Subgroups — #36470180

Order 22784.

888 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	#26022001	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19151408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151408	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021980	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021880	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3584	C₂	1	1	yes	maximal, characteristic
8	C₂×#15667952	C₂²	1	1	yes	characteristic, complemented
9	C₂×#15667952	C₂²	1	1	yes	characteristic, complemented
10	C₂×#15667948	C₂²	1	1	yes	characteristic, complemented
11	C₂×#15667944	C₂²	1	1	yes	characteristic, complemented
12	#19151599	—	2	1	no	—
13	#19151414	—	2	1	no	—
14	#19151411	—	2	1	no	—
15	#19151408	—	2	2	no	—
16	#19151408	—	2	2	no	—
17	#19151405	—	2	2	no	—
18	#19151382	—	2	2	no	—
19	#19151366	—	2	1	no	—
20	#585×C₈₉	—	2	1	no	—
21	#578×C₈₉	—	2	1	no	—
22	#578×C₈₉	C₄	1	2	yes	complemented
23	#577×C₈₉	—	2	2	no	—
24	#577×C₈₉	—	2	2	no	—
25	#576×C₈₉	—	2	1	no	—
26	#576×C₈₉	C₄	1	2	yes	complemented
27	#575×C₈₉	—	2	2	no	—
28	#575×C₈₉	—	2	1	no	—
29	C₂×#135×C₈₉	—	2	2	no	—
30	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#13083558	—	2	1	no	—
34	C₂×C₄⋊Dic₈₉	—	2	1	no	—
35	#15667952	—	2	1	no	—
36	#15667952	—	2	1	no	—
37	#15667952	—	2	1	no	—
38	#15667952	—	2	1	no	—
39	C₂×#13083549	—	2	1	no	—
40	C₂×#13083549	—	2	1	no	—
41	#15667948	—	2	1	no	—
42	#15667948	—	2	1	no	—
43	#15667944	—	2	1	no	—
44	#15667944	—	2	1	no	—
45	#15667936	—	4	1	no	—
46	#15667933	—	4	1	no	—
47	2₋¹⁺⁴×C₈₉	—	2	2	no	—
48	2₋¹⁺⁴×C₈₉	—	2	2	no	—
49	2₋¹⁺⁴×C₈₉	—	4	1	no	—
50	H(5,𝔽₂)×C₈₉	—	2	2	no	—
51	H(5,𝔽₂)×C₈₉	—	2	2	no	—
52	H(5,𝔽₂)×C₈₉	—	4	2	no	—
53	H(5,𝔽₂)×C₈₉	—	4	1	no	—
54	C₂×#41×C₈₉	—	2	4	no	—
55	C₂×#41×C₈₉	—	2	1	no	—
56	C₂×#41×C₈₉	—	2	1	no	—
57	C₂×#41×C₈₉	—	4	2	no	—
58	C₂×#41×C₈₉	—	4	2	no	—
59	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
60	#137×C₈₉	—	2	2	no	—
61	#137×C₈₉	—	2	4	no	—
62	#137×C₈₉	—	2	4	no	—
63	#137×C₈₉	—	2	2	no	—
64	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
65	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
66	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
67	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
68	#135×C₈₉	—	2	4	no	—
69	#135×C₈₉	—	2	4	no	—
70	#135×C₈₉	—	2	2	no	—
71	#135×C₈₉	—	2	2	no	—
72	#135×C₈₉	—	2	1	no	—
73	#135×C₈₉	—	2	1	no	—
74	#135×C₈₉	—	2	1	no	—
75	#135×C₈₉	—	2	1	no	—
76	#135×C₈₉	C₂×C₄	1	2	yes	—
77	#135×C₈₉	D₄	1	2	yes	—
78	#135×C₈₉	D₄	1	2	yes	—
79	#135×C₈₉	D₄	1	2	yes	—
80	C₂×Q₁₆×C₈₉	—	2	2	no	—
81	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
82	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₈₉	—	2	4	no	—
84	C₂×SD₁₆×C₈₉	—	2	1	no	—
