Subgroups — #15770451

Order 3328.

966 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×#11718792	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718792	C₂	1	1	yes	maximal, characteristic
3	C₂²×#88063	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114574	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₅₂	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×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₁₃×#430	—	2	2	no	—
16	C₁₃×#430	—	2	2	no	—
17	C₂×C₁₃×#108	—	2	2	no	—
18	#11718792	—	2	2	no	—
19	#11718792	—	2	2	no	—
20	#11718792	—	2	2	no	—
21	#11718792	—	2	2	no	—
22	C₂×#88063	—	2	2	no	—
23	C₂×#88063	—	2	2	no	—
24	C₂×#88063	C₄	1	4	yes	complemented
25	C₂×#88061	—	2	2	no	—
26	C₂×#88061	—	2	2	no	—
27	#11718151	—	2	2	no	—
28	#11718147	—	2	2	no	—
29	#11718146	—	2	2	no	—
30	C₂⁴×D₁₃	—	2	1	no	—
31	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×D₅₂	—	2	1	no	—
33	C₂²×D₅₂	—	2	1	no	—
34	C₂²×D₅₂	—	2	1	no	—
35	C₂²×D₅₂	—	2	1	no	—
36	C₂²×D₅₂	—	2	1	no	—
37	C₂²×D₅₂	—	2	1	no	—
38	C₂²×D₅₂	—	2	1	no	—
39	C₂²×D₅₂	—	2	1	no	—
40	C₂²×D₅₂	—	2	1	no	—
41	C₂²×D₅₂	—	2	1	no	—
42	C₂²×D₅₂	—	2	1	no	—
43	C₂²×D₅₂	C₂×C₄	1	2	yes	—
44	C₂²×D₅₂	D₄	1	2	yes	—
45	C₂²×D₅₂	Q₈	1	2	yes	—
46	C₂×C₁₃×M₁₆	—	2	1	no	—
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
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	—	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	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	C₂×C₄	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	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
64	C₂²×C₈×C₁₃	—	2	1	no	—
65	C₂²×C₈×C₁₃	—	2	1	no	—
66	C₂²×C₈×C₁₃	—	2	1	no	—
67	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
68	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
69	#88180	—	2	1	no	—
70	#88180	—	2	1	no	—
71	#88180	—	2	1	no	—
72	#88180	—	2	1	no	—
73	#88180	—	2	1	no	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	D₄	1	2	yes	—
77	C₂×C₄⋊Dic₁₃	—	2	1	no	—
78	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
79	C₂×C₄×Dic₁₃	—	2	1	no	—
80	C₂×C₄×Dic₁₃	—	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	C₂×C₄	1	2	yes	—
87	C₂²×#1055	—	2	1	no	—
88	C₁₃×#108	—	2	8	no	—
89	#88063	—	2	8	no	—
90	#88061	—	2	8	no	—
91	#88061	—	2	8	no	—
92	#11142	—	13	1	no	maximal, Sylow
93	C₂⁴×C₁₃	#41	1	1	yes	characteristic
94	C₂³×D₁₃	—	2	2	no	—
95	C₂³×D₁₃	—	2	2	no	—
96	C₂³×D₁₃	—	2	2	no	—
97	C₂³×D₁₃	—	4	1	no	—
98	C₂³×D₁₃	—	4	1	no	—
99	C₂³×D₁₃	—	4	1	no	—
100	C₂³×D₁₃	—	4	1	no	—
101	C₂³×D₁₃	—	8	4	no	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	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×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	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×Dic₁₃	—	2	2	no	—
117	C₂²×Dic₁₃	—	4	1	no	—
118	C₂×D₅₂	—	2	2	no	—
119	C₂×D₅₂	—	2	2	no	—
120	C₂×D₅₂	—	2	2	no	—
