Subgroups — #15769391

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718793	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718667	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718771	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	C₂×C₁₃×#405	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	C₁₃×#405	—	2	2	no	—
16	C₁₃×#405	—	2	2	no	—
17	C₂×C₁₃×#97	—	2	1	no	—
18	C₂×C₄×C₈×C₁₃	—	2	1	no	—
19	C₂×#88064	C₄	1	2	yes	complemented
20	#11718793	—	2	2	no	—
21	#11718793	—	2	2	no	—
22	C₂×#88063	C₄	1	2	yes	complemented
23	#11718771	—	2	2	no	—
24	#11718771	—	2	1	no	—
25	#11718771	—	2	1	no	—
26	C₂×#88060	C₄	1	4	yes	complemented
27	#11718667	—	2	2	no	—
28	#11718667	—	2	2	no	—
29	C₂×#88046	C₄	1	4	yes	—
30	#11718151	—	2	2	no	—
31	#11718142	—	2	2	no	—
32	#11718125	—	2	2	no	—
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
35	C₂×#6127	—	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	—	2	1	no	—
47	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
49	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
55	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
56	C₂²×C₈×C₁₃	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₁₃	D₄	1	2	yes	—
63	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	D₄	1	2	yes	—
68	C₁₃×#117	D₄	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
73	#88180	—	2	1	no	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	—	2	1	no	—
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	—	2	1	no	—
90	C₂×#6099	C₂×C₄	1	2	yes	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	C₂×C₄	1	2	yes	—
93	C₁₃×#97	—	2	4	no	—
94	C₄×C₈×C₁₃	—	2	4	no	—
95	#88064	—	2	4	no	—
96	#88063	—	2	4	no	—
97	#88060	—	2	4	no	—
98	#88060	—	2	4	no	—
99	#88046	—	2	8	no	—
100	#10961	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂³×D₁₃	C₄²	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₃	—	2	2	no	—
119	C₂×C₂²⋊D₁₃	—	2	2	no	—
120	C₂×C₂²⋊D₁₃	—	2	2	no	—
121	C₂×C₂²⋊D₁₃	—	2	2	no	—
122	C₂×C₂²⋊D₁₃	—	2	2	no	—
123	C₂×C₂²⋊D₁₃	—	2	2	no	—
124	C₂²×Dic₁₃	—	2	2	no	—
125	C₂²×Dic₁₃	C₄²	1	2	yes	—
126	#6127	—	4	1	no	—
127	#6127	—	4	1	no	—
128	#6127	—	4	1	no	—
129	#6127	—	4	1	no	—
130	#6127	—	4	1	no	—
131	#6127	—	4	1	no	—
132	#6127	—	4	1	no	—
133	#6127	—	4	1	no	—
134	#6127	—	4	1	no	—
135	#6127	—	4	1	no	—
136	#6127	—	4	1	no	—
137	#6127	—	4	1	no	—
138	#6127	—	4	1	no	—
139	#6127	—	4	1	no	—
140	#6127	—	4	1	no	—
141	#6127	—	4	1	no	—
142	C₂×D₅₂	—	2	1	no	—
143	C₂×D₅₂	—	2	1	no	—
144	C₂×D₅₂	—	2	1	no	—
145	C₂×D₅₂	—	2	1	no	—
146	C₂×D₅₂	—	2	1	no	—
147	C₂×D₅₂	—	2	1	no	—
148	C₂×C₄×D₁₃	—	2	2	no	—
149	C₂×C₄×D₁₃	—	2	2	no	—
150	C₂×C₄×D₁₃	—	2	2	no	—
151	C₂×C₄×D₁₃	—	2	2	no	—
152	C₂×C₄×D₁₃	—	2	2	no	—