85	C₂×SD₁₆×C₈₉	—	2	1	no	—
86	C₂×D₈×C₈₉	—	2	2	no	—
87	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
89	#131×C₈₉	—	2	1	no	—
90	#131×C₈₉	—	2	1	no	—
91	#131×C₈₉	C₂×C₄	1	2	yes	—
92	#131×C₈₉	D₄	1	2	yes	—
93	C₂×M₁₆×C₈₉	—	2	1	no	—
94	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	—	2	1	no	—
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Dic₈₉	—	4	1	no	—
98	#13083558	—	4	1	no	—
99	#13083558	—	4	1	no	—
100	C₂×#10623494	—	4	1	no	—
101	C₄⋊Dic₈₉	—	4	1	no	—
102	C₄⋊Dic₈₉	—	4	1	no	—
103	#13083549	—	4	1	no	—
104	#13083549	—	4	1	no	—
105	#41×C₈₉	—	2	1	no	—
106	#41×C₈₉	—	2	1	no	—
107	#41×C₈₉	—	2	4	no	—
108	#41×C₈₉	—	2	4	no	—
109	#41×C₈₉	—	2	2	no	—
110	#41×C₈₉	—	2	2	no	—
111	#41×C₈₉	—	2	2	no	—
112	#41×C₈₉	—	2	2	no	—
113	#41×C₈₉	—	4	4	no	—
114	#41×C₈₉	—	4	4	no	—
115	#41×C₈₉	—	4	4	no	—
116	#41×C₈₉	—	4	4	no	—
117	#41×C₈₉	—	4	2	no	—
118	#41×C₈₉	—	4	2	no	—
119	#41×C₈₉	—	4	2	no	—
120	#41×C₈₉	—	4	2	no	—
121	#41×C₈₉	—	4	1	no	—
122	#41×C₈₉	—	4	1	no	—
123	#41×C₈₉	—	4	1	no	—
124	#41×C₈₉	—	4	1	no	—
125	#41×C₈₉	C₂²⋊C₄	1	2	yes	—
126	#41×C₈₉	SD₁₆	1	2	yes	—
127	C₂×Q₈×C₈₉	—	2	4	no	—
128	C₂×Q₈×C₈₉	—	2	1	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	4	2	no	—
131	C₂×Q₈×C₈₉	—	4	2	no	—
132	C₂×Q₈×C₈₉	D₈	1	1	yes	characteristic
133	C₂×D₄×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	2	4	no	—
135	C₂×D₄×C₈₉	—	2	1	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	4	4	no	—
138	C₂×D₄×C₈₉	—	4	4	no	—
139	C₂×D₄×C₈₉	—	4	2	no	—
140	C₂×D₄×C₈₉	—	4	4	no	—
141	C₂×D₄×C₈₉	—	4	1	no	—
142	C₂×D₄×C₈₉	—	4	1	no	—
143	C₂×D₄×C₈₉	—	4	2	no	—
144	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	4	4	no	—
147	C₂²×C₄×C₈₉	—	4	1	no	—
148	C₂²×C₄×C₈₉	—	4	1	no	—
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	Q₁₆×C₈₉	—	2	4	no	—
151	Q₁₆×C₈₉	—	2	1	no	—
152	Q₁₆×C₈₉	—	2	1	no	—
153	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
154	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
155	SD₁₆×C₈₉	—	2	4	no	—
156	SD₁₆×C₈₉	—	2	4	no	—
157	SD₁₆×C₈₉	—	2	2	no	—
158	SD₁₆×C₈₉	—	2	2	no	—
159	SD₁₆×C₈₉	—	2	2	no	—
160	SD₁₆×C₈₉	—	2	2	no	—
161	D₈×C₈₉	—	2	4	no	—
162	D₈×C₈₉	—	2	1	no	—
163	D₈×C₈₉	—	2	1	no	—
164	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
165	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
166	M₁₆×C₈₉	—	2	1	no	—
167	M₁₆×C₈₉	—	2	2	no	—
168	M₁₆×C₈₉	—	2	2	no	—
169	M₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	—	2	2	no	—
172	C₂×C₈×C₈₉	—	2	2	no	—
173	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₂³×C₈₉	—	2	1	no	—
180	C₂³×C₈₉	—	4	4	no	—
181	C₂³×C₈₉	—	4	1	no	—
182	C₂³×C₈₉	—	4	1	no	—
183	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	Q₈×C₈₉	—	2	1	no	—
185	Q₈×C₈₉	—	2	2	no	—
186	Q₈×C₈₉	—	2	2	no	—
187	Q₈×C₈₉	—	4	4	no	—