121	C₂×D₅₂	—	2	2	no	—
122	C₂×D₅₂	—	2	2	no	—
123	C₂×D₅₂	—	2	2	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	2	2	no	—
126	C₂×D₅₂	—	2	2	no	—
127	C₂×D₅₂	—	2	2	no	—
128	C₂×D₅₂	—	2	2	no	—
129	C₂×D₅₂	—	2	2	no	—
130	C₂×D₅₂	—	2	2	no	—
131	C₂×D₅₂	—	2	2	no	—
132	C₂×D₅₂	—	2	2	no	—
133	C₂×D₅₂	—	4	1	no	—
134	C₂×D₅₂	—	4	1	no	—
135	C₂×D₅₂	—	4	1	no	—
136	C₂×D₅₂	—	4	1	no	—
137	C₂×D₅₂	—	4	1	no	—
138	C₂×D₅₂	—	4	1	no	—
139	C₂×D₅₂	—	4	1	no	—
140	C₂×D₅₂	—	4	1	no	—
141	C₂×D₅₂	—	4	1	no	—
142	C₂×D₅₂	—	4	1	no	—
143	C₂×D₅₂	—	4	1	no	—
144	C₂×D₅₂	—	4	1	no	—
145	C₂×D₅₂	C₄⋊C₄	1	4	yes	—
146	C₁₃×M₁₆	—	2	2	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	2	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	4	1	no	—
154	C₁₃×M₁₆	—	4	1	no	—
155	C₁₃×M₁₆	—	4	1	no	—
156	C₁₃×M₁₆	—	4	1	no	—
157	C₁₃×M₁₆	C₂²⋊C₄	1	4	yes	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	4	1	no	—
164	C₂×C₈×C₁₃	—	4	1	no	—
165	C₂×C₈×C₁₃	—	4	1	no	—
166	C₂×C₈×C₁₃	—	4	1	no	—
167	C₂²⋊Dic₁₃	—	2	2	no	—
168	C₂²⋊Dic₁₃	—	4	1	no	—
169	C₂²⋊Dic₁₃	—	4	1	no	—
170	C₂²⋊Dic₁₃	—	4	1	no	—
171	C₄⋊Dic₁₃	—	2	2	no	—
172	C₄⋊Dic₁₃	—	2	2	no	—
173	C₄⋊Dic₁₃	—	2	2	no	—
174	C₄⋊Dic₁₃	—	4	1	no	—
175	C₄×Dic₁₃	—	2	2	no	—
176	C₄×Dic₁₃	—	4	1	no	—
177	C₄×Dic₁₃	—	4	1	no	—
178	C₄×Dic₁₃	—	4	1	no	—
179	#6099	—	2	2	no	—
180	#6099	—	2	2	no	—
181	#6099	—	4	1	no	—
182	#6099	—	4	1	no	—
183	C₂×#1055	—	2	2	no	—
184	C₂×#1055	—	4	1	no	—
185	C₂×#1055	—	4	1	no	—
186	C₂×#430	D₁₃	1	1	yes	characteristic, complemented
187	C₂×#418	—	13	1	no	—
188	C₂×#418	—	13	1	no	—
189	C₂²×#100	—	13	1	no	—
190	C₂×#344	—	13	1	no	—
191	#1742	—	13	1	no	—
192	#1733	—	13	1	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	#117	1	1	yes	characteristic
195	C₂³×C₁₃	#121	1	1	yes	characteristic
196	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂³×C₁₃	#123	1	1	yes	characteristic
198	C₂³×C₁₃	#123	1	1	yes	characteristic
199	C₂³×C₁₃	#124	1	1	yes	characteristic
200	C₂³×C₁₃	#124	1	1	yes	characteristic
201	C₂²×D₁₃	—	2	4	no	—
202	C₂²×D₁₃	—	4	2	no	—
203	C₂²×D₁₃	—	4	2	no	—
204	C₂²×D₁₃	—	4	2	no	—
205	C₂²×D₁₃	—	4	2	no	—
206	C₂²×D₁₃	—	4	2	no	—
207	C₂²×D₁₃	—	4	2	no	—
208	C₂²×D₁₃	—	8	4	no	—
209	C₂²×D₁₃	—	8	4	no	—
210	C₂²×D₁₃	—	8	4	no	—
211	C₂²×D₁₃	—	8	4	no	—
212	C₂²×D₁₃	—	8	4	no	—
213	C₂²×D₁₃	—	8	4	no	—
214	C₂²×D₁₃	—	8	4	no	—
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
243	C₂×Dic₁₃	—	4	2	no	—
244	C₂×Dic₁₃	—	4	2	no	—
245	C₂×Dic₁₃	—	8	2	no	—
246	C₂×Dic₁₃	—	8	2	no	—
247	D₅₂	—	2	4	no	—
248	D₅₂	—	2	4	no	—
249	D₅₂	—	4	2	no	—
250	D₅₂	—	4	2	no	—
251	D₅₂	—	4	2	no	—
252	D₅₂	—	4	2	no	—
253	D₅₂	—	4	2	no	—
254	D₅₂	—	4	2	no	—
255	C₈×C₁₃	—	2	4	no	—
256	C₈×C₁₃	—	4	2	no	—
257	C₈×C₁₃	—	4	2	no	—
258	#1055	—	4	2	no	—
259	C₂³×D₄	—	13	1	no	—
260	C₂²×M₁₆	—	13	1	no	—
261	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
262	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
