Subgroups — C₈₉×#63066 #36440914

Order 22784.

7352 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3558	C₂	1	6	yes	maximal, complemented
2	C₈₉×#3551	C₂	1	6	yes	maximal, complemented
3	C₈₉×#3549	C₂	1	3	yes	maximal, complemented
4	C₈₉×#3543	C₂	1	12	yes	maximal, complemented
5	C₈₉×#3542	C₂	1	12	yes	maximal, complemented
6	C₈₉×#3537	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3529	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3524	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3517	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3498	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3488	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3487	C₂	1	2	yes	maximal, complemented
14	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#41×C₈₉	C₂²	1	2	yes	complemented
18	#563×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	#563×C₈₉	C₂²	1	6	yes	complemented
20	#562×C₈₉	C₂²	1	12	yes	complemented
21	#562×C₈₉	C₂²	1	6	yes	complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	3	yes	complemented
23	H(3,𝔽₄)×C₈₉	C₂²	1	6	yes	complemented
24	#560×C₈₉	C₂²	1	6	yes	complemented
25	#560×C₈₉	C₂²	1	12	yes	complemented
26	#560×C₈₉	C₂²	1	12	yes	complemented
27	#560×C₈₉	C₂²	1	12	yes	complemented
28	#559×C₈₉	C₂²	1	12	yes	complemented
29	#557×C₈₉	C₂²	1	2	yes	complemented
30	#555×C₈₉	C₂²	1	12	yes	complemented
31	#555×C₈₉	C₂²	1	6	yes	complemented
32	#553×C₈₉	C₂²	1	12	yes	complemented
33	#553×C₈₉	C₂²	1	12	yes	complemented
34	#552×C₈₉	C₂²	1	12	yes	complemented
35	#551×C₈₉	C₂²	1	12	yes	complemented
36	#550×C₈₉	C₂²	1	4	yes	complemented
37	#550×C₈₉	C₂²	1	12	yes	complemented
38	#550×C₈₉	C₂²	1	2	yes	complemented
39	#550×C₈₉	C₂²	1	4	yes	complemented
40	#550×C₈₉	C₂²	1	6	yes	complemented
41	#548×C₈₉	C₂²	1	4	yes	complemented
42	#548×C₈₉	C₂²	1	12	yes	complemented
43	#548×C₈₉	C₂²	1	4	yes	complemented
44	#547×C₈₉	C₂²	1	6	yes	complemented
45	#546×C₈₉	C₂²	1	12	yes	complemented
46	#546×C₈₉	C₂²	1	12	yes	complemented
47	#546×C₈₉	C₂²	1	12	yes	complemented
48	#546×C₈₉	C₂²	1	24	yes	complemented
49	D₄²×C₈₉	C₂²	1	12	yes	complemented
50	D₄²×C₈₉	C₂²	1	12	yes	complemented
51	D₄²×C₈₉	C₂²	1	12	yes	complemented
52	D₄²×C₈₉	C₂²	1	12	yes	complemented
53	D₄²×C₈₉	C₂²	1	6	yes	complemented
54	D₄²×C₈₉	C₂²	1	12	yes	complemented
55	#542×C₈₉	C₂²	1	12	yes	complemented
56	#540×C₈₉	C₂²	1	12	yes	complemented
57	#540×C₈₉	C₂²	1	12	yes	complemented
58	#540×C₈₉	C₂²	1	24	yes	complemented
59	#538×C₈₉	C₂²	1	24	yes	complemented
60	#538×C₈₉	C₂²	1	12	yes	complemented
61	#537×C₈₉	C₂²	1	12	yes	complemented
62	#536×C₈₉	C₂²	1	3	yes	complemented
63	#535×C₈₉	C₂²	1	6	yes	complemented
64	#535×C₈₉	C₂²	1	6	yes	complemented
65	#535×C₈₉	C₂²	1	12	yes	complemented
66	#535×C₈₉	C₂²	1	6	yes	complemented
67	#535×C₈₉	C₂²	1	6	yes	complemented
68	#535×C₈₉	C₂²	1	3	yes	complemented
69	#535×C₈₉	C₂²	1	24	yes	complemented
70	#534×C₈₉	C₂²	1	24	yes	complemented
