Subgroups — C₁₃×#22116 #15708455

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1943	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1936	C₂	1	2	yes	maximal
8	C₁₃×#1926	C₂	1	2	yes	maximal
9	C₁₃×#1921	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	—	2	1	no	—
16	C₁₃×#474	C₄	1	8	yes	complemented
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₁₃×#391	—	2	1	no	—
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#388	—	2	1	no	—
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₄³×C₁₃	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×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
51	C₄×Q₈×C₁₃	—	4	4	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
54	C₁₃×#117	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂×C₄	1	8	yes	—
81	C₁₃×#106	—	4	2	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
84	C₁₃×#102	—	4	2	no	—
85	C₁₃×#102	C₂×C₄	1	8	yes	—
86	C₁₃×#97	—	4	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	2	no	—
92	#22116	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	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	4	yes	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	4	1	no	—
153	C₄²×C₁₃	—	4	4	no	—
154	C₄²×C₁₃	—	4	2	no	—
155	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₃	#41	1	2	yes	—
157	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
158	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2293	C₂×C₁₃	1	1	yes	characteristic
160	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1943	C₂×C₁₃	1	2	yes	complemented
163	#1936	C₂×C₁₃	1	2	yes	—
164	#1926	C₂×C₁₃	1	2	yes	—
165	#1921	C₂×C₁₃	1	2	yes	complemented
166	#1802	C₂×C₁₃	1	1	yes	characteristic
167	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₃	—	4	8	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	1	no	—
180	D₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₁₃	#137	1	2	yes	—
215	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₃	—	2	4	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄×Q₈	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#117	—	2	1	no	—
227	#474	C₄×C₁₃	1	8	yes	complemented
228	C₂×#107	C₂²×C₁₃	1	2	yes	—
229	C₂×#106	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#102	C₂²×C₁₃	1	2	yes	—
233	C₂×#102	C₂²×C₁₃	1	2	yes	—
234	C₂×#97	C₂²×C₁₃	1	2	yes	—
235	#391	—	2	1	no	—
236	#390	C₂²×C₁₃	1	1	yes	characteristic
237	#390	C₂²×C₁₃	1	1	yes	characteristic
238	#389	—	2	1	no	—
239	#389	C₂²×C₁₃	1	2	yes	—
240	#389	C₂²×C₁₃	1	1	yes	characteristic
241	#389	C₂²×C₁₃	1	1	yes	characteristic
242	#388	—	2	1	no	—
243	#388	—	2	1	no	—
244	#384	C₂²×C₁₃	1	1	yes	characteristic
245	C₄×C₄⋊C₄	—	2	1	no	—
246	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₄×C₂²⋊C₄	—	2	1	no	—
249	C₄³	C₂²×C₁₃	1	1	yes	characteristic
250	#340	C₂²×C₁₃	1	2	yes	—
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	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	8	1	no	—
259	C₂²×C₁₃	—	8	1	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂²×C₁₃	#536	1	1	yes	characteristic
264	C₂²×C₁₃	#537	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
268	C₂²×C₁₃	#575	1	1	yes	characteristic
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	1	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	—	8	1	no	—
279	C₄×C₁₃	#442	1	4	yes	—
280	C₄×C₁₃	#519	1	1	yes	characteristic
281	C₄×C₁₃	#520	1	1	yes	characteristic
282	C₄×C₁₃	#541	1	1	yes	characteristic
283	C₄×C₁₃	#542	1	1	yes	characteristic
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
291	C₄×Q₈	—	4	4	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
294	#117	—	4	4	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	#107	C₂×C₄×C₁₃	1	8	yes	—
321	#106	—	4	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
324	#102	—	4	2	no	—
325	#102	C₂×C₄×C₁₃	1	8	yes	—
326	#97	—	4	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	2	no	—
332	C₂×C₁₃	—	8	2	no	—
333	C₂×C₁₃	#2323	1	1	yes	characteristic
334	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
335	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
336	C₂×C₁₃	#3235	1	1	yes	characteristic
337	C₂×C₁₃	#3239	1	1	yes	characteristic
338	C₂×C₁₃	#3251	1	1	yes	characteristic
339	C₂×C₁₃	#3254	1	1	yes	characteristic
340	C₂⁴	—	2	1	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
403	C₄²	C₁₃×#41	1	2	yes	—
404	C₁₃	#22116	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	—	2	2	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	Q₈	—	4	8	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
448	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
449	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
450	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
451	C₂×C₄	C₁₃×#137	1	2	yes	—
452	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
454	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
457	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
468	C₂²	C₁₃×#536	1	1	yes	characteristic
469	C₂²	C₁₃×#537	1	1	yes	characteristic
470	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
473	C₂²	C₁₃×#575	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	1	no	—
484	C₄	C₁₃×#442	1	4	yes	—
485	C₄	C₁₃×#519	1	1	yes	characteristic
486	C₄	C₁₃×#520	1	1	yes	characteristic
487	C₄	C₁₃×#541	1	1	yes	characteristic
488	C₄	C₁₃×#542	1	1	yes	characteristic
489	C₂	—	8	2	no	—
490	C₂	C₁₃×#2323	1	1	yes	characteristic
491	C₂	C₂×C₁₃×#442	1	1	yes	characteristic
492	C₂	C₄×C₁₃×#137	1	1	yes	characteristic
493	C₂	C₁₃×#3235	1	1	yes	characteristic
494	C₂	C₁₃×#3239	1	1	yes	characteristic
495	C₂	C₁₃×#3251	1	1	yes	characteristic
496	C₂	C₁₃×#3254	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
4. C₁₃×#1988	C₂	semidirect
5. C₁₃×#1948	C₂	semidirect
6. C₁₃×#1943	C₂	semidirect
9. C₁₃×#1921	C₂	semidirect
11. C₁₃×#1767	C₂	semidirect
16. C₁₃×#474	C₄	semidirect
92. #22116	C₁₃	direct (N × H)
158. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
160. #1988	C₂×C₁₃	semidirect
161. #1948	C₂×C₁₃	semidirect
162. #1943	C₂×C₁₃	semidirect
165. #1921	C₂×C₁₃	semidirect
167. #1767	C₂×C₁₃	semidirect
227. #474	C₄×C₁₃	semidirect
404. C₁₃	#22116	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×#474	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2293	2
C₁₃×#1988	2
C₁₃×#1948	2
C₁₃×#1943	2
C₁₃×#1936	2
C₁₃×#1926	2
C₁₃×#1921	2
C₁₃×#1802	2
C₁₃×#1767	2
#22116	13

Subgroups — C13×#22116 #15708455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22116 #15708455