Subgroups — #15869869

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124556	C₂	1	1	yes	maximal, characteristic
2	#13123737	C₂	1	2	yes	maximal, complemented
3	C₂×#11718378	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115734	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115626	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115505	C₂	1	2	yes	maximal, complemented
7	#13115337	C₂	1	2	yes	maximal, complemented
8	#13114890	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114720	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114637	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	#11719527	C₂²	1	2	yes	—
16	C₂×#88158	C₂²	1	1	yes	characteristic
17	C₂×#88155	C₂²	1	2	yes	—
18	C₁₃×#405	—	2	1	no	—
19	C₁₃×#405	—	2	1	no	—
20	C₁₃×#405	C₂²	1	1	yes	characteristic
21	C₁₃×#405	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×M₁₆	—	2	1	no	—
23	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#97	—	2	1	no	—
25	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
26	#11718897	C₂²	1	2	yes	—
27	#11718806	—	2	4	no	—
28	#11718805	—	2	4	no	—
29	#11718804	C₄	1	2	yes	complemented
30	#11718803	C₄	1	2	yes	complemented
31	#11718802	C₄	1	4	yes	complemented
32	#11718800	C₂²	1	2	yes	—
33	#11718793	C₂²	1	2	yes	—
34	#11718785	C₂²	1	2	yes	—
35	C₂×#88059	C₂²	1	1	yes	characteristic
36	C₂×#88059	C₂²	1	1	yes	characteristic
37	#11718767	C₂²	1	1	yes	characteristic
38	#11718762	C₂²	1	2	yes	—
39	#11718667	C₂²	1	2	yes	—
40	C₂×#88045	C₂²	1	2	yes	—
41	#11718378	—	2	1	no	—
42	#11718378	—	2	1	no	—
43	#11718378	—	2	1	no	—
44	#11718378	—	2	1	no	—
45	#11718151	C₂²	1	2	yes	—
46	#11718125	C₂²	1	2	yes	—
47	#11718115	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂×#6127	C₂³	1	2	yes	—
50	C₁₃×#131	—	2	1	no	—
51	C₁₃×#131	—	2	1	no	—
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	C₂×C₄	1	2	yes	—
54	C₁₃×#131	C₂×C₄	1	2	yes	—
55	C₁₃×#131	D₄	1	4	yes	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	#88205	C₂×C₄	1	4	yes	—
72	#88204	—	2	4	no	—
73	#88203	C₂×C₄	1	4	yes	—
74	#88196	—	2	2	no	—
75	#88186	—	2	2	no	—
76	#88180	C₂³	1	2	yes	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂×#6099	C₂³	1	2	yes	—
79	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
80	#88158	—	2	1	no	—
81	#88158	—	2	1	no	—
82	#88158	—	2	1	no	—
83	#88158	—	2	1	no	—
84	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂×#6095	C₂×C₄	1	2	yes	complemented
86	#88155	—	2	2	no	—
87	#88155	—	2	2	no	—
88	#88155	—	2	2	no	—
89	#88155	—	2	2	no	—
90	C₂×#6094	—	2	2	no	—
91	C₂×C₈×D₁₃	—	2	2	no	—
92	C₁₃×#97	—	2	1	no	—
93	C₁₃×#97	—	2	1	no	—
94	C₁₃×#97	—	2	1	no	—
95	C₁₃×#97	D₄	1	1	yes	characteristic
96	C₁₃×#97	D₄	1	1	yes	characteristic
97	C₁₃×#97	D₄	1	1	yes	characteristic
98	C₁₃×#97	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃	—	2	1	no	—
100	C₄×C₈×C₁₃	—	2	1	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	#88077	—	2	4	no	—
103	#88065	—	2	4	no	—
104	#88064	C₂×C₄	1	4	yes	complemented
105	#88063	C₂×C₄	1	4	yes	complemented
106	#88062	—	2	4	no	—
107	#88059	—	2	1	no	—
108	#88059	—	2	1	no	—
109	#88059	C₂×C₄	1	2	yes	complemented
110	#88059	C₂×C₄	1	2	yes	complemented
111	#88058	—	2	1	no	—
112	#88057	—	2	1	no	—
113	#88055	—	2	2	no	—
114	C₈×Dic₁₃	—	2	2	no	—
115	#88046	—	2	4	no	—
116	#88045	—	2	2	no	—
117	#88045	—	2	2	no	—
