Subgroups — #15768352

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88155	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718793	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718667	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114532	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6127	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂×#88155	—	2	2	no	—
16	C₂×#88155	—	2	2	no	—
17	C₂×#88155	—	2	2	no	—
18	C₂×#88155	—	2	2	no	—
19	C₂×#88155	—	2	2	no	—
20	C₂×#88155	—	2	2	no	—
21	C₂²×#6094	C₄	1	2	yes	complemented
22	C₂²×C₈×D₁₃	C₄	1	2	yes	complemented
23	C₂×#88064	C₄	1	2	yes	complemented
24	#11718793	—	2	2	no	—
25	#11718793	—	2	2	no	—
26	C₂×#88063	C₄	1	2	yes	complemented
27	#11718667	—	2	2	no	—
28	#11718667	—	2	2	no	—
29	C₂×#88046	C₄	1	4	yes	—
30	C₁₃×#336	—	2	2	no	—
31	#11718151	—	2	2	no	—
32	#11718142	—	2	2	no	—
33	#11718125	—	2	2	no	—
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
36	C₂×#6127	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₂×#6127	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	D₄	1	2	yes	—
45	C₂×#6127	D₄	1	2	yes	—
46	C₂×#6127	D₄	1	2	yes	—
47	C₂×#6127	Q₈	1	2	yes	—
48	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
50	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	D₄	1	2	yes	—
65	C₂²×C₈×C₁₃	D₄	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	—	2	1	no	—
77	#88180	—	2	1	no	—
78	C₂×C₄⋊Dic₁₃	—	2	1	no	—
79	C₂×C₄×Dic₁₃	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	—	2	1	no	—
89	C₂×#6099	C₂×C₄	1	2	yes	—
90	C₂×#6099	D₄	1	2	yes	—
91	C₂×#6099	D₄	1	2	yes	—
92	C₂²×#1055	—	2	1	no	—
93	C₂²×#1055	C₂×C₄	1	2	yes	—
94	#88155	—	2	8	no	—
95	#88155	—	2	8	no	—
96	#88155	—	2	8	no	—
97	#88155	—	2	8	no	—
98	C₂×#6094	—	2	4	no	—
99	C₂×#6094	—	2	4	no	—
100	C₂×#6094	—	2	4	no	—
101	C₂×C₈×D₁₃	—	2	4	no	—
102	C₂×C₈×D₁₃	—	2	4	no	—
103	C₂×C₈×D₁₃	—	2	4	no	—
104	#88064	—	2	4	no	—
105	#88063	—	2	4	no	—
106	#88046	—	2	8	no	—
107	#10764	—	13	1	no	maximal, Sylow
108	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂³×D₁₃	C₄²	1	2	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₁₃	—	2	2	no	—
126	C₂×C₂²⋊D₁₃	—	2	2	no	—
127	C₂×C₂²⋊D₁₃	—	2	2	no	—
128	C₂×C₂²⋊D₁₃	—	2	2	no	—
129	C₂×C₂²⋊D₁₃	C₂²⋊C₄	1	4	yes	—
130	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	4	yes	—
131	C₂²×Dic₁₃	—	2	2	no	—
132	C₂²×Dic₁₃	C₄²	1	2	yes	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	#6127	—	2	2	no	—
136	#6127	—	2	2	no	—
137	#6127	—	2	2	no	—
138	#6127	—	2	2	no	—
139	#6127	—	2	2	no	—
140	#6127	—	2	2	no	—
141	#6127	—	2	2	no	—
142	#6127	—	2	2	no	—
143	#6127	—	2	2	no	—
144	#6127	—	2	2	no	—
145	#6127	—	2	2	no	—
146	#6127	—	2	2	no	—
147	#6127	—	2	2	no	—
148	#6127	—	2	2	no	—
149	C₂×D₅₂	—	2	1	no	—
150	C₂×D₅₂	—	2	1	no	—
151	C₂×D₅₂	—	2	1	no	—
152	C₂×D₅₂	—	2	1	no	—
153	C₂×D₅₂	C₂²⋊C₄	1	2	yes	—
154	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
155	C₂×C₄×D₁₃	—	2	2	no	—
