Subgroups — #36581004

Order 22784.

756 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030700	C₂	1	1	yes	maximal, characteristic
2	#26020741	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020738	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020737	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020736	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020735	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020733	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020732	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020648	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020647	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020635	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020632	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020402	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020400	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1903	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668040	C₂²	1	1	yes	characteristic
17	C₂×#15668038	C₂²	1	1	yes	characteristic
18	C₂×#15668037	C₂²	1	1	yes	characteristic
19	#19152364	C₂²	1	1	yes	characteristic
20	#19152144	C₂²	1	1	yes	characteristic
21	C₂×#15668008	C₂²	1	1	yes	characteristic
22	#19152073	C₂²	1	1	yes	characteristic
23	#19152072	C₂²	1	1	yes	characteristic
24	#19151986	C₄	1	2	yes	complemented
25	#19151984	C₄	1	2	yes	complemented
26	#19151973	C₄	1	2	yes	complemented
27	#19151969	C₄	1	2	yes	complemented
28	#19151615	C₂²	1	1	yes	characteristic
29	#19151614	C₂²	1	1	yes	characteristic
30	#19151614	C₂²	1	1	yes	characteristic
31	#19151604	C₂²	1	1	yes	characteristic
32	#19151604	C₂²	1	1	yes	characteristic
33	#19151603	C₂²	1	1	yes	characteristic
34	C₂×#15667928	C₂²	1	1	yes	characteristic
35	#19151572	C₂²	1	1	yes	characteristic
36	#19151571	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
38	#19151370	C₂²	1	1	yes	characteristic
39	#19151370	C₂²	1	1	yes	characteristic
40	#19151369	C₂²	1	1	yes	characteristic
41	#19151359	C₂²	1	1	yes	characteristic
42	#19151359	C₂²	1	1	yes	characteristic
43	#19151359	C₂²	1	1	yes	characteristic
44	#19151357	C₂²	1	1	yes	characteristic
45	#19151356	C₂²	1	1	yes	characteristic
46	#19151355	C₂²	1	1	yes	characteristic
47	#19151354	C₂²	1	1	yes	characteristic
48	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
49	#568×C₈₉	C₂²	1	1	yes	characteristic
50	#421×C₈₉	C₂²	1	1	yes	characteristic
51	#418×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
53	#344×C₈₉	C₂²	1	1	yes	characteristic
54	#338×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#13083574	C₂³	1	1	yes	characteristic
