Subgroups — C₄×C₁₃×#440 #15706840

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#440	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1763	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1762	C₂	1	2	yes	maximal
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#97	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×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃	—	2	1	no	—
18	C₁₃×#440	C₄	1	16	yes	direct product factor
19	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₄³×C₁₃	—	2	1	no	—
39	C₄³×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	4	4	no	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂×C₄	1	8	yes	complemented
81	C₁₃×#106	C₂×C₄	1	4	yes	complemented
82	C₁₃×#103	C₂×C₄	1	4	yes	complemented
83	C₁₃×#103	C₂×C₄	1	8	yes	complemented
84	C₁₃×#102	C₂×C₄	1	4	yes	—
85	C₁₃×#102	C₂×C₄	1	8	yes	—
86	C₁₃×#97	—	2	4	no	—
87	C₁₃×#97	C₂×C₄	1	8	yes	complemented
88	C₄×C₈×C₁₃	—	2	2	no	—
89	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₄×#440	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	2	no	—
98	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
120	C₁₃×SD₁₆	C₄²	1	16	yes	complemented
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	8	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	—	2	2	no	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₁₃×C₂²⋊C₄	—	2	4	no	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₄²×C₁₃	—	4	4	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
150	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₄²×C₁₃	#41	1	4	yes	—
153	C₂×#440	C₂×C₁₃	1	2	yes	—
154	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
155	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
157	#1776	C₂×C₁₃	1	2	yes	complemented
158	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1763	C₂×C₁₃	1	2	yes	complemented
160	#1762	C₂×C₁₃	1	2	yes	—
161	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
163	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	C₂×C₄²	1	4	yes	complemented
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	C₂×C₄²	1	4	yes	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	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	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	4	16	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
197	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
206	C₈×C₁₃	—	2	4	no	—
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	C₂×C₄²	1	4	yes	complemented
209	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₄²	—	2	1	no	—
215	#440	C₄×C₁₃	1	16	yes	direct product factor
216	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
217	C₂×#107	C₂²×C₁₃	1	2	yes	—
218	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#102	C₂²×C₁₃	1	2	yes	—
223	C₂×#97	C₂²×C₁₃	1	2	yes	—
224	C₂×#97	C₂²×C₁₃	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	—	2	2	no	—
229	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
233	C₄×C₂²⋊C₄	—	2	1	no	—
234	C₄×C₂²⋊C₄	—	2	2	no	—
235	C₄³	—	2	1	no	—
236	C₄³	C₂²×C₁₃	1	1	yes	characteristic
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
247	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
249	C₂²×C₁₃	#575	1	2	yes	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	4	no	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	4	no	—
257	C₄×C₁₃	—	4	4	no	—
258	C₄×C₁₃	#440	1	4	yes	direct product factor
259	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
260	C₄×C₁₃	C₄×#41	1	2	yes	—
261	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
267	C₂×SD₁₆	C₂×C₄×C₁₃	1	8	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
274	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
278	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	4	4	no	—
294	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	D₄×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
299	#107	C₂×C₄×C₁₃	1	8	yes	complemented
300	#106	C₂×C₄×C₁₃	1	4	yes	complemented
301	#103	C₂×C₄×C₁₃	1	4	yes	complemented
302	#103	C₂×C₄×C₁₃	1	8	yes	complemented
303	#102	C₂×C₄×C₁₃	1	4	yes	—
