Subgroups — #36570399

Order 22784.

1320 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029169	C₂	1	1	yes	maximal, characteristic, complemented
2	#135×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028799	C₂	1	2	yes	maximal, complemented
4	#26021151	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021141	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020755	C₂	1	2	yes	maximal, complemented
7	#26020616	C₂	1	2	yes	maximal, complemented
8	#26020306	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020216	C₂	1	2	yes	maximal, complemented
10	#26020087	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3584	C₂	1	1	yes	maximal, characteristic
12	#19152365	C₂²	1	2	yes	complemented
13	#41×Dic₈₉	C₂²	1	2	yes	complemented
14	#19151720	—	2	2	no	—
15	#19151715	—	2	2	no	—
16	Q₁₆×Dic₈₉	—	2	1	no	—
17	SD₁₆×Dic₈₉	—	2	2	no	—
18	D₈×Dic₈₉	—	2	1	no	—
19	C₂×#15667948	C₂²	1	1	yes	characteristic, complemented
20	#19151636	C₂²	1	1	yes	characteristic, complemented
21	#19151615	—	2	4	no	—
22	#19151615	C₂²	1	2	yes	—
23	#19151615	C₂²	1	2	yes	complemented
24	#19151615	C₂²	1	2	yes	complemented
25	C₂×#15667939	—	2	4	no	—
26	C₂×#15667939	C₂²	1	1	yes	characteristic
27	C₂×#15667939	C₂²	1	2	yes	complemented
28	#19151594	C₂²	1	1	yes	characteristic
29	#19151594	C₂²	1	2	yes	complemented
30	#19151572	C₂²	1	2	yes	complemented
31	#19151565	C₂²	1	2	yes	complemented
32	#19151553	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
34	#19151370	C₂²	1	2	yes	complemented
35	#19151362	C₂²	1	1	yes	characteristic, complemented
36	#19151359	C₂²	1	1	yes	characteristic, complemented
37	#585×C₈₉	C₂²	1	2	yes	—
38	#578×C₈₉	—	2	1	no	—
39	#578×C₈₉	C₄	1	2	yes	complemented
40	#577×C₈₉	—	2	2	no	—
41	#577×C₈₉	C₄	1	4	yes	complemented
42	#576×C₈₉	—	2	1	no	—
43	#576×C₈₉	C₄	1	2	yes	complemented
44	#575×C₈₉	—	2	2	no	—
45	#575×C₈₉	C₂²	1	2	yes	—
46	C₂×#135×C₈₉	—	2	2	no	—
47	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
50	#15668019	—	2	4	no	—
51	#15668019	—	4	2	no	—
52	C₂×#13083558	—	2	4	no	—
53	C₂×#13083558	C₂³	1	2	yes	—
54	C₂×#13083558	C₂³	1	1	yes	characteristic
55	C₂²×#10623494	C₂³	1	1	yes	characteristic
56	Q₈×Dic₈₉	—	2	2	no	—
57	D₄×Dic₈₉	—	2	2	no	—
58	D₄×Dic₈₉	—	4	2	no	—
59	#15667971	—	2	2	no	—
60	#15667971	C₂³	1	2	yes	—
61	#15667971	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₈₉	—	2	2	no	—
63	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
64	#15667948	—	2	1	no	—
65	#15667948	—	2	1	no	—
66	#15667946	—	2	1	no	—
67	#15667944	—	2	1	no	—
68	#15667939	—	2	4	no	—
69	#15667939	—	2	2	no	—
70	#15667939	—	2	2	no	—
71	#15667939	—	2	4	no	—
72	#15667939	—	2	4	no	—
73	#15667939	D₄	1	2	yes	—
74	#15667939	D₄	1	2	yes	—
75	#15667936	—	2	2	no	—
76	#15667936	—	2	1	no	—
77	#15667933	—	2	2	no	—
78	#15667933	—	2	1	no	—