56	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
57	C₂²×C₂²⋊D₈₉	—	4	1	no	—
58	#15668040	—	4	1	no	—
59	#15668040	—	4	1	no	—
60	#15668038	—	4	1	no	—
61	#15668038	—	4	1	no	—
62	#15668037	—	4	1	no	—
63	#15668037	—	4	1	no	—
64	C₂×#13083563	C₂×C₄	1	2	yes	complemented
65	C₂×#13083562	C₂×C₄	1	2	yes	complemented
66	C₂×#13083561	C₂×C₄	1	2	yes	complemented
67	C₂×D₇₁₂	C₂×C₄	1	2	yes	complemented
68	C₂×#13083559	C₂×C₄	1	2	yes	complemented
69	C₂×#13083559	C₂×C₄	1	2	yes	complemented
70	#15668020	—	4	1	no	—
71	#15668018	—	4	1	no	—
72	C₂×#13083558	C₂³	1	1	yes	characteristic
73	C₂×#13083558	C₂³	1	1	yes	characteristic
74	M₁₆×D₈₉	—	4	1	no	—
75	#15668010	C₂×C₄	1	1	yes	characteristic, complemented
76	#15668008	—	4	1	no	—
77	#15668008	C₂×C₄	1	2	yes	—
78	#15668008	C₂×C₄	1	2	yes	—
79	#15668008	C₂×C₄	1	1	yes	characteristic, complemented
80	#15668001	C₂×C₄	1	1	yes	characteristic, complemented
81	#15667999	C₂×C₄	1	1	yes	characteristic, complemented
82	#15667984	—	4	1	no	—
83	C₄×D₃₅₆	—	4	1	no	—
84	D₄×Dic₈₉	—	4	1	no	—
85	D₄×Dic₈₉	—	4	1	no	—
86	#15667974	—	4	1	no	—
87	C₄×C₂²⋊D₈₉	—	4	1	no	—
88	#15667971	C₂³	1	1	yes	characteristic
89	#15667971	C₂³	1	1	yes	characteristic
90	#15667971	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₈₉	—	4	1	no	—
92	C₂²⋊C₄×D₈₉	—	4	1	no	—
93	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
94	#15667939	—	4	1	no	—
95	#15667938	—	4	1	no	—
96	#15667938	—	4	1	no	—
97	#15667934	—	4	1	no	—
98	#15667934	—	4	1	no	—
99	#15667933	—	4	1	no	—
100	#15667928	—	4	1	no	—
101	#15667927	—	4	1	no	—
102	#15667926	—	4	1	no	—
103	#15667922	C₂×C₄	1	2	yes	complemented
104	C₈×Dic₈₉	C₂×C₄	1	2	yes	complemented
105	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
107	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
108	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
109	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
110	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	complemented
111	#131×C₈₉	—	4	1	no	—
112	#131×C₈₉	—	4	1	no	—
113	C₂×M₁₆×C₈₉	—	4	1	no	—
114	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	#117×C₈₉	C₂³	1	1	yes	characteristic
119	#104×C₈₉	—	4	1	no	—
120	#102×C₈₉	—	4	1	no	—
121	#100×C₈₉	—	4	1	no	—
122	C₂³×D₈₉	—	2	1	no	—
123	#13083574	—	2	1	no	—
124	#13083574	—	2	1	no	—
125	#13083574	—	2	1	no	—
126	#13083574	—	2	1	no	—
127	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₃₅₆	—	2	1	no	—
129	C₂×D₃₅₆	—	2	1	no	—
130	C₂×D₃₅₆	—	2	1	no	—
131	C₂×D₃₅₆	—	2	1	no	—
132	C₂×D₃₅₆	—	2	1	no	—
133	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
