Subgroups — C₄×#11718803 #15869799

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 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×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115746	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115621	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115498	C₂	1	2	yes	maximal, complemented
7	#13115344	C₂	1	2	yes	maximal, complemented
8	#13114900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88059	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88063	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#131	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×C₄×C₈×C₁₃	—	2	1	no	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	#11718893	C₂²	1	2	yes	—
27	#11718803	C₄	1	8	yes	direct product factor
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×#88058	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	C₄×D₁₀₄	—	2	1	no	—
42	C₄×D₁₀₄	—	2	1	no	—
43	C₄×D₁₀₄	—	2	1	no	—
44	C₄×D₁₀₄	—	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	1	yes	characteristic
64	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
68	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₁₃×#117	—	2	1	no	—
70	C₁₃×#117	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	#88203	—	2	4	no	—
74	#88203	C₂×C₄	1	8	yes	complemented
75	C₂×#6106	—	2	2	no	—
76	C₂×#6104	—	2	2	no	—
77	C₂×#6103	—	2	2	no	—
78	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
79	C₂×#6099	C₂³	1	2	yes	—
80	C₂×#6099	C₂³	1	2	yes	—
81	C₂×D₁₀₄	—	2	1	no	—
82	C₂×D₁₀₄	—	2	1	no	—
83	C₂×D₁₀₄	—	2	2	no	—
84	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
85	C₄×D₅₂	—	2	2	no	—
86	C₄×D₅₂	—	2	2	no	—
87	C₄×D₅₂	—	2	2	no	—
88	C₄×D₅₂	—	2	2	no	—
89	C₁₃×#97	—	2	1	no	—
90	C₁₃×#97	—	2	1	no	—
91	C₁₃×#97	—	2	1	no	—
92	C₄×C₈×C₁₃	—	2	1	no	—
93	C₄×C₈×C₁₃	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
97	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
99	#88075	—	2	2	no	—
100	#88072	—	2	2	no	—
101	#88063	—	2	4	no	—
102	#88063	C₂×C₄	1	8	yes	complemented
103	#88061	—	2	2	no	—
104	#88061	—	2	2	no	—
105	#88059	—	2	2	no	—
106	#88059	C₂×C₄	1	4	yes	complemented
107	#88058	—	2	1	no	—
108	#88058	—	2	1	no	—
109	#88049	—	2	2	no	—
110	#88049	—	2	2	no	—
111	#88048	—	2	2	no	—
112	#88047	—	2	2	no	—
113	#88043	—	2	2	no	—
114	C₄×#1055	—	2	2	no	—
115	C₄×#472	—	13	1	no	maximal, Sylow
116	C₂³×D₁₃	—	2	2	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₁₃×#41	C₂²×C₄	1	2	yes	—
120	C₁₃×#41	#41	1	2	yes	—
121	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂²×Dic₁₃	—	2	2	no	—
131	C₂×D₅₂	—	2	2	no	—
132	C₂×D₅₂	—	2	2	no	—
133	C₂×D₅₂	—	2	2	no	—
134	C₂×D₅₂	—	2	2	no	—
135	C₂×D₅₂	—	2	2	no	—
136	C₂×D₅₂	C₂²×C₄	1	4	yes	—
137	C₂×C₄×D₁₃	—	4	2	no	—
138	C₂×C₄×D₁₃	—	4	2	no	—
139	C₂×C₄×D₁₃	—	8	4	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	—	2	1	no	—
142	C₁₃×M₁₆	—	2	1	no	—
143	C₁₃×M₁₆	—	2	4	no	—
144	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