153	C₂×C₄×D₁₃	—	2	2	no	—
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	—	2	1	no	—
156	C₂×Dic₂₆	—	2	1	no	—
157	C₂×Dic₂₆	—	2	1	no	—
158	C₂×Dic₂₆	—	2	1	no	—
159	C₂×Dic₂₆	—	2	1	no	—
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	C₂²⋊C₄	1	4	yes	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
176	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₂²⋊Dic₁₃	—	2	2	no	—
184	C₂²⋊Dic₁₃	—	2	2	no	—
185	C₄⋊Dic₁₃	—	4	1	no	—
186	C₄⋊Dic₁₃	—	4	1	no	—
187	C₄×Dic₁₃	—	4	1	no	—
188	C₄×Dic₁₃	—	4	1	no	—
189	#6099	—	2	2	no	—
190	#6099	—	2	2	no	—
191	#6099	—	4	1	no	—
192	#6099	—	4	1	no	—
193	#6099	—	4	1	no	—
194	#6099	—	4	1	no	—
195	#6099	—	4	1	no	—
196	#6099	—	4	1	no	—
197	C₂×#1055	—	2	2	no	—
198	C₂×#1055	—	2	2	no	—
199	C₂×#1055	—	2	2	no	—
200	C₂×#1055	—	2	2	no	—
201	C₂×#1055	—	4	1	no	—
202	C₂×#1055	—	4	1	no	—
203	C₂×#413	—	13	1	no	—
204	C₂×#410	—	13	1	no	—
205	C₂×#408	—	13	1	no	—
206	C₂×#405	D₁₃	1	1	yes	characteristic, complemented
207	C₂×#344	—	13	1	no	—
208	C₂×#344	—	13	1	no	—
209	#1729	—	13	1	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
212	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₁₃	#117	1	1	yes	characteristic
214	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
217	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂²×D₁₃	—	2	2	no	—
219	C₂²×D₁₃	—	2	2	no	—
220	C₂²×D₁₃	—	2	2	no	—
221	C₂²×D₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	2	2	no	—
257	C₂×Dic₁₃	—	2	2	no	—
258	C₂×Dic₁₃	—	2	2	no	—
259	C₂×Dic₁₃	—	4	4	no	—
260	C₂×Dic₁₃	—	4	2	no	—
261	D₅₂	—	4	1	no	—
262	D₅₂	—	4	1	no	—
263	D₅₂	—	4	1	no	—
264	D₅₂	—	4	1	no	—
265	C₄×D₁₃	—	4	2	no	—
266	C₄×D₁₃	—	4	2	no	—
267	C₄×D₁₃	—	4	2	no	—
268	C₄×D₁₃	—	4	2	no	—
269	Dic₂₆	—	4	1	no	—
270	Dic₂₆	—	4	1	no	—
271	Dic₂₆	—	4	1	no	—
272	Dic₂₆	—	4	1	no	—
273	C₈×C₁₃	—	2	2	no	—
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	2	4	no	—
276	#1055	—	4	2	no	—
277	#1055	—	4	2	no	—
278	C₂²×#41	—	13	1	no	—
279	C₂²×M₁₆	—	13	1	no	—
280	C₂²×M₁₆	—	13	1	no	—
281	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
282	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
283	C₂×#117	—	13	1	no	—
284	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
285	#413	—	26	2	no	—
286	#413	—	26	2	no	—
287	C₂×#101	—	13	2	no	—
288	C₂×#100	—	13	2	no	—
289	#410	—	26	2	no	—
290	#410	—	26	2	no	—
291	C₂×#99	—	13	4	no	—
292	#408	—	26	2	no	—
293	#408	—	26	1	no	—
294	#408	—	26	1	no	—
295	C₂×C₂²⋊C₈	—	13	4	no	—
296	#405	—	2	2	no	—
297	#405	—	2	2	no	—
298	C₂×#97	—	2	1	no	—
299	C₂×C₄×C₈	—	2	1	no	—
300	#344	—	26	2	no	—
301	#344	—	26	2	no	—
302	#336	—	26	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
313	C₂²×C₁₃	#386	1	1	yes	characteristic
