Subgroups — #15769300

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88045	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718793	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114562	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₁₃×M₁₆	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	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	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	C₄×C₁₃×M₁₆	—	2	2	no	—
16	C₄×C₁₃×M₁₆	—	2	2	no	—
17	C₂×C₁₃×#97	—	2	1	no	—
18	C₂×C₄×C₈×C₁₃	—	2	1	no	—
19	#11718800	—	2	2	no	—
20	#11718800	C₄	1	4	yes	complemented
21	C₂×#88065	—	2	2	no	—
22	C₂×#88064	C₄	1	2	yes	complemented
23	#11718793	—	2	2	no	—
24	#11718793	—	2	2	no	—
25	C₂×#88063	C₄	1	2	yes	complemented
26	C₂×#88045	—	2	2	no	—
27	C₂×#88045	—	2	1	no	—
28	C₂×#88045	—	2	1	no	—
29	C₂×#88045	C₄	1	4	yes	complemented
30	#11718151	—	2	2	no	—
31	#11718150	—	2	2	no	—
32	#11718115	—	2	2	no	—
33	C₂³×C₄×C₁₃	—	2	1	no	—
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₂²⋊D₁₃	—	2	1	no	—
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	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	C₂×C₄	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	2	yes	—
48	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	—	2	1	no	—
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	—	2	1	no	—
57	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
60	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
61	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
62	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₃	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
73	#88180	—	2	1	no	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊Dic₁₃	—	2	1	no	—
78	C₂×C₄×Dic₁₃	—	2	1	no	—
79	C₂×#6099	—	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	C₂×C₄	1	2	yes	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	—	2	1	no	—
93	C₁₃×#97	—	2	4	no	—
94	C₄×C₈×C₁₃	—	2	4	no	—
95	#88065	—	2	8	no	—
96	#88064	—	2	4	no	—
97	#88063	—	2	4	no	—
98	#88045	—	2	4	no	—
99	#88045	—	2	4	no	—
100	#10946	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₂³×D₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₂×C₂²⋊D₁₃	—	2	2	no	—
123	C₂×C₂²⋊D₁₃	—	2	2	no	—
124	C₂×C₂²⋊D₁₃	—	4	1	no	—
125	C₂×C₂²⋊D₁₃	—	4	1	no	—
126	C₂×C₂²⋊D₁₃	—	4	1	no	—
127	C₂×C₂²⋊D₁₃	—	4	1	no	—
128	C₂²×Dic₁₃	—	2	1	no	—
129	C₂²×Dic₁₃	—	4	1	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
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	—	4	1	no	—
139	#6127	—	4	1	no	—
140	#6127	—	4	1	no	—
141	#6127	—	4	1	no	—
142	#6127	—	4	1	no	—
143	#6127	—	4	1	no	—
144	#6127	—	4	1	no	—
145	#6127	—	4	1	no	—
146	C₂×D₅₂	—	2	1	no	—
147	C₂×D₅₂	—	2	1	no	—
148	C₂×D₅₂	—	2	1	no	—
149	C₂×D₅₂	—	2	1	no	—
150	C₂×D₅₂	—	2	1	no	—
151	C₂×D₅₂	C₄²	1	2	yes	—
152	C₂×C₄×D₁₃	—	2	2	no	—
153	C₂×C₄×D₁₃	—	2	2	no	—
154	C₂×C₄×D₁₃	—	4	1	no	—
155	C₂×C₄×D₁₃	—	4	1	no	—
156	C₂×C₄×D₁₃	—	4	1	no	—
