Subgroups — #15869821

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718803	C₂	1	1	yes	maximal, characteristic
2	C₄×#88203	C₂	1	2	yes	maximal, complemented
3	C₂×#11718372	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115746	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115616	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115498	C₂	1	2	yes	maximal, complemented
7	#13115344	C₂	1	2	yes	maximal, complemented
8	#13114895	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114742	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88063	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	C₂×#88203	C₂²	1	2	yes	—
16	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅₂	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	#11718893	C₂²	1	2	yes	—
27	#11718803	C₄	1	8	yes	complemented
28	C₂×#88063	C₂²	1	2	yes	—
29	C₂×#88063	C₂²	1	2	yes	—
30	C₂×#88061	C₂²	1	2	yes	—
31	C₂×#88059	C₂²	1	1	yes	characteristic
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	C₂×#88057	C₂²	1	1	yes	characteristic
34	#11718687	—	2	2	no	—
35	C₄×#6106	—	2	2	no	—
36	#11718675	—	2	2	no	—
37	C₄×#6104	—	2	2	no	—
38	#11718662	C₂²	1	2	yes	—
39	#11718656	C₂²	1	2	yes	—
40	C₄×#6099	C₂²	1	2	yes	—
41	#11718372	—	2	1	no	—
42	#11718372	—	2	1	no	—
43	#11718372	—	2	1	no	—
44	#11718372	—	2	1	no	—
45	#11718146	C₂²	1	2	yes	—
46	#11718146	C₂²	1	2	yes	—
47	#11718144	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂²×D₅₂	C₂³	1	2	yes	—
50	C₂²×C₄×D₁₃	—	2	2	no	—
51	C₁₃×#131	—	2	2	no	—
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	—	2	2	no	—
54	C₁₃×#131	C₂×C₄	1	4	yes	complemented
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₁₃	D₄	1	2	yes	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	D₄	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	#88203	—	2	4	no	—
71	#88203	C₂×C₄	1	8	yes	complemented
72	C₂×#6106	—	2	2	no	—
73	C₂×#6104	—	2	2	no	—
74	C₂×#6103	—	2	2	no	—
75	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
76	C₂×#6099	C₂³	1	2	yes	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂×D₁₀₄	—	2	1	no	—
79	C₂×D₁₀₄	—	2	1	no	—
80	C₂×D₁₀₄	—	2	2	no	—
81	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
82	C₄×D₅₂	—	2	2	no	—
83	C₄×D₅₂	—	2	2	no	—
84	C₄×D₅₂	—	2	2	no	—
85	C₄×D₅₂	—	2	2	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₁₃×#97	—	2	1	no	—
88	C₁₃×#97	—	2	1	no	—
89	C₁₃×#97	D₄	1	1	yes	characteristic
90	C₁₃×#97	D₄	1	1	yes	characteristic
91	C₁₃×#97	D₄	1	1	yes	characteristic
92	C₁₃×#97	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	#88075	—	2	2	no	—
97	#88072	—	2	2	no	—
98	#88063	—	2	4	no	—
99	#88063	C₂×C₄	1	8	yes	complemented
100	#88061	—	2	2	no	—
101	#88061	—	2	2	no	—
102	#88059	—	2	2	no	—
103	#88059	C₂×C₄	1	4	yes	complemented
104	#88057	—	2	1	no	—
105	#88057	—	2	1	no	—
106	#88049	—	2	2	no	—
107	#88049	—	2	2	no	—
108	#88048	—	2	2	no	—
109	#88047	—	2	2	no	—
110	#88043	—	2	2	no	—
111	C₄×#1055	—	2	2	no	—
112	#21555	—	13	1	no	maximal, Sylow
113	C₂³×D₁₃	—	2	2	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	C₂²×C₄	1	2	yes	—