71	#534×C₈₉	C₂²	1	12	yes	complemented
72	#532×C₈₉	C₂²	1	6	yes	complemented
73	#532×C₈₉	C₂²	1	3	yes	complemented
74	#532×C₈₉	C₂²	1	6	yes	complemented
75	C₂×#127×C₈₉	C₂²	1	6	yes	complemented
76	#529×C₈₉	C₂²	1	6	yes	complemented
77	#529×C₈₉	C₂²	1	12	yes	complemented
78	#529×C₈₉	C₂²	1	12	yes	complemented
79	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
80	#525×C₈₉	C₂²	1	6	yes	complemented
81	#525×C₈₉	C₂²	1	6	yes	complemented
82	#525×C₈₉	C₂²	1	12	yes	complemented
83	C₂×#121×C₈₉	C₂²	1	12	yes	complemented
84	#520×C₈₉	C₂²	1	4	yes	complemented
85	#519×C₈₉	C₂²	1	2	yes	complemented
86	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
87	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
88	2₋¹⁺⁴×C₈₉	—	4	4	no	—
89	H(5,𝔽₂)×C₈₉	—	4	8	no	—
90	H(5,𝔽₂)×C₈₉	—	4	4	no	—
91	C₂×#41×C₈₉	—	4	8	no	—
92	C₂×#41×C₈₉	C₂³	1	2	yes	—
93	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×#41×C₈₉	C₂³	1	4	yes	—
95	C₂×#41×C₈₉	C₂³	1	3	yes	—
96	C₂×#41×C₈₉	C₂³	1	6	yes	—
97	C₂×#41×C₈₉	C₂³	1	6	yes	—
98	C₂×#41×C₈₉	C₂³	1	3	yes	—
99	C₂×#41×C₈₉	C₂³	1	12	yes	—
100	C₂×#41×C₈₉	C₂³	1	12	yes	—
101	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
103	C₂²×D₄×C₈₉	C₂³	1	12	yes	—
104	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
105	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
106	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
107	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
108	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
109	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
114	#127×C₈₉	C₂³	1	6	yes	—
115	#127×C₈₉	C₂³	1	12	yes	—
116	#127×C₈₉	C₂³	1	12	yes	—
117	#127×C₈₉	C₂³	1	12	yes	—
118	#127×C₈₉	C₂³	1	6	yes	—
119	#127×C₈₉	C₂³	1	3	yes	—
120	#127×C₈₉	C₂³	1	12	yes	—
121	#126×C₈₉	C₂³	1	4	yes	—
122	#126×C₈₉	C₂³	1	12	yes	—
123	#126×C₈₉	C₂³	1	12	yes	—
124	#126×C₈₉	C₂³	1	24	yes	—
125	#125×C₈₉	C₂³	1	2	yes	—
126	#125×C₈₉	C₂³	1	12	yes	—
127	#125×C₈₉	C₂³	1	12	yes	—
128	#124×C₈₉	C₂³	1	3	yes	—
129	#124×C₈₉	C₂³	1	6	yes	—
130	#124×C₈₉	C₂³	1	12	yes	—
131	#124×C₈₉	C₂³	1	6	yes	—
132	#124×C₈₉	C₂³	1	12	yes	—
133	#124×C₈₉	C₂³	1	12	yes	—
134	#124×C₈₉	C₂³	1	1	yes	characteristic
135	#124×C₈₉	C₂³	1	6	yes	—
136	#124×C₈₉	C₂³	1	6	yes	—
137	#124×C₈₉	C₂³	1	12	yes	—
138	#124×C₈₉	C₂³	1	24	yes	—
139	#123×C₈₉	C₂³	1	2	yes	—
140	#123×C₈₉	C₂³	1	6	yes	—
141	#123×C₈₉	C₂³	1	12	yes	—
142	#123×C₈₉	C₂³	1	12	yes	—
143	#123×C₈₉	C₂³	1	24	yes	—
144	#123×C₈₉	C₂³	1	12	yes	—
145	#123×C₈₉	C₂³	1	12	yes	—
146	#123×C₈₉	C₂³	1	12	yes	—
147	#123×C₈₉	C₂³	1	24	yes	—
148	#123×C₈₉	C₂³	1	24	yes	—
149	#123×C₈₉	C₂³	1	12	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
156	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
157	#121×C₈₉	C₂³	1	12	yes	—
158	#121×C₈₉	C₂³	1	24	yes	—
159	#121×C₈₉	C₂³	1	12	yes	—
160	#121×C₈₉	C₂³	1	12	yes	—
161	#121×C₈₉	C₂³	1	12	yes	—
162	#121×C₈₉	C₂³	1	12	yes	—
163	#121×C₈₉	C₂³	1	12	yes	—
164	#121×C₈₉	C₂³	1	12	yes	—