79	#15667927	—	4	2	no	—
80	C₂²⋊#10623494	—	4	2	no	—
81	#15667922	—	2	1	no	—
82	C₈×Dic₈₉	—	2	1	no	—
83	C₈×Dic₈₉	—	2	1	no	—
84	C₈×Dic₈₉	—	2	1	no	—
85	2₋¹⁺⁴×C₈₉	—	2	2	no	—
86	2₋¹⁺⁴×C₈₉	—	2	2	no	—
87	2₋¹⁺⁴×C₈₉	C₂×C₄	1	4	yes	complemented
88	H(5,𝔽₂)×C₈₉	—	2	2	no	—
89	H(5,𝔽₂)×C₈₉	—	2	2	no	—
90	H(5,𝔽₂)×C₈₉	—	4	2	no	—
91	H(5,𝔽₂)×C₈₉	C₂×C₄	1	4	yes	complemented
92	C₂×#41×C₈₉	—	2	4	no	—
93	C₂×#41×C₈₉	—	2	4	no	—
94	C₂×#41×C₈₉	—	4	2	no	—
95	C₂×#41×C₈₉	C₂³	1	2	yes	—
96	C₂×#41×C₈₉	C₂³	1	2	yes	—
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	#137×C₈₉	—	2	2	no	—
99	#137×C₈₉	—	2	4	no	—
100	#137×C₈₉	—	2	4	no	—
101	#137×C₈₉	C₂×C₄	1	4	yes	complemented
102	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
103	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
104	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
105	AGL(1,ℤ/8)×C₈₉	C₂×C₄	1	4	yes	complemented
106	#135×C₈₉	—	2	4	no	—
107	#135×C₈₉	—	2	2	no	—
108	#135×C₈₉	—	2	4	no	—
109	#135×C₈₉	—	2	2	no	—
110	#135×C₈₉	—	2	1	no	—
111	#135×C₈₉	—	2	1	no	—
112	#135×C₈₉	—	2	1	no	—
113	#135×C₈₉	—	2	1	no	—
114	#135×C₈₉	C₂×C₄	1	2	yes	—
115	#135×C₈₉	C₂×C₄	1	2	yes	—
116	#135×C₈₉	D₄	1	2	yes	—
117	#135×C₈₉	D₄	1	2	yes	—
118	C₂×Q₁₆×C₈₉	—	2	2	no	—
119	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
121	C₂×SD₁₆×C₈₉	—	2	4	no	—
122	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
123	C₂×SD₁₆×C₈₉	D₄	1	2	yes	—
124	C₂×D₈×C₈₉	—	2	2	no	—
125	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
127	#131×C₈₉	—	2	1	no	—
128	#131×C₈₉	—	2	1	no	—
129	#131×C₈₉	C₂×C₄	1	2	yes	complemented
130	#131×C₈₉	C₂×C₄	1	2	yes	complemented
131	C₂×M₁₆×C₈₉	—	2	1	no	—
132	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₈₉	—	2	1	no	—
134	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₈₉	—	2	1	no	—
136	C₂²×Dic₈₉	—	4	2	no	—
137	#13083558	—	2	1	no	—
138	#13083558	—	2	2	no	—
139	#13083558	—	2	2	no	—
140	#13083558	—	4	4	no	—
141	#13083558	C₂×D₄	1	2	yes	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	—	2	1	no	—
146	C₂×#10623494	—	2	2	no	—
147	C₂×#10623494	—	4	4	no	—
148	C₄⋊Dic₈₉	—	2	2	no	—
149	C₄⋊Dic₈₉	—	2	1	no	—
150	C₄⋊Dic₈₉	—	4	2	no	—
151	C₂²⋊Dic₈₉	—	2	2	no	—
152	C₂²⋊Dic₈₉	—	2	1	no	—
153	C₂²⋊Dic₈₉	—	4	2	no	—
154	C₄×Dic₈₉	—	2	1	no	—
155	C₄×Dic₈₉	—	2	2	no	—
156	C₄×Dic₈₉	—	2	1	no	—
157	C₄×Dic₈₉	—	4	2	no	—
158	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
160	#41×C₈₉	—	2	1	no	—
161	#41×C₈₉	—	2	2	no	—
162	#41×C₈₉	—	2	2	no	—
163	#41×C₈₉	—	2	1	no	—
164	#41×C₈₉	—	2	4	no	—
165	#41×C₈₉	—	2	4	no	—
166	#41×C₈₉	—	2	4	no	—
167	#41×C₈₉	—	2	4	no	—
168	#41×C₈₉	—	2	2	no	—
169	#41×C₈₉	—	2	2	no	—
170	#41×C₈₉	—	2	2	no	—
171	#41×C₈₉	—	2	2	no	—
172	#41×C₈₉	—	4	4	no	—
173	#41×C₈₉	—	4	4	no	—
174	#41×C₈₉	—	4	4	no	—
175	#41×C₈₉	—	4	4	no	—
176	#41×C₈₉	—	4	2	no	—
177	#41×C₈₉	—	4	2	no	—