117	C₁₃×#41	#41	1	2	yes	—
118	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	#41	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₁₃	—	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	C₂²×C₄	1	4	yes	—
132	C₂×C₄×D₁₃	—	4	2	no	—
133	C₂×C₄×D₁₃	—	4	2	no	—
134	C₂×C₄×D₁₃	—	8	4	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	—	2	1	no	—
137	C₁₃×M₁₆	—	2	1	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
140	C₁₃×M₁₆	#41	1	2	yes	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂×D₄	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	#41	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
162	#6106	—	2	8	no	—
163	#6104	—	2	8	no	—
164	#6103	—	4	2	no	—
165	#6103	—	4	2	no	—
166	C₄⋊Dic₁₃	—	2	2	no	—
167	C₄⋊Dic₁₃	—	2	2	no	—
168	#6099	—	2	2	no	—
169	#6099	—	2	2	no	—
170	#6099	—	2	2	no	—
171	#6099	C₂²×C₄	1	4	yes	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	2	2	no	—
174	D₁₀₄	—	2	4	no	—
175	D₁₀₄	—	2	4	no	—
176	C₂×#472	—	13	1	no	—
177	C₄×AGL(1,ℤ/8)	—	13	2	no	—
178	C₂×#442	—	13	1	no	—
179	#2875	D₁₃	1	1	yes	characteristic, complemented
180	#1978	—	13	1	no	—
181	#1951	—	13	1	no	—
182	#1931	—	13	2	no	—
183	#1907	—	13	2	no	—
184	#1815	—	13	1	no	—
185	#1778	—	13	1	no	—
186	C₄×#100	—	13	2	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂²×D₁₃	—	2	4	no	—
190	C₂²×D₁₃	—	4	2	no	—
191	C₂²×D₁₃	—	4	2	no	—
192	C₂²×D₁₃	—	8	2	no	—
193	C₂²×D₁₃	—	8	2	no	—
194	Q₈×C₁₃	—	2	1	no	—
195	Q₈×C₁₃	C₄×D₄	1	2	yes	—
196	D₄×C₁₃	—	2	2	no	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	2	1	no	—
199	D₄×C₁₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	8	2	no	—
206	C₂×C₄×C₁₃	#121	1	2	yes	—
207	C₂×C₄×C₁₃	#121	1	2	yes	—
208	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×Dic₁₃	—	4	2	no	—
215	C₂×Dic₁₃	—	8	2	no	—
216	D₅₂	—	2	4	no	—
217	D₅₂	—	2	4	no	—
218	D₅₂	—	4	2	no	—
219	D₅₂	—	4	2	no	—
220	C₄×D₁₃	—	8	4	no	—
221	C₄×D₁₃	—	8	4	no	—
222	C₈×C₁₃	—	2	2	no	—
223	C₈×C₁₃	—	2	1	no	—
224	C₈×C₁₃	—	2	2	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	C₄×D₄	1	2	yes	—
227	C₈×C₁₃	C₄×D₄	1	2	yes	—
228	#1055	—	2	4	no	—
229	#1055	—	4	2	no	—
230	C₂×AGL(1,ℤ/8)	—	13	2	no	—
231	C₂²×D₈	—	13	1	no	—
232	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
233	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
234	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
235	C₂×C₄×D₄	—	13	2	no	—
236	#472	—	13	8	no	—
237	#442	—	26	2	no	—
238	#442	—	26	1	no	—
239	#442	—	26	1	no	—
240	#442	—	26	1	no	—
241	#442	—	26	1	no	—
242	#440	—	26	2	no	—
243	C₄×SD₁₆	—	26	2	no	—
244	C₄×D₈	—	26	2	no	—
245	C₂×#108	—	13	1	no	—
246	C₂×#108	—	13	1	no	—
247	#428	—	13	2	no	—
248	C₂×#106	—	13	1	no	—
249	#418	—	13	2	no	—
250	#417	—	13	2	no	—
251	C₂×#102	—	13	2	no	—
252	C₂×#100	—	13	2	no	—
253	C₂×#100	—	13	2	no	—
254	#405	—	2	1	no	—
255	#405	—	2	1	no	—
256	#405	C₂×D₁₃	1	1	yes	characteristic
257	#405	C₂×D₁₃	1	1	yes	characteristic
258	C₄×M₁₆	—	2	1	no	—
259	C₄×M₁₆	—	13	2	no	—
260	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
261	C₂×#97	—	2	1	no	—
262	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