165	#121×C₈₉	C₂³	1	12	yes	—
166	#121×C₈₉	C₂³	1	6	yes	—
167	#121×C₈₉	C₂³	1	12	yes	—
168	#121×C₈₉	C₂³	1	12	yes	—
169	#121×C₈₉	C₂³	1	12	yes	—
170	#121×C₈₉	C₂³	1	12	yes	—
171	#121×C₈₉	C₂³	1	12	yes	—
172	#121×C₈₉	C₂³	1	12	yes	—
173	#121×C₈₉	C₂³	1	12	yes	—
174	#121×C₈₉	C₂³	1	24	yes	—
175	#121×C₈₉	C₂³	1	24	yes	—
176	#121×C₈₉	C₂³	1	24	yes	—
177	#121×C₈₉	C₂³	1	24	yes	—
178	#121×C₈₉	C₂³	1	24	yes	—
179	#120×C₈₉	C₂³	1	12	yes	—
180	#120×C₈₉	C₂³	1	12	yes	—
181	#120×C₈₉	C₂³	1	6	yes	—
182	#120×C₈₉	C₂³	1	6	yes	—
183	#120×C₈₉	C₂³	1	12	yes	—
184	#120×C₈₉	C₂³	1	12	yes	—
185	#120×C₈₉	C₂³	1	24	yes	—
186	#120×C₈₉	C₂³	1	24	yes	—
187	#120×C₈₉	C₂³	1	24	yes	—
188	#120×C₈₉	C₂³	1	12	yes	—
189	#120×C₈₉	C₂³	1	12	yes	—
190	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
191	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
192	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
193	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
194	C₄×D₄×C₈₉	C₂³	1	6	yes	—
195	C₄×D₄×C₈₉	C₂³	1	12	yes	—
196	C₄×D₄×C₈₉	C₂³	1	12	yes	—
197	C₄×D₄×C₈₉	C₂³	1	12	yes	—
198	C₄×D₄×C₈₉	C₂³	1	12	yes	—
199	C₄×D₄×C₈₉	C₂³	1	6	yes	—
200	C₄×D₄×C₈₉	C₂³	1	12	yes	—
201	C₄×D₄×C₈₉	C₂³	1	12	yes	—
202	C₄×D₄×C₈₉	C₂³	1	12	yes	—
203	C₄×D₄×C₈₉	C₂³	1	24	yes	—
204	C₄×D₄×C₈₉	C₂³	1	24	yes	—
205	C₄×D₄×C₈₉	C₂³	1	12	yes	—
206	#117×C₈₉	C₂³	1	6	yes	—
207	#117×C₈₉	C₂³	1	3	yes	—
208	#117×C₈₉	C₂³	1	6	yes	—
209	#117×C₈₉	C₂³	1	6	yes	—
210	#117×C₈₉	C₂³	1	12	yes	—
211	#117×C₈₉	C₂³	1	24	yes	—
212	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	—
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
215	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
216	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
217	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
218	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
219	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
220	#41×C₈₉	—	2	16	no	—
221	#41×C₈₉	—	2	8	no	—
222	#41×C₈₉	—	2	4	no	—
223	#41×C₈₉	—	4	12	no	—
224	#41×C₈₉	—	4	6	no	—
225	#41×C₈₉	—	4	6	no	—
226	#41×C₈₉	—	4	24	no	—
227	#41×C₈₉	—	4	12	no	—
228	#41×C₈₉	—	8	12	no	—
229	C₂×Q₈×C₈₉	—	2	8	no	—
230	C₂×Q₈×C₈₉	—	4	6	no	—
231	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
232	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
233	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
235	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₈₉	—	4	12	no	—
238	C₂×D₄×C₈₉	—	4	24	no	—
239	C₂×D₄×C₈₉	—	4	12	no	—
240	C₂×D₄×C₈₉	—	4	12	no	—
241	C₂×D₄×C₈₉	—	4	6	no	—
242	C₂×D₄×C₈₉	—	8	24	no	—
243	C₂×D₄×C₈₉	—	8	24	no	—
244	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
245	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
246	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
247	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
248	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
249	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