178	#41×C₈₉	C₂²×C₄	1	4	yes	—
179	#41×C₈₉	C₂²×C₄	1	2	yes	—
180	#41×C₈₉	C₂×D₄	1	4	yes	—
181	#41×C₈₉	C₂×D₄	1	2	yes	—
182	C₂×Q₈×C₈₉	—	2	4	no	—
183	C₂×Q₈×C₈₉	—	2	4	no	—
184	C₂×Q₈×C₈₉	—	4	2	no	—
185	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
186	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
187	C₂×Q₈×C₈₉	#41	1	1	yes	characteristic
188	C₂×D₄×C₈₉	—	2	2	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	4	4	no	—
194	C₂×D₄×C₈₉	—	4	2	no	—
195	C₂×D₄×C₈₉	—	4	4	no	—
196	C₂×D₄×C₈₉	—	4	4	no	—
197	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
198	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₈₉	#41	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	—	2	2	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	2	no	—
203	C₂²×C₄×C₈₉	—	4	4	no	—
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	Q₁₆×C₈₉	—	2	4	no	—
206	Q₁₆×C₈₉	—	2	1	no	—
207	Q₁₆×C₈₉	—	2	1	no	—
208	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
209	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
210	SD₁₆×C₈₉	—	2	4	no	—
211	SD₁₆×C₈₉	—	2	4	no	—
212	SD₁₆×C₈₉	—	2	2	no	—
213	SD₁₆×C₈₉	—	2	2	no	—
214	SD₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
215	SD₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
216	D₈×C₈₉	—	2	4	no	—
217	D₈×C₈₉	—	2	1	no	—
218	D₈×C₈₉	—	2	1	no	—
219	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
220	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
221	M₁₆×C₈₉	—	2	1	no	—
222	M₁₆×C₈₉	—	2	2	no	—
223	M₁₆×C₈₉	—	2	2	no	—
224	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	2	no	—
227	C₂×C₈×C₈₉	—	2	2	no	—
228	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₈₉	—	2	2	no	—
235	C₂³×C₈₉	—	2	1	no	—
236	C₂³×C₈₉	—	2	2	no	—
237	C₂³×C₈₉	—	4	4	no	—
238	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
239	Q₈×C₈₉	—	2	1	no	—
240	Q₈×C₈₉	—	2	2	no	—
241	Q₈×C₈₉	—	2	2	no	—
242	Q₈×C₈₉	—	2	2	no	—
243	Q₈×C₈₉	—	4	4	no	—
244	Q₈×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
245	Q₈×C₈₉	C₄×D₄	1	2	yes	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	2	4	no	—
248	D₄×C₈₉	—	2	2	no	—
249	D₄×C₈₉	—	2	4	no	—
250	D₄×C₈₉	—	2	2	no	—
251	D₄×C₈₉	—	2	2	no	—
252	D₄×C₈₉	—	2	1	no	—
253	D₄×C₈₉	—	2	2	no	—
254	D₄×C₈₉	—	4	4	no	—
255	D₄×C₈₉	—	4	4	no	—
256	D₄×C₈₉	—	4	4	no	—
257	D₄×C₈₉	—	4	2	no	—
258	D₄×C₈₉	—	4	2	no	—
259	D₄×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
260	D₄×C₈₉	C₄×D₄	1	2	yes	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	—	2	1	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	4	no	—
267	C₂×C₄×C₈₉	—	2	2	no	—
268	C₂×C₄×C₈₉	—	4	4	no	—
269	C₂×C₄×C₈₉	—	4	4	no	—
270	C₂×C₄×C₈₉	—	4	4	no	—
271	C₂×C₄×C₈₉	—	4	2	no	—
272	C₂×C₄×C₈₉	—	4	2	no	—
273	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×Dic₈₉	—	2	1	no	—
280	C₂×Dic₈₉	—	2	1	no	—
281	C₂×Dic₈₉	—	4	2	no	—