263	#343	—	13	2	no	—
264	#343	—	13	2	no	—
265	#341	—	13	2	no	—
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
271	C₂²×C₁₃	#529	1	1	yes	characteristic
272	C₂×D₁₃	—	4	4	no	—
273	C₂×D₁₃	—	8	4	no	—
274	C₂×D₁₃	—	8	2	no	—
275	C₂×D₁₃	—	8	2	no	—
276	C₂×D₁₃	—	8	4	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₁₃	#525	1	1	yes	characteristic
284	C₄×C₁₃	#532	1	1	yes	characteristic
285	Dic₁₃	—	8	2	no	—
286	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×D₄	—	13	2	no	—
288	C₂³×C₄	—	26	2	no	—
289	AGL(1,ℤ/8)	—	13	8	no	—
290	AGL(1,ℤ/8)	—	26	4	no	—
291	C₂×SD₁₆	—	26	2	no	—
292	C₂×D₈	—	13	4	no	—
293	C₂×D₈	—	26	2	no	—
294	C₂×D₈	—	26	2	no	—
295	C₂×D₈	—	26	1	no	—
296	C₂×D₈	—	26	1	no	—
297	#131	—	2	2	no	—
298	#131	—	2	2	no	—
299	#131	—	2	2	no	—
300	#131	C₄×D₁₃	1	4	yes	complemented
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	13	2	no	—
304	C₂×M₁₆	—	13	2	no	—
305	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×Q₈	D₅₂	1	2	yes	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	26	2	no	—
314	C₄×D₄	—	26	2	no	—
315	C₄×D₄	—	26	2	no	—
316	C₄×D₄	—	26	2	no	—
317	C₄×D₄	D₅₂	1	2	yes	—
318	#117	—	2	1	no	—
319	#117	C₂²×D₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	—	13	2	no	—
321	C₂×C₂²⋊C₄	—	26	2	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
324	#108	—	13	4	no	—
325	#108	—	26	2	no	—
326	#107	—	26	2	no	—
327	#106	—	26	1	no	—
328	#106	—	26	1	no	—
329	#106	—	26	2	no	—
330	#103	—	26	2	no	—
331	#102	—	26	2	no	—
332	#102	—	26	2	no	—
333	#102	—	26	2	no	—
334	#102	—	26	2	no	—
335	#102	—	26	2	no	—
336	#100	—	13	8	no	—
337	#100	—	26	4	no	—
338	#97	—	2	1	no	—
339	#97	—	2	1	no	—
340	#97	—	2	1	no	—
341	#97	—	26	2	no	—
342	#97	C₂²⋊D₁₃	1	1	yes	characteristic
343	#97	C₂²⋊D₁₃	1	1	yes	characteristic
344	#97	C₂²⋊D₁₃	1	1	yes	characteristic
345	#97	C₂²⋊D₁₃	1	1	yes	characteristic
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	26	2	no	—
350	C₂×C₁₃	—	2	1	no	—
351	C₂×C₁₃	—	2	1	no	—
352	C₂×C₁₃	—	4	2	no	—
353	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
354	C₂×C₁₃	#3068	1	2	yes	—
355	D₁₃	—	8	4	no	—
356	C₂⁴	—	26	2	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	C₂×C₄×D₁₃	1	2	yes	—
360	#41	#6127	1	2	yes	—
361	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	13	4	no	—
364	C₂×D₄	—	26	2	no	—
365	C₂×D₄	—	26	2	no	—
366	C₂×D₄	—	26	2	no	—
367	C₂×D₄	—	26	2	no	—
368	C₂×D₄	—	26	2	no	—
369	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	26	2	no	—
373	C₂²×C₄	—	52	2	no	—
374	C₂²×C₄	—	52	2	no	—
375	C₂²×C₄	—	104	4	no	—
376	C₂²×C₄	#6127	1	2	yes	—
377	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
378	SD₁₆	—	26	8	no	—
379	D₈	—	26	8	no	—
380	D₈	—	26	4	no	—
381	D₈	—	26	4	no	—
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	13	4	no	—
387	M₁₆	—	26	2	no	—
388	M₁₆	—	26	2	no	—
389	M₁₆	—	26	2	no	—
390	M₁₆	C₂×C₄×D₁₃	1	2	yes	—
391	M₁₆	#6127	1	2	yes	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
401	C₂×C₈	#6127	1	2	yes	—
402	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
403	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