118	#21559	—	13	1	no	maximal, Sylow
119	C₁₃×#41	—	2	1	no	—
120	C₁₃×#41	—	2	1	no	—
121	C₁₃×#41	C₂²×C₄	1	2	yes	—
122	C₁₃×#41	C₂×D₄	1	2	yes	—
123	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	C₂×D₅₂	C₂²×C₄	1	2	yes	—
136	C₂×C₄×D₁₃	—	2	2	no	—
137	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
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	4	no	—
143	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
144	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	4	no	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
158	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
159	C₂×C₈×C₁₃	#41	1	2	yes	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₁₃×C₂²⋊C₄	#41	1	2	yes	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²⋊Dic₁₃	—	2	2	no	—
170	#6107	—	2	4	no	—
171	#6106	—	2	4	no	—
172	#6105	—	2	4	no	—
173	#6104	—	2	4	no	—
174	C₄⋊Dic₁₃	—	2	2	no	—
175	C₄×Dic₁₃	—	2	2	no	—
176	#6099	—	2	2	no	—
177	#6099	—	2	2	no	—
178	#6099	—	2	2	no	—
179	#6099	C₂²×C₄	1	4	yes	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	Dic₅₂	—	2	1	no	—
183	Dic₅₂	—	2	1	no	—
184	D₁₀₄	—	2	1	no	—
185	D₁₀₄	—	2	1	no	—
186	#6095	—	2	2	no	—
187	#6095	—	2	2	no	—
188	#6094	—	4	2	no	—
189	#6094	—	4	2	no	—
190	C₈×D₁₃	—	4	2	no	—
191	C₈×D₁₃	—	4	2	no	—
192	#3067	—	13	1	no	—
193	#2955	—	13	2	no	—
194	C₂×#444	—	13	1	no	—
195	#2875	D₁₃	1	1	yes	characteristic, complemented
196	#1976	—	13	1	no	—
197	#1953	—	13	1	no	—
198	#1932	—	13	2	no	—
199	#1906	—	13	2	no	—
200	#1814	—	13	1	no	—
201	#1773	—	13	1	no	—
202	#1757	—	13	2	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂²×D₁₃	—	2	2	no	—
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	C₄×D₄	1	2	yes	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	8	1	no	—
219	C₂×C₄×C₁₃	—	8	2	no	—
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	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂²⋊D₁₃	—	4	2	no	—
227	C₂²⋊D₁₃	—	4	2	no	—
228	C₂×Dic₁₃	—	2	2	no	—
229	C₂×Dic₁₃	—	4	2	no	—
230	D₅₂	—	2	2	no	—
231	D₅₂	—	2	2	no	—
232	C₄×D₁₃	—	4	2	no	—
233	C₄×D₁₃	—	4	2	no	—
234	Dic₂₆	—	2	2	no	—
235	Dic₂₆	—	2	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
241	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
242	C₈×C₁₃	#121	1	2	yes	—
243	C₈×C₁₃	#121	1	2	yes	—
244	#1055	—	2	4	no	—
245	#1055	—	4	2	no	—
246	#575	—	13	2	no	—
247	C₂×#135	—	13	1	no	—
248	C₂×#131	—	13	2	no	—
249	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
250	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
251	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
252	#473	—	13	2	no	—
253	#472	—	13	2	no	—
254	#471	—	13	4	no	—
255	#444	—	26	4	no	—
256	#444	—	26	1	no	—
257	#444	—	26	1	no	—
258	#444	—	26	1	no	—
259	#444	—	26	1	no	—
260	#443	—	26	4	no	—
261	#430	—	13	2	no	—
262	C₂×#108	—	13	1	no	—
263	C₂×#108	—	13	1	no	—
264	#427	—	13	1	no	—
265	#421	—	13	2	no	—
266	#421	—	13	2	no	—
267	C₂×#104	—	13	2	no	—
268	#413	—	13	2	no	—
269	#410	—	13	2	no	—
270	#405	—	2	1	no	—
271	#405	—	2	1	no	—
272	#405	—	13	2	no	—
273	#405	C₂×D₁₃	1	1	yes	characteristic
274	#405	C₂×D₁₃	1	1	yes	characteristic
275	C₄×M₁₆	—	2	1	no	—
276	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
277	C₂×#97	—	2	1	no	—
278	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
279	#344	—	13	2	no	—
280	#344	—	13	2	no	—
