Subgroups — #15905519

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124566	C₂	1	2	yes	maximal, complemented
2	C₂×#11718803	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718803	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123447	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116233	C₂	1	2	yes	maximal, complemented
6	#13116110	C₂	1	2	yes	maximal, complemented
7	#13115746	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115626	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115314	C₂	1	2	yes	maximal, complemented
10	#13114886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
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×#88203	C₂²	1	2	yes	—
16	C₂×#88203	C₂²	1	2	yes	—
17	#11719524	C₂²	1	2	yes	—
18	C₂²×D₁₀₄	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	#11718864	—	2	4	no	—
27	#11718860	—	2	4	no	—
28	#11718803	—	2	2	no	—
29	#11718803	—	2	2	no	—
30	#11718803	—	2	2	no	—
31	#11718803	—	2	2	no	—
32	C₂×#88063	C₂²	1	2	yes	—
33	C₂×#88063	C₂²	1	2	yes	—
34	C₂×#88063	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	#11718662	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×D₅₂	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	#88203	—	2	4	no	—
71	#88203	—	2	4	no	—
72	#88203	—	2	4	no	—
73	#88203	—	4	2	no	—
74	#88202	—	2	4	no	—
75	#88202	—	4	2	no	—
76	C₂×#6106	—	2	2	no	—
77	C₂×#6106	—	2	2	no	—
78	C₂×#6104	—	2	2	no	—
79	C₂×#6104	—	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×D₁₀₄	—	2	1	no	—
85	C₂×D₁₀₄	—	2	1	no	—
86	C₂×D₁₀₄	—	2	1	no	—
87	C₂×D₁₀₄	—	2	1	no	—
88	C₂×D₁₀₄	—	2	1	no	—
89	C₂×D₁₀₄	—	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	#88063	—	2	4	no	—
98	#88063	—	2	4	no	—
99	#88063	—	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	#88049	—	4	2	no	—
109	#24809	—	13	1	no	maximal, Sylow
110	C₂³×D₁₃	—	2	2	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	—	2	1	no	—
117	C₁₃×#41	C₂×D₄	1	2	yes	—
118	C₁₃×#41	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	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	#6106	—	4	4	no	—
165	#6106	—	4	4	no	—
166	#6104	—	4	4	no	—
167	#6104	—	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	D₁₀₄	—	4	1	no	—
180	D₁₀₄	—	4	1	no	—
181	D₁₀₄	—	4	1	no	—
182	D₁₀₄	—	4	1	no	—
183	#3068	—	13	2	no	—
184	C₂×#472	—	13	1	no	—
185	C₂×#472	—	13	1	no	—
186	#2955	D₁₃	1	1	yes	characteristic, complemented
187	#2916	—	13	1	no	—
188	#2069	—	13	2	no	—
189	#2048	—	13	2	no	—
190	#1978	—	13	1	no	—
191	#1953	—	13	1	no	—
192	#1903	—	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	C₂²×D₁₃	—	4	2	no	—
198	C₂²×D₁₃	—	4	2	no	—
199	C₂²×D₁₃	—	4	2	no	—
200	C₂²×D₁₃	—	16	2	no	—
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	2	1	no	—
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	#121	1	2	yes	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	#121	1	2	yes	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
226	D₅₂	—	4	2	no	—
227	D₅₂	—	4	2	no	—
228	D₅₂	—	4	2	no	—
229	D₅₂	—	4	2	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	4	1	no	—
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	C₈×C₁₃	#121	1	1	yes	characteristic
237	#1055	—	2	4	no	—
238	#1055	—	4	2	no	—
239	#1055	—	4	2	no	—
240	#575	C₂×D₁₃	1	1	yes	characteristic
241	C₂×AGL(1,ℤ/8)	—	13	2	no	—
242	C₂×AGL(1,ℤ/8)	—	13	2	no	—
