Subgroups — #15865701

Order 3328.

1106 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115444	C₂	1	2	yes	maximal, complemented
4	#13115395	C₂	1	2	yes	maximal, complemented
5	#13115129	C₂	1	2	yes	maximal
6	#13115016	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114582	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×#1055	C₂²	1	2	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
24	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₄³×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
29	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
30	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
31	#11718586	—	2	4	no	—
32	C₂×C₄⋊#1055	C₂²	1	2	yes	—
33	C₂×C₄⋊#1055	C₂²	1	2	yes	—
34	C₂×C₄×#1055	—	2	4	no	—
35	C₂×C₄×#1055	C₂²	1	2	yes	—
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
40	#11718116	C₂²	1	2	yes	—
41	#11718116	C₂²	1	2	yes	—
42	#11718116	C₂²	1	2	yes	—
43	#11718116	C₂²	1	2	yes	—
44	#11718116	C₂²	1	2	yes	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×D₄×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	C₈	1	8	yes	complemented
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	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	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×#1055	—	2	4	no	—
82	C₂²×#1055	—	2	4	no	—
83	C₂²×#1055	—	2	4	no	—
84	C₂²×#1055	C₂³	1	2	yes	—
85	C₂²×#1055	C₂³	1	2	yes	—
86	C₂²×#1055	C₂³	1	2	yes	—
87	C₂²×#1055	C₂³	1	2	yes	—
88	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊#1055	—	2	4	no	—
95	C₂²⋊#1055	—	2	4	no	—
96	C₂²⋊#1055	—	2	4	no	—
97	C₄⋊#1055	—	2	4	no	—
98	C₄⋊#1055	—	2	4	no	—
99	C₄×#1055	—	2	2	no	—
100	C₄×#1055	—	2	2	no	—
101	C₄×#1055	—	2	2	no	—
102	C₄×#1055	—	2	4	no	—
103	C₄×#1055	D₄	1	4	yes	complemented
104	#21101	—	13	1	no	maximal, Sylow
105	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	complemented
128	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	#41	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
146	C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
151	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	C₂×C₈	1	4	yes	complemented
166	C₄²×C₁₃	C₂×D₄	1	2	yes	—
167	C₄²×C₁₃	#41	1	2	yes	—
168	C₂×#1055	—	2	16	no	—
169	C₂×#1055	—	2	2	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	2	2	no	—
174	C₂×#1055	—	2	2	no	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	—	2	2	no	—
177	C₂×#1055	—	2	2	no	—
178	C₂×#1055	—	2	2	no	—
179	C₂×#1055	C₂×D₄	1	4	yes	—
180	C₂×#1055	#41	1	4	yes	—
181	C₂×#431	—	13	1	no	—
182	C₂²×C₄×C₈	—	13	1	no	—
183	C₄²×D₄	D₁₃	1	1	yes	characteristic
184	#1923	—	13	2	no	—
185	#1916	—	13	2	no	—
186	#1869	—	13	2	no	—
187	#1850	—	13	2	no	—
188	C₄×C₄⋊C₈	—	13	1	no	—
189	C₄×C₂²⋊C₈	—	13	1	no	—
190	C₄×C₂²⋊C₈	—	13	1	no	—
191	#1744	—	13	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	#117	1	2	yes	—
203	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
204	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
205	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
206	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	D₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	2	8	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	#117	1	2	yes	—
241	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
246	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
248	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