281	#339	—	13	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
286	C₂²×C₁₃	#525	1	1	yes	characteristic
287	C₂²×C₁₃	#532	1	1	yes	characteristic
288	C₂×D₁₃	—	4	2	no	—
289	C₂×D₁₃	—	8	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
296	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
297	C₄×C₁₃	#529	1	1	yes	characteristic
298	Dic₁₃	—	4	2	no	—
299	Dic₁₃	—	8	2	no	—
300	C₂×#41	—	13	2	no	—
301	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
302	#137	—	13	4	no	—
303	#137	—	26	2	no	—
304	AGL(1,ℤ/8)	—	13	4	no	—
305	AGL(1,ℤ/8)	—	26	2	no	—
306	#135	—	26	4	no	—
307	#135	—	26	1	no	—
308	#135	—	26	1	no	—
309	#135	—	26	1	no	—
310	#135	—	26	1	no	—
311	C₂×Q₁₆	—	13	1	no	—
312	C₂×SD₁₆	—	13	2	no	—
313	C₂×D₈	—	13	1	no	—
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	2	2	no	—
317	#131	—	26	2	no	—
318	#131	—	26	2	no	—
319	#131	—	26	2	no	—
320	#131	—	26	2	no	—
321	#131	C₄×D₁₃	1	2	yes	—
322	#131	C₄×D₁₃	1	2	yes	—
323	#131	D₅₂	1	4	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	—	26	2	no	—
329	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
330	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	26	2	no	—
334	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
336	C₄×Q₈	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	2	no	—
339	#117	—	2	1	no	—
340	#117	—	13	2	no	—
341	#117	C₂²×D₁₃	1	1	yes	characteristic
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
344	#108	—	13	2	no	—
345	#108	—	13	2	no	—
346	#108	—	26	4	no	—
347	#108	—	26	1	no	—
348	#108	—	26	1	no	—
349	#107	—	26	1	no	—
350	#106	—	26	1	no	—
351	#104	—	26	4	no	—
352	#104	—	26	4	no	—
353	#104	—	26	2	no	—
354	#104	—	26	2	no	—
355	#101	—	13	4	no	—
356	#100	—	13	4	no	—
357	#99	—	26	4	no	—
358	#97	—	2	1	no	—
359	#97	—	2	1	no	—
360	#97	—	2	1	no	—
361	#97	—	26	2	no	—
362	#97	C₂²⋊D₁₃	1	1	yes	characteristic
363	#97	C₂²⋊D₁₃	1	1	yes	characteristic
364	#97	C₂²⋊D₁₃	1	1	yes	characteristic
365	#97	C₂²⋊D₁₃	1	1	yes	characteristic
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	2	1	no	—
369	C₄×C₈	—	26	2	no	—
370	C₂×C₁₃	—	2	1	no	—
371	C₂×C₁₃	—	2	1	no	—
372	C₂×C₁₃	—	2	1	no	—
373	C₂×C₁₃	—	4	2	no	—
374	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
375	D₁₃	—	8	2	no	—
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	26	2	no	—
379	#41	—	26	2	no	—
380	#41	—	26	2	no	—
381	#41	—	26	2	no	—
382	#41	C₂×C₄×D₁₃	1	2	yes	—
383	#41	C₂×D₅₂	1	2	yes	—
384	C₂×Q₈	—	13	2	no	—
385	C₂×Q₈	#6127	1	1	yes	characteristic
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	13	2	no	—
388	C₂×D₄	—	26	2	no	—
389	C₂×D₄	#6127	1	1	yes	characteristic
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	26	2	no	—
394	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
395	Q₁₆	—	26	4	no	—
396	Q₁₆	—	26	1	no	—
397	Q₁₆	—	26	1	no	—
398	SD₁₆	—	26	4	no	—
399	SD₁₆	—	26	4	no	—
400	SD₁₆	—	26	2	no	—
401	SD₁₆	—	26	2	no	—
402	D₈	—	26	4	no	—
403	D₈	—	26	1	no	—
404	D₈	—	26	1	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	13	4	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	—	26	2	no	—
413	M₁₆	—	26	2	no	—
414	M₁₆	—	52	2	no	—
415	M₁₆	—	52	2	no	—
416	M₁₆	C₂×C₄×D₁₃	1	2	yes	—
417	M₁₆	C₂×D₅₂	1	2	yes	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	4	no	—
423	C₂×C₈	—	26	2	no	—
424	C₂×C₈	—	26	2	no	—
425	C₂×C₈	—	52	2	no	—
426	C₂×C₈	—	52	2	no	—