243	C₂²×D₈	—	13	1	no	—
244	#568	—	13	2	no	—
245	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
246	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
247	#472	—	26	2	no	—
248	#472	—	26	2	no	—
249	#472	—	26	4	no	—
250	#472	—	26	2	no	—
251	#472	—	26	2	no	—
252	#471	—	26	4	no	—
253	#444	—	2	2	no	—
254	#443	—	2	2	no	—
255	#430	—	13	2	no	—
256	#430	—	13	2	no	—
257	#430	—	26	2	no	—
258	#430	C₂×D₁₃	1	1	yes	characteristic
259	C₂×#108	—	13	1	no	—
260	C₂×#108	—	13	1	no	—
261	C₂×#108	—	13	1	no	—
262	C₂×#108	—	26	2	no	—
263	#421	C₂×D₁₃	1	1	yes	characteristic
264	#421	C₂×D₁₃	1	1	yes	characteristic
265	#418	—	13	2	no	—
266	#413	—	13	2	no	—
267	C₂×#100	—	13	2	no	—
268	C₂×#100	—	13	2	no	—
269	C₂×#100	—	13	2	no	—
270	#405	C₂×D₁₃	1	1	yes	characteristic
271	#344	—	13	2	no	—
272	#338	—	13	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	#537	1	1	yes	characteristic
279	C₂²×C₁₃	#547	1	1	yes	characteristic
280	C₂²×C₁₃	#548	1	1	yes	characteristic
281	C₂×D₁₃	—	8	2	no	—
282	C₂×D₁₃	—	16	2	no	—
283	C₂×D₁₃	—	16	2	no	—
284	C₂×D₁₃	—	16	2	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	8	1	no	—
288	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
289	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
290	C₄×C₁₃	D₄²	1	1	yes	characteristic
291	C₄×C₁₃	#553	1	1	yes	characteristic
292	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
293	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
294	C₂²×D₄	—	13	2	no	—
295	#137	—	2	1	no	—
296	#137	D₅₂	1	2	yes	—
297	AGL(1,ℤ/8)	—	2	1	no	—
298	AGL(1,ℤ/8)	—	26	4	no	—
299	AGL(1,ℤ/8)	—	26	4	no	—
300	AGL(1,ℤ/8)	—	26	4	no	—
301	AGL(1,ℤ/8)	—	52	2	no	—
302	AGL(1,ℤ/8)	D₅₂	1	2	yes	—
303	#135	—	2	2	no	—
304	C₂×SD₁₆	—	26	2	no	—
305	C₂×SD₁₆	—	26	2	no	—
306	C₂×D₈	—	26	2	no	—
307	C₂×D₈	—	26	2	no	—
308	C₂×D₈	—	26	1	no	—
309	C₂×D₈	—	26	1	no	—
310	C₂×D₈	—	26	1	no	—
311	C₂×D₈	—	26	1	no	—
312	C₂×D₈	—	26	1	no	—
313	C₂×D₈	—	26	1	no	—
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	2	1	no	—
317	#131	—	2	1	no	—
318	#131	—	2	1	no	—
319	#131	—	2	1	no	—
320	#131	—	26	4	no	—
321	#131	—	52	2	no	—
322	#131	C₂²⋊D₁₃	1	2	yes	—
323	#131	C₂²⋊D₁₃	1	2	yes	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂×M₁₆	—	13	2	no	—
328	C₂×M₁₆	—	13	2	no	—
329	C₂×M₁₆	—	26	4	no	—
330	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
331	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
336	#117	C₂²×D₁₃	1	1	yes	characteristic
337	#108	—	2	2	no	—
338	#108	—	13	2	no	—
339	#108	—	13	2	no	—
340	#108	—	26	4	no	—
341	#108	—	26	4	no	—
342	#108	—	26	1	no	—
343	#108	—	26	1	no	—
344	#108	—	26	1	no	—
345	#108	—	26	1	no	—
346	#104	—	2	2	no	—
347	#104	—	2	2	no	—
348	#102	—	52	2	no	—
349	#101	—	26	2	no	—
350	#100	—	26	4	no	—
351	#100	—	26	2	no	—
352	#100	—	26	4	no	—
353	#100	—	26	4	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	—	2	1	no	—
358	C₂×C₁₃	—	2	1	no	—
359	C₂×C₁₃	—	4	2	no	—
360	C₂×C₁₃	—	8	1	no	—
361	C₂×C₁₃	#2416	1	1	yes	characteristic
362	D₁₃	—	16	2	no	—
363	C₂⁴	—	26	2	no	—
364	#41	—	2	1	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	C₂×D₅₂	1	2	yes	—
371	#41	C₂×C₂²⋊D₁₃	1	2	yes	—
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	—	26	2	no	—
377	C₂×D₄	—	26	2	no	—
378	C₂×D₄	—	26	2	no	—
379	C₂×D₄	—	26	2	no	—
380	C₂×D₄	—	26	2	no	—
381	C₂×D₄	—	26	2	no	—
