Subgroups — #15885460

Order 3328.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124417	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123557	C₂	1	2	yes	maximal, complemented
4	C₂²×#88059	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115724	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115584	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115485	C₂	1	2	yes	maximal, complemented
8	#13115136	C₂	1	2	yes	maximal, complemented
9	#13115114	C₂	1	2	yes	maximal, complemented
10	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#11719496	C₂²	1	2	yes	—
14	C₂²×#6099	C₂²	1	2	yes	—
15	C₂×#88158	C₂²	1	1	yes	characteristic
16	C₂×#88155	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	#11718777	C₄	1	1	yes	characteristic, complemented
22	#11718777	C₄	1	1	yes	characteristic, complemented
23	#11718776	C₄	1	1	yes	characteristic, complemented
24	#11718776	C₄	1	1	yes	characteristic, complemented
25	#11718775	C₄	1	2	yes	complemented
26	#11718775	C₄	1	2	yes	complemented
27	#11718774	C₂²	1	2	yes	—
28	#11718771	C₂²	1	2	yes	—
29	C₂×#88059	—	2	4	no	—
30	C₂×#88059	C₂²	1	1	yes	characteristic
31	C₂×#88059	C₂²	1	2	yes	—
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718763	C₂²	1	2	yes	—
35	#11718762	C₂²	1	2	yes	—
36	C₂×#88045	C₂²	1	2	yes	—
37	C₂×#88045	C₂²	1	2	yes	—
38	#11718391	—	2	2	no	—
39	#11718390	—	2	2	no	—
40	#11718389	—	2	2	no	—
41	#11718386	—	2	2	no	—
42	#11718361	—	2	4	no	—
43	C₁₃×#336	C₂²	1	1	yes	characteristic
44	C₁₃×#336	C₂²	1	1	yes	characteristic
45	#11718115	C₂²	1	2	yes	—
46	#11718115	C₂²	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×#6127	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	#88207	—	2	2	no	—
63	#88184	C₂×C₄	1	2	yes	—
64	#88184	C₂×C₄	1	2	yes	—
65	#88183	—	2	2	no	—
66	C₄×C₂²⋊D₁₃	—	2	2	no	—
67	C₄×C₂²⋊D₁₃	—	2	2	no	—
68	#88180	C₂³	1	2	yes	—
69	#88178	C₂×C₄	1	2	yes	—
70	#88178	C₂×C₄	1	2	yes	—
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	—	2	4	no	—
73	C₂×#6099	—	4	2	no	—
74	C₂×#6099	C₂³	1	2	yes	—
75	C₂×#6099	C₂³	1	2	yes	—
76	C₂²×#1055	—	2	2	no	—
77	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
78	#88158	—	2	2	no	—
79	#88158	—	2	2	no	—
80	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
81	C₂×#6095	C₂×C₄	1	2	yes	—
82	#88155	—	2	4	no	—
83	#88155	—	4	2	no	—
84	C₂×#6094	—	2	2	no	—
85	C₂×C₈×D₁₃	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
87	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
88	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
89	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	#88061	C₂×C₄	1	2	yes	—
94	#88061	C₂×C₄	1	2	yes	—
95	#88060	—	2	2	no	—
96	#88060	—	2	2	no	—
97	#88059	—	2	2	no	—
98	#88059	—	2	4	no	—
99	#88059	D₄	1	4	yes	complemented
100	#88058	C₂×C₄	1	1	yes	characteristic
101	#88058	C₂×C₄	1	1	yes	characteristic
102	#88057	C₂×C₄	1	2	yes	—
103	#88056	C₂×C₄	1	2	yes	—
104	#88056	C₂×C₄	1	2	yes	—
105	#88055	—	2	2	no	—
106	#88054	—	2	2	no	—
107	#88054	—	2	2	no	—
108	C₈×Dic₁₃	—	2	2	no	—
109	#88045	—	2	4	no	—