282	C₂×Dic₈₉	—	4	2	no	—
283	C₂×Dic₈₉	—	4	1	no	—
284	C₂×Dic₈₉	—	8	4	no	—
285	C₈×C₈₉	—	2	2	no	—
286	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	#10623494	—	2	2	no	—
291	#10623494	—	4	2	no	—
292	#10623494	—	4	1	no	—
293	C₂²×C₈₉	—	2	2	no	—
294	C₂²×C₈₉	—	2	4	no	—
295	C₂²×C₈₉	—	4	1	no	—
296	C₂²×C₈₉	—	4	2	no	—
297	C₂²×C₈₉	—	8	2	no	—
298	C₂²×C₈₉	—	8	1	no	—
299	C₂²×C₈₉	—	8	2	no	—
300	C₂²×C₈₉	—	16	4	no	—
301	C₂²×C₈₉	#518	1	1	yes	characteristic
302	C₂²×C₈₉	D₄²	1	1	yes	characteristic
303	C₂²×C₈₉	#546	1	1	yes	characteristic
304	C₄×C₈₉	—	2	2	no	—
305	C₄×C₈₉	—	2	4	no	—
306	C₄×C₈₉	—	4	2	no	—
307	C₄×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
308	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₈₉	D₄²	1	1	yes	characteristic
310	C₄×C₈₉	#546	1	1	yes	characteristic
311	Dic₈₉	—	2	2	no	—
312	Dic₈₉	—	4	1	no	—
313	Dic₈₉	—	8	1	no	—
314	Dic₈₉	—	8	2	no	—
315	#22462	—	89	1	no	maximal, Sylow
316	C₂×C₈₉	—	2	1	no	—
317	C₂×C₈₉	—	2	1	no	—
318	C₂×C₈₉	—	2	1	no	—
319	C₂×C₈₉	—	4	4	no	—
320	C₂×C₈₉	—	4	2	no	—
321	C₂×C₈₉	—	8	2	no	—
322	C₂×C₈₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
323	#3584	D₈₉	1	1	yes	characteristic
324	#2957	—	89	1	no	—
325	C₄×#135	—	89	1	no	—
326	#2901	—	89	2	no	—
327	#1976	—	89	1	no	—
328	#1974	—	89	1	no	—
329	#1906	—	89	2	no	—
330	#1881	—	89	2	no	—
331	#1814	—	89	1	no	—
332	#1794	—	89	2	no	—
333	#1764	—	89	1	no	—
334	C₈₉	#22462	1	1	yes	characteristic, complemented, Sylow
335	#585	C₂×D₈₉	1	2	yes	—
336	#578	—	2	1	no	—
337	#578	Dic₈₉	1	2	yes	complemented
338	#577	—	2	2	no	—
339	#577	Dic₈₉	1	4	yes	complemented
340	#576	—	2	1	no	—
341	#576	Dic₈₉	1	2	yes	complemented
342	#575	—	2	2	no	—
343	#575	C₂×D₈₉	1	2	yes	—
344	C₂×#135	—	2	2	no	—
345	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
346	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
347	#568	—	89	2	no	—
348	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
349	C₄×#41	—	89	2	no	—
350	#444	—	178	2	no	—
351	#443	—	178	2	no	—
352	C₄×Q₁₆	—	178	1	no	—
353	C₄×SD₁₆	—	178	2	no	—
354	C₄×D₈	—	178	1	no	—
355	C₂×#108	—	89	1	no	—
356	#427	—	89	1	no	—
357	#421	—	89	2	no	—
358	#421	—	89	2	no	—
359	#421	—	89	2	no	—
360	#421	—	178	4	no	—
361	C₂×#104	—	89	1	no	—
362	C₂×#104	—	89	2	no	—
363	C₂×#104	—	178	4	no	—
364	#416	—	89	1	no	—
365	#416	—	89	2	no	—
366	#410	—	89	2	no	—
367	#408	—	89	2	no	—
368	#405	—	89	1	no	—
369	C₂×C₄×C₈	—	89	1	no	—
370	#344	—	89	2	no	—
371	#341	—	89	1	no	—
372	#339	—	89	1	no	—
373	2₋¹⁺⁴	—	2	2	no	—
374	2₋¹⁺⁴	—	2	2	no	—
375	2₋¹⁺⁴	C₂×Dic₈₉	1	4	yes	complemented
376	H(5,𝔽₂)	—	2	2	no	—
377	H(5,𝔽₂)	—	2	2	no	—
378	H(5,𝔽₂)	—	4	2	no	—
379	H(5,𝔽₂)	C₂×Dic₈₉	1	4	yes	complemented
380	C₂×#41	—	2	4	no	—
381	C₂×#41	—	2	4	no	—
382	C₂×#41	—	4	2	no	—
383	C₂×#41	C₂²×D₈₉	1	2	yes	—
384	C₂×#41	C₂²×D₈₉	1	2	yes	—