145	C₁₃×M₁₆	#41	1	2	yes	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	4	no	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	#6106	—	2	8	no	—
173	#6104	—	2	8	no	—
174	#6103	—	4	2	no	—
175	#6103	—	4	2	no	—
176	C₄⋊Dic₁₃	—	2	2	no	—
177	C₄⋊Dic₁₃	—	2	2	no	—
178	#6099	—	2	2	no	—
179	#6099	—	2	2	no	—
180	#6099	—	2	2	no	—
181	#6099	C₂²×C₄	1	4	yes	—
182	C₂×#1055	—	2	2	no	—
183	C₂×#1055	—	2	2	no	—
184	D₁₀₄	—	2	4	no	—
185	D₁₀₄	—	2	4	no	—
186	C₂×#472	—	13	1	no	—
187	C₄×AGL(1,ℤ/8)	—	13	2	no	—
188	C₂×C₄×D₈	—	13	1	no	—
189	C₄×#131	D₁₃	1	1	yes	characteristic, complemented
190	#1978	—	13	1	no	—
191	#1952	—	13	1	no	—
192	#1931	—	13	2	no	—
193	#1907	—	13	2	no	—
194	#1816	—	13	1	no	—
195	C₄×#108	—	13	1	no	—
196	C₄×#100	—	13	2	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂²×D₁₃	—	2	4	no	—
200	C₂²×D₁₃	—	4	2	no	—
201	C₂²×D₁₃	—	4	2	no	—
202	C₂²×D₁₃	—	8	2	no	—
203	C₂²×D₁₃	—	8	2	no	—
204	Q₈×C₁₃	—	2	1	no	—
205	Q₈×C₁₃	C₄×D₄	1	2	yes	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×Dic₁₃	—	4	2	no	—
230	C₂×Dic₁₃	—	8	2	no	—
231	D₅₂	—	2	4	no	—
232	D₅₂	—	2	4	no	—
233	D₅₂	—	4	2	no	—
234	D₅₂	—	4	2	no	—
235	C₄×D₁₃	—	8	4	no	—
236	C₄×D₁₃	—	8	4	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	1	no	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	1	no	—
241	C₈×C₁₃	C₄×D₄	1	2	yes	—
242	C₈×C₁₃	C₄×D₄	1	2	yes	—
243	#1055	—	2	4	no	—
244	#1055	—	4	2	no	—
245	C₂×AGL(1,ℤ/8)	—	13	2	no	—
246	C₂²×D₈	—	13	1	no	—
247	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
248	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
249	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
250	C₂×C₄×D₄	—	13	2	no	—
251	#472	—	13	8	no	—
252	#442	—	26	2	no	—
253	#440	—	26	2	no	—
254	C₄×SD₁₆	—	26	2	no	—
255	C₄×D₈	—	26	2	no	—
256	C₄×D₈	—	26	1	no	—
257	C₄×D₈	—	26	1	no	—
258	C₄×D₈	—	26	1	no	—
259	C₄×D₈	—	26	1	no	—
260	C₂×#108	—	13	1	no	—
261	C₂×#108	—	13	1	no	—
262	#428	—	13	2	no	—
263	C₂×#107	—	13	1	no	—
264	#418	—	13	2	no	—
265	#417	—	13	2	no	—
266	C₂×#102	—	13	2	no	—
267	C₂×#100	—	13	2	no	—
268	C₂×#100	—	13	2	no	—
269	#405	—	2	1	no	—
270	#405	—	2	1	no	—
271	#405	C₂×D₁₃	1	1	yes	characteristic
272	#405	C₂×D₁₃	1	1	yes	characteristic
273	C₄×M₁₆	—	2	1	no	—
274	C₄×M₁₆	—	13	2	no	—
275	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
276	C₂×C₄×C₈	—	2	1	no	—
277	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
278	#343	—	13	2	no	—
279	#343	—	13	2	no	—
280	#341	—	13	2	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
287	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
288	C₂²×C₁₃	#529	1	1	yes	characteristic
289	C₂×D₁₃	—	4	4	no	—
290	C₂×D₁₃	—	8	4	no	—
291	C₂×D₁₃	—	8	2	no	—
292	C₂×D₁₃	—	8	2	no	—
293	C₂×D₁₃	—	8	4	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	#472	1	2	yes	complemented
301	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₁₃	#525	1	1	yes	characteristic
304	C₄×C₁₃	#532	1	1	yes	characteristic
305	Dic₁₃	—	8	2	no	—
306	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
307	C₂²×D₄	—	13	2	no	—
308	C₂³×C₄	—	26	2	no	—
309	AGL(1,ℤ/8)	—	13	8	no	—
310	AGL(1,ℤ/8)	—	26	4	no	—
311	C₂×SD₁₆	—	26	2	no	—