188	Q₈×C₈₉	—	4	1	no	—
189	Q₈×C₈₉	—	4	1	no	—
190	Q₈×C₈₉	#102	1	2	yes	—
191	D₄×C₈₉	—	2	2	no	—
192	D₄×C₈₉	—	2	2	no	—
193	D₄×C₈₉	—	2	2	no	—
194	D₄×C₈₉	—	2	2	no	—
195	D₄×C₈₉	—	2	1	no	—
196	D₄×C₈₉	—	4	4	no	—
197	D₄×C₈₉	—	4	4	no	—
198	D₄×C₈₉	—	4	4	no	—
199	D₄×C₈₉	—	4	2	no	—
200	D₄×C₈₉	—	4	2	no	—
201	D₄×C₈₉	—	4	2	no	—
202	D₄×C₈₉	—	4	2	no	—
203	D₄×C₈₉	—	4	1	no	—
204	D₄×C₈₉	—	4	1	no	—
205	D₄×C₈₉	#102	1	2	yes	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	4	4	no	—
210	C₂×C₄×C₈₉	—	4	4	no	—
211	C₂×C₄×C₈₉	—	4	4	no	—
212	C₂×C₄×C₈₉	—	4	1	no	—
213	C₂×C₄×C₈₉	—	4	1	no	—
214	C₂×C₄×C₈₉	—	4	2	no	—
215	C₂×C₄×C₈₉	—	4	2	no	—
216	C₂×C₄×C₈₉	—	4	2	no	—
217	C₂×C₄×C₈₉	—	4	2	no	—
218	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
223	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂×Dic₈₉	—	8	1	no	—
225	C₂×Dic₈₉	—	16	1	no	—
226	C₈×C₈₉	—	2	2	no	—
227	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₈×C₈₉	#120	1	1	yes	characteristic
230	C₈×C₈₉	#120	1	1	yes	characteristic
231	#10623494	—	8	1	no	—
232	C₂²×C₈₉	—	2	2	no	—
233	C₂²×C₈₉	—	4	1	no	—
234	C₂²×C₈₉	—	4	2	no	—
235	C₂²×C₈₉	—	4	2	no	—
236	C₂²×C₈₉	—	8	1	no	—
237	C₂²×C₈₉	—	16	1	no	—
238	C₂²×C₈₉	—	16	1	no	—
239	C₂²×C₈₉	—	16	4	no	—
240	C₂²×C₈₉	#418	1	1	yes	characteristic
241	C₂²×C₈₉	#447	1	1	yes	characteristic
242	C₂²×C₈₉	#450	1	1	yes	characteristic
243	C₄×C₈₉	—	2	2	no	—
244	C₄×C₈₉	—	4	2	no	—
245	C₄×C₈₉	—	4	2	no	—
246	C₄×C₈₉	#379	1	1	yes	characteristic
247	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
248	C₄×C₈₉	#447	1	1	yes	characteristic
249	C₄×C₈₉	#450	1	1	yes	characteristic
250	Dic₈₉	—	16	1	no	—
251	#12752	—	89	1	no	maximal, Sylow
252	C₂×C₈₉	—	2	1	no	—
253	C₂×C₈₉	—	2	1	no	—
254	C₂×C₈₉	—	2	1	no	—
255	C₂×C₈₉	—	4	2	no	—
256	C₂×C₈₉	—	8	2	no	—
257	C₂×C₈₉	—	8	2	no	—
258	C₂×C₈₉	#1786	1	1	yes	characteristic
259	#3584	D₈₉	1	1	yes	characteristic
260	#2148	—	89	1	no	—
261	C₂×#360	—	89	1	no	—
262	C₂×#360	—	89	1	no	—
263	#2143	—	89	1	no	—
264	#2117	—	89	1	no	—
265	#1815	—	89	1	no	—
266	C₈₉	#12752	1	1	yes	characteristic, complemented, Sylow
267	#585	—	2	1	no	—
268	#578	—	2	1	no	—
269	#578	Dic₈₉	1	2	yes	complemented
270	#577	—	2	2	no	—
271	#577	—	2	2	no	—
272	#576	—	2	1	no	—
273	#576	Dic₈₉	1	2	yes	complemented
274	#575	—	2	2	no	—
275	#575	—	2	1	no	—
276	C₂×#135	—	2	2	no	—
277	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
278	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
279	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
280	C₂×M₃₂	—	89	1	no	—
281	C₂×M₃₂	—	89	1	no	—
282	C₂×#108	—	89	1	no	—
283	C₂×#106	—	89	1	no	—
284	#417	—	178	1	no	—
285	#362	—	178	1	no	—
286	#361	—	178	1	no	—
287	#360	—	178	2	no	—
288	#360	—	178	2	no	—
289	#359	—	178	2	no	—