385	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
386	#137	—	2	2	no	—
387	#137	—	2	4	no	—
388	#137	—	2	4	no	—
389	#137	C₂×Dic₈₉	1	4	yes	complemented
390	AGL(1,ℤ/8)	—	2	2	no	—
391	AGL(1,ℤ/8)	—	2	4	no	—
392	AGL(1,ℤ/8)	—	2	4	no	—
393	AGL(1,ℤ/8)	C₂×Dic₈₉	1	4	yes	complemented
394	#135	—	2	4	no	—
395	#135	—	2	2	no	—
396	#135	—	2	4	no	—
397	#135	—	2	2	no	—
398	#135	—	2	1	no	—
399	#135	—	2	1	no	—
400	#135	—	2	1	no	—
401	#135	—	2	1	no	—
402	#135	C₂×Dic₈₉	1	2	yes	—
403	#135	C₂×Dic₈₉	1	2	yes	—
404	#135	C₂²⋊D₈₉	1	2	yes	—
405	#135	C₂²⋊D₈₉	1	2	yes	—
406	C₂×Q₁₆	—	2	2	no	—
407	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic, complemented
408	C₂×Q₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
409	C₂×SD₁₆	—	2	4	no	—
410	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	complemented
411	C₂×SD₁₆	C₂²⋊D₈₉	1	2	yes	—
412	C₂×D₈	—	2	2	no	—
413	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic, complemented
414	C₂×D₈	C₂²⋊D₈₉	1	1	yes	characteristic
415	#131	—	2	1	no	—
416	#131	—	2	1	no	—
417	#131	—	356	2	no	—
418	#131	—	178	4	no	—
419	#131	C₂×Dic₈₉	1	2	yes	complemented
420	#131	C₂×Dic₈₉	1	2	yes	complemented
421	C₂×M₁₆	—	2	1	no	—
422	C₂×M₁₆	—	89	1	no	—
423	C₂×M₁₆	—	89	2	no	—
424	C₂×M₁₆	—	178	4	no	—
425	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	—	89	1	no	—
428	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
429	C₄×Q₈	—	178	2	no	—
430	C₄×D₄	—	356	2	no	—
431	C₄×D₄	—	178	2	no	—
432	#117	—	89	2	no	—
433	#117	—	89	1	no	—
434	#117	—	178	2	no	—
435	C₂×C₄²	—	89	1	no	—
436	C₂×C₄²	—	178	2	no	—
437	#108	—	178	1	no	—
438	#108	—	178	1	no	—
439	#107	—	178	1	no	—
440	#106	—	178	1	no	—
441	#104	—	89	2	no	—
442	#104	—	89	2	no	—
443	#104	—	178	2	no	—
444	#104	—	178	2	no	—
445	#104	—	178	4	no	—
446	#104	—	178	4	no	—
447	#104	—	178	4	no	—
448	#103	—	178	2	no	—
449	#103	—	178	1	no	—
450	#102	—	178	2	no	—
451	#102	—	178	1	no	—
452	#99	—	356	2	no	—
453	C₂²⋊C₈	—	356	2	no	—
454	#97	—	178	1	no	—
455	C₄×C₈	—	178	1	no	—
456	C₄×C₈	—	178	1	no	—
457	C₄×C₈	—	178	1	no	—
458	#41	—	2	1	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	2	1	no	—
462	#41	—	2	4	no	—
463	#41	—	2	4	no	—
464	#41	—	2	4	no	—
465	#41	—	2	4	no	—
466	#41	—	2	2	no	—
467	#41	—	2	2	no	—
468	#41	—	2	2	no	—
469	#41	—	2	2	no	—
470	#41	—	4	4	no	—
471	#41	—	4	4	no	—
472	#41	—	4	4	no	—
473	#41	—	4	4	no	—
474	#41	—	4	2	no	—
475	#41	—	4	2	no	—
476	#41	C₂²×Dic₈₉	1	2	yes	—
477	#41	C₂²×Dic₈₉	1	4	yes	—
478	#41	D₄×D₈₉	1	2	yes	—
479	#41	C₂×C₂²⋊D₈₉	1	4	yes	—
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	4	no	—
482	C₂×Q₈	—	4	2	no	—
483	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
484	C₂×Q₈	C₂×C₂²⋊D₈₉	1	2	yes	—
485	C₂×Q₈	#13083573	1	1	yes	characteristic
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	4	no	—
494	C₂×D₄	—	4	4	no	—