312	C₂×D₈	—	13	4	no	—
313	C₂×D₈	—	26	2	no	—
314	C₂×D₈	—	26	2	no	—
315	C₂×D₈	—	26	1	no	—
316	C₂×D₈	—	26	1	no	—
317	#131	—	2	2	no	—
318	#131	—	2	2	no	—
319	#131	—	2	2	no	—
320	#131	C₄×D₁₃	1	4	yes	complemented
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	13	2	no	—
324	C₂×M₁₆	—	13	2	no	—
325	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
326	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
331	C₄×Q₈	D₅₂	1	1	yes	characteristic
332	C₄×Q₈	D₅₂	1	1	yes	characteristic
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	26	2	no	—
336	C₄×D₄	—	26	2	no	—
337	C₄×D₄	—	26	2	no	—
338	C₄×D₄	—	26	2	no	—
339	C₄×D₄	D₅₂	1	1	yes	characteristic
340	C₄×D₄	D₅₂	1	1	yes	characteristic
341	#117	—	2	1	no	—
342	#117	C₂²×D₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	—	13	2	no	—
344	C₂×C₂²⋊C₄	—	26	2	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
347	#108	—	13	4	no	—
348	#108	—	26	2	no	—
349	#107	—	26	1	no	—
350	#107	—	26	1	no	—
351	#107	—	26	2	no	—
352	#106	—	26	2	no	—
353	#103	—	26	2	no	—
354	#102	—	26	2	no	—
355	#102	—	26	2	no	—
356	#102	—	26	2	no	—
357	#102	—	26	2	no	—
358	#102	—	26	2	no	—
359	#100	—	13	8	no	—
360	#100	—	26	4	no	—
361	#97	—	2	1	no	—
362	#97	—	2	1	no	—
363	#97	—	2	1	no	—
364	#97	—	26	2	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	26	2	no	—
369	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
371	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
372	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
373	C₂×C₁₃	—	2	1	no	—
374	C₂×C₁₃	—	2	1	no	—
375	C₂×C₁₃	—	4	2	no	—
376	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
378	C₂×C₁₃	#3067	1	1	yes	characteristic
379	D₁₃	—	8	4	no	—
380	C₂⁴	—	26	2	no	—
381	#41	—	2	1	no	—
382	#41	—	2	1	no	—
383	#41	C₂×C₄×D₁₃	1	2	yes	—
384	#41	#6127	1	2	yes	—
385	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	13	4	no	—
388	C₂×D₄	—	26	2	no	—
389	C₂×D₄	—	26	2	no	—
390	C₂×D₄	—	26	2	no	—
391	C₂×D₄	—	26	2	no	—
392	C₂×D₄	—	26	2	no	—
393	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	26	2	no	—
398	C₂²×C₄	—	52	2	no	—
399	C₂²×C₄	—	52	2	no	—
400	C₂²×C₄	—	104	4	no	—
401	C₂²×C₄	#6127	1	1	yes	characteristic
402	C₂²×C₄	#6127	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
404	SD₁₆	—	26	8	no	—
405	D₈	—	26	8	no	—
406	D₈	—	26	4	no	—
407	D₈	—	26	4	no	—
408	M₁₆	—	2	4	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	1	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	13	4	no	—
413	M₁₆	—	26	2	no	—
414	M₁₆	—	26	2	no	—
415	M₁₆	—	26	2	no	—
416	M₁₆	C₂×C₄×D₁₃	1	2	yes	—
417	M₁₆	#6127	1	2	yes	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	—	26	2	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
427	C₂×C₈	#6127	1	2	yes	—
428	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	26	2	no	—
435	C₄⋊C₄	—	26	2	no	—
436	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
437	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	52	2	no	—
442	C₂²⋊C₄	—	52	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	C₂×D₅₂	1	1	yes	characteristic