157	C₂×C₄×D₁₃	—	4	1	no	—
158	C₂×Dic₂₆	—	2	1	no	—
159	C₂×Dic₂₆	—	2	1	no	—
160	C₂×Dic₂₆	—	2	1	no	—
161	C₂×Dic₂₆	—	2	1	no	—
162	C₂×Dic₂₆	—	2	1	no	—
163	C₂×Dic₂₆	C₄²	1	2	yes	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	C₂²⋊C₄	1	4	yes	—
171	C₁₃×M₁₆	C₂²⋊C₄	1	4	yes	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
183	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
184	C₂²⋊Dic₁₃	—	2	2	no	—
185	C₂²⋊Dic₁₃	—	4	1	no	—
186	C₄⋊Dic₁₃	—	2	2	no	—
187	C₄⋊Dic₁₃	—	4	1	no	—
188	C₄×Dic₁₃	—	2	2	no	—
189	C₄×Dic₁₃	—	4	1	no	—
190	#6099	—	2	2	no	—
191	#6099	—	2	2	no	—
192	#6099	—	2	2	no	—
193	#6099	—	2	2	no	—
194	#6099	—	4	1	no	—
195	#6099	—	4	1	no	—
196	#6099	—	4	1	no	—
197	#6099	—	4	1	no	—
198	C₂×#1055	—	2	2	no	—
199	C₂×#1055	—	2	2	no	—
200	C₂×#1055	—	4	1	no	—
201	C₂×#1055	—	4	1	no	—
202	C₂×#1055	—	4	1	no	—
203	C₂×#1055	—	4	1	no	—
204	C₂×#421	—	13	1	no	—
205	C₂²×#104	—	13	1	no	—
206	C₂×#413	—	13	1	no	—
207	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic, complemented
208	C₂×#344	—	13	1	no	—
209	#1738	—	13	1	no	—
210	C₂×#339	—	13	1	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	#117	1	1	yes	characteristic
213	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	#121	1	1	yes	characteristic
216	C₂³×C₁₃	#123	1	1	yes	characteristic
217	C₂³×C₁₃	#124	1	1	yes	characteristic
218	C₂³×C₁₃	#126	1	1	yes	characteristic
219	C₂²×D₁₃	—	2	2	no	—
220	C₂²×D₁₃	—	4	1	no	—
221	C₂²×D₁₃	—	4	1	no	—
222	C₂²×D₁₃	—	8	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	4	4	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₄×D₄	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	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#121	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	#123	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
255	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
256	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	—	4	2	no	—
261	C₂×Dic₁₃	—	2	2	no	—
262	C₂×Dic₁₃	—	4	1	no	—
263	C₂×Dic₁₃	—	4	1	no	—
264	C₂×Dic₁₃	—	4	2	no	—
265	C₂×Dic₁₃	—	8	2	no	—
266	D₅₂	—	2	2	no	—
267	D₅₂	—	2	2	no	—
268	D₅₂	—	4	1	no	—
269	D₅₂	—	4	1	no	—
270	C₄×D₁₃	—	4	2	no	—
271	C₄×D₁₃	—	4	2	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	—	4	2	no	—
274	Dic₂₆	—	2	2	no	—
275	Dic₂₆	—	2	2	no	—
276	Dic₂₆	—	4	1	no	—
277	Dic₂₆	—	4	1	no	—
278	C₈×C₁₃	—	2	4	no	—
279	C₈×C₁₃	—	2	4	no	—
280	#1055	—	4	2	no	—
281	#1055	—	4	2	no	—
282	C₂²×#41	—	13	1	no	—
283	C₂²×M₁₆	—	13	1	no	—
284	C₂²×M₁₆	—	13	1	no	—
285	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
286	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
287	C₂×#117	—	13	1	no	—
288	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
289	#421	—	13	4	no	—
290	#421	—	26	2	no	—
291	C₂×#104	—	13	4	no	—
292	C₂×#104	—	26	2	no	—
293	C₂×#104	—	26	2	no	—
294	C₂×#104	—	26	1	no	—
295	C₂×#104	—	26	1	no	—
296	#413	—	26	2	no	—
297	#413	—	26	2	no	—