135	C₂×C₂²⋊D₈₉	—	2	1	no	—
136	C₂×C₂²⋊D₈₉	—	4	1	no	—
137	C₂×C₂²⋊D₈₉	—	4	2	no	—
138	C₂×C₂²⋊D₈₉	—	4	2	no	—
139	C₂×C₂²⋊D₈₉	—	8	4	no	—
140	C₂²×Dic₈₉	—	2	1	no	—
141	C₂²×Dic₈₉	—	4	2	no	—
142	C₂×C₄×D₈₉	—	2	1	no	—
143	C₂×C₄×D₈₉	—	4	2	no	—
144	#13083563	—	4	2	no	—
145	#13083562	—	4	2	no	—
146	#13083561	—	4	2	no	—
147	D₇₁₂	—	4	2	no	—
148	#13083559	—	4	2	no	—
149	#13083559	—	4	2	no	—
150	#13083558	—	2	1	no	—
151	#13083558	—	2	1	no	—
152	#13083558	—	2	1	no	—
153	#13083558	—	2	1	no	—
154	#13083557	—	4	2	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	C₂²×C₄	1	2	yes	—
157	C₈×D₈₉	—	4	2	no	—
158	C₄⋊Dic₈₉	—	2	1	no	—
159	C₄⋊Dic₈₉	—	2	1	no	—
160	C₄⋊Dic₈₉	—	2	1	no	—
161	#13083553	—	4	1	no	—
162	C₂²⋊Dic₈₉	—	2	1	no	—
163	C₂²⋊Dic₈₉	—	2	1	no	—
164	C₂²⋊Dic₈₉	—	2	1	no	—
165	C₂²⋊Dic₈₉	—	4	1	no	—
166	C₂²⋊Dic₈₉	—	4	2	no	—
167	#13083551	—	4	1	no	—
168	#13083551	—	4	2	no	—
169	C₄×Dic₈₉	—	2	1	no	—
170	C₄×Dic₈₉	—	2	1	no	—
171	C₄×Dic₈₉	—	2	1	no	—
172	C₄×Dic₈₉	—	2	1	no	—
173	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₂⁴×C₈₉	—	2	1	no	—
176	#41×C₈₉	—	2	1	no	—
177	#41×C₈₉	—	2	1	no	—
178	#41×C₈₉	—	2	1	no	—
179	#41×C₈₉	—	2	1	no	—
180	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	C₂×D₄×C₈₉	—	2	1	no	—
187	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	SD₁₆×C₈₉	—	4	2	no	—
192	D₈×C₈₉	—	4	2	no	—
193	M₁₆×C₈₉	—	2	1	no	—
194	M₁₆×C₈₉	—	2	1	no	—
195	M₁₆×C₈₉	—	2	1	no	—
196	M₁₆×C₈₉	—	2	1	no	—
197	M₁₆×C₈₉	—	2	1	no	—
198	M₁₆×C₈₉	—	2	1	no	—
199	M₁₆×C₈₉	—	2	1	no	—
200	M₁₆×C₈₉	—	2	1	no	—
201	M₁₆×C₈₉	—	4	2	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	4	2	no	—
206	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₈₉	—	2	1	no	—
208	C₂²⋊C₄×C₈₉	—	2	1	no	—
209	C₄²×C₈₉	—	2	1	no	—
210	C₂³×C₈₉	—	2	1	no	—
211	C₂³×C₈₉	—	2	2	no	—
212	C₂³×C₈₉	—	4	1	no	—
213	C₂³×C₈₉	—	4	1	no	—
214	C₂³×C₈₉	—	8	2	no	—
215	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×D₈₉	—	2	1	no	—
217	C₂²×D₈₉	—	2	2	no	—
218	C₂²×D₈₉	—	4	1	no	—
219	C₂²×D₈₉	—	4	1	no	—
220	C₂²×D₈₉	—	8	2	no	—
221	Q₈×C₈₉	—	2	1	no	—
222	Q₈×C₈₉	—	2	1	no	—
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	2	2	no	—
225	D₄×C₈₉	—	2	2	no	—
226	D₄×C₈₉	—	2	1	no	—
227	D₄×C₈₉	—	4	1	no	—
228	D₄×C₈₉	—	4	1	no	—
229	D₄×C₈₉	—	4	1	no	—
230	D₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	4	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂²⋊D₈₉	—	4	1	no	—
242	C₂²⋊D₈₉	—	4	1	no	—
243	C₂²⋊D₈₉	—	8	2	no	—
244	C₂²⋊D₈₉	—	8	4	no	—
245	C₂²⋊D₈₉	—	8	4	no	—
246	C₂×Dic₈₉	—	2	1	no	—
247	C₂×Dic₈₉	—	2	1	no	—
248	C₂×Dic₈₉	—	2	1	no	—
249	C₂×Dic₈₉	—	4	2	no	—