263	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
264	C₂×#117	—	13	1	no	—
265	C₂×#117	—	13	1	no	—
266	#430	—	2	2	no	—
267	#430	—	2	2	no	—
268	C₂×#108	—	2	2	no	—
269	#418	—	26	2	no	—
270	#418	—	26	2	no	—
271	#418	—	26	2	no	—
272	#418	—	26	2	no	—
273	C₂×#102	—	26	2	no	—
274	C₂×#102	—	26	2	no	—
275	C₂×#100	—	13	4	no	—
276	C₂×#100	—	26	2	no	—
277	C₂×#100	—	26	2	no	—
278	#344	—	26	2	no	—
279	#343	—	26	2	no	—
280	#339	—	26	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	#380	1	1	yes	characteristic
289	C₂²×C₁₃	#388	1	1	yes	characteristic
290	C₂²×C₁₃	#388	1	1	yes	characteristic
291	C₂²×C₁₃	#393	1	1	yes	characteristic
292	C₂²×C₁₃	#394	1	1	yes	characteristic
293	C₂²×C₁₃	#394	1	1	yes	characteristic
294	C₂²×C₁₃	#399	1	1	yes	characteristic
295	C₂×D₁₃	—	4	4	no	—
296	C₂×D₁₃	—	8	4	no	—
297	C₂×D₁₃	—	8	4	no	—
298	C₂×D₁₃	—	8	4	no	—
299	C₂×D₁₃	—	8	4	no	—
300	C₂×D₁₃	—	8	4	no	—
301	C₂×D₁₃	—	8	4	no	—
302	C₂×D₁₃	—	8	4	no	—
303	C₄×C₁₃	#385	1	1	yes	characteristic
304	C₄×C₁₃	#385	1	1	yes	characteristic
305	C₄×C₁₃	#386	1	1	yes	characteristic
306	C₄×C₁₃	#390	1	1	yes	characteristic
307	C₄×C₁₃	#392	1	1	yes	characteristic
308	C₄×C₁₃	#396	1	1	yes	characteristic
309	C₄×C₁₃	#396	1	1	yes	characteristic
310	C₄×C₁₃	#397	1	1	yes	characteristic
311	Dic₁₃	—	8	2	no	—
312	Dic₁₃	—	8	2	no	—
313	C₂⁵	—	26	1	no	—
314	C₂²×D₄	—	13	2	no	—
315	C₂²×D₄	—	13	2	no	—
316	C₂²×D₄	—	13	2	no	—
317	C₂²×D₄	—	26	1	no	—
318	C₂²×D₄	—	26	1	no	—
319	C₂²×D₄	—	26	1	no	—
320	C₂²×D₄	—	26	1	no	—
321	C₂²×D₄	—	26	1	no	—
322	C₂²×D₄	—	26	1	no	—
323	C₂²×D₄	—	26	1	no	—
324	C₂²×D₄	—	26	1	no	—
325	C₂²×D₄	—	26	1	no	—
326	C₂²×D₄	—	26	1	no	—
327	C₂²×D₄	—	26	1	no	—
328	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	13	2	no	—
343	C₂×M₁₆	—	26	1	no	—
344	C₂×M₁₆	—	26	1	no	—
345	C₂×M₁₆	—	26	1	no	—
346	C₂×M₁₆	—	26	1	no	—
347	C₂×M₁₆	—	26	1	no	—
348	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
349	C₂×M₁₆	D₅₂	1	2	yes	—
350	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
351	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
352	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	26	1	no	—
357	#117	—	13	2	no	—
358	#117	—	26	1	no	—
359	#117	—	26	1	no	—
360	#117	—	26	1	no	—
361	#117	—	26	1	no	—
362	#117	—	26	1	no	—
363	#117	—	26	1	no	—
364	#117	—	26	1	no	—
365	C₂×C₄⋊C₄	—	13	2	no	—
366	C₂×C₄⋊C₄	—	26	1	no	—
367	C₂×C₂²⋊C₄	—	26	1	no	—
368	C₂×C₂²⋊C₄	—	26	1	no	—
369	C₂×C₄²	—	26	1	no	—
370	C₂×C₄²	—	26	1	no	—
371	#108	—	2	8	no	—
372	#102	—	26	8	no	—
373	#102	—	26	8	no	—
374	#100	—	26	8	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	2	1	no	—
378	C₂×C₁₃	—	2	1	no	—
379	C₂×C₁₃	—	2	1	no	—
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	#1439	1	1	yes	characteristic
382	C₂×C₁₃	#2048	1	2	yes	—
383	D₁₃	—	8	4	no	—
384	C₂⁴	—	26	2	no	—
385	C₂⁴	—	26	2	no	—
386	C₂⁴	—	26	2	no	—
387	C₂⁴	—	52	1	no	—
388	C₂⁴	—	52	1	no	—