250	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
251	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
252	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
253	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
254	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
255	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
257	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
259	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
260	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
261	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
262	C₂²×C₄×C₈₉	—	4	12	no	—
263	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
266	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
268	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
270	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
283	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
285	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
287	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
288	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
289	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
290	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
291	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
296	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
298	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
299	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
300	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
301	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
302	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
303	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₄²×C₈₉	C₂⁴	1	2	yes	—
305	C₄²×C₈₉	C₂⁴	1	6	yes	—
306	C₄²×C₈₉	C₂⁴	1	6	yes	—
307	C₄²×C₈₉	C₂⁴	1	12	yes	—
308	C₄²×C₈₉	C₂⁴	1	3	yes	—
309	C₄²×C₈₉	C₂⁴	1	12	yes	—
310	C₂³×C₈₉	—	4	6	no	—
311	C₂³×C₈₉	—	4	12	no	—
312	C₂³×C₈₉	—	4	6	no	—
313	C₂³×C₈₉	—	4	12	no	—
314	C₂³×C₈₉	—	4	24	no	—
315	C₂³×C₈₉	—	4	12	no	—
316	C₂³×C₈₉	C₂⁵	1	6	yes	—
317	C₂³×C₈₉	C₂⁵	1	2	yes	—
318	C₂³×C₈₉	C₂⁵	1	12	yes	—
319	C₂³×C₈₉	C₂⁵	1	3	yes	—
320	Q₈×C₈₉	—	2	12	no	—
321	Q₈×C₈₉	—	4	3	no	—
322	Q₈×C₈₉	—	4	2	no	—
323	Q₈×C₈₉	—	4	1	no	—
324	Q₈×C₈₉	—	4	6	no	—
325	Q₈×C₈₉	H(5,𝔽₂)	1	4	yes	—
326	D₄×C₈₉	—	2	12	no	—
327	D₄×C₈₉	—	2	24	no	—
328	D₄×C₈₉	—	2	6	no	—
329	D₄×C₈₉	—	4	12	no	—
330	D₄×C₈₉	—	4	6	no	—
331	D₄×C₈₉	—	4	6	no	—
332	D₄×C₈₉	—	4	3	no	—
333	D₄×C₈₉	—	4	12	no	—
334	D₄×C₈₉	—	4	12	no	—
335	D₄×C₈₉	—	4	12	no	—
336	D₄×C₈₉	—	4	12	no	—
337	D₄×C₈₉	—	4	12	no	—
338	D₄×C₈₉	—	4	24	no	—
339	D₄×C₈₉	—	4	12	no	—
340	D₄×C₈₉	—	4	24	no	—
341	D₄×C₈₉	—	4	1	no	—
342	D₄×C₈₉	—	4	6	no	—
343	D₄×C₈₉	—	4	6	no	—
344	C₂×C₄×C₈₉	—	2	12	no	—
345	C₂×C₄×C₈₉	—	2	24	no	—
346	C₂×C₄×C₈₉	—	2	12	no	—
347	C₂×C₄×C₈₉	—	2	6	no	—
348	C₂×C₄×C₈₉	—	4	2	no	—
349	C₂×C₄×C₈₉	—	4	12	no	—
350	C₂×C₄×C₈₉	—	4	12	no	—
351	C₂×C₄×C₈₉	—	4	24	no	—
352	C₂×C₄×C₈₉	—	4	6	no	—
353	C₂×C₄×C₈₉	—	4	6	no	—