298	C₂×#101	—	13	2	no	—
299	C₂×#100	—	13	2	no	—
300	C₄×M₁₆	—	2	2	no	—
301	C₄×M₁₆	—	2	2	no	—
302	C₂×#97	—	2	1	no	—
303	C₂×C₄×C₈	—	2	1	no	—
304	#344	—	26	2	no	—
305	#341	—	26	2	no	—
306	#339	—	26	2	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	4	1	no	—
311	C₂²×C₁₃	—	4	1	no	—
312	C₂²×C₁₃	—	4	1	no	—
313	C₂²×C₁₃	—	4	1	no	—
314	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₁₃	#386	1	1	yes	characteristic
316	C₂²×C₁₃	#388	1	1	yes	characteristic
317	C₂²×C₁₃	#388	1	1	yes	characteristic
318	C₂²×C₁₃	#388	1	1	yes	characteristic
319	C₂²×C₁₃	#388	1	1	yes	characteristic
320	C₂²×C₁₃	#390	1	1	yes	characteristic
321	C₂×D₁₃	—	4	2	no	—
322	C₂×D₁₃	—	8	2	no	—
323	C₂×D₁₃	—	8	2	no	—
324	C₂×D₁₃	—	8	2	no	—
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	—	4	2	no	—
327	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
328	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
329	C₄×C₁₃	#386	1	1	yes	characteristic
330	C₄×C₁₃	#386	1	1	yes	characteristic
331	C₄×C₁₃	#388	1	1	yes	characteristic
332	C₄×C₁₃	#388	1	1	yes	characteristic
333	C₄×C₁₃	#390	1	1	yes	characteristic
334	C₄×C₁₃	#390	1	1	yes	characteristic
335	Dic₁₃	—	4	2	no	—
336	Dic₁₃	—	8	2	no	—
337	C₂×#41	—	13	2	no	—
338	C₂×#41	—	13	2	no	—
339	C₂×#41	—	26	1	no	—
340	C₂×#41	—	26	1	no	—
341	C₂×#41	—	26	1	no	—
342	C₂×#41	—	26	1	no	—
343	C₂×#41	—	26	1	no	—
344	C₂×#41	—	26	1	no	—
345	C₂×#41	—	26	1	no	—
346	C₂×#41	—	26	1	no	—
347	C₂×#41	—	26	1	no	—
348	C₂×#41	—	26	1	no	—
349	C₂²×Q₈	—	13	1	no	—
350	C₂²×D₄	—	13	1	no	—
351	C₂²×D₄	—	26	1	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	26	1	no	—
354	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	13	2	no	—
362	C₂×M₁₆	—	13	2	no	—
363	C₂×M₁₆	—	26	1	no	—
364	C₂×M₁₆	—	26	1	no	—
365	C₂×M₁₆	—	26	1	no	—
366	C₂×M₁₆	—	26	1	no	—
367	C₂×M₁₆	—	26	1	no	—
368	C₂×M₁₆	—	26	1	no	—
369	C₂×M₁₆	—	26	1	no	—
370	C₂×M₁₆	—	26	1	no	—
371	C₂×M₁₆	—	26	1	no	—
372	C₂×M₁₆	—	26	1	no	—
373	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
374	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
375	C₂×M₁₆	D₅₂	1	2	yes	—
376	C₂×M₁₆	D₅₂	1	2	yes	—
377	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
378	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	26	1	no	—
382	C₂²×C₈	—	26	1	no	—
383	#117	—	13	2	no	—
384	#117	—	26	1	no	—
385	#117	—	26	1	no	—
386	#117	—	26	1	no	—
387	C₂×C₄⋊C₄	—	26	1	no	—
388	C₂×C₂²⋊C₄	—	26	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	26	1	no	—
393	C₂×C₄²	C₄×D₁₃	1	2	yes	—
394	C₂×C₄²	D₅₂	1	2	yes	—
395	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
396	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
397	#104	—	26	8	no	—
398	#104	—	26	4	no	—
399	#104	—	26	4	no	—
400	#101	—	26	4	no	—
401	#100	—	26	4	no	—
402	#97	—	2	4	no	—
403	C₄×C₈	—	2	4	no	—
404	C₂×C₁₃	—	2	1	no	—
405	C₂×C₁₃	—	2	1	no	—
406	C₂×C₁₃	—	2	1	no	—
407	C₂×C₁₃	—	2	1	no	—
408	C₂×C₁₃	—	2	1	no	—
409	C₂×C₁₃	—	2	1	no	—
410	C₂×C₁₃	#1437	1	1	yes	characteristic