389	C₂⁴	—	52	1	no	—
390	C₂⁴	—	52	1	no	—
391	C₂⁴	—	104	4	no	—
392	C₂⁴	#6131	1	1	yes	characteristic
393	C₂×D₄	—	13	4	no	—
394	C₂×D₄	—	26	2	no	—
395	C₂×D₄	—	26	2	no	—
396	C₂×D₄	—	26	2	no	—
397	C₂×D₄	—	26	2	no	—
398	C₂×D₄	—	26	2	no	—
399	C₂×D₄	—	26	2	no	—
400	C₂×D₄	—	26	2	no	—
401	C₂×D₄	—	26	2	no	—
402	C₂×D₄	—	26	2	no	—
403	C₂×D₄	—	26	2	no	—
404	C₂×D₄	—	26	2	no	—
405	C₂×D₄	—	26	2	no	—
406	C₂×D₄	—	26	2	no	—
407	C₂×D₄	—	26	2	no	—
408	C₂×D₄	—	26	2	no	—
409	C₂×D₄	—	52	1	no	—
410	C₂×D₄	—	52	1	no	—
411	C₂×D₄	—	52	1	no	—
412	C₂×D₄	—	52	1	no	—
413	C₂×D₄	—	52	1	no	—
414	C₂×D₄	—	52	1	no	—
415	C₂×D₄	—	52	1	no	—
416	C₂×D₄	—	52	1	no	—
417	C₂×D₄	—	52	1	no	—
418	C₂×D₄	—	52	1	no	—
419	C₂×D₄	—	52	1	no	—
420	C₂×D₄	—	52	1	no	—
421	C₂²×C₄	—	26	2	no	—
422	C₂²×C₄	—	52	1	no	—
423	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
425	C₂²×C₄	#6127	1	1	yes	characteristic
426	C₂²×C₄	#6127	1	1	yes	characteristic
427	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
428	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
429	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
430	C₂²×C₄	#6129	1	1	yes	characteristic
431	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
432	C₂²×C₄	#6131	1	1	yes	characteristic
433	C₂²×C₄	#6131	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	M₁₆	—	4	1	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	26	2	no	—
449	M₁₆	—	26	2	no	—
450	M₁₆	—	52	1	no	—
451	M₁₆	—	52	1	no	—
452	M₁₆	#6103	1	4	yes	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	—	4	1	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	26	2	no	—
463	C₂×C₈	—	52	1	no	—
464	C₂×C₈	—	52	1	no	—
465	C₄⋊C₄	—	26	2	no	—
466	C₄⋊C₄	—	26	2	no	—
467	C₄⋊C₄	—	26	2	no	—
468	C₄⋊C₄	—	52	1	no	—
469	C₂²⋊C₄	—	26	2	no	—
470	C₂²⋊C₄	—	52	1	no	—
471	C₂²⋊C₄	—	52	1	no	—
472	C₂²⋊C₄	—	52	1	no	—
473	C₄²	—	26	2	no	—
474	C₄²	—	52	1	no	—
475	C₄²	—	52	1	no	—
476	C₄²	—	52	1	no	—
477	C₁₃	#11142	1	1	yes	characteristic, complemented, Sylow
478	C₂³	—	4	2	no	—
479	C₂³	—	26	4	no	—
480	C₂³	—	52	2	no	—
481	C₂³	—	52	2	no	—
482	C₂³	—	52	2	no	—
483	C₂³	—	52	2	no	—
484	C₂³	—	52	2	no	—
485	C₂³	—	52	2	no	—
486	C₂³	—	104	4	no	—
487	C₂³	—	104	4	no	—
488	C₂³	—	104	4	no	—
489	C₂³	—	104	4	no	—
490	C₂³	—	104	4	no	—
491	C₂³	—	104	4	no	—
492	C₂³	—	104	4	no	—
493	C₂³	#88146	1	1	yes	characteristic
494	C₂³	#88148	1	1	yes	characteristic
495	C₂³	#88148	1	1	yes	characteristic
496	C₂³	#88149	1	1	yes	characteristic
497	C₂³	#88200	1	1	yes	characteristic
498	C₂³	#88201	1	1	yes	characteristic
499	C₂³	#88201	1	1	yes	characteristic
500	D₄	—	26	4	no	—
501	D₄	—	26	4	no	—
502	D₄	—	52	2	no	—
503	D₄	—	52	2	no	—
504	D₄	—	52	2	no	—
505	D₄	—	52	2	no	—
506	D₄	—	52	2	no	—
507	D₄	—	52	2	no	—
508	C₂×C₄	—	52	2	no	—
509	C₂×C₄	—	52	2	no	—
510	C₂×C₄	—	104	2	no	—
511	C₂×C₄	—	104	2	no	—
512	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