354	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
355	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
356	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
357	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
358	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
359	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
360	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
361	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
362	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	2	3	no	—
365	C₂²×C₈₉	—	2	12	no	—
366	C₂²×C₈₉	—	2	6	no	—
367	C₂²×C₈₉	—	2	12	no	—
368	C₂²×C₈₉	—	2	6	no	—
369	C₂²×C₈₉	—	2	12	no	—
370	C₂²×C₈₉	—	2	4	no	—
371	C₂²×C₈₉	—	2	12	no	—
372	C₂²×C₈₉	—	8	12	no	—
373	C₂²×C₈₉	—	16	12	no	—
374	C₂²×C₈₉	—	16	6	no	—
375	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
376	C₄×C₈₉	—	2	4	no	—
377	C₄×C₈₉	—	2	2	no	—
378	C₄×C₈₉	—	2	1	no	—
379	C₄×C₈₉	—	2	6	no	—
380	C₄×C₈₉	—	2	6	no	—
381	C₄×C₈₉	—	2	4	no	—
382	C₄×C₈₉	—	2	12	no	—
383	C₄×C₈₉	—	2	2	no	—
384	C₄×C₈₉	C₂×H(5,𝔽₂)	1	6	yes	—
385	#63066	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂×C₈₉	—	4	2	no	—
387	C₂×C₈₉	—	4	12	no	—
388	C₂×C₈₉	—	4	3	no	—
389	C₂×C₈₉	—	4	6	no	—
390	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₈₉	H(7,𝔽₂)	1	2	yes	—
392	#3558	C₂×C₈₉	1	6	yes	complemented
393	#3551	C₂×C₈₉	1	6	yes	complemented
394	#3549	C₂×C₈₉	1	3	yes	complemented
395	#3543	C₂×C₈₉	1	12	yes	complemented
396	#3542	C₂×C₈₉	1	12	yes	complemented
397	#3537	C₂×C₈₉	1	6	yes	complemented
398	#3529	C₂×C₈₉	1	3	yes	complemented
399	#3524	C₂×C₈₉	1	4	yes	complemented
400	#3517	C₂×C₈₉	1	2	yes	complemented
401	#3500	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#3498	C₂×C₈₉	1	2	yes	complemented
403	#3488	C₂×C₈₉	1	4	yes	complemented
404	#3487	C₂×C₈₉	1	2	yes	complemented
405	C₈₉	#63066	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
407	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
408	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic, complemented
409	C₂²×#41	C₂²×C₈₉	1	2	yes	complemented
410	#563	C₂²×C₈₉	1	1	yes	characteristic, complemented
411	#563	C₂²×C₈₉	1	6	yes	complemented
412	#562	C₂²×C₈₉	1	12	yes	complemented
413	#562	C₂²×C₈₉	1	6	yes	complemented
414	H(3,𝔽₄)	C₂²×C₈₉	1	3	yes	complemented
415	H(3,𝔽₄)	C₂²×C₈₉	1	6	yes	complemented
416	#560	C₂²×C₈₉	1	6	yes	complemented
417	#560	C₂²×C₈₉	1	12	yes	complemented
418	#560	C₂²×C₈₉	1	12	yes	complemented
419	#560	C₂²×C₈₉	1	12	yes	complemented
420	#559	C₂²×C₈₉	1	12	yes	complemented
421	#557	C₂²×C₈₉	1	2	yes	complemented
422	#555	C₂²×C₈₉	1	12	yes	complemented
423	#555	C₂²×C₈₉	1	6	yes	complemented
424	#553	C₂²×C₈₉	1	12	yes	complemented
425	#553	C₂²×C₈₉	1	12	yes	complemented
426	#552	C₂²×C₈₉	1	12	yes	complemented
427	#551	C₂²×C₈₉	1	12	yes	complemented
428	#550	C₂²×C₈₉	1	4	yes	complemented
429	#550	C₂²×C₈₉	1	12	yes	complemented
430	#550	C₂²×C₈₉	1	2	yes	complemented
431	#550	C₂²×C₈₉	1	4	yes	complemented