110	#88045	—	4	2	no	—
111	#23018	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	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	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	C₂×D₅₂	C₂²×C₄	1	2	yes	—
133	C₂×C₄×D₁₃	—	2	2	no	—
134	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	#41	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₂²⋊Dic₁₃	—	2	2	no	—
161	C₂²⋊Dic₁₃	—	2	2	no	—
162	C₂²⋊Dic₁₃	—	2	2	no	—
163	#6103	—	2	2	no	—
164	#6103	—	2	2	no	—
165	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
166	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
167	#6101	—	2	2	no	—
168	#6101	—	2	2	no	—
169	C₄×Dic₁₃	—	2	2	no	—
170	#6099	—	2	2	no	—
171	#6099	—	2	2	no	—
172	#6099	—	2	2	no	—
173	#6099	—	4	4	no	—
174	#6099	C₂×D₄	1	4	yes	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	—	2	2	no	—
177	C₂×#1055	—	4	4	no	—
178	Dic₅₂	—	2	2	no	—
179	D₁₀₄	—	2	2	no	—
180	#6095	—	2	4	no	—
181	#6094	—	4	4	no	—
182	C₈×D₁₃	—	4	4	no	—
183	#3050	—	13	1	no	—
184	C₂×#443	—	13	1	no	—
185	#2933	—	13	2	no	—
186	C₂²×#108	—	13	1	no	—
187	#1974	—	13	1	no	—
188	#1945	—	13	1	no	—
189	#1929	—	13	2	no	—
190	#1871	—	13	2	no	—
191	#1866	—	13	2	no	—
192	#1772	—	13	1	no	—
193	C₈×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂²×D₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	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	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂²⋊D₁₃	—	4	2	no	—
227	C₂²⋊D₁₃	—	4	2	no	—
228	C₂²⋊D₁₃	—	4	4	no	—
229	C₂²⋊D₁₃	—	8	2	no	—
230	C₂×Dic₁₃	—	2	2	no	—
231	C₂×Dic₁₃	—	2	2	no	—
232	C₂×Dic₁₃	—	2	2	no	—
233	D₅₂	—	2	2	no	—
234	D₅₂	—	2	2	no	—
235	C₄×D₁₃	—	4	2	no	—
236	C₄×D₁₃	—	4	2	no	—
237	Dic₂₆	—	2	2	no	—
238	Dic₂₆	—	2	2	no	—
239	C₈×C₁₃	—	2	1	no	—
240	C₈×C₁₃	—	2	1	no	—
241	C₈×C₁₃	—	2	1	no	—
242	C₈×C₁₃	—	2	1	no	—
243	C₈×C₁₃	—	2	1	no	—
244	C₈×C₁₃	—	2	1	no	—
245	C₈×C₁₃	C₄×D₄	1	2	yes	—
246	C₈×C₁₃	C₄×D₄	1	2	yes	—
247	#1055	—	2	4	no	—
248	#1055	—	4	2	no	—
249	C₂×#135	—	13	1	no	—
250	C₂×#131	—	13	2	no	—
251	C₂²×M₁₆	—	13	2	no	—
252	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
253	#525	—	13	2	no	—
254	#467	—	13	1	no	—
255	#467	—	13	1	no	—
256	#466	—	13	1	no	—
257	#466	—	13	1	no	—
258	#465	—	13	2	no	—
259	#465	—	13	2	no	—
260	#443	—	26	4	no	—
261	#436	—	26	2	no	—
262	#435	—	26	2	no	—
263	#435	—	26	2	no	—
264	C₈×D₄	—	26	2	no	—
265	C₂×#108	—	13	1	no	—
266	C₂×#108	—	13	2	no	—
267	C₂×#108	—	13	1	no	—
268	C₂×#108	—	26	4	no	—
269	#427	—	13	1	no	—
270	#424	—	13	2	no	—
271	C₂×#104	—	13	2	no	—
272	C₂×#104	—	13	2	no	—
273	#416	—	13	2	no	—
274	#408	—	13	2	no	—
275	C₂×C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic
276	#405	—	13	2	no	—
277	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
280	#339	—	13	2	no	—
281	#339	—	13	2	no	—
282	#336	C₂×D₁₃	1	1	yes	characteristic
283	#336	C₂×D₁₃	1	1	yes	characteristic
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	#443	1	2	yes	complemented
294	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₁₃	#548	1	1	yes	characteristic
296	C₂²×C₁₃	#553	1	1	yes	characteristic