411	C₂×C₁₃	#1932	1	2	yes	—
412	D₁₃	—	8	2	no	—
413	C₂⁴	—	26	1	no	—
414	C₂⁴	#6127	1	1	yes	characteristic
415	#41	—	26	2	no	—
416	#41	—	26	2	no	—
417	#41	—	26	2	no	—
418	#41	—	26	2	no	—
419	#41	—	26	2	no	—
420	#41	—	26	2	no	—
421	#41	—	26	2	no	—
422	#41	—	26	2	no	—
423	#41	—	52	1	no	—
424	#41	—	52	1	no	—
425	#41	—	52	1	no	—
426	#41	—	52	1	no	—
427	#41	—	52	1	no	—
428	#41	—	52	1	no	—
429	#41	—	52	1	no	—
430	#41	—	52	1	no	—
431	C₂×Q₈	—	13	2	no	—
432	C₂×Q₈	—	26	1	no	—
433	C₂×Q₈	—	26	1	no	—
434	C₂×Q₈	—	26	1	no	—
435	C₂×Q₈	—	26	1	no	—
436	C₂×Q₈	—	26	1	no	—
437	C₂×D₄	—	13	2	no	—
438	C₂×D₄	—	26	2	no	—
439	C₂×D₄	—	26	2	no	—
440	C₂×D₄	—	26	1	no	—
441	C₂×D₄	—	26	1	no	—
442	C₂×D₄	—	26	1	no	—
443	C₂×D₄	—	26	1	no	—
444	C₂×D₄	—	26	1	no	—
445	C₂×D₄	—	52	1	no	—
446	C₂×D₄	—	52	1	no	—
447	C₂×D₄	—	52	1	no	—
448	C₂×D₄	—	52	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	26	1	no	—
455	C₂²×C₄	—	26	2	no	—
456	C₂²×C₄	—	26	2	no	—
457	C₂²×C₄	—	52	1	no	—
458	C₂²×C₄	—	52	1	no	—
459	C₂²×C₄	—	52	1	no	—
460	C₂²×C₄	—	52	1	no	—
461	C₂²×C₄	—	52	1	no	—
462	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
468	C₂²×C₄	#6127	1	1	yes	characteristic
469	C₂²×C₄	#6127	1	1	yes	characteristic
470	C₂²×C₄	#6127	1	1	yes	characteristic
471	C₂²×C₄	#6127	1	1	yes	characteristic
472	C₂²×C₄	#6127	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	26	2	no	—
483	M₁₆	—	26	2	no	—
484	M₁₆	—	26	2	no	—
485	M₁₆	—	26	2	no	—
486	M₁₆	—	52	1	no	—
487	M₁₆	—	52	1	no	—
488	M₁₆	—	52	1	no	—
489	M₁₆	—	52	1	no	—
490	M₁₆	#6103	1	4	yes	—
491	M₁₆	#6103	1	4	yes	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	26	2	no	—
499	C₂×C₈	—	26	2	no	—
500	C₂×C₈	—	52	1	no	—
501	C₂×C₈	—	52	1	no	—
502	C₂×C₈	—	52	1	no	—
503	C₂×C₈	—	52	1	no	—
504	C₄⋊C₄	—	26	2	no	—
505	C₄⋊C₄	—	52	1	no	—
506	C₂²⋊C₄	—	26	2	no	—
507	C₂²⋊C₄	—	52	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	26	2	no	—
513	C₄²	—	52	1	no	—
514	C₄²	#6103	1	2	yes	—
515	C₄²	#6103	1	2	yes	—
516	C₁₃	#10946	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	4	2	no	—
518	C₂³	—	26	2	no	—
519	C₂³	—	52	1	no	—
520	C₂³	—	52	1	no	—
521	C₂³	—	104	2	no	—
522	C₂³	#88126	1	1	yes	characteristic
523	C₂³	C₄×D₅₂	1	1	yes	characteristic
524	C₂³	#88129	1	1	yes	characteristic
525	C₂³	#88130	1	1	yes	characteristic
526	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
527	C₂³	#88183	1	1	yes	characteristic
528	C₂³	#88184	1	1	yes	characteristic
529	Q₈	—	26	2	no	—
530	Q₈	—	26	2	no	—
531	Q₈	—	52	1	no	—
532	Q₈	—	52	1	no	—
533	D₄	—	26	2	no	—
534	D₄	—	26	2	no	—
535	D₄	—	52	2	no	—
536	D₄	—	52	2	no	—
537	D₄	—	52	2	no	—
538	D₄	—	52	2	no	—
539	D₄	—	52	1	no	—
540	D₄	—	52	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	26	2	no	—
548	C₂×C₄	—	52	1	no	—
549	C₂×C₄	—	52	1	no	—
550	C₂×C₄	—	52	2	no	—
551	C₂×C₄	—	52	2	no	—
552	C₂×C₄	—	52	2	no	—
553	C₂×C₄	—	52	2	no	—
554	C₂×C₄	—	52	2	no	—
555	C₂×C₄	—	104	2	no	—