314	C₂²×C₁₃	#388	1	1	yes	characteristic
315	C₂²×C₁₃	#388	1	1	yes	characteristic
316	C₂²×C₁₃	#390	1	1	yes	characteristic
317	C₂×D₁₃	—	4	2	no	—
318	C₂×D₁₃	—	4	4	no	—
319	C₂×D₁₃	—	8	2	no	—
320	C₂×D₁₃	—	8	2	no	—
321	C₄×C₁₃	—	4	4	no	—
322	C₄×C₁₃	#386	1	1	yes	characteristic
323	C₄×C₁₃	#386	1	1	yes	characteristic
324	C₄×C₁₃	#388	1	1	yes	characteristic
325	C₄×C₁₃	#388	1	1	yes	characteristic
326	C₄×C₁₃	#388	1	1	yes	characteristic
327	C₄×C₁₃	#388	1	1	yes	characteristic
328	C₄×C₁₃	#390	1	1	yes	characteristic
329	C₄×C₁₃	#390	1	1	yes	characteristic
330	Dic₁₃	—	4	2	no	—
331	Dic₁₃	—	8	2	no	—
332	C₂×#41	—	26	1	no	—
333	C₂×#41	—	26	1	no	—
334	C₂×#41	—	26	1	no	—
335	C₂×#41	—	26	1	no	—
336	C₂×#41	—	26	1	no	—
337	C₂×#41	—	26	1	no	—
338	C₂×#41	—	26	1	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	C₂²×Q₈	—	13	1	no	—
345	C₂²×D₄	—	13	2	no	—
346	C₂²×D₄	—	13	1	no	—
347	C₂³×C₄	—	13	2	no	—
348	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	13	2	no	—
353	C₂×M₁₆	—	26	1	no	—
354	C₂×M₁₆	—	26	1	no	—
355	C₂×M₁₆	—	26	1	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	—	26	1	no	—
358	C₂×M₁₆	—	26	1	no	—
359	C₂×M₁₆	—	26	1	no	—
360	C₂×M₁₆	—	26	1	no	—
361	C₂×M₁₆	—	26	1	no	—
362	C₂×M₁₆	—	26	1	no	—
363	C₂×M₁₆	—	26	1	no	—
364	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
365	C₂×M₁₆	D₅₂	1	2	yes	—
366	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	13	2	no	—
373	C₂²×C₈	—	26	1	no	—
374	C₂²×C₈	C₄×D₁₃	1	2	yes	—
375	C₂²×C₈	D₅₂	1	2	yes	—
376	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	26	1	no	—
381	#117	—	26	1	no	—
382	#117	—	26	1	no	—
383	#117	—	26	1	no	—
384	#117	D₅₂	1	2	yes	—
385	#117	C₂²⋊D₁₃	1	2	yes	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	26	1	no	—
388	C₂×C₂²⋊C₄	—	13	2	no	—
389	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	26	1	no	—
392	#101	—	26	4	no	—
393	#100	—	26	4	no	—
394	#99	—	26	8	no	—
395	C₂²⋊C₈	—	26	4	no	—
396	C₂²⋊C₈	—	26	4	no	—
397	#97	—	2	4	no	—
398	C₄×C₈	—	2	4	no	—
399	C₂×C₁₃	—	2	1	no	—
400	C₂×C₁₃	—	2	1	no	—
401	C₂×C₁₃	—	2	1	no	—
402	C₂×C₁₃	—	2	1	no	—
403	C₂×C₁₃	—	2	1	no	—
404	C₂×C₁₃	—	2	1	no	—
405	C₂×C₁₃	#1437	1	1	yes	characteristic
406	C₂×C₁₃	#1757	1	2	yes	—
407	D₁₃	—	8	2	no	—
408	C₂⁴	—	13	2	no	—
409	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
410	#41	—	52	1	no	—
411	#41	—	52	1	no	—
412	#41	—	52	1	no	—
413	#41	—	52	1	no	—
414	#41	—	52	1	no	—
415	#41	—	52	1	no	—
416	#41	—	52	1	no	—
417	#41	—	52	1	no	—
418	#41	—	52	1	no	—
419	#41	—	52	1	no	—
420	#41	—	52	1	no	—
421	#41	—	52	1	no	—
422	#41	—	52	1	no	—
423	#41	—	52	1	no	—
424	#41	—	52	1	no	—
425	#41	—	52	1	no	—
426	C₂×Q₈	—	26	1	no	—
427	C₂×Q₈	—	26	1	no	—
428	C₂×Q₈	—	26	1	no	—
