Subgroups — C₄×C₁₃×#435 #15706825

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#435	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1752	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#435	C₄	1	16	yes	direct product factor
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₄×C₁₃×M₁₆	—	2	4	no	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	C₂²	1	2	yes	—
25	C₂×C₁₃×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	—	2	4	no	—
27	C₂×C₄×C₈×C₁₃	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	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₄³×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	4	no	—
48	C₂×C₁₃×M₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	complemented
50	C₂²×C₈×C₁₃	—	2	4	no	—
51	C₂²×C₈×C₁₃	—	2	4	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₄×D₄×C₁₃	—	2	8	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
80	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
81	C₁₃×#97	—	2	4	no	—
82	C₁₃×#97	—	2	4	no	—
83	C₁₃×#97	C₂×C₄	1	8	yes	complemented
84	C₄×C₈×C₁₃	—	2	4	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
89	C₁₃×#95	C₂×C₄	1	2	yes	—
90	C₁₃×#95	C₂×C₄	1	2	yes	—
91	C₁₃×#95	C₂×C₄	1	2	yes	—
92	C₄×#435	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	C₄²	1	4	yes	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	M₁₆	1	8	yes	complemented
109	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×M₁₆	—	2	16	no	—
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	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	16	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₃	#41	1	4	yes	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
139	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	2	4	no	—
143	C₄²×C₁₃	—	2	4	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₂×#435	C₂×C₁₃	1	2	yes	—
153	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
156	#1771	C₂×C₁₃	1	2	yes	complemented
157	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1753	C₂×C₁₃	1	2	yes	complemented
159	#1752	C₂×C₁₃	1	2	yes	complemented
160	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
171	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
172	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
173	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	D₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	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	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	16	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	—	2	2	no	—
194	C₂×C₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
196	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
199	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
200	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
201	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
202	C₂×C₄×C₁₃	#131	1	4	yes	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₃	—	2	4	no	—
208	C₈×C₁₃	—	2	4	no	—
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	C₄×D₄	1	8	yes	complemented
211	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
212	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
214	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
217	#435	C₄×C₁₃	1	16	yes	direct product factor
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
221	C₄×M₁₆	—	2	4	no	—
222	C₂×#97	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	—	2	4	no	—
226	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
234	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
235	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₄³	C₂²×C₁₃	1	1	yes	characteristic
238	#336	C₂²×C₁₃	1	2	yes	—
239	#336	C₂²×C₁₃	1	2	yes	—
240	#336	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	2	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	C₄×M₁₆	1	4	yes	complemented
251	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
254	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
255	C₂²×C₁₃	C₂×#131	1	2	yes	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	#435	1	8	yes	direct product factor
264	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
265	C₄×C₁₃	C₄×#41	1	2	yes	—
266	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
268	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	—	2	4	no	—
276	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
277	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
281	C₄×D₄	—	2	8	no	—
282	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
294	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
295	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
296	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
303	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
304	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
305	#97	—	2	4	no	—
306	#97	—	2	4	no	—
307	#97	C₂×C₄×C₁₃	1	8	yes	complemented
308	C₄×C₈	—	2	4	no	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
313	#95	C₂×C₄×C₁₃	1	2	yes	—
314	#95	C₂×C₄×C₁₃	1	2	yes	—
315	#95	C₂×C₄×C₁₃	1	2	yes	—
316	C₂×C₁₃	—	2	4	no	—
317	C₂×C₁₃	—	4	2	no	—
318	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
319	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
320	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#435	1	2	yes	—
322	C₂×C₁₃	#2965	1	2	yes	—
323	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	C₄²×C₁₃	1	4	yes	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	C₁₃×M₁₆	1	8	yes	complemented
339	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	M₁₆	—	2	16	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	16	no	—
358	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
359	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
360	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
361	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
362	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
363	C₂×C₈	C₁₃×#41	1	4	yes	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
369	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
380	C₄²	C₂×D₄×C₁₃	1	2	yes	—
381	C₄²	C₁₃×#41	1	2	yes	—
382	C₁₃	C₄×#435	1	1	yes	characteristic, direct product factor, Sylow
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
391	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
392	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
393	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
394	D₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	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	8	no	—
415	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
416	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
417	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
418	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
419	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
420	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
421	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
422	C₂×C₄	C₁₃×#131	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
426	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	2	4	no	—
429	C₈	—	2	4	no	—
430	C₈	C₄×D₄×C₁₃	1	8	yes	complemented
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	C₄×C₁₃×M₁₆	1	4	yes	complemented
441	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
442	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
443	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
444	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
445	C₂²	C₂×C₁₃×#131	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	C₁₃×#435	1	8	yes	direct product factor
454	C₄	C₂×C₄×D₄×C₁₃	1	2	yes	—
455	C₄	C₄×C₁₃×#41	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	2	no	—
458	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
459	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
460	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#435	1	2	yes	—
462	C₂	C₁₃×#2965	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
3. C₂²×C₄×C₈×C₁₃	C₂	semidirect
5. C₁₃×#1771	C₂	semidirect
6. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
7. C₁₃×#1753	C₂	semidirect
8. C₁₃×#1752	C₂	semidirect
9. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
10. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
11. C₄×C₁₃×#97	C₂	semidirect
18. C₁₃×#435	C₄	direct (N × H)
49. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
52. C₂²×C₈×C₁₃	C₂×C₄	semidirect
78. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
79. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
80. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
83. C₁₃×#97	C₂×C₄	semidirect
88. C₄×C₈×C₁₃	D₄	semidirect
92. C₄×#435	C₁₃	direct (N × H)
108. C₂²×C₄×C₁₃	M₁₆	semidirect
153. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
154. C₂²×C₄×C₈	C₂×C₁₃	semidirect
156. #1771	C₂×C₁₃	semidirect
157. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
158. #1753	C₂×C₁₃	semidirect
159. #1752	C₂×C₁₃	semidirect
160. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
161. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
162. C₄×#97	C₂×C₁₃	semidirect
210. C₈×C₁₃	C₄×D₄	semidirect
217. #435	C₄×C₁₃	direct (N × H)
250. C₂²×C₁₃	C₄×M₁₆	semidirect
263. C₄×C₁₃	#435	direct (N × H)
273. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
276. C₂²×C₈	C₂×C₄×C₁₃	semidirect
302. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
303. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
304. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
307. #97	C₂×C₄×C₁₃	semidirect
312. C₄×C₈	D₄×C₁₃	semidirect
338. C₂²×C₄	C₁₃×M₁₆	semidirect
382. C₁₃	C₄×#435	direct (N × H)
430. C₈	C₄×D₄×C₁₃	semidirect
440. C₂²	C₄×C₁₃×M₁₆	semidirect
453. C₄	C₁₃×#435	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×#435	2
C₂×C₄×C₁₃×M₁₆	2
C₂²×C₄×C₈×C₁₃	2
C₄²×D₄×C₁₃	2
C₁₃×#1771	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
C₁₃×#1752	2
C₄×C₁₃×C₂²⋊C₈	2
C₄×C₁₃×#97	2
C₄×#435	13

Subgroups — C4×C13×#435 #15706825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#435 #15706825