432	#550	C₂²×C₈₉	1	6	yes	complemented
433	#548	C₂²×C₈₉	1	4	yes	complemented
434	#548	C₂²×C₈₉	1	12	yes	complemented
435	#548	C₂²×C₈₉	1	4	yes	complemented
436	#547	C₂²×C₈₉	1	6	yes	complemented
437	#546	C₂²×C₈₉	1	12	yes	complemented
438	#546	C₂²×C₈₉	1	12	yes	complemented
439	#546	C₂²×C₈₉	1	12	yes	complemented
440	#546	C₂²×C₈₉	1	24	yes	complemented
441	D₄²	C₂²×C₈₉	1	12	yes	complemented
442	D₄²	C₂²×C₈₉	1	12	yes	complemented
443	D₄²	C₂²×C₈₉	1	12	yes	complemented
444	D₄²	C₂²×C₈₉	1	12	yes	complemented
445	D₄²	C₂²×C₈₉	1	6	yes	complemented
446	D₄²	C₂²×C₈₉	1	12	yes	complemented
447	#542	C₂²×C₈₉	1	12	yes	complemented
448	#540	C₂²×C₈₉	1	12	yes	complemented
449	#540	C₂²×C₈₉	1	12	yes	complemented
450	#540	C₂²×C₈₉	1	24	yes	complemented
451	#538	C₂²×C₈₉	1	24	yes	complemented
452	#538	C₂²×C₈₉	1	12	yes	complemented
453	#537	C₂²×C₈₉	1	12	yes	complemented
454	#536	C₂²×C₈₉	1	3	yes	complemented
455	#535	C₂²×C₈₉	1	6	yes	complemented
456	#535	C₂²×C₈₉	1	6	yes	complemented
457	#535	C₂²×C₈₉	1	12	yes	complemented
458	#535	C₂²×C₈₉	1	6	yes	complemented
459	#535	C₂²×C₈₉	1	6	yes	complemented
460	#535	C₂²×C₈₉	1	3	yes	complemented
461	#535	C₂²×C₈₉	1	24	yes	complemented
462	#534	C₂²×C₈₉	1	24	yes	complemented
463	#534	C₂²×C₈₉	1	12	yes	complemented
464	#532	C₂²×C₈₉	1	6	yes	complemented
465	#532	C₂²×C₈₉	1	3	yes	complemented
466	#532	C₂²×C₈₉	1	6	yes	complemented
467	C₂×#127	C₂²×C₈₉	1	6	yes	complemented
468	#529	C₂²×C₈₉	1	6	yes	complemented
469	#529	C₂²×C₈₉	1	12	yes	complemented
470	#529	C₂²×C₈₉	1	12	yes	complemented
471	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
472	#525	C₂²×C₈₉	1	6	yes	complemented
473	#525	C₂²×C₈₉	1	6	yes	complemented
474	#525	C₂²×C₈₉	1	12	yes	complemented
475	C₂×#121	C₂²×C₈₉	1	12	yes	complemented
476	#520	C₂²×C₈₉	1	4	yes	complemented
477	#519	C₂²×C₈₉	1	2	yes	complemented
478	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
479	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	2₋¹⁺⁴	—	4	4	no	—
481	H(5,𝔽₂)	—	4	8	no	—
482	H(5,𝔽₂)	—	4	4	no	—
483	C₂×#41	—	4	8	no	—
484	C₂×#41	C₂³×C₈₉	1	2	yes	—
485	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×#41	C₂³×C₈₉	1	4	yes	—
487	C₂×#41	C₂³×C₈₉	1	3	yes	—
488	C₂×#41	C₂³×C₈₉	1	6	yes	—
489	C₂×#41	C₂³×C₈₉	1	6	yes	—
490	C₂×#41	C₂³×C₈₉	1	3	yes	—
491	C₂×#41	C₂³×C₈₉	1	12	yes	—
492	C₂×#41	C₂³×C₈₉	1	12	yes	—
493	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
494	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
495	C₂²×D₄	C₂³×C₈₉	1	12	yes	—
496	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
497	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
498	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
499	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
500	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
501	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
502	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