513	C₂×C₄	#88147	1	1	yes	characteristic
514	C₂×C₄	#88147	1	1	yes	characteristic
515	C₂×C₄	#88148	1	1	yes	characteristic
516	C₂×C₄	#88148	1	1	yes	characteristic
517	C₂×C₄	#88149	1	1	yes	characteristic
518	C₂×C₄	#88149	1	1	yes	characteristic
519	C₂×C₄	#88150	1	1	yes	characteristic
520	C₂×C₄	#88150	1	1	yes	characteristic
521	C₂×C₄	#88151	1	1	yes	characteristic
522	C₂×C₄	#88152	1	1	yes	characteristic
523	C₂×C₄	#88152	1	1	yes	characteristic
524	C₂×C₄	C₂×#6103	1	1	yes	characteristic
525	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
526	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
527	C₂×C₄	#88183	1	1	yes	characteristic
528	C₂×C₄	#88184	1	1	yes	characteristic
529	C₂×C₄	#88184	1	1	yes	characteristic
530	C₂×C₄	#88191	1	1	yes	characteristic
531	C₂×C₄	#88191	1	1	yes	characteristic
532	C₂×C₄	#88192	1	1	yes	characteristic
533	C₂×C₄	#88193	1	1	yes	characteristic
534	C₂×C₄	#88193	1	1	yes	characteristic
535	C₂×C₄	#88194	1	1	yes	characteristic
536	C₂×C₄	#88200	1	1	yes	characteristic
537	C₂×C₄	#88200	1	1	yes	characteristic
538	C₂×C₄	#88201	1	1	yes	characteristic
539	C₂×C₄	#88207	1	1	yes	characteristic
540	C₈	—	2	4	no	—
541	C₈	—	4	2	no	—
542	C₈	—	4	2	no	—
543	C₈	—	52	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	52	4	no	—
552	C₂²	—	104	4	no	—
553	C₂²	—	104	4	no	—
554	C₂²	—	104	4	no	—
555	C₂²	—	104	4	no	—
556	C₂²	—	104	4	no	—
557	C₂²	—	104	4	no	—
558	C₂²	—	104	4	no	—
559	C₂²	#11718648	1	1	yes	characteristic
560	C₂²	#11718651	1	1	yes	characteristic
561	C₂²	#11718651	1	1	yes	characteristic
562	C₂²	#11718652	1	1	yes	characteristic
563	C₂²	#11718652	1	1	yes	characteristic
564	C₂²	#11718653	1	1	yes	characteristic
565	C₂²	#11718892	1	1	yes	characteristic
566	C₄	—	104	2	no	—
567	C₄	—	104	2	no	—
568	C₄	#11718649	1	1	yes	characteristic
569	C₄	#11718650	1	1	yes	characteristic
570	C₄	#11718650	1	1	yes	characteristic
571	C₄	#11718654	1	1	yes	characteristic
572	C₄	#11718655	1	1	yes	characteristic
573	C₄	#11718655	1	1	yes	characteristic
574	C₄	#11718874	1	1	yes	characteristic
575	C₄	#11718884	1	1	yes	characteristic
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	104	4	no	—
583	C₂	#13113078	1	1	yes	characteristic
584	C₂	#13116111	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718652
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#430	C₂
socle	C₂²×C₁₃	#394
prime radical	C₂³×D₅₂	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#430	D₁₃
hypocenter	C₁₃	#11142
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
4. C₂×#11718151	C₂	semidirect
5. #13114574	C₂	semidirect
6. #13114547	C₂	semidirect
7. C₂×C₁₃×#430	C₂	semidirect
24. C₂×#88063	C₄	semidirect
186. C₂×#430	D₁₃	semidirect
477. C₁₃	#11142	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718792	2
C₂²×#88063	2
C₂×#11718151	2
#13114574	2
#13114547	2
C₂×C₁₃×#430	2
#11142	13