Subgroups — #15905530

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124575	C₂	1	2	yes	maximal
2	C₂×#11718804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718804	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123447	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116236	C₂	1	2	yes	maximal, complemented
6	#13116117	C₂	1	2	yes	maximal, complemented
7	#13115751	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115626	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115307	C₂	1	2	yes	maximal, complemented
10	#13114886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#575	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂×#88205	C₂²	1	2	yes	—
16	C₂×#88205	C₂²	1	2	yes	—
17	#11719524	C₂²	1	2	yes	—
18	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
19	C₁₃×#444	—	2	2	no	—
20	C₁₃×#443	—	2	2	no	—
21	C₁₃×#430	C₂²	1	1	yes	characteristic
22	C₁₃×#421	C₂²	1	1	yes	characteristic
23	C₁₃×#421	C₂²	1	1	yes	characteristic
24	C₁₃×#405	C₂²	1	1	yes	characteristic
25	#11718898	C₂²	1	2	yes	—
26	#11718865	—	2	4	no	—
27	#11718861	—	2	4	no	—
28	#11718804	—	2	2	no	—
29	#11718804	—	2	2	no	—
30	#11718804	—	2	2	no	—
31	#11718804	—	2	2	no	—
32	C₂×#88064	C₂²	1	2	yes	—
33	C₂×#88064	C₂²	1	2	yes	—
34	C₂×#88064	C₂²	1	2	yes	—
35	#11718786	—	2	2	no	—
36	#11718786	C₂²	1	2	yes	—
37	#11718785	C₂²	1	2	yes	—
38	C₂×#88059	—	2	2	no	—
39	C₂×#88059	C₂²	1	1	yes	characteristic
40	C₂×#88059	C₂²	1	1	yes	characteristic
41	C₂×#88059	C₂²	1	1	yes	characteristic
42	#11718665	C₂²	1	2	yes	—
43	#11718152	C₂²	1	2	yes	—
44	#11718125	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₂²×Dic₂₆	C₂³	1	2	yes	—
48	C₁₃×#137	—	2	1	no	—
49	C₁₃×#137	D₄	1	2	yes	—
50	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
51	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#131	—	2	1	no	—
54	C₁₃×#131	—	2	1	no	—
55	C₁₃×#131	—	2	1	no	—
56	C₁₃×#131	—	2	1	no	—
57	C₁₃×#131	—	2	1	no	—
58	C₁₃×#131	—	2	1	no	—
59	C₁₃×#131	D₄	1	2	yes	—
60	C₁₃×#131	D₄	1	2	yes	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	—	2	1	no	—
67	C₂²×C₈×C₁₃	—	2	1	no	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#117	C₂³	1	1	yes	characteristic
70	#88205	—	2	4	no	—
71	#88205	—	2	4	no	—
72	#88205	—	2	4	no	—
73	#88205	—	4	2	no	—
74	#88202	—	2	4	no	—
75	#88202	—	4	2	no	—
76	C₂×#6107	—	2	2	no	—
77	C₂×#6107	—	2	2	no	—
78	C₂×#6105	—	2	2	no	—
79	C₂×#6105	—	2	2	no	—
80	C₂×#6099	—	2	4	no	—
81	C₂×#6099	C₂³	1	2	yes	—
82	C₂×#6099	C₂³	1	2	yes	—
83	C₂×#6099	C₂³	1	2	yes	—
84	C₂×Dic₅₂	—	2	1	no	—
85	C₂×Dic₅₂	—	2	1	no	—
86	C₂×Dic₅₂	—	2	1	no	—
87	C₂×Dic₅₂	—	2	1	no	—
88	C₂×Dic₅₂	—	2	1	no	—
89	C₂×Dic₅₂	—	2	1	no	—
90	C₁₃×#108	—	2	2	no	—
91	C₁₃×#104	—	2	2	no	—
92	C₁₃×#104	—	2	2	no	—
93	C₁₃×#97	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	#88076	—	2	2	no	—
96	#88073	—	2	2	no	—
97	#88064	—	2	4	no	—
98	#88064	—	2	4	no	—
99	#88064	—	2	4	no	—
100	#88062	—	2	4	no	—
101	#88059	—	2	1	no	—
102	#88059	—	2	1	no	—
103	#88059	—	2	1	no	—
104	#88059	—	2	1	no	—
105	#88059	—	2	4	no	—
106	#88059	D₄	1	2	yes	—