250	C₂×C₄×C₁₃	#131	1	2	yes	—
251	C₂×C₄×C₁₃	#131	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	#1055	—	2	4	no	—
257	#1055	—	2	4	no	—
258	#1055	—	4	2	no	—
259	#1055	—	4	2	no	—
260	C₂³×C₈	—	13	2	no	—
261	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
262	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
264	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
265	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
266	#431	—	26	4	no	—
267	C₂×C₄⋊C₈	—	13	2	no	—
268	C₂×C₄⋊C₈	—	13	2	no	—
269	C₂×C₂²⋊C₈	—	13	2	no	—
270	C₂×C₂²⋊C₈	—	13	2	no	—
271	C₂×C₂²⋊C₈	—	13	2	no	—
272	C₂×C₄×C₈	—	13	1	no	—
273	C₂×C₄×C₈	—	13	2	no	—
274	C₂×C₄×C₈	—	13	1	no	—
275	C₂×C₄×C₈	—	13	1	no	—
276	C₂×C₄×C₈	—	13	1	no	—
277	C₂×C₄×C₈	—	26	4	no	—
278	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
279	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
287	C₄³	C₂×D₁₃	1	1	yes	characteristic
288	#336	—	13	2	no	—
289	#336	—	13	2	no	—
290	#336	—	13	2	no	—
291	#336	—	13	2	no	—
292	#336	—	13	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	#431	1	4	yes	complemented
307	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
308	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
310	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
311	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	4	1	no	—
321	C₄×C₁₃	—	4	1	no	—
322	C₄×C₁₃	—	4	1	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	C₈×D₄	1	4	yes	—
325	C₄×C₁₃	#435	1	4	yes	—
326	C₄×C₁₃	#525	1	2	yes	—
327	C₄×C₁₃	#529	1	2	yes	—
328	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
334	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
335	C₂²×C₈	—	13	2	no	—
336	C₂²×C₈	—	13	2	no	—
337	C₂²×C₈	—	13	2	no	—
338	C₂²×C₈	—	13	2	no	—
339	C₂²×C₈	—	26	4	no	—
340	C₂²×C₈	—	26	4	no	—
341	C₂²×C₈	—	26	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	#1055	1	8	yes	complemented
345	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
360	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
361	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
371	C₄⋊C₈	—	26	4	no	—
372	C₄⋊C₈	—	26	4	no	—
373	C₂²⋊C₈	—	26	4	no	—
374	C₂²⋊C₈	—	26	4	no	—
375	C₂²⋊C₈	—	26	4	no	—
376	C₄×C₈	—	13	4	no	—
377	C₄×C₈	—	26	4	no	—
378	C₄×C₈	—	26	2	no	—
379	C₄×C₈	—	26	2	no	—
380	C₄×C₈	—	26	2	no	—
381	#95	C₂×Dic₁₃	1	1	yes	characteristic
382	#95	C₂×Dic₁₃	1	1	yes	characteristic
383	#95	C₂×Dic₁₃	1	1	yes	characteristic
384	#95	C₂×Dic₁₃	1	1	yes	characteristic
385	#95	C₂×Dic₁₃	1	1	yes	characteristic
386	#95	C₂×Dic₁₃	1	1	yes	characteristic
387	C₂×C₁₃	—	2	4	no	—
388	C₂×C₁₃	—	4	2	no	—
389	C₂×C₁₃	#2290	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
391	C₂×C₁₃	#2922	1	1	yes	characteristic
392	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
393	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
394	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
395	C₂×C₁₃	#2965	1	1	yes	characteristic
396	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
397	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	C₂×#1055	1	4	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	C₂×#1055	1	4	yes	—
418	C₂²×C₄	C₂×#1055	1	4	yes	complemented
419	C₂²×C₄	#6099	1	4	yes	—
420	C₂²×C₄	#6127	1	4	yes	—
421	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
434	C₂×C₈	—	13	4	no	—
435	C₂×C₈	—	13	4	no	—
436	C₂×C₈	—	26	16	no	—
437	C₂×C₈	—	26	2	no	—
438	C₂×C₈	—	26	2	no	—
439	C₂×C₈	—	26	2	no	—