250	C₂×Dic₈₉	—	4	1	no	—
251	C₂×Dic₈₉	—	4	1	no	—
252	C₂×Dic₈₉	—	4	1	no	—
253	C₂×Dic₈₉	—	16	2	no	—
254	D₃₅₆	—	2	1	no	—
255	D₃₅₆	—	2	2	no	—
256	D₃₅₆	—	2	1	no	—
257	D₃₅₆	—	2	2	no	—
258	D₃₅₆	—	4	1	no	—
259	D₃₅₆	—	4	1	no	—
260	C₄×D₈₉	—	4	1	no	—
261	C₄×D₈₉	—	4	1	no	—
262	C₄×D₈₉	—	16	2	no	—
263	Dic₁₇₈	—	2	1	no	—
264	Dic₁₇₈	—	2	1	no	—
265	C₈×C₈₉	—	2	2	no	—
266	C₈×C₈₉	—	4	1	no	—
267	C₈×C₈₉	—	4	1	no	—
268	C₈×C₈₉	—	4	1	no	—
269	#10623494	—	2	2	no	—
270	#10623494	—	4	1	no	—
271	C₂²×C₈₉	—	4	1	no	—
272	C₂²×C₈₉	—	4	1	no	—
273	C₂²×C₈₉	—	4	2	no	—
274	C₂²×C₈₉	—	8	2	no	—
275	C₂²×C₈₉	—	8	2	no	—
276	C₂²×C₈₉	—	8	1	no	—
277	C₂²×C₈₉	—	16	1	no	—
278	C₂²×C₈₉	#518	1	1	yes	characteristic
279	C₂²×C₈₉	#560	1	1	yes	characteristic
280	C₂²×C₈₉	#560	1	1	yes	characteristic
281	C₂×D₈₉	—	4	1	no	—
282	C₂×D₈₉	—	4	2	no	—
283	C₂×D₈₉	—	8	2	no	—
284	C₂×D₈₉	—	8	2	no	—
285	C₂×D₈₉	—	8	1	no	—
286	C₂×D₈₉	—	16	1	no	—
287	C₄×C₈₉	—	4	1	no	—
288	C₄×C₈₉	—	8	1	no	—
289	C₄×C₈₉	#518	1	1	yes	characteristic
290	C₄×C₈₉	#518	1	1	yes	characteristic
291	C₄×C₈₉	#560	1	1	yes	characteristic
292	C₄×C₈₉	#560	1	1	yes	characteristic
293	Dic₈₉	—	2	2	no	—
294	Dic₈₉	—	4	1	no	—
295	Dic₈₉	—	4	1	no	—
296	Dic₈₉	—	8	1	no	—
297	Dic₈₉	—	8	1	no	—
298	Dic₈₉	—	8	1	no	—
299	#23361	—	89	1	no	maximal, Sylow
300	C₂×C₈₉	—	2	1	no	—
301	C₂×C₈₉	—	2	1	no	—
302	C₂×C₈₉	—	2	1	no	—
303	C₂×C₈₉	—	8	1	no	—
304	C₂×C₈₉	—	8	2	no	—
305	C₂×C₈₉	#2380	1	1	yes	characteristic
306	D₈₉	—	8	1	no	—
307	D₈₉	—	8	2	no	—
308	#3151	—	89	1	no	—
309	#1904	—	89	1	no	—
310	#1904	—	89	1	no	—
311	#1904	—	89	1	no	—
312	#1904	—	89	1	no	—
313	#1903	—	89	1	no	—
314	#1903	—	89	1	no	—
315	#1903	—	89	1	no	—
316	#1903	D₈₉	1	1	yes	characteristic, complemented
317	#1887	—	89	1	no	—
318	#1887	—	89	1	no	—
319	#1884	—	89	1	no	—
320	#1884	—	89	1	no	—
321	#1841	—	89	1	no	—
322	#1841	—	89	1	no	—
323	C₈₉	#23361	1	1	yes	characteristic, complemented, Sylow
324	C₂×AGL(1,ℤ/8)	—	89	1	no	—
325	C₂×AGL(1,ℤ/8)	—	89	1	no	—
326	C₂×AGL(1,ℤ/8)	—	89	1	no	—
327	C₂×AGL(1,ℤ/8)	C₂×D₈₉	1	1	yes	characteristic
328	#568	—	89	1	no	—
329	#568	C₂×D₈₉	1	1	yes	characteristic
330	#532	—	89	1	no	—
331	C₂×#127	—	89	1	no	—
332	#518	—	89	1	no	—
333	#518	—	89	1	no	—
334	#496	—	89	2	no	—
335	#496	—	89	2	no	—
336	#493	—	89	2	no	—
337	#492	—	89	2	no	—
338	#421	—	89	1	no	—
339	#421	—	89	1	no	—
340	#421	—	89	1	no	—
341	#421	C₂×D₈₉	1	1	yes	characteristic
342	#418	—	89	1	no	—
343	#418	—	89	1	no	—
344	#418	—	89	1	no	—
345	#418	C₂×D₈₉	1	1	yes	characteristic
346	C₂×#100	—	89	1	no	—
347	C₂×#100	C₂×D₈₉	1	1	yes	characteristic
348	#410	—	89	1	no	—
349	#410	—	89	1	no	—
350	C₄×M₁₆	—	89	1	no	—
