Subgroups — C₁₃×#22811 #15709150

Order 3328.

846 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1973	C₂	1	2	yes	maximal
5	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1925	C₂	1	2	yes	maximal
7	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	—	2	1	no	—
16	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#391	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#388	—	2	2	no	—
30	C₁₃×#387	—	2	2	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	—	2	1	no	—
34	C₁₃×#380	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×SD₁₆	—	2	2	no	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
55	C₁₃×#117	—	4	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	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	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#106	C₂×C₄	1	4	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#103	—	4	2	no	—
80	C₁₃×#103	C₂×C₄	1	4	yes	—
81	C₁₃×#102	—	4	2	no	—
82	C₁₃×#102	C₂×C₄	1	4	yes	—
83	C₁₃×#97	—	2	4	no	—
84	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	2	yes	—
90	#22811	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×SD₁₆	—	2	8	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	8	1	no	—
139	C₁₃×C₄⋊C₄	—	8	1	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	4	4	no	—
149	C₄²×C₁₃	—	8	2	no	—
150	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
153	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2354	C₂×C₁₃	1	1	yes	characteristic
155	#1973	C₂×C₁₃	1	2	yes	—
156	#1928	C₂×C₁₃	1	2	yes	complemented
157	#1925	C₂×C₁₃	1	2	yes	—
158	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1802	C₂×C₁₃	1	1	yes	characteristic
161	#1776	C₂×C₁₃	1	2	yes	complemented
162	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	4	1	no	—
174	Q₈×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	4	1	no	—
178	D₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	8	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	—	4	2	no	—
203	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃	#137	1	2	yes	—
207	C₂×C₄×C₁₃	C₂³×C₄	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	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	4	2	no	—
215	C₈×C₁₃	#117	1	4	yes	complemented
216	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#117	—	2	1	no	—
220	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
221	C₂×#107	C₂²×C₁₃	1	2	yes	—
222	C₂×#107	C₂²×C₁₃	1	2	yes	—
223	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₃	1	2	yes	—
226	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#102	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#97	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	#391	C₂²×C₁₃	1	2	yes	—
232	#390	C₂²×C₁₃	1	2	yes	—
233	#388	—	2	2	no	—
234	#387	—	2	2	no	—
235	#384	C₂²×C₁₃	1	1	yes	characteristic
236	#384	C₂²×C₁₃	1	1	yes	characteristic
237	#382	—	2	1	no	—
238	#380	—	2	1	no	—
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	—	8	1	no	—
252	C₂²×C₁₃	—	8	1	no	—
253	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₁₃	#547	1	1	yes	characteristic
255	C₂²×C₁₃	#550	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
258	C₂²×C₁₃	#576	1	1	yes	characteristic
259	C₂²×C₁₃	#578	1	1	yes	characteristic
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	#440	1	4	yes	—
269	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
270	C₄×C₁₃	#520	1	1	yes	characteristic
271	C₄×C₁₃	#555	1	1	yes	characteristic
272	C₄×C₁₃	#556	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
286	#117	—	4	4	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	2	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	4	no	—
307	#107	—	4	2	no	—
308	#106	C₂×C₄×C₁₃	1	4	yes	—
309	C₄⋊C₈	—	2	2	no	—
310	#103	—	4	2	no	—
311	#103	C₂×C₄×C₁₃	1	4	yes	—
312	#102	—	4	2	no	—
313	#102	C₂×C₄×C₁₃	1	4	yes	—
314	#97	—	2	4	no	—
315	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	D₄×C₁₃	1	2	yes	—
321	C₂×C₁₃	—	8	2	no	—
322	C₂×C₁₃	#2354	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
324	C₂×C₁₃	#2951	1	1	yes	characteristic
325	C₂×C₁₃	#3353	1	1	yes	characteristic
326	C₂×C₁₃	#3357	1	1	yes	characteristic
327	C₂×C₁₃	#3398	1	1	yes	characteristic
328	C₂×C₁₃	#3399	1	1	yes	characteristic
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
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	—	2	1	no	—
341	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
355	SD₁₆	—	2	8	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
362	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
363	C₂×C₈	C₁₃×#41	1	2	yes	—
364	C₂×C₈	C₁₃×#41	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	8	1	no	—
377	C₄⋊C₄	—	8	1	no	—
378	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
379	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	4	no	—
387	C₄²	—	8	2	no	—
388	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
389	C₄²	C₁₃×#41	1	2	yes	—
390	C₁₃	#22811	1	1	yes	characteristic, direct product factor, Sylow
391	C₂³	—	2	2	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	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	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
432	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
433	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
434	C₂×C₄	C₁₃×#137	1	2	yes	—
435	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
438	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
439	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	4	2	no	—
443	C₈	C₁₃×#117	1	4	yes	complemented
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
452	C₂²	C₁₃×#547	1	1	yes	characteristic
453	C₂²	C₁₃×#550	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
456	C₂²	C₁₃×#576	1	1	yes	characteristic
457	C₂²	C₁₃×#578	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₁₃×#440	1	4	yes	—
467	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
468	C₄	C₁₃×#520	1	1	yes	characteristic
469	C₄	C₁₃×#555	1	1	yes	characteristic
470	C₄	C₁₃×#556	1	1	yes	characteristic
471	C₂	—	8	2	no	—
472	C₂	C₁₃×#2354	1	1	yes	characteristic
473	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
474	C₂	C₁₃×#2951	1	1	yes	characteristic
475	C₂	C₁₃×#3353	1	1	yes	characteristic
476	C₂	C₁₃×#3357	1	1	yes	characteristic
477	C₂	C₁₃×#3398	1	1	yes	characteristic
478	C₂	C₁₃×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×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
2. C₁₃×#2355	C₂	semidirect
5. C₁₃×#1928	C₂	semidirect
7. C₁₃×#1845	C₂	semidirect
8. C₁₃×#1803	C₂	semidirect
10. C₁₃×#1776	C₂	semidirect
11. C₁₃×#1770	C₂	semidirect
16. C₄×C₁₃×SD₁₆	C₄	semidirect
90. #22811	C₁₃	direct (N × H)
153. #2355	C₂×C₁₃	semidirect
156. #1928	C₂×C₁₃	semidirect
158. #1845	C₂×C₁₃	semidirect
159. #1803	C₂×C₁₃	semidirect
161. #1776	C₂×C₁₃	semidirect
162. #1770	C₂×C₁₃	semidirect
215. C₈×C₁₃	#117	semidirect
220. C₄×SD₁₆	C₄×C₁₃	semidirect
390. C₁₃	#22811	direct (N × H)
443. C₈	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2355	2
C₁₃×#2354	2
C₁₃×#1973	2
C₁₃×#1928	2
C₁₃×#1925	2
C₁₃×#1845	2
C₁₃×#1803	2
C₁₃×#1802	2
C₁₃×#1776	2
C₁₃×#1770	2
#22811	13

Subgroups — C13×#22811 #15709150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22811 #15709150