556	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
557	C₂×C₄	#88126	1	1	yes	characteristic
558	C₂×C₄	#88126	1	1	yes	characteristic
559	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
560	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
561	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
562	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
563	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
564	C₂×C₄	#88128	1	1	yes	characteristic
565	C₂×C₄	#88129	1	1	yes	characteristic
566	C₂×C₄	#88129	1	1	yes	characteristic
567	C₂×C₄	#88130	1	1	yes	characteristic
568	C₂×C₄	C₂×#6103	1	1	yes	characteristic
569	C₂×C₄	C₂×#6103	1	1	yes	characteristic
570	C₂×C₄	C₂×#6103	1	1	yes	characteristic
571	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
574	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
575	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
576	C₂×C₄	#88183	1	1	yes	characteristic
577	C₂×C₄	#88183	1	1	yes	characteristic
578	C₂×C₄	#88184	1	1	yes	characteristic
579	C₂×C₄	#88184	1	1	yes	characteristic
580	C₂×C₄	#88184	1	1	yes	characteristic
581	C₂×C₄	#88184	1	1	yes	characteristic
582	C₂×C₄	#88184	1	1	yes	characteristic
583	C₂×C₄	#88207	1	1	yes	characteristic
584	C₈	—	2	4	no	—
585	C₈	—	2	4	no	—
586	C₈	—	52	2	no	—
587	C₈	—	52	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	52	2	no	—
596	C₂²	—	104	2	no	—
597	C₂²	—	104	2	no	—
598	C₂²	—	104	2	no	—
599	C₂²	C₄×#6103	1	1	yes	characteristic
600	C₂²	#11718600	1	1	yes	characteristic
601	C₂²	#11718601	1	1	yes	characteristic
602	C₂²	#11718601	1	1	yes	characteristic
603	C₂²	#11718601	1	1	yes	characteristic
604	C₂²	#11718601	1	1	yes	characteristic
605	C₂²	#11718874	1	1	yes	characteristic
606	C₄	—	2	4	no	—
607	C₄	—	4	2	no	—
608	C₄	—	52	2	no	—
609	C₄	—	104	2	no	—
610	C₄	C₄×#6103	1	1	yes	characteristic
611	C₄	C₄×#6103	1	1	yes	characteristic
612	C₄	#11718600	1	1	yes	characteristic
613	C₄	#11718600	1	1	yes	characteristic
614	C₄	#11718601	1	1	yes	characteristic
615	C₄	#11718601	1	1	yes	characteristic
616	C₄	#11718874	1	1	yes	characteristic
617	C₄	#11718874	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	104	2	no	—
625	C₂	#13113074	1	1	yes	characteristic
626	C₂	#13115505	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#88184
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	#388
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	#10946
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₂×#11718151	C₂	semidirect
5. #13114562	C₂	semidirect
6. C₂×#11718115	C₂	semidirect
7. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
20. #11718800	C₄	semidirect
22. C₂×#88064	C₄	semidirect
25. C₂×#88063	C₄	semidirect
29. C₂×#88045	C₄	semidirect
207. C₂×C₄×M₁₆	D₁₃	semidirect
516. C₁₃	#10946	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718800	2
C₂²×#88045	2
C₂×#11718793	2
C₂×#11718151	2
#13114562	2
C₂×#11718115	2
C₂×C₄×C₁₃×M₁₆	2
#10946	13