107	#88059	D₄	1	2	yes	—
108	#88050	—	4	2	no	—
109	#24810	—	13	1	no	maximal, Sylow
110	C₁₃×#41	—	2	1	no	—
111	C₁₃×#41	—	2	1	no	—
112	C₁₃×#41	—	2	1	no	—
113	C₁₃×#41	—	2	1	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	C₂×D₄	1	2	yes	—
117	C₁₃×#41	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂²×Dic₁₃	—	2	2	no	—
128	C₂×Dic₂₆	—	2	2	no	—
129	C₂×Dic₂₆	—	2	2	no	—
130	C₂×Dic₂₆	—	2	2	no	—
131	C₂×Dic₂₆	—	2	2	no	—
132	C₂×Dic₂₆	—	2	2	no	—
133	C₂×Dic₂₆	—	2	2	no	—
134	C₁₃×Q₁₆	—	2	2	no	—
135	C₁₃×SD₁₆	—	2	2	no	—
136	C₁₃×SD₁₆	—	2	2	no	—
137	C₁₃×D₈	—	2	2	no	—
138	C₁₃×M₁₆	—	2	1	no	—
139	C₁₃×M₁₆	—	2	1	no	—
140	C₁₃×M₁₆	—	2	2	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	1	no	—
143	C₁₃×M₁₆	—	2	1	no	—
144	C₁₃×M₁₆	—	4	1	no	—
145	C₁₃×M₁₆	—	4	1	no	—
146	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
147	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	4	1	no	—
154	C₂×C₈×C₁₃	—	4	1	no	—
155	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
160	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	#6107	—	4	4	no	—
165	#6107	—	4	4	no	—
166	#6105	—	4	4	no	—
167	#6105	—	4	4	no	—
168	#6099	—	2	2	no	—
169	#6099	—	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	—	2	2	no	—
178	C₂×#1055	—	4	4	no	—
179	Dic₅₂	—	4	1	no	—
180	Dic₅₂	—	4	1	no	—
181	Dic₅₂	—	4	1	no	—
182	Dic₅₂	—	4	1	no	—
183	#3069	—	13	2	no	—
184	C₂×#473	—	13	1	no	—
185	C₂×#473	—	13	1	no	—
186	#2955	D₁₃	1	1	yes	characteristic
187	#2916	—	13	1	no	—
188	#2070	—	13	2	no	—
189	#2049	—	13	2	no	—
190	#1979	—	13	1	no	—
191	#1953	—	13	1	no	—
192	#1902	—	13	2	no	—
193	#1813	—	13	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	2	1	no	—
200	Q₈×C₁₃	#121	1	2	yes	—
201	D₄×C₁₃	—	2	2	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	1	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	2	1	no	—
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	#121	1	2	yes	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×Dic₁₃	—	4	2	no	—
223	C₂×Dic₁₃	—	4	2	no	—
224	C₂×Dic₁₃	—	4	2	no	—
225	Dic₂₆	—	4	2	no	—
226	Dic₂₆	—	4	2	no	—
227	Dic₂₆	—	4	2	no	—
228	Dic₂₆	—	4	2	no	—
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	4	1	no	—
232	C₈×C₁₃	#121	1	1	yes	characteristic
233	C₈×C₁₃	#121	1	1	yes	characteristic
234	C₈×C₁₃	#121	1	1	yes	characteristic
235	C₈×C₁₃	#121	1	1	yes	characteristic
236	#1055	—	2	4	no	—
237	#1055	—	4	2	no	—
238	#1055	—	4	2	no	—
239	#575	C₂×D₁₃	1	1	yes	characteristic
240	C₂×#137	—	13	2	no	—
241	C₂×#137	—	13	2	no	—
242	C₂²×Q₁₆	—	13	1	no	—
243	#568	—	13	2	no	—
244	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
245	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
246	#473	—	26	2	no	—
247	#473	—	26	2	no	—
248	#473	—	26	4	no	—
249	#473	—	26	2	no	—
250	#473	—	26	2	no	—
251	#471	—	26	4	no	—
252	#444	—	2	2	no	—
253	#443	—	2	2	no	—
254	#430	—	13	2	no	—
255	#430	—	13	2	no	—
256	#430	—	26	2	no	—
257	#430	C₂×D₁₃	1	1	yes	characteristic
258	C₂×#108	—	13	1	no	—
259	C₂×#108	—	13	1	no	—
260	C₂×#108	—	13	1	no	—
261	C₂×#108	—	26	2	no	—