404	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	26	2	no	—
408	C₄⋊C₄	—	26	2	no	—
409	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	52	2	no	—
413	C₂²⋊C₄	—	52	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	1	no	—
416	C₄²	C₂×D₅₂	1	2	yes	—
417	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
418	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
419	C₁₃	#21555	1	1	yes	characteristic, complemented, Sylow
420	C₂³	—	2	1	no	—
421	C₂³	—	26	4	no	—
422	C₂³	—	52	2	no	—
423	C₂³	—	52	2	no	—
424	C₂³	—	104	2	no	—
425	C₂³	—	104	2	no	—
426	C₂³	C₂×#6127	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	C₄×D₅₂	1	2	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	26	4	no	—
433	D₄	—	26	4	no	—
434	D₄	—	52	2	no	—
435	D₄	—	52	2	no	—
436	D₄	C₄×D₅₂	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	52	2	no	—
444	C₂×C₄	—	104	4	no	—
445	C₂×C₄	—	104	4	no	—
446	C₂×C₄	—	104	2	no	—
447	C₂×C₄	#88184	1	2	yes	—
448	C₂×C₄	#88184	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
451	C₂×C₄	C₂×#6127	1	1	yes	characteristic
452	C₂×C₄	C₂×#6127	1	1	yes	characteristic
453	C₂×C₄	C₂×#6127	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	26	4	no	—
460	C₈	—	52	2	no	—
461	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
462	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	52	4	no	—
467	C₂²	—	104	4	no	—
468	C₂²	—	104	4	no	—
469	C₂²	—	104	2	no	—
470	C₂²	—	104	2	no	—
471	C₂²	C₄×#6127	1	1	yes	characteristic
472	C₂²	#11719184	1	1	yes	characteristic
473	C₂²	C₂×#88184	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	104	2	no	—
479	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
480	C₄	#11719182	1	1	yes	characteristic
481	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
482	C₄	#11719496	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	—	104	4	no	—
487	C₂	C₄×#88184	1	1	yes	characteristic
488	C₂	#13124564	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#88184
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2875	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×#11718803	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2875	D₁₃
hypocenter	C₁₃	#21555
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2875

Complements

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

N	H ≅ G/N	type
2. C₄×#88203	C₂	semidirect
3. C₂×#11718372	C₂	semidirect
4. #13115746	C₂	semidirect
5. #13115616	C₂	semidirect
6. #13115498	C₂	semidirect
7. #13115344	C₂	semidirect
8. #13114895	C₂	semidirect
9. #13114742	C₂	semidirect
10. C₄×#88063	C₂	semidirect
11. C₁₃×#2875	C₂	semidirect
27. #11718803	C₄	semidirect
54. C₁₃×#131	C₂×C₄	semidirect
71. #88203	C₂×C₄	semidirect
81. C₂×D₁₀₄	C₂×C₄	semidirect
99. #88063	C₂×C₄	semidirect
103. #88059	C₂×C₄	semidirect
179. #2875	D₁₃	semidirect
300. #131	C₄×D₁₃	semidirect
419. C₁₃	#21555	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718803	2
C₄×#88203	2
C₂×#11718372	2
#13115746	2
#13115616	2
#13115498	2
#13115344	2
#13114895	2
#13114742	2
C₄×#88063	2
C₁₃×#2875	2
#21555	13