447	C₄²	C₂×D₅₂	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
450	C₁₃	C₄×#472	1	1	yes	characteristic, complemented, Sylow
451	C₂³	—	2	1	no	—
452	C₂³	—	26	4	no	—
453	C₂³	—	52	2	no	—
454	C₂³	—	52	2	no	—
455	C₂³	—	104	2	no	—
456	C₂³	—	104	2	no	—
457	C₂³	C₂×#6127	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	C₄×D₅₂	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	26	4	no	—
464	D₄	—	26	4	no	—
465	D₄	—	52	2	no	—
466	D₄	—	52	2	no	—
467	D₄	C₄×D₅₂	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	52	2	no	—
478	C₂×C₄	—	104	4	no	—
479	C₂×C₄	—	104	4	no	—
480	C₂×C₄	—	104	2	no	—
481	C₂×C₄	#88184	1	1	yes	characteristic
482	C₂×C₄	#88184	1	1	yes	characteristic
483	C₂×C₄	#88184	1	1	yes	characteristic
484	C₂×C₄	#88184	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
487	C₂×C₄	C₂×#6127	1	1	yes	characteristic
488	C₂×C₄	C₂×#6127	1	1	yes	characteristic
489	C₂×C₄	C₂×#6127	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	1	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	1	no	—
495	C₈	—	26	4	no	—
496	C₈	—	52	2	no	—
497	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
498	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	52	4	no	—
505	C₂²	—	104	4	no	—
506	C₂²	—	104	4	no	—
507	C₂²	—	104	2	no	—
508	C₂²	—	104	2	no	—
509	C₂²	C₄×#6127	1	1	yes	characteristic
510	C₂²	#11719184	1	1	yes	characteristic
511	C₂²	C₂×#88184	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	104	2	no	—
519	C₄	#11718803	1	2	yes	direct product factor
520	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
521	C₄	#11719182	1	1	yes	characteristic
522	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
523	C₄	#11719496	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	104	4	no	—
528	C₂	C₄×#88184	1	1	yes	characteristic
529	C₂	C₂×#11718803	1	1	yes	characteristic
530	C₂	#13124556	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88184
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#131	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×#11718803	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#131	D₁₃
hypocenter	C₁₃	C₄×#472
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₄×#88203	C₂	semidirect
3. C₂×C₄×D₁₀₄	C₂	semidirect
4. #13115746	C₂	semidirect
5. #13115621	C₂	semidirect
6. #13115498	C₂	semidirect
7. #13115344	C₂	semidirect
8. #13114900	C₂	semidirect
9. C₄×#88059	C₂	semidirect
10. C₄×#88063	C₂	semidirect
11. C₄×C₁₃×#131	C₂	semidirect
27. #11718803	C₄	direct (N × H)
54. C₁₃×#131	C₂×C₄	semidirect
74. #88203	C₂×C₄	semidirect
84. C₂×D₁₀₄	C₂×C₄	semidirect
102. #88063	C₂×C₄	semidirect
106. #88059	C₂×C₄	semidirect
189. C₄×#131	D₁₃	semidirect
300. C₄×C₁₃	#472	semidirect
320. #131	C₄×D₁₃	semidirect
450. C₁₃	C₄×#472	semidirect
519. C₄	#11718803	direct (N × H)

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×C₄×D₁₀₄	2
#13115746	2
#13115621	2
#13115498	2
#13115344	2
#13114900	2
C₄×#88059	2
C₄×#88063	2
C₄×C₁₃×#131	2
C₄×#472	13

Subgroups — C4×#11718803 #15869799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718803 #15869799