156	C₂×C₄×D₁₃	—	2	2	no	—
157	C₂×C₄×D₁₃	—	2	2	no	—
158	C₂×C₄×D₁₃	—	2	2	no	—
159	C₂×C₄×D₁₃	C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
161	C₂×Dic₂₆	—	2	1	no	—
162	C₂×Dic₂₆	—	2	1	no	—
163	C₂×Dic₂₆	—	2	1	no	—
164	C₂×Dic₂₆	—	2	1	no	—
165	C₂×Dic₂₆	C₂²⋊C₄	1	2	yes	—
166	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	4	1	no	—
170	C₁₃×M₁₆	—	4	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₂×C₈×C₁₃	—	2	2	no	—
180	C₂×C₈×C₁₃	—	4	1	no	—
181	C₂×C₈×C₁₃	—	4	1	no	—
182	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
183	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	—	4	1	no	—
185	C₁₃×C₄⋊C₄	—	4	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₄²×C₁₃	—	4	1	no	—
189	C₄²×C₁₃	—	4	1	no	—
190	C₂²⋊Dic₁₃	—	2	2	no	—
191	C₂²⋊Dic₁₃	—	2	2	no	—
192	C₄⋊Dic₁₃	—	4	1	no	—
193	C₄⋊Dic₁₃	—	4	1	no	—
194	C₄×Dic₁₃	—	4	1	no	—
195	C₄×Dic₁₃	—	4	1	no	—
196	#6099	—	2	2	no	—
197	#6099	—	2	2	no	—
198	#6099	—	2	2	no	—
199	#6099	—	2	2	no	—
200	#6099	—	2	2	no	—
201	#6099	—	2	2	no	—
202	#6099	—	4	1	no	—
203	#6099	—	4	1	no	—
204	C₂×#1055	—	2	2	no	—
205	C₂×#1055	—	2	2	no	—
206	C₂×#1055	—	2	2	no	—
207	C₂×#1055	—	4	1	no	—
208	C₂×#1055	—	4	1	no	—
209	C₂×#1055	C₂²⋊C₄	1	4	yes	—
210	#6094	—	2	16	no	—
211	C₈×D₁₃	—	2	16	no	—
212	C₂²×#131	—	13	1	no	—
213	C₂×#413	—	13	1	no	—
214	C₂×#410	—	13	1	no	—
215	C₂×#344	—	13	1	no	—
216	C₂×#344	—	13	1	no	—
217	#1729	—	13	1	no	—
218	#1729	D₁₃	1	1	yes	characteristic, complemented
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
221	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
224	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
225	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂²×D₁₃	—	2	2	no	—
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	4	4	no	—
230	C₂²×D₁₃	#95	1	4	yes	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
258	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
261	C₂²⋊D₁₃	—	2	4	no	—
262	C₂²⋊D₁₃	—	2	4	no	—
263	C₂²⋊D₁₃	—	2	4	no	—
264	C₂²⋊D₁₃	—	2	4	no	—
265	C₂×Dic₁₃	—	2	2	no	—
266	C₂×Dic₁₃	—	2	2	no	—
267	C₂×Dic₁₃	—	4	4	no	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	#95	1	4	yes	—
270	D₅₂	—	2	2	no	—
271	D₅₂	—	2	2	no	—
272	D₅₂	—	2	2	no	—
273	D₅₂	—	2	2	no	—
274	C₄×D₁₃	—	2	4	no	—
275	C₄×D₁₃	—	2	4	no	—
276	C₄×D₁₃	—	2	4	no	—
277	C₄×D₁₃	—	2	4	no	—
278	Dic₂₆	—	2	2	no	—
279	Dic₂₆	—	2	2	no	—
280	Dic₂₆	—	2	2	no	—
281	Dic₂₆	—	2	2	no	—
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	2	2	no	—
284	C₈×C₁₃	—	4	2	no	—
285	#1055	—	2	4	no	—
286	#1055	—	4	2	no	—
287	C₂²×#41	—	13	1	no	—
288	C₂×#131	—	26	2	no	—
289	C₂×#131	—	26	2	no	—
290	C₂×#131	—	26	2	no	—
291	C₂×#131	—	26	2	no	—
292	C₂×#131	—	26	2	no	—
293	C₂×#131	—	26	2	no	—
294	C₂²×M₁₆	—	13	1	no	—
295	C₂²×M₁₆	—	13	2	no	—
296	C₂²×M₁₆	—	13	1	no	—
297	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
298	C₂³×C₈	—	13	2	no	—
299	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