351	#344	—	89	1	no	—
352	#344	—	89	1	no	—
353	#344	—	89	1	no	—
354	#344	C₂×D₈₉	1	1	yes	characteristic
355	#339	—	89	1	no	—
356	#339	—	89	1	no	—
357	#339	—	89	1	no	—
358	#339	—	89	1	no	—
359	#338	—	89	1	no	—
360	#338	C₂×D₈₉	1	1	yes	characteristic
361	H(3,ℤ/4)	—	89	1	no	—
362	H(3,ℤ/4)	—	89	1	no	—
363	C₂×#41	—	89	1	no	—
364	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
365	C₂²×D₄	—	89	1	no	—
366	C₂²×D₄	—	356	1	no	—
367	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
368	AGL(1,ℤ/8)	—	4	1	no	—
369	AGL(1,ℤ/8)	—	4	1	no	—
370	AGL(1,ℤ/8)	—	356	1	no	—
371	AGL(1,ℤ/8)	—	356	1	no	—
372	AGL(1,ℤ/8)	—	356	1	no	—
373	AGL(1,ℤ/8)	—	356	1	no	—
374	AGL(1,ℤ/8)	—	356	1	no	—
375	AGL(1,ℤ/8)	—	356	1	no	—
376	C₂×SD₁₆	—	89	2	no	—
377	C₂×SD₁₆	—	89	2	no	—
378	C₂×SD₁₆	—	89	2	no	—
379	C₂×SD₁₆	C₄×D₈₉	1	2	yes	complemented
380	C₂×D₈	—	89	2	no	—
381	C₂×D₈	—	89	2	no	—
382	C₂×D₈	—	89	2	no	—
383	C₂×D₈	C₄×D₈₉	1	2	yes	complemented
384	#131	—	4	1	no	—
385	#131	—	4	1	no	—
386	#131	—	356	1	no	—
387	#131	—	356	1	no	—
388	C₂×M₁₆	—	4	1	no	—
389	C₂×M₁₆	—	89	1	no	—
390	C₂×M₁₆	—	89	1	no	—
391	C₂×M₁₆	—	356	1	no	—
392	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
393	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
394	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
395	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
396	C₄⋊Q₈	—	89	1	no	—
397	#127	—	89	2	no	—
398	#127	—	89	2	no	—
399	#127	—	89	1	no	—
400	#127	—	356	1	no	—
401	#124	—	89	1	no	—
402	#124	—	89	1	no	—
403	#121	—	356	1	no	—
404	C₄×D₄	—	356	1	no	—
405	C₄×D₄	—	356	1	no	—
406	C₄×D₄	—	356	1	no	—
407	C₄×D₄	—	356	1	no	—
408	C₄×D₄	—	356	1	no	—
409	#117	—	89	1	no	—
410	#117	—	89	1	no	—
411	#117	—	89	1	no	—
412	#117	C₂²×D₈₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	356	1	no	—
414	C₂×C₂²⋊C₄	—	356	1	no	—
415	C₂×C₄²	—	89	1	no	—
416	#104	—	4	1	no	—
417	#104	—	356	1	no	—
418	#104	—	356	1	no	—
419	#104	—	356	1	no	—
420	#102	—	4	1	no	—
421	#102	—	356	1	no	—
422	#102	—	356	1	no	—
423	#102	—	356	1	no	—
424	#100	—	4	1	no	—
425	#100	—	356	1	no	—
426	#99	—	356	1	no	—
427	#99	—	356	1	no	—
428	#97	—	89	2	no	—
429	C₄×C₈	—	89	2	no	—
430	C₂⁴	—	2	1	no	—
431	C₂⁴	—	178	1	no	—
432	#41	—	2	1	no	—
433	#41	—	2	1	no	—
434	#41	—	2	1	no	—
435	#41	—	2	1	no	—
436	#41	—	178	1	no	—
437	#41	—	178	1	no	—
438	#41	—	178	1	no	—
439	#41	—	178	1	no	—
440	C₂×Q₈	—	89	1	no	—
441	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	89	1	no	—
449	C₂×D₄	—	89	2	no	—
450	C₂×D₄	—	356	1	no	—
451	C₂×D₄	—	356	2	no	—
452	C₂×D₄	—	356	2	no	—
453	C₂×D₄	—	178	1	no	—
454	C₂×D₄	—	178	1	no	—