495	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
496	C₂×D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
497	C₂×D₄	#13083573	1	1	yes	characteristic
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	356	2	no	—
503	C₂²×C₄	—	178	1	no	—
504	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
505	Q₁₆	—	2	4	no	—
506	Q₁₆	—	2	1	no	—
507	Q₁₆	—	2	1	no	—
508	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
509	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
510	SD₁₆	—	2	4	no	—
511	SD₁₆	—	2	4	no	—
512	SD₁₆	—	2	2	no	—
513	SD₁₆	—	2	2	no	—
514	SD₁₆	C₂²⋊Dic₈₉	1	4	yes	—
515	SD₁₆	C₂²⋊Dic₈₉	1	4	yes	—
516	D₈	—	2	4	no	—
517	D₈	—	2	1	no	—
518	D₈	—	2	1	no	—
519	D₈	C₂²⋊Dic₈₉	1	2	yes	—
520	D₈	C₂²⋊Dic₈₉	1	2	yes	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	2	no	—
523	M₁₆	—	2	2	no	—
524	M₁₆	—	89	2	no	—
525	M₁₆	—	356	4	no	—
526	M₁₆	—	178	2	no	—
527	M₁₆	—	178	2	no	—
528	M₁₆	—	178	1	no	—
529	M₁₆	C₂²×Dic₈₉	1	2	yes	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	356	4	no	—
534	C₂×C₈	—	178	1	no	—
535	C₂×C₈	—	178	1	no	—
536	C₂×C₈	—	178	1	no	—
537	C₂×C₈	—	178	2	no	—
538	C₂×C₈	—	178	1	no	—
539	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
540	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
541	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
542	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
543	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
544	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
545	C₄⋊C₄	—	356	2	no	—
546	C₄⋊C₄	—	178	2	no	—
547	C₄⋊C₄	—	178	1	no	—
548	C₂²⋊C₄	—	356	2	no	—
549	C₂²⋊C₄	—	178	1	no	—
550	C₂²⋊C₄	—	178	2	no	—
551	C₄²	—	89	1	no	—
552	C₄²	—	89	1	no	—
553	C₄²	—	356	2	no	—
554	C₄²	—	178	2	no	—
555	C₄²	—	178	1	no	—
556	C₄²	—	178	1	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	4	4	no	—
561	C₂³	#15668057	1	1	yes	characteristic
562	Q₈	—	2	1	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	4	no	—
567	Q₈	C₂×C₂²⋊Dic₈₉	1	4	yes	—
568	Q₈	D₄×Dic₈₉	1	2	yes	—
569	D₄	—	2	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	4	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	C₂×C₂²⋊Dic₈₉	1	4	yes	—
583	D₄	D₄×Dic₈₉	1	2	yes	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	356	2	no	—
597	C₂×C₄	—	356	2	no	—
598	C₂×C₄	—	356	1	no	—
599	C₂×C₄	—	178	1	no	—
600	C₂×C₄	—	178	1	no	—
601	C₂×C₄	—	712	4	no	—
602	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
603	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
604	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
606	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
607	C₂×C₄	#15668057	1	1	yes	characteristic
608	C₈	—	2	2	no	—
609	C₈	—	356	2	no	—
610	C₈	—	356	1	no	—
611	C₈	—	178	2	no	—
612	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