382	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
383	C₂×D₄	#6127	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
387	Q₁₆	—	2	2	no	—
388	SD₁₆	—	2	2	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	52	4	no	—
391	SD₁₆	—	52	4	no	—
392	D₈	—	2	2	no	—
393	D₈	—	52	4	no	—
394	D₈	—	52	4	no	—
395	D₈	—	52	1	no	—
396	D₈	—	52	1	no	—
397	D₈	—	52	1	no	—
398	D₈	—	52	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	4	1	no	—
406	M₁₆	—	4	1	no	—
407	M₁₆	—	13	4	no	—
408	M₁₆	—	26	2	no	—
409	M₁₆	—	26	2	no	—
410	M₁₆	—	26	2	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	—	26	2	no	—
413	M₁₆	—	52	4	no	—
414	M₁₆	C₂×D₅₂	1	2	yes	—
415	M₁₆	C₂×C₂²⋊D₁₃	1	2	yes	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	—	26	2	no	—
424	C₂×C₈	—	26	2	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	—	52	4	no	—
427	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
428	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₈	#6129	1	1	yes	characteristic
430	C₂×C₈	#6129	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
433	C₄⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₁₃	#24809	1	1	yes	characteristic, complemented, Sylow
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	52	2	no	—
440	C₂³	—	52	2	no	—
441	C₂³	—	52	2	no	—
442	C₂³	—	208	2	no	—
443	C₂³	#88257	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	Q₈	#88184	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	2	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	52	2	no	—
456	D₄	—	52	2	no	—
457	D₄	—	52	2	no	—
458	D₄	—	52	2	no	—
459	D₄	#88184	1	2	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
468	C₂×C₄	C₂×#6127	1	1	yes	characteristic
469	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×#6129	1	1	yes	characteristic
471	C₂×C₄	#88256	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	26	4	no	—
477	C₈	—	52	2	no	—
478	C₈	—	52	2	no	—
479	C₈	#88193	1	1	yes	characteristic
480	C₈	#88193	1	1	yes	characteristic
481	C₈	#88193	1	1	yes	characteristic
482	C₈	#88193	1	1	yes	characteristic
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	104	2	no	—
489	C₂²	—	208	2	no	—
490	C₂²	—	208	2	no	—
491	C₂²	—	208	2	no	—
492	C₂²	#11719257	1	1	yes	characteristic
493	C₂²	#11719260	1	1	yes	characteristic
494	C₂²	#11719538	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	1	no	—
498	C₄	D₄×D₅₂	1	1	yes	characteristic
499	C₄	#11719270	1	1	yes	characteristic
500	C₄	C₂×#88184	1	1	yes	characteristic
501	C₄	C₂×#88193	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	4	2	no	—
506	C₂	—	8	1	no	—
507	C₂	—	208	2	no	—
508	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
hypercenter	#2955	D₁₃
hypocenter	C₁₃	#24809
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
1. #13124566	C₂	semidirect
2. C₂×#11718803	C₂	semidirect
3. C₂×#11718803	C₂	semidirect
4. #13123447	C₂	semidirect
5. #13116233	C₂	semidirect
6. #13116110	C₂	semidirect
7. #13115746	C₂	semidirect
8. #13115626	C₂	semidirect
9. #13115314	C₂	semidirect
10. #13114886	C₂	semidirect
11. C₁₃×#2955	C₂	semidirect
186. #2955	D₁₃	semidirect
436. C₁₃	#24809	semidirect

Maximal subgroups

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

subgroup	index
#13124566	2
C₂×#11718803	2
#13123447	2
#13116233	2
#13116110	2
#13115746	2
#13115626	2
#13115314	2
#13114886	2
C₁₃×#2955	2
#24809	13