455	C₂×D₄	—	178	1	no	—
456	C₂×D₄	—	178	1	no	—
457	C₂×D₄	—	178	1	no	—
458	C₂×D₄	—	178	1	no	—
459	C₂×D₄	—	712	4	no	—
460	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
461	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	356	2	no	—
464	C₂²×C₄	—	356	2	no	—
465	C₂²×C₄	—	178	1	no	—
466	C₂²×C₄	—	178	1	no	—
467	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
468	SD₁₆	—	4	2	no	—
469	SD₁₆	—	356	2	no	—
470	SD₁₆	—	356	2	no	—
471	SD₁₆	—	356	2	no	—
472	D₈	—	4	2	no	—
473	D₈	—	356	2	no	—
474	D₈	—	356	2	no	—
475	D₈	—	356	2	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	1	no	—
480	M₁₆	—	2	1	no	—
481	M₁₆	—	2	1	no	—
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	356	2	no	—
486	M₁₆	—	178	1	no	—
487	M₁₆	—	178	1	no	—
488	M₁₆	—	178	1	no	—
489	M₁₆	—	178	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	4	2	no	—
494	C₂×C₈	—	89	2	no	—
495	C₂×C₈	—	356	2	no	—
496	C₂×C₈	—	178	1	no	—
497	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	356	1	no	—
500	C₄⋊C₄	—	178	1	no	—
501	C₄⋊C₄	—	178	1	no	—
502	C₄⋊C₄	—	178	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	356	1	no	—
505	C₂²⋊C₄	—	356	2	no	—
506	C₂²⋊C₄	—	356	2	no	—
507	C₂²⋊C₄	—	356	1	no	—
508	C₂²⋊C₄	—	178	1	no	—
509	C₂²⋊C₄	—	178	1	no	—
510	C₂²⋊C₄	—	178	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	89	1	no	—
513	C₄²	—	89	1	no	—
514	C₄²	—	178	1	no	—
515	C₄²	—	178	1	no	—
516	C₄²	—	178	1	no	—
517	C₄²	—	178	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	8	2	no	—
523	C₂³	—	356	1	no	—
524	C₂³	—	356	1	no	—
525	C₂³	—	178	1	no	—
526	C₂³	—	178	2	no	—
527	C₂³	—	712	2	no	—
528	C₂³	#15668058	1	1	yes	characteristic
529	Q₈	—	2	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	178	1	no	—
532	Q₈	—	178	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	356	1	no	—
542	D₄	—	356	1	no	—
543	D₄	—	356	1	no	—
544	D₄	—	356	1	no	—
545	D₄	—	178	1	no	—
546	D₄	—	178	2	no	—
547	D₄	—	178	1	no	—
548	D₄	—	178	2	no	—
549	D₄	—	712	4	no	—
550	D₄	—	712	2	no	—
551	D₄	—	712	4	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	356	2	no	—
557	C₂×C₄	—	356	1	no	—
558	C₂×C₄	—	356	1	no	—
559	C₂×C₄	—	356	1	no	—
560	C₂×C₄	—	356	1	no	—
561	C₂×C₄	—	356	1	no	—
562	C₂×C₄	—	1424	2	no	—
563	C₂×C₄	—	1424	2	no	—
564	C₂×C₄	—	178	1	no	—
565	C₂×C₄	—	178	1	no	—
566	C₂×C₄	—	178	1	no	—
567	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
568	C₂×C₄	#15668057	1	1	yes	characteristic
569	C₂×C₄	#15668057	1	1	yes	characteristic
570	C₂×C₄	#15668057	1	1	yes	characteristic
571	C₂×C₄	#15668057	1	1	yes	characteristic
572	C₂×C₄	#15668058	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	356	1	no	—