290	#350	—	178	2	no	—
291	#343	—	178	1	no	—
292	2₋¹⁺⁴	—	2	2	no	—
293	2₋¹⁺⁴	—	2	2	no	—
294	2₋¹⁺⁴	—	4	1	no	—
295	H(5,𝔽₂)	—	2	2	no	—
296	H(5,𝔽₂)	—	2	2	no	—
297	H(5,𝔽₂)	—	4	2	no	—
298	H(5,𝔽₂)	—	4	1	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	1	no	—
302	C₂×#41	—	4	2	no	—
303	C₂×#41	—	4	2	no	—
304	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
305	#137	—	2	2	no	—
306	#137	—	2	4	no	—
307	#137	—	2	4	no	—
308	#137	—	2	2	no	—
309	AGL(1,ℤ/8)	—	2	2	no	—
310	AGL(1,ℤ/8)	—	2	4	no	—
311	AGL(1,ℤ/8)	—	2	4	no	—
312	AGL(1,ℤ/8)	—	2	2	no	—
313	#135	—	2	4	no	—
314	#135	—	2	4	no	—
315	#135	—	2	2	no	—
316	#135	—	2	2	no	—
317	#135	—	2	1	no	—
318	#135	—	2	1	no	—
319	#135	—	2	1	no	—
320	#135	—	2	1	no	—
321	#135	C₂×Dic₈₉	1	2	yes	—
322	#135	C₂²⋊D₈₉	1	2	yes	—
323	#135	C₂²⋊D₈₉	1	2	yes	—
324	#135	C₂²⋊D₈₉	1	2	yes	—
325	C₂×Q₁₆	—	2	2	no	—
326	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
327	C₂×Q₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
328	C₂×SD₁₆	—	2	4	no	—
329	C₂×SD₁₆	—	2	1	no	—
330	C₂×SD₁₆	—	2	1	no	—
331	C₂×D₈	—	2	2	no	—
332	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
333	C₂×D₈	C₂²⋊D₈₉	1	1	yes	characteristic
334	#131	—	2	1	no	—
335	#131	—	2	1	no	—
336	#131	C₂×Dic₈₉	1	2	yes	—
337	#131	C₂²⋊D₈₉	1	2	yes	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	178	1	no	—
340	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	—	178	1	no	—
344	M₃₂	—	178	1	no	—
345	M₃₂	—	178	1	no	—
346	M₃₂	—	178	1	no	—
347	M₃₂	—	178	1	no	—
348	C₂×C₁₆	—	178	1	no	—
349	C₂×C₁₆	—	178	1	no	—
350	#108	—	178	1	no	—
351	#108	—	178	1	no	—
352	#106	—	178	1	no	—
353	#106	—	178	1	no	—
354	#103	—	356	1	no	—
355	#102	—	356	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	4	4	no	—
365	#41	—	4	4	no	—
366	#41	—	4	4	no	—
367	#41	—	4	4	no	—
368	#41	—	4	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	1	no	—
373	#41	—	4	1	no	—
374	#41	—	4	1	no	—
375	#41	—	4	1	no	—
376	#41	C₂²⋊Dic₈₉	1	2	yes	—
377	#41	#13083562	1	2	yes	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×Q₈	#13083559	1	1	yes	characteristic
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	#13083559	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	356	1	no	—
401	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
402	Q₁₆	—	2	4	no	—
403	Q₁₆	—	2	1	no	—
404	Q₁₆	—	2	1	no	—
405	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
406	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
407	SD₁₆	—	2	4	no	—
408	SD₁₆	—	2	4	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	2	2	no	—
413	D₈	—	2	4	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	D₈	C₂²⋊Dic₈₉	1	2	yes	—
417	D₈	C₂²⋊Dic₈₉	1	2	yes	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	356	1	no	—
