	—	4	8	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	4	2	no	—
285	C₄×Q₈	D₄×C₁₃	1	4	yes	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	4	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	4	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	4	no	—
312	#102	—	2	2	no	—
313	#102	—	4	2	no	—
314	#97	—	2	2	no	—
315	#95	—	2	1	no	—
316	#95	—	2	2	no	—
317	#95	—	2	1	no	—
318	#95	D₄×C₁₃	1	1	yes	characteristic
319	#95	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₁₃	—	8	2	no	—
321	C₂×C₁₃	#2417	1	1	yes	characteristic
322	C₂×C₁₃	#3038	1	1	yes	characteristic
323	C₂×C₁₃	#3044	1	1	yes	characteristic
324	C₂×C₁₃	#3308	1	2	yes	—
325	C₂×C₁₃	#3386	1	2	yes	—
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
333	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
334	C₂×Q₈	C₁₃×#41	1	2	yes	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	SD₁₆	—	2	8	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	4	no	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₄²	C₁₃×#41	1	2	yes	—
387	C₁₃	#24827	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	4	no	—
398	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	C₁₃×#121	1	2	yes	—
425	C₂×C₄	C₁₃×#121	1	2	yes	—
426	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
431	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
442	C₂²	C₁₃×#546	1	1	yes	characteristic
443	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
445	C₂²	C₁₃×#578	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
456	C₄	C₁₃×#537	1	1	yes	characteristic
457	C₄	C₁₃×#552	1	1	yes	characteristic
458	C₄	C₁₃×#554	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₁₃×#2417	1	1	yes	characteristic
461	C₂	C₁₃×#3038	1	1	yes	characteristic
462	C₂	C₁₃×#3044	1	1	yes	characteristic
463	C₂	C₁₃×#3308	1	2	yes	—
464	C₂	C₁₃×#3386	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#477	C₂	semidirect
4. C₁₃×#2351	C₂	semidirect
5. C₁₃×#2083	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1940	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
49. C₂×C₁₃×SD₁₆	Q₈	semidirect
94. #24827	C₁₃	direct (N × H)
156. C₂×#477	C₂×C₁₃	semidirect
159. #2351	C₂×C₁₃	semidirect
160. #2083	C₂×C₁₃	semidirect
162. #1993	C₂×C₁₃	semidirect
163. #1940	C₂×C₁₃	semidirect
166. #1803	C₂×C₁₃	semidirect
177. Q₈×C₁₃	C₂²⋊Q₈	semidirect
275. C₂×SD₁₆	Q₈×C₁₃	semidirect
387. C₁₃	#24827	direct (N × H)
398. Q₈	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#477	2
C₂×C₁₃×#440	2
C₁₃×#2542	2
C₁₃×#2351	2
C₁₃×#2083	2
C₁₃×#2067	2
C₁₃×#1993	2
C₁₃×#1940	2
C₁₃×#1880	2
C₁₃×#1804	2
C₁₃×#1803	2
#24827	13

Subgroups — C13×#24827 #15711166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24827 #15711166