262	#421	C₂×D₁₃	1	1	yes	characteristic
263	#421	C₂×D₁₃	1	1	yes	characteristic
264	#419	—	13	2	no	—
265	#413	—	13	2	no	—
266	C₂×#101	—	13	2	no	—
267	C₂×#101	—	13	2	no	—
268	C₂×#101	—	13	2	no	—
269	#405	C₂×D₁₃	1	1	yes	characteristic
270	#344	—	13	2	no	—
271	#338	—	13	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	#537	1	1	yes	characteristic
278	C₂²×C₁₃	#547	1	1	yes	characteristic
279	C₂²×C₁₃	#548	1	1	yes	characteristic
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
284	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
285	C₄×C₁₃	D₄²	1	1	yes	characteristic
286	C₄×C₁₃	#553	1	1	yes	characteristic
287	Dic₁₃	—	8	2	no	—
288	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
289	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
290	C₂²×Q₈	—	13	2	no	—
291	#137	—	2	1	no	—
292	#137	—	26	4	no	—
293	#137	—	26	4	no	—
294	#137	—	26	4	no	—
295	#137	—	52	2	no	—
296	#137	D₅₂	1	2	yes	—
297	AGL(1,ℤ/8)	—	2	1	no	—
298	AGL(1,ℤ/8)	D₅₂	1	2	yes	—
299	#135	—	2	2	no	—
300	C₂×Q₁₆	—	26	2	no	—
301	C₂×Q₁₆	—	26	2	no	—
302	C₂×Q₁₆	—	26	1	no	—
303	C₂×Q₁₆	—	26	1	no	—
304	C₂×Q₁₆	—	26	1	no	—
305	C₂×Q₁₆	—	26	1	no	—
306	C₂×Q₁₆	—	26	1	no	—
307	C₂×Q₁₆	—	26	1	no	—
308	C₂×SD₁₆	—	26	2	no	—
309	C₂×SD₁₆	—	26	2	no	—
310	#131	—	2	1	no	—
311	#131	—	2	1	no	—
312	#131	—	2	1	no	—
313	#131	—	2	1	no	—
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	26	4	no	—
317	#131	—	52	2	no	—
318	#131	C₂²⋊D₁₃	1	2	yes	—
319	#131	C₂²⋊D₁₃	1	2	yes	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	13	2	no	—
323	C₂×M₁₆	—	13	2	no	—
324	C₂×M₁₆	—	13	2	no	—
325	C₂×M₁₆	—	26	4	no	—
326	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
327	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
328	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
332	#117	C₂²×D₁₃	1	1	yes	characteristic
333	#108	—	2	2	no	—
334	#108	—	13	2	no	—
335	#108	—	13	2	no	—
336	#108	—	26	4	no	—
337	#108	—	26	4	no	—
338	#108	—	26	1	no	—
339	#108	—	26	1	no	—
340	#108	—	26	1	no	—
341	#108	—	26	1	no	—
342	#104	—	2	2	no	—
343	#104	—	2	2	no	—
344	#103	—	52	2	no	—
345	#101	—	26	4	no	—
346	#101	—	26	2	no	—
347	#101	—	26	4	no	—
348	#101	—	26	4	no	—
349	#100	—	26	2	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂×C₁₃	—	2	1	no	—
353	C₂×C₁₃	—	2	1	no	—
354	C₂×C₁₃	—	2	1	no	—
355	C₂×C₁₃	—	4	2	no	—
356	C₂×C₁₃	—	8	1	no	—
357	C₂×C₁₃	#2416	1	1	yes	characteristic
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	—	2	1	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	C₂×D₅₂	1	2	yes	—
365	#41	C₂×C₂²⋊D₁₃	1	2	yes	—
366	C₂×Q₈	—	26	2	no	—
367	C₂×Q₈	—	26	2	no	—
368	C₂×Q₈	—	26	2	no	—
369	C₂×Q₈	—	26	2	no	—
370	C₂×Q₈	—	26	2	no	—
371	C₂×Q₈	—	26	2	no	—
372	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
373	C₂×Q₈	#6127	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
377	C₂×D₄	#6127	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	26	2	no	—
381	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
382	Q₁₆	—	2	2	no	—
383	Q₁₆	—	52	4	no	—
384	Q₁₆	—	52	4	no	—
385	Q₁₆	—	52	1	no	—
386	Q₁₆	—	52	1	no	—