422	M₁₆	—	356	1	no	—
423	M₁₆	C₂²⋊Dic₈₉	1	2	yes	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	356	1	no	—
428	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
433	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
434	C₄⋊C₄	—	356	1	no	—
435	C₄⋊C₄	—	356	1	no	—
436	C₁₆	—	356	1	no	—
437	C₁₆	—	356	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	#15668038	1	1	yes	characteristic
443	Q₈	—	2	1	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	4	no	—
447	Q₈	—	4	1	no	—
448	Q₈	—	4	1	no	—
449	Q₈	#15667933	1	2	yes	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	2	1	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	#15667933	1	2	yes	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	1424	1	no	—
478	C₂×C₄	—	712	1	no	—
479	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
480	C₂×C₄	#15667981	1	1	yes	characteristic
481	C₂×C₄	#15667981	1	1	yes	characteristic
482	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
483	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
484	C₂×C₄	#15668038	1	1	yes	characteristic
485	C₈	—	2	2	no	—
486	C₈	—	712	1	no	—
487	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
488	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
489	C₈	#15667981	1	1	yes	characteristic
490	C₈	#15667981	1	1	yes	characteristic
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	16	1	no	—
497	C₂²	—	16	1	no	—
498	C₂²	—	16	4	no	—
499	C₂²	#19151603	1	1	yes	characteristic
500	C₂²	#19151732	1	1	yes	characteristic
501	C₂²	#19151749	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	1424	1	no	—
506	C₄	#19151454	1	1	yes	characteristic
507	C₄	C₂×#15667933	1	1	yes	characteristic
508	C₄	#19151732	1	1	yes	characteristic
509	C₄	#19151749	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	4	2	no	—
514	C₂	—	8	2	no	—
515	C₂	—	8	2	no	—
516	C₂	#26020183	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26020183
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting, prime radical	C₈₉×#3584	C₂
socle	C₂×C₈₉	#1786
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#3584	D₈₉
hypocenter	C₈₉	#12752
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #26022001	C₂	semidirect
2. C₂×#19151408	C₂	semidirect
3. C₂×#19151408	C₂	semidirect
4. #26021980	C₂	semidirect
5. #26021880	C₂	semidirect
6. #26020311	C₂	semidirect
8. C₂×#15667952	C₂²	semidirect
9. C₂×#15667952	C₂²	semidirect
10. C₂×#15667948	C₂²	semidirect
11. C₂×#15667944	C₂²	semidirect
22. #578×C₈₉	C₄	semidirect
26. #576×C₈₉	C₄	semidirect
266. C₈₉	#12752	semidirect
269. #578	Dic₈₉	semidirect
273. #576	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26022001	2
C₂×#19151408	2
#26021980	2
#26021880	2
#26020311	2
C₈₉×#3584	2
#12752	89