297	C₂×D₁₃	—	4	2	no	—
298	C₂×D₁₃	—	4	2	no	—
299	C₂×D₁₃	—	4	2	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₁₃	#520	1	1	yes	characteristic
306	C₄×C₁₃	D₄²	1	1	yes	characteristic
307	C₄×C₁₃	#547	1	1	yes	characteristic
308	Dic₁₃	—	4	2	no	—
309	Dic₁₃	—	4	2	no	—
310	Dic₁₃	—	4	2	no	—
311	C₂×#41	—	13	2	no	—
312	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
313	#135	—	26	2	no	—
314	#135	—	26	2	no	—
315	C₂×Q₁₆	—	13	1	no	—
316	C₂×SD₁₆	—	13	2	no	—
317	C₂×D₈	—	13	1	no	—
318	#131	—	26	4	no	—
319	#131	—	52	2	no	—
320	C₂×M₁₆	—	13	2	no	—
321	C₂×M₁₆	—	13	2	no	—
322	C₂×M₁₆	—	26	2	no	—
323	C₂×M₁₆	—	26	2	no	—
324	C₂×M₁₆	—	26	4	no	—
325	C₂×M₁₆	—	52	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	26	2	no	—
329	C₂²×C₈	—	26	2	no	—
330	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
332	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
337	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
338	#123	—	26	2	no	—
339	C₂²⋊Q₈	—	13	2	no	—
340	C₂²⋊Q₈	—	13	2	no	—
341	#121	—	13	2	no	—
342	#121	—	13	2	no	—
343	#120	—	26	2	no	—
344	C₄×D₄	—	26	2	no	—
345	C₄×D₄	—	26	2	no	—
346	#117	—	13	2	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
350	#108	—	13	4	no	—
351	#108	—	26	4	no	—
352	#108	—	26	2	no	—
353	#107	—	13	1	no	—
354	#107	—	13	1	no	—
355	#106	—	13	2	no	—
356	C₄⋊C₈	—	26	2	no	—
357	C₄⋊C₈	—	26	2	no	—
358	#104	—	26	4	no	—
359	#104	—	52	2	no	—
360	#103	—	13	2	no	—
361	#103	—	13	2	no	—
362	#102	—	13	2	no	—
363	#102	—	13	2	no	—
364	C₂²⋊C₈	—	26	2	no	—
365	C₂²⋊C₈	—	26	2	no	—
366	C₂²⋊C₈	D₅₂	1	1	yes	characteristic
367	C₂²⋊C₈	D₅₂	1	1	yes	characteristic
368	C₂²⋊C₈	D₅₂	1	1	yes	characteristic
369	C₂²⋊C₈	D₅₂	1	1	yes	characteristic
370	#97	—	26	2	no	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	26	2	no	—
374	#95	—	2	1	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	2	2	no	—
378	C₂×C₁₃	—	4	1	no	—
379	C₂×C₁₃	#2361	1	1	yes	characteristic
380	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
381	C₂×C₁₃	#2957	1	1	yes	characteristic
382	D₁₃	—	8	2	no	—
383	C₂⁴	#6127	1	1	yes	characteristic
384	#41	—	26	2	no	—
385	#41	—	26	2	no	—
386	#41	—	26	2	no	—
387	#41	—	26	2	no	—
388	C₂×Q₈	—	13	2	no	—
389	C₂×D₄	—	13	2	no	—
390	C₂×D₄	—	26	2	no	—
391	C₂×D₄	—	26	2	no	—
392	C₂×D₄	—	26	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	26	2	no	—
400	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
404	C₂²×C₄	#6127	1	1	yes	characteristic
405	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
406	Q₁₆	—	26	2	no	—
407	SD₁₆	—	26	4	no	—
408	D₈	—	26	2	no	—
409	M₁₆	—	13	4	no	—
410	M₁₆	—	26	2	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	—	26	2	no	—
413	M₁₆	—	52	4	no	—
414	M₁₆	—	52	4	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	—	26	2	no	—
427	C₂×C₈	—	52	4	no	—
428	C₂×C₈	—	52	4	no	—
429	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
433	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
434	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
435	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