300	C₂×#117	—	13	1	no	—
301	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
302	#413	—	26	2	no	—
303	#413	—	26	2	no	—
304	C₂×#101	—	13	2	no	—
305	C₂×#100	—	13	2	no	—
306	#410	—	26	2	no	—
307	#410	—	26	2	no	—
308	C₂×#99	—	13	4	no	—
309	#344	—	26	2	no	—
310	#344	—	26	2	no	—
311	#336	—	2	2	no	—
312	#336	—	26	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	4	1	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
321	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₁₃	#385	1	1	yes	characteristic
324	C₂²×C₁₃	#385	1	1	yes	characteristic
325	C₂²×C₁₃	#386	1	1	yes	characteristic
326	C₂²×C₁₃	#386	1	1	yes	characteristic
327	C₂×D₁₃	—	2	4	no	—
328	C₂×D₁₃	—	4	4	no	—
329	C₂×D₁₃	—	4	4	no	—
330	C₂×D₁₃	—	4	4	no	—
331	C₄×C₁₃	—	8	2	no	—
332	C₄×C₁₃	#379	1	1	yes	characteristic
333	C₄×C₁₃	#380	1	1	yes	characteristic
334	C₄×C₁₃	#380	1	1	yes	characteristic
335	C₄×C₁₃	#381	1	1	yes	characteristic
336	C₄×C₁₃	#385	1	1	yes	characteristic
337	C₄×C₁₃	#385	1	1	yes	characteristic
338	C₄×C₁₃	#386	1	1	yes	characteristic
339	C₄×C₁₃	#386	1	1	yes	characteristic
340	Dic₁₃	—	2	4	no	—
341	Dic₁₃	—	8	2	no	—
342	C₂×#41	—	13	2	no	—
343	C₂×#41	—	13	2	no	—
344	C₂×#41	—	13	2	no	—
345	C₂×#41	—	13	2	no	—
346	C₂×#41	—	26	1	no	—
347	C₂×#41	—	26	1	no	—
348	C₂×#41	—	26	1	no	—
349	C₂×#41	—	26	1	no	—
350	C₂×#41	—	26	1	no	—
351	C₂×#41	—	26	1	no	—
352	C₂×#41	—	26	1	no	—
353	C₂×#41	—	26	1	no	—
354	C₂²×Q₈	—	13	1	no	—
355	C₂²×D₄	—	13	2	no	—
356	C₂²×D₄	—	13	1	no	—
357	C₂³×C₄	—	13	2	no	—
358	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
359	#131	—	26	8	no	—
360	#131	—	26	8	no	—
361	#131	—	26	8	no	—
362	#131	—	26	8	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	13	2	no	—
369	C₂×M₁₆	—	13	2	no	—
370	C₂×M₁₆	—	13	2	no	—
371	C₂×M₁₆	—	26	4	no	—
372	C₂×M₁₆	—	26	4	no	—
373	C₂×M₁₆	—	26	1	no	—
374	C₂×M₁₆	—	26	1	no	—
375	C₂×M₁₆	—	26	1	no	—
376	C₂×M₁₆	—	26	1	no	—
377	C₂×M₁₆	—	26	1	no	—
378	C₂×M₁₆	—	26	4	no	—
379	C₂×M₁₆	—	26	1	no	—
380	C₂×M₁₆	—	26	1	no	—
381	C₂×M₁₆	—	26	1	no	—
382	C₂×M₁₆	—	26	1	no	—
383	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	13	2	no	—
390	C₂²×C₈	—	26	4	no	—
391	C₂²×C₈	—	26	4	no	—
392	C₂²×C₈	—	26	4	no	—
393	C₂²×C₈	—	26	1	no	—
394	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
396	C₂²×C₈	D₅₂	1	2	yes	—
397	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	26	1	no	—
403	#117	—	26	1	no	—
404	#117	—	26	1	no	—
405	#117	—	26	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	26	1	no	—
408	C₂×C₂²⋊C₄	—	13	2	no	—
409	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	26	1	no	—
412	#101	—	26	4	no	—
413	#100	—	26	4	no	—
414	#99	—	26	8	no	—
415	C₂×C₁₃	—	2	1	no	—
416	C₂×C₁₃	—	2	1	no	—
417	C₂×C₁₃	—	2	1	no	—
418	C₂×C₁₃	—	2	1	no	—
419	C₂×C₁₃	—	2	1	no	—
420	C₂×C₁₃	—	2	1	no	—
421	C₂×C₁₃	C₂²⋊#95	1	1	yes	characteristic
422	C₂×C₁₃	#1757	1	2	yes	—
423	D₁₃	—	4	4	no	—
424	C₂⁴	—	13	2	no	—
425	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