440	C₂×C₈	—	26	2	no	—
441	C₂×C₈	—	26	2	no	—
442	C₂×C₈	—	26	2	no	—
443	C₂×C₈	—	26	2	no	—
444	C₂×C₈	—	26	2	no	—
445	C₂×C₈	—	26	2	no	—
446	C₂×C₈	—	26	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	C₂×#1055	1	4	yes	complemented
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	C₂×#1055	1	4	yes	—
455	C₂²⋊C₄	C₂×#1055	1	4	yes	complemented
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	2	no	—
469	C₄²	C₂×#1055	1	4	yes	complemented
470	C₄²	D₄×D₁₃	1	2	yes	—
471	C₄²	#6129	1	2	yes	—
472	C₁₃	#21101	1	1	yes	characteristic, complemented, Sylow
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	C₂²×#1055	1	2	yes	—
484	C₂³	C₂²×#1055	1	2	yes	—
485	C₂³	C₂×#6099	1	2	yes	—
486	C₂³	#88180	1	2	yes	—
487	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
488	D₄	—	2	8	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	C₂²×#1055	1	2	yes	—
522	C₂×C₄	C₂²×#1055	1	2	yes	—
523	C₂×C₄	C₂²×#1055	1	2	yes	—
524	C₂×C₄	C₂²×#1055	1	2	yes	—
525	C₂×C₄	C₂²×#1055	1	2	yes	—
526	C₂×C₄	C₂×#6099	1	2	yes	—
527	C₂×C₄	C₂×#6099	1	2	yes	—
528	C₂×C₄	#88180	1	2	yes	—
529	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
530	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
531	C₂×C₄	#88202	1	2	yes	—
532	C₂×C₄	#88202	1	2	yes	—
533	C₂×C₄	C₂×#6127	1	2	yes	—
534	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
535	C₂×C₄	C₂×#6129	1	1	yes	characteristic
536	C₂×C₄	#41×D₁₃	1	2	yes	—
537	C₈	—	26	4	no	—
538	C₈	—	26	4	no	—
539	C₈	—	52	2	no	—
540	C₈	—	52	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	#11718586	1	4	yes	complemented
555	C₂²	C₂³×#1055	1	1	yes	characteristic
556	C₂²	C₂²×#6099	1	1	yes	characteristic
557	C₂²	C₂×#88180	1	1	yes	characteristic
558	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
559	C₂²	C₂×#88202	1	1	yes	characteristic
560	C₂²	C₂×#88202	1	1	yes	characteristic
561	C₂²	#41×Dic₁₃	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	D₄×#1055	1	4	yes	—
573	C₄	#11718672	1	4	yes	—
574	C₄	#11719243	1	2	yes	—
575	C₄	#11719252	1	2	yes	—
576	C₂	—	2	4	no	—
577	C₂	—	4	2	no	—
578	C₂	#13117281	1	1	yes	characteristic
579	C₂	C₂×#11718586	1	1	yes	characteristic
580	C₂	#13123480	1	1	yes	characteristic
581	C₂	C₂×D₄×#1055	1	1	yes	characteristic
582	C₂	C₂×#11718672	1	1	yes	characteristic
583	C₂	#41×#1055	1	1	yes	characteristic
584	C₂	#13123803	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄²×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄²×D₄	D₁₃
hypocenter	C₁₃	#21101
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11718586	C₂	semidirect
2. C₂²×C₄×#1055	C₂	semidirect
3. #13115444	C₂	semidirect
4. #13115395	C₂	semidirect
6. #13115016	C₂	semidirect
7. C₄×C₄⋊#1055	C₂	semidirect
8. C₄×C₂²⋊#1055	C₂	semidirect
9. C₄×C₂²⋊#1055	C₂	semidirect
10. #13114582	C₂	semidirect
54. C₄×D₄×C₁₃	C₈	semidirect
103. C₄×#1055	D₄	semidirect
127. C₂²×C₄×C₁₃	C₂×C₈	semidirect
145. C₁₃×C₄⋊C₄	C₂×C₈	semidirect
151. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
165. C₄²×C₁₃	C₂×C₈	semidirect
306. C₂²×C₁₃	#431	semidirect
344. C₄×D₄	#1055	semidirect
418. C₂²×C₄	C₂×#1055	semidirect
449. C₄⋊C₄	C₂×#1055	semidirect
455. C₂²⋊C₄	C₂×#1055	semidirect
469. C₄²	C₂×#1055	semidirect
472. C₁₃	#21101	semidirect
554. C₂²	#11718586	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
C₂²×C₄×#1055	2
#13115444	2
#13115395	2
#13115129	2
#13115016	2
C₄×C₄⋊#1055	2
C₄×C₂²⋊#1055	2
#13114582	2
C₄²×D₄×C₁₃	2
#21101	13