387	Q₁₆	—	52	1	no	—
388	Q₁₆	—	52	1	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	52	4	no	—
392	SD₁₆	—	52	4	no	—
393	D₈	—	2	2	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	4	1	no	—
401	M₁₆	—	4	1	no	—
402	M₁₆	—	13	4	no	—
403	M₁₆	—	26	2	no	—
404	M₁₆	—	26	2	no	—
405	M₁₆	—	26	2	no	—
406	M₁₆	—	26	2	no	—
407	M₁₆	—	26	2	no	—
408	M₁₆	—	52	4	no	—
409	M₁₆	C₂×D₅₂	1	2	yes	—
410	M₁₆	C₂×C₂²⋊D₁₃	1	2	yes	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	4	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	26	2	no	—
419	C₂×C₈	—	26	2	no	—
420	C₂×C₈	—	26	2	no	—
421	C₂×C₈	—	52	4	no	—
422	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
423	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
424	C₂×C₈	#6129	1	1	yes	characteristic
425	C₂×C₈	#6129	1	1	yes	characteristic
426	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₁₃	#24810	1	1	yes	characteristic, complemented, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	#88257	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	—	52	2	no	—
439	Q₈	—	52	2	no	—
440	Q₈	—	52	2	no	—
441	Q₈	—	52	2	no	—
442	Q₈	#88184	1	2	yes	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	#88184	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	52	2	no	—
459	C₂×C₄	—	52	2	no	—
460	C₂×C₄	—	52	2	no	—
461	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
462	C₂×C₄	C₂×#6127	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#6129	1	1	yes	characteristic
465	C₂×C₄	#88256	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	1	no	—
470	C₈	—	26	4	no	—
471	C₈	—	52	2	no	—
472	C₈	—	52	2	no	—
473	C₈	#88193	1	1	yes	characteristic
474	C₈	#88193	1	1	yes	characteristic
475	C₈	#88193	1	1	yes	characteristic
476	C₈	#88193	1	1	yes	characteristic
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	#11719257	1	1	yes	characteristic
483	C₂²	#11719260	1	1	yes	characteristic
484	C₂²	#11719538	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	104	2	no	—
489	C₄	D₄×D₅₂	1	1	yes	characteristic
490	C₄	#11719270	1	1	yes	characteristic
491	C₄	C₂×#88184	1	1	yes	characteristic
492	C₄	C₂×#88193	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	#13118276	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13118276
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2955	C₂
socle	C₂×C₁₃	#2416
prime radical	C₁₃×#575	C₂²
hypercenter	#2955	D₁₃
hypocenter	C₁₃	#24810
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2955

Complements

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

N	H ≅ G/N	type
2. C₂×#11718804	C₂	semidirect
3. C₂×#11718804	C₂	semidirect
4. #13123447	C₂	semidirect
5. #13116236	C₂	semidirect
6. #13116117	C₂	semidirect
7. #13115751	C₂	semidirect
8. #13115626	C₂	semidirect
9. #13115307	C₂	semidirect
10. #13114886	C₂	semidirect
431. C₁₃	#24810	semidirect

Maximal subgroups

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

subgroup	index
#13124575	2
C₂×#11718804	2
#13123447	2
#13116236	2
#13116117	2
#13115751	2
#13115626	2
#13115307	2
#13114886	2
C₁₃×#2955	2
#24810	13