426	#41	—	26	2	no	—
427	#41	—	26	2	no	—
428	#41	—	26	2	no	—
429	#41	—	26	2	no	—
430	#41	—	26	2	no	—
431	#41	—	26	2	no	—
432	#41	—	26	2	no	—
433	#41	—	26	2	no	—
434	#41	—	26	2	no	—
435	#41	—	26	2	no	—
436	#41	—	26	2	no	—
437	#41	—	26	2	no	—
438	#41	—	26	2	no	—
439	#41	—	26	2	no	—
440	#41	—	26	2	no	—
441	#41	—	26	2	no	—
442	C₂×Q₈	—	13	2	no	—
443	C₂×Q₈	—	13	2	no	—
444	C₂×Q₈	—	26	1	no	—
445	C₂×Q₈	—	26	1	no	—
446	C₂×Q₈	—	26	1	no	—
447	C₂×Q₈	—	26	1	no	—
448	C₂×D₄	—	13	4	no	—
449	C₂×D₄	—	13	4	no	—
450	C₂×D₄	—	13	2	no	—
451	C₂×D₄	—	13	2	no	—
452	C₂×D₄	—	26	2	no	—
453	C₂×D₄	—	26	2	no	—
454	C₂×D₄	—	26	2	no	—
455	C₂×D₄	—	26	2	no	—
456	C₂×D₄	—	26	1	no	—
457	C₂×D₄	—	26	1	no	—
458	C₂×D₄	—	26	1	no	—
459	C₂×D₄	—	26	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	13	2	no	—
462	C₂²×C₄	—	13	4	no	—
463	C₂²×C₄	—	13	4	no	—
464	C₂²×C₄	—	26	2	no	—
465	C₂²×C₄	—	26	2	no	—
466	C₂²×C₄	—	26	2	no	—
467	C₂²×C₄	—	26	2	no	—
468	C₂²×C₄	—	26	2	no	—
469	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
472	C₂²×C₄	#6127	1	1	yes	characteristic
473	C₂²×C₄	#6127	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
479	C₂²×C₄	#6129	1	1	yes	characteristic
480	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
481	C₂²×C₄	#6131	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	4	1	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	—	26	16	no	—
488	M₁₆	—	26	2	no	—
489	M₁₆	—	26	2	no	—
490	M₁₆	—	26	2	no	—
491	M₁₆	—	26	2	no	—
492	M₁₆	—	26	2	no	—
493	M₁₆	—	26	2	no	—
494	M₁₆	—	52	1	no	—
495	M₁₆	—	52	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	13	4	no	—
508	C₂×C₈	—	26	16	no	—
509	C₂×C₈	—	26	2	no	—
510	C₂×C₈	—	26	2	no	—
511	C₂×C₈	—	26	2	no	—
512	C₂×C₈	—	52	1	no	—
513	C₂×C₈	—	52	1	no	—
514	C₂×C₈	#6103	1	2	yes	—
515	C₂×C₈	#6103	1	2	yes	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₄⋊C₄	—	52	1	no	—
519	C₄⋊C₄	—	52	1	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	26	2	no	—
523	C₂²⋊C₄	—	26	2	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	1	no	—
526	C₄²	—	52	1	no	—
527	C₄²	—	52	1	no	—
528	C₁₃	#10764	1	1	yes	characteristic, complemented, Sylow
529	C₂³	—	4	2	no	—
530	C₂³	—	13	4	no	—
531	C₂³	—	26	2	no	—
532	C₂³	—	26	2	no	—
533	C₂³	—	52	4	no	—
534	C₂³	C₄²×D₁₃	1	1	yes	characteristic
535	C₂³	C₄×D₅₂	1	1	yes	characteristic
536	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
537	C₂³	#88135	1	1	yes	characteristic
538	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
539	C₂³	#88147	1	1	yes	characteristic
540	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
541	Q₈	—	26	2	no	—
542	Q₈	—	26	2	no	—
543	Q₈	—	26	2	no	—
544	Q₈	—	26	2	no	—
545	D₄	—	26	4	no	—
546	D₄	—	26	4	no	—
547	D₄	—	26	4	no	—
548	D₄	—	26	4	no	—
549	D₄	—	26	2	no	—
550	D₄	—	26	2	no	—
551	D₄	—	26	2	no	—
552	D₄	—	26	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	13	4	no	—
556	C₂×C₄	—	26	2	no	—
557	C₂×C₄	—	26	2	no	—