429	C₂×Q₈	—	26	1	no	—
430	C₂×Q₈	—	26	1	no	—
431	C₂×Q₈	—	26	1	no	—
432	C₂×D₄	—	26	2	no	—
433	C₂×D₄	—	26	2	no	—
434	C₂×D₄	—	26	2	no	—
435	C₂×D₄	—	26	2	no	—
436	C₂×D₄	—	26	2	no	—
437	C₂×D₄	—	26	2	no	—
438	C₂×D₄	—	26	1	no	—
439	C₂×D₄	—	26	1	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	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	13	2	no	—
446	C₂²×C₄	—	26	2	no	—
447	C₂²×C₄	—	26	2	no	—
448	C₂²×C₄	—	26	2	no	—
449	C₂²×C₄	—	26	2	no	—
450	C₂²×C₄	—	26	2	no	—
451	C₂²×C₄	—	26	2	no	—
452	C₂²×C₄	—	26	2	no	—
453	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
458	C₂²×C₄	#6127	1	1	yes	characteristic
459	C₂²×C₄	#6127	1	1	yes	characteristic
460	C₂²×C₄	#6127	1	1	yes	characteristic
461	C₂²×C₄	#6127	1	1	yes	characteristic
462	C₂²×C₄	#6127	1	1	yes	characteristic
463	C₂²×C₄	#6127	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	26	2	no	—
471	M₁₆	—	26	2	no	—
472	M₁₆	—	52	1	no	—
473	M₁₆	—	52	1	no	—
474	M₁₆	—	52	1	no	—
475	M₁₆	—	52	1	no	—
476	M₁₆	—	52	1	no	—
477	M₁₆	—	52	1	no	—
478	M₁₆	#6103	1	4	yes	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	26	2	no	—
491	C₂×C₈	—	26	2	no	—
492	C₂×C₈	—	26	2	no	—
493	C₂×C₈	—	26	2	no	—
494	C₂×C₈	—	52	1	no	—
495	C₂×C₈	—	52	1	no	—
496	C₂×C₈	#6103	1	2	yes	—
497	C₂×C₈	#6103	1	2	yes	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	52	1	no	—
501	C₄⋊C₄	—	52	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	26	2	no	—
504	C₂²⋊C₄	—	26	2	no	—
505	C₂²⋊C₄	#6103	1	4	yes	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	52	1	no	—
509	C₄²	—	52	1	no	—
510	C₁₃	#10961	1	1	yes	characteristic, complemented, Sylow
511	C₂³	—	4	2	no	—
512	C₂³	—	26	2	no	—
513	C₂³	—	26	2	no	—
514	C₂³	—	26	2	no	—
515	C₂³	—	52	4	no	—
516	C₂³	C₄²×D₁₃	1	1	yes	characteristic
517	C₂³	#88126	1	1	yes	characteristic
518	C₂³	C₄×D₅₂	1	1	yes	characteristic
519	C₂³	C₄×D₅₂	1	1	yes	characteristic
520	C₂³	C₂×#6103	1	1	yes	characteristic
521	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
522	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
523	Q₈	—	52	1	no	—
524	Q₈	—	52	1	no	—
525	Q₈	—	52	1	no	—
526	Q₈	—	52	1	no	—
527	D₄	—	52	2	no	—
528	D₄	—	52	2	no	—
529	D₄	—	52	2	no	—
530	D₄	—	52	2	no	—
531	D₄	—	52	1	no	—
532	D₄	—	52	1	no	—
533	D₄	—	52	1	no	—
534	D₄	—	52	1	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	26	2	no	—
538	C₂×C₄	—	26	2	no	—
539	C₂×C₄	—	26	2	no	—
540	C₂×C₄	—	52	2	no	—
541	C₂×C₄	—	52	2	no	—
542	C₂×C₄	—	52	2	no	—
543	C₂×C₄	—	52	2	no	—
544	C₂×C₄	—	52	4	no	—
545	C₂×C₄	—	52	2	no	—
546	C₂×C₄	#88126	1	1	yes	characteristic
547	C₂×C₄	#88126	1	1	yes	characteristic
548	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
549	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