304	#102	C₂×C₄×C₁₃	1	8	yes	—
305	#97	—	2	4	no	—
306	#97	C₂×C₄×C₁₃	1	8	yes	complemented
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	C₂×C₁₃	—	4	4	no	—
314	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
316	C₂×C₁₃	#2943	1	1	yes	characteristic
317	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
318	C₂×C₁₃	C₄×#137	1	2	yes	—
319	C₂⁴	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
323	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
327	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
344	SD₁₆	C₄²×C₁₃	1	16	yes	complemented
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
350	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
359	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
360	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	4	4	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
374	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
375	C₄²	C₁₃×#41	1	2	yes	—
376	C₄²	C₁₃×#41	1	4	yes	—
377	C₁₃	C₄×#440	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	C₂×C₄²×C₁₃	1	4	yes	complemented
387	D₄	—	2	2	no	—
388	D₄	—	2	4	no	—
389	D₄	C₂×C₄²×C₁₃	1	4	yes	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	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	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
412	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
413	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
414	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
415	C₂×C₄	C₁₃×#137	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
418	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
420	C₈	—	2	4	no	—
421	C₈	—	2	2	no	—
422	C₈	C₂×C₄²×C₁₃	1	4	yes	complemented
423	C₂²	—	2	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
429	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
430	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
432	C₂²	C₁₃×#575	1	2	yes	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₁₃×#440	1	4	yes	direct product factor
442	C₄	C₂²×C₄²×C₁₃	1	1	yes	characteristic
443	C₄	C₄×C₁₃×#41	1	2	yes	—
444	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
445	C₂	—	4	4	no	—
446	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
447	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
448	C₂	C₁₃×#2943	1	1	yes	characteristic
449	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
450	C₂	C₄×C₁₃×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×Q₈×C₁₃	C₂	semidirect
5. C₁₃×#1776	C₂	semidirect
6. C₄×C₁₃×#107	C₂	semidirect
7. C₁₃×#1763	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
11. C₄×C₁₃×#97	C₂	semidirect
18. C₁₃×#440	C₄	direct (N × H)
19. C₄×C₁₃×SD₁₆	C₄	semidirect
54. C₄×Q₈×C₁₃	C₂×C₄	semidirect
55. C₄×Q₈×C₁₃	C₂×C₄	semidirect
80. C₁₃×#107	C₂×C₄	semidirect
81. C₁₃×#106	C₂×C₄	semidirect
82. C₁₃×#103	C₂×C₄	semidirect
83. C₁₃×#103	C₂×C₄	semidirect
87. C₁₃×#97	C₂×C₄	semidirect
89. C₄×C₈×C₁₃	C₂×C₄	semidirect
94. C₄×#440	C₁₃	direct (N × H)
120. C₁₃×SD₁₆	C₄²	semidirect
155. C₄²×Q₈	C₂×C₁₃	semidirect
157. #1776	C₂×C₁₃	semidirect
158. C₄×#107	C₂×C₁₃	semidirect
159. #1763	C₂×C₁₃	semidirect
161. C₄×#103	C₂×C₁₃	semidirect
163. C₄×#97	C₂×C₁₃	semidirect
172. Q₈×C₁₃	C₂×C₄²	semidirect
208. C₈×C₁₃	C₂×C₄²	semidirect
215. #440	C₄×C₁₃	direct (N × H)
216. C₄×SD₁₆	C₄×C₁₃	semidirect
258. C₄×C₁₃	#440	direct (N × H)
273. C₄×Q₈	C₂×C₄×C₁₃	semidirect
274. C₄×Q₈	C₂×C₄×C₁₃	semidirect
299. #107	C₂×C₄×C₁₃	semidirect
300. #106	C₂×C₄×C₁₃	semidirect
301. #103	C₂×C₄×C₁₃	semidirect
302. #103	C₂×C₄×C₁₃	semidirect
306. #97	C₂×C₄×C₁₃	semidirect
308. C₄×C₈	C₂×C₄×C₁₃	semidirect
344. SD₁₆	C₄²×C₁₃	semidirect
377. C₁₃	C₄×#440	direct (N × H)
386. Q₈	C₂×C₄²×C₁₃	semidirect
422. C₈	C₂×C₄²×C₁₃	semidirect
441. C₄	C₁₃×#440	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×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₄²×Q₈×C₁₃	2
C₄²×D₄×C₁₃	2
C₁₃×#1776	2
C₄×C₁₃×#107	2
C₁₃×#1763	2
C₁₃×#1762	2
C₄×C₁₃×#103	2
C₄×C₁₃×#102	2
C₄×C₁₃×#97	2
C₄×#440	13

Subgroups — C4×C13×#440 #15706840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#440 #15706840