558	C₂×C₄	—	26	4	no	—
559	C₂×C₄	—	26	4	no	—
560	C₂×C₄	—	26	4	no	—
561	C₂×C₄	—	26	4	no	—
562	C₂×C₄	—	52	4	no	—
563	C₂×C₄	—	52	2	no	—
564	C₂×C₄	#88126	1	1	yes	characteristic
565	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
569	C₂×C₄	#88135	1	1	yes	characteristic
570	C₂×C₄	#88136	1	1	yes	characteristic
571	C₂×C₄	#88136	1	1	yes	characteristic
572	C₂×C₄	#88137	1	1	yes	characteristic
573	C₂×C₄	#88137	1	1	yes	characteristic
574	C₂×C₄	#88138	1	1	yes	characteristic
575	C₂×C₄	#88138	1	1	yes	characteristic
576	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
577	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
578	C₂×C₄	#88146	1	1	yes	characteristic
579	C₂×C₄	#88147	1	1	yes	characteristic
580	C₂×C₄	#88148	1	1	yes	characteristic
581	C₂×C₄	#88148	1	1	yes	characteristic
582	C₂×C₄	#88149	1	1	yes	characteristic
583	C₂×C₄	#88150	1	1	yes	characteristic
584	C₂×C₄	#88150	1	1	yes	characteristic
585	C₂×C₄	#88151	1	1	yes	characteristic
586	C₂×C₄	C₂×#6103	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
588	C₂×C₄	#88191	1	1	yes	characteristic
589	C₂×C₄	#88191	1	1	yes	characteristic
590	C₂×C₄	#88192	1	1	yes	characteristic
591	C₂×C₄	#88200	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	2	2	no	—
594	C₈	—	4	2	no	—
595	C₈	—	26	4	no	—
596	C₈	—	52	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	26	4	no	—
605	C₂²	—	52	4	no	—
606	C₂²	—	52	4	no	—
607	C₂²	—	52	4	no	—
608	C₂²	D₁₃×#95	1	1	yes	characteristic
609	C₂²	#11718326	1	1	yes	characteristic
610	C₂²	#11718327	1	1	yes	characteristic
611	C₂²	#11718329	1	1	yes	characteristic
612	C₂²	C₄×#6103	1	1	yes	characteristic
613	C₂²	#11718617	1	1	yes	characteristic
614	C₂²	#11718650	1	1	yes	characteristic
615	C₄	—	8	2	no	—
616	C₄	—	26	4	no	—
617	C₄	—	104	2	no	—
618	C₄	#11718325	1	1	yes	characteristic
619	C₄	#11718326	1	1	yes	characteristic
620	C₄	#11718328	1	1	yes	characteristic
621	C₄	#11718329	1	1	yes	characteristic
622	C₄	#11718616	1	1	yes	characteristic
623	C₄	#11718617	1	1	yes	characteristic
624	C₄	#11718648	1	1	yes	characteristic
625	C₄	#11718650	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	52	4	no	—
633	C₂	#13113057	1	1	yes	characteristic
634	C₂	#13114637	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂³×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₁₃×#1729	C₂
socle	C₂²×C₁₃	C₄×C₂²⋊C₄
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	#1729	D₁₃
hypocenter	C₁₃	#10764
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. C₂×#11718151	C₂	semidirect
5. C₂×#11718125	C₂	semidirect
6. #13114532	C₂	semidirect
7. C₁₃×#1729	C₂	semidirect
21. C₂²×#6094	C₄	semidirect
22. C₂²×C₈×D₁₃	C₄	semidirect
23. C₂×#88064	C₄	semidirect
26. C₂×#88063	C₄	semidirect
218. #1729	D₁₃	semidirect
528. C₁₃	#10764	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88155	2
C₂×#11718793	2
C₂×#11718667	2
C₂×#11718151	2
C₂×#11718125	2
#13114532	2
C₁₃×#1729	2
#10764	13