613	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
614	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
615	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	8	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	2	no	—
623	C₂²	—	16	4	no	—
624	C₂²	#19152073	1	1	yes	characteristic
625	C₂²	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
626	C₂²	#19152242	1	1	yes	characteristic
627	C₄	—	2	2	no	—
628	C₄	—	2	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	356	1	no	—
631	C₄	—	178	2	no	—
632	C₄	—	712	2	no	—
633	C₄	—	712	1	no	—
634	C₄	C₂²×C₂²⋊Dic₈₉	1	1	yes	characteristic
635	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
636	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
637	C₄	#19152242	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	4	4	no	—
642	C₂	—	4	2	no	—
643	C₂	—	8	2	no	—
644	C₂	D₄×C₂²⋊Dic₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3584	C₂
socle	C₂×C₈₉	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3584	D₈₉
hypocenter	C₈₉	#22462
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #26029169	C₂	semidirect
2. #135×Dic₈₉	C₂	semidirect
3. #26028799	C₂	semidirect
4. #26021151	C₂	semidirect
5. #26021141	C₂	semidirect
6. #26020755	C₂	semidirect
7. #26020616	C₂	semidirect
8. #26020306	C₂	semidirect
9. #26020216	C₂	semidirect
10. #26020087	C₂	semidirect
12. #19152365	C₂²	semidirect
13. #41×Dic₈₉	C₂²	semidirect
19. C₂×#15667948	C₂²	semidirect
20. #19151636	C₂²	semidirect
23. #19151615	C₂²	semidirect
24. #19151615	C₂²	semidirect
27. C₂×#15667939	C₂²	semidirect
29. #19151594	C₂²	semidirect
30. #19151572	C₂²	semidirect
31. #19151565	C₂²	semidirect
32. #19151553	C₂²	semidirect
33. C₂×C₈×Dic₈₉	C₂²	semidirect
34. #19151370	C₂²	semidirect
35. #19151362	C₂²	semidirect
36. #19151359	C₂²	semidirect
39. #578×C₈₉	C₄	semidirect
41. #577×C₈₉	C₄	semidirect
43. #576×C₈₉	C₄	semidirect
87. 2₋¹⁺⁴×C₈₉	C₂×C₄	semidirect
91. H(5,𝔽₂)×C₈₉	C₂×C₄	semidirect
101. #137×C₈₉	C₂×C₄	semidirect
105. AGL(1,ℤ/8)×C₈₉	C₂×C₄	semidirect
119. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
122. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
125. C₂×D₈×C₈₉	C₂×C₄	semidirect
129. #131×C₈₉	C₂×C₄	semidirect
130. #131×C₈₉	C₂×C₄	semidirect
334. C₈₉	#22462	semidirect
337. #578	Dic₈₉	semidirect
339. #577	Dic₈₉	semidirect
341. #576	Dic₈₉	semidirect
375. 2₋¹⁺⁴	C₂×Dic₈₉	semidirect
379. H(5,𝔽₂)	C₂×Dic₈₉	semidirect
389. #137	C₂×Dic₈₉	semidirect
393. AGL(1,ℤ/8)	C₂×Dic₈₉	semidirect
407. C₂×Q₁₆	C₂×Dic₈₉	semidirect
410. C₂×SD₁₆	C₂×Dic₈₉	semidirect
413. C₂×D₈	C₂×Dic₈₉	semidirect
419. #131	C₂×Dic₈₉	semidirect
420. #131	C₂×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029169	2
#135×Dic₈₉	2
#26028799	2
#26021151	2
#26021141	2
#26020755	2
#26020616	2
#26020306	2
#26020216	2
#26020087	2
C₈₉×#3584	2
#22462	89