578	C₈	—	178	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	16	1	no	—
586	C₂²	—	356	1	no	—
587	C₂²	—	356	2	no	—
588	C₂²	—	1424	1	no	—
589	C₂²	—	712	2	no	—
590	C₂²	—	712	1	no	—
591	C₂²	—	712	2	no	—
592	C₂²	#19152070	1	1	yes	characteristic
593	C₂²	#19152336	1	1	yes	characteristic
594	C₂²	#19152338	1	1	yes	characteristic
595	C₄	—	4	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	356	1	no	—
598	C₄	—	356	1	no	—
599	C₄	—	178	2	no	—
600	C₄	—	712	1	no	—
601	C₄	—	712	1	no	—
602	C₄	—	712	1	no	—
603	C₄	#19152070	1	1	yes	characteristic
604	C₄	#19152071	1	1	yes	characteristic
605	C₄	#19152336	1	1	yes	characteristic
606	C₄	#19152337	1	1	yes	characteristic
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	8	1	no	—
611	C₂	—	8	2	no	—
612	C₂	—	712	2	no	—
613	C₂	—	712	1	no	—
614	C₂	#26023427	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26023427
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1903	C₂
socle	C₂×C₈₉	#2380
prime radical	#26030700	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1903	D₈₉
hypocenter	C₈₉	#23361
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1903

Complements

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

N	H ≅ G/N	type
2. #26020741	C₂	semidirect
3. #26020738	C₂	semidirect
4. #26020737	C₂	semidirect
5. #26020736	C₂	semidirect
6. #26020735	C₂	semidirect
7. #26020733	C₂	semidirect
8. #26020732	C₂	semidirect
9. #26020648	C₂	semidirect
10. #26020647	C₂	semidirect
11. #26020635	C₂	semidirect
12. #26020632	C₂	semidirect
13. #26020402	C₂	semidirect
14. #26020400	C₂	semidirect
15. C₈₉×#1903	C₂	semidirect
24. #19151986	C₄	semidirect
25. #19151984	C₄	semidirect
26. #19151973	C₄	semidirect
27. #19151969	C₄	semidirect
64. C₂×#13083563	C₂×C₄	semidirect
65. C₂×#13083562	C₂×C₄	semidirect
66. C₂×#13083561	C₂×C₄	semidirect
67. C₂×D₇₁₂	C₂×C₄	semidirect
68. C₂×#13083559	C₂×C₄	semidirect
69. C₂×#13083559	C₂×C₄	semidirect
75. #15668010	C₂×C₄	semidirect
79. #15668008	C₂×C₄	semidirect
80. #15668001	C₂×C₄	semidirect
81. #15667999	C₂×C₄	semidirect
103. #15667922	C₂×C₄	semidirect
104. C₈×Dic₈₉	C₂×C₄	semidirect
109. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
110. C₂×D₈×C₈₉	C₂×C₄	semidirect
316. #1903	D₈₉	semidirect
323. C₈₉	#23361	semidirect
379. C₂×SD₁₆	C₄×D₈₉	semidirect
383. C₂×D₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030700	2
#26020741	2
#26020738	2
#26020737	2
#26020736	2
#26020735	2
#26020733	2
#26020732	2
#26020648	2
#26020647	2
#26020635	2
#26020632	2
#26020402	2
#26020400	2
C₈₉×#1903	2
#23361	89