550	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
551	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
552	C₂×C₄	#88128	1	1	yes	characteristic
553	C₂×C₄	#88129	1	1	yes	characteristic
554	C₂×C₄	#88129	1	1	yes	characteristic
555	C₂×C₄	#88129	1	1	yes	characteristic
556	C₂×C₄	#88130	1	1	yes	characteristic
557	C₂×C₄	#88130	1	1	yes	characteristic
558	C₂×C₄	C₂×#6103	1	1	yes	characteristic
559	C₂×C₄	C₂×#6103	1	1	yes	characteristic
560	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
561	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
562	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
563	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
564	C₂×C₄	#88183	1	1	yes	characteristic
565	C₂×C₄	#88183	1	1	yes	characteristic
566	C₂×C₄	#88183	1	1	yes	characteristic
567	C₂×C₄	#88184	1	1	yes	characteristic
568	C₂×C₄	#88184	1	1	yes	characteristic
569	C₂×C₄	#88184	1	1	yes	characteristic
570	C₂×C₄	#88184	1	1	yes	characteristic
571	C₂×C₄	#88184	1	1	yes	characteristic
572	C₂×C₄	#88184	1	1	yes	characteristic
573	C₂×C₄	#88207	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₈	—	52	2	no	—
578	C₈	—	52	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	52	4	no	—
587	C₂²	—	52	2	no	—
588	C₂²	—	104	2	no	—
589	C₂²	—	104	2	no	—
590	C₂²	C₄×#6103	1	1	yes	characteristic
591	C₂²	C₄×#6103	1	1	yes	characteristic
592	C₂²	C₄×#6103	1	1	yes	characteristic
593	C₂²	#11718600	1	1	yes	characteristic
594	C₂²	#11718601	1	1	yes	characteristic
595	C₂²	#11718601	1	1	yes	characteristic
596	C₂²	#11718874	1	1	yes	characteristic
597	C₄	—	4	4	no	—
598	C₄	—	52	2	no	—
599	C₄	—	104	2	no	—
600	C₄	#11718600	1	1	yes	characteristic
601	C₄	#11718600	1	1	yes	characteristic
602	C₄	#11718601	1	1	yes	characteristic
603	C₄	#11718601	1	1	yes	characteristic
604	C₄	#11718601	1	1	yes	characteristic
605	C₄	#11718601	1	1	yes	characteristic
606	C₄	#11718874	1	1	yes	characteristic
607	C₄	#11718874	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	104	2	no	—
615	C₂	#13113074	1	1	yes	characteristic
616	C₂	#13114637	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂³×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₄×C₂²⋊C₄
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#10961
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂×#405

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. C₂×C₁₃×#405	C₂	semidirect
19. C₂×#88064	C₄	semidirect
22. C₂×#88063	C₄	semidirect
26. C₂×#88060	C₄	semidirect
206. C₂×#405	D₁₃	semidirect
510. C₁₃	#10961	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718793	2
C₂×#11718667	2
C₂×#11718771	2
C₂×#11718151	2
C₂×#11718125	2
#13114532	2
C₂×C₁₃×#405	2
#10961	13