436	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
437	C₂×C₈	D₄×D₁₃	1	2	yes	—
438	C₂×C₈	#6129	1	2	yes	—
439	C₄⋊C₄	—	13	2	no	—
440	C₄⋊C₄	—	13	2	no	—
441	C₄⋊C₄	—	26	2	no	—
442	C₄⋊C₄	—	26	2	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	26	2	no	—
445	C₂²⋊C₄	—	26	2	no	—
446	C₂²⋊C₄	—	26	2	no	—
447	C₂²⋊C₄	—	26	2	no	—
448	C₂²⋊C₄	—	26	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	26	2	no	—
454	C₁₃	#23018	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	26	2	no	—
460	C₂³	C₄×D₅₂	1	1	yes	characteristic
461	C₂³	C₄×D₅₂	1	1	yes	characteristic
462	C₂³	C₂×#6127	1	1	yes	characteristic
463	Q₈	—	26	2	no	—
464	Q₈	—	26	2	no	—
465	D₄	—	26	2	no	—
466	D₄	—	26	2	no	—
467	D₄	—	52	2	no	—
468	D₄	—	52	2	no	—
469	D₄	—	52	4	no	—
470	D₄	—	104	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	26	2	no	—
488	C₂×C₄	—	26	2	no	—
489	C₂×C₄	—	26	2	no	—
490	C₂×C₄	—	52	2	no	—
491	C₂×C₄	—	52	2	no	—
492	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
493	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂×#6129	1	1	yes	characteristic
498	C₂×C₄	#88256	1	1	yes	characteristic
499	C₂×C₄	#88257	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	26	4	no	—
507	C₈	—	52	2	no	—
508	C₈	#88135	1	2	yes	—
509	C₈	#88135	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	52	2	no	—
520	C₂²	—	52	2	no	—
521	C₂²	—	52	2	no	—
522	C₂²	#11718361	1	2	yes	complemented
523	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
524	C₂²	#11719257	1	1	yes	characteristic
525	C₂²	#11719270	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	52	2	no	—
531	C₄	—	52	2	no	—
532	C₄	—	52	2	no	—
533	C₄	C₂×#88135	1	1	yes	characteristic
534	C₄	#11719228	1	1	yes	characteristic
535	C₄	D₄×D₅₂	1	1	yes	characteristic
536	C₄	#11719260	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	104	2	no	—
542	C₂	#13117850	1	1	yes	characteristic
543	C₂	C₂×#11718361	1	1	yes	characteristic
544	C₂	#13123754	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₈×C₁₃×C₂²⋊C₄	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124417	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	#23018
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#11718361	C₂	semidirect
3. #13123557	C₂	semidirect
4. C₂²×#88059	C₂	semidirect
5. #13115724	C₂	semidirect
6. #13115584	C₂	semidirect
7. #13115485	C₂	semidirect
8. #13115136	C₂	semidirect
9. #13115114	C₂	semidirect
10. #13114715	C₂	semidirect
11. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
21. #11718777	C₄	semidirect
22. #11718777	C₄	semidirect
23. #11718776	C₄	semidirect
24. #11718776	C₄	semidirect
25. #11718775	C₄	semidirect
26. #11718775	C₄	semidirect
99. #88059	D₄	semidirect
193. C₈×C₂²⋊C₄	D₁₃	semidirect
293. C₂²×C₁₃	#443	semidirect
454. C₁₃	#23018	semidirect
522. C₂²	#11718361	semidirect

Maximal subgroups

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

subgroup	index
#13124417	2
C₂×#11718361	2
#13123557	2
C₂²×#88059	2
#13115724	2
#13115584	2
#13115485	2
#13115136	2
#13115114	2
#13114715	2
C₈×C₁₃×C₂²⋊C₄	2
#23018	13