427	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
428	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂×D₅₂	1	2	yes	—
430	C₂×C₈	#6127	1	1	yes	characteristic
431	C₂×C₈	#6127	1	1	yes	characteristic
432	C₂×C₈	#6127	1	2	yes	—
433	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
434	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	26	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	26	2	no	—
442	C₂²⋊C₄	#6127	1	2	yes	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	26	2	no	—
447	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
449	C₁₃	#21559	1	1	yes	characteristic, complemented, Sylow
450	C₂³	—	2	1	no	—
451	C₂³	—	26	2	no	—
452	C₂³	C₂×#6127	1	1	yes	characteristic
453	Q₈	—	2	1	no	—
454	Q₈	—	26	2	no	—
455	Q₈	—	26	2	no	—
456	Q₈	C₄×D₅₂	1	2	yes	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	1	no	—
460	D₄	—	26	2	no	—
461	D₄	—	26	2	no	—
462	D₄	—	52	2	no	—
463	D₄	—	52	2	no	—
464	D₄	C₄×D₅₂	1	2	yes	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	26	2	no	—
474	C₂×C₄	—	52	2	no	—
475	C₂×C₄	—	52	2	no	—
476	C₂×C₄	—	52	2	no	—
477	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
479	C₂×C₄	C₂×#6127	1	1	yes	characteristic
480	C₂×C₄	C₂×#6127	1	1	yes	characteristic
481	C₂×C₄	C₂×#6127	1	1	yes	characteristic
482	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	26	4	no	—
486	C₈	—	52	2	no	—
487	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
488	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
490	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
491	C₈	#88184	1	2	yes	—
492	C₈	#88184	1	2	yes	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	52	2	no	—
497	C₂²	—	104	2	no	—
498	C₂²	C₄×#6127	1	1	yes	characteristic
499	C₂²	#11719182	1	1	yes	characteristic
500	C₂²	#11719496	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	52	2	no	—
506	C₄	—	104	2	no	—
507	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
508	C₄	#11719184	1	1	yes	characteristic
509	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
510	C₄	C₂×#88184	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	2	no	—
515	C₂	—	104	2	no	—
516	C₂	C₄×#88184	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#88184
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2875	C₂
socle	C₂×C₁₃	C₄×#121
prime radical	#13124556	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2875	D₁₃
hypocenter	C₁₃	#21559
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #13123737	C₂	semidirect
3. C₂×#11718378	C₂	semidirect
4. #13115734	C₂	semidirect
5. #13115626	C₂	semidirect
6. #13115505	C₂	semidirect
7. #13115337	C₂	semidirect
8. #13114890	C₂	semidirect
9. #13114720	C₂	semidirect
10. #13114637	C₂	semidirect
11. C₁₃×#2875	C₂	semidirect
29. #11718804	C₄	semidirect
30. #11718803	C₄	semidirect
31. #11718802	C₄	semidirect
79. C₂×Dic₅₂	C₂×C₄	semidirect
84. C₂×D₁₀₄	C₂×C₄	semidirect
85. C₂×#6095	C₂×C₄	semidirect
104. #88064	C₂×C₄	semidirect
105. #88063	C₂×C₄	semidirect
109. #88059	C₂×C₄	semidirect
110. #88059	C₂×C₄	semidirect
195. #2875	D₁₃	semidirect
449. C₁₃	#21559	semidirect

Maximal subgroups

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

subgroup	index
#13124556	2
#13123737	2
C₂×#11718378	2
#13115734	2
#13115626	2
#13115505	2
#13115337	2
#13114890	2
#13114720	2
#13114637	2
C₁₃×#2875	2
#21559	13