503	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
505	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
506	#127	C₂³×C₈₉	1	6	yes	—
507	#127	C₂³×C₈₉	1	12	yes	—
508	#127	C₂³×C₈₉	1	12	yes	—
509	#127	C₂³×C₈₉	1	12	yes	—
510	#127	C₂³×C₈₉	1	6	yes	—
511	#127	C₂³×C₈₉	1	3	yes	—
512	#127	C₂³×C₈₉	1	12	yes	—
513	#126	C₂³×C₈₉	1	4	yes	—
514	#126	C₂³×C₈₉	1	12	yes	—
515	#126	C₂³×C₈₉	1	12	yes	—
516	#126	C₂³×C₈₉	1	24	yes	—
517	#125	C₂³×C₈₉	1	2	yes	—
518	#125	C₂³×C₈₉	1	12	yes	—
519	#125	C₂³×C₈₉	1	12	yes	—
520	#124	C₂³×C₈₉	1	3	yes	—
521	#124	C₂³×C₈₉	1	6	yes	—
522	#124	C₂³×C₈₉	1	12	yes	—
523	#124	C₂³×C₈₉	1	6	yes	—
524	#124	C₂³×C₈₉	1	12	yes	—
525	#124	C₂³×C₈₉	1	12	yes	—
526	#124	C₂³×C₈₉	1	1	yes	characteristic
527	#124	C₂³×C₈₉	1	6	yes	—
528	#124	C₂³×C₈₉	1	6	yes	—
529	#124	C₂³×C₈₉	1	12	yes	—
530	#124	C₂³×C₈₉	1	24	yes	—
531	#123	C₂³×C₈₉	1	2	yes	—
532	#123	C₂³×C₈₉	1	6	yes	—
533	#123	C₂³×C₈₉	1	12	yes	—
534	#123	C₂³×C₈₉	1	12	yes	—
535	#123	C₂³×C₈₉	1	24	yes	—
536	#123	C₂³×C₈₉	1	12	yes	—
537	#123	C₂³×C₈₉	1	12	yes	—
538	#123	C₂³×C₈₉	1	12	yes	—
539	#123	C₂³×C₈₉	1	24	yes	—
540	#123	C₂³×C₈₉	1	24	yes	—
541	#123	C₂³×C₈₉	1	12	yes	—
542	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
543	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
545	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
546	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
547	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
548	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
549	#121	C₂³×C₈₉	1	12	yes	—
550	#121	C₂³×C₈₉	1	24	yes	—
551	#121	C₂³×C₈₉	1	12	yes	—
552	#121	C₂³×C₈₉	1	12	yes	—
553	#121	C₂³×C₈₉	1	12	yes	—
554	#121	C₂³×C₈₉	1	12	yes	—
555	#121	C₂³×C₈₉	1	12	yes	—
556	#121	C₂³×C₈₉	1	12	yes	—
557	#121	C₂³×C₈₉	1	12	yes	—
558	#121	C₂³×C₈₉	1	6	yes	—
559	#121	C₂³×C₈₉	1	12	yes	—
560	#121	C₂³×C₈₉	1	12	yes	—
561	#121	C₂³×C₈₉	1	12	yes	—
562	#121	C₂³×C₈₉	1	12	yes	—
563	#121	C₂³×C₈₉	1	12	yes	—
564	#121	C₂³×C₈₉	1	12	yes	—
565	#121	C₂³×C₈₉	1	12	yes	—
566	#121	C₂³×C₈₉	1	24	yes	—
567	#121	C₂³×C₈₉	1	24	yes	—
568	#121	C₂³×C₈₉	1	24	yes	—
569	#121	C₂³×C₈₉	1	24	yes	—
570	#121	C₂³×C₈₉	1	24	yes	—
571	#120	C₂³×C₈₉	1	12	yes	—
572	#120	C₂³×C₈₉	1	12	yes	—
573	#120	C₂³×C₈₉	1	6	yes	—
574	#120	C₂³×C₈₉	1	6	yes	—
575	#120	C₂³×C₈₉	1	12	yes	—
576	#120	C₂³×C₈₉	1	12	yes	—
577	#120	C₂³×C₈₉	1	24	yes	—
578	#120	C₂³×C₈₉	1	24	yes	—
579	#120	C₂³×C₈₉	1	24	yes	—
580	#120	C₂³×C₈₉	1	12	yes	—
581	#120	C₂³×C₈₉	1	12	yes	—
582	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
583	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
584	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
585	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
586	C₄×D₄	C₂³×C₈₉	1	6	yes	—
587	C₄×D₄	C₂³×C₈₉	1	12	yes	—
588	C₄×D₄	C₂³×C₈₉	1	12	yes	—
589	C₄×D₄	C₂³×C₈₉	1	12	yes	—
590	C₄×D₄	C₂³×C₈₉	1	12	yes	—
591	C₄×D₄	C₂³×C₈₉	1	6	yes	—
592	C₄×D₄	C₂³×C₈₉	1	12	yes	—
593	C₄×D₄	C₂³×C₈₉	1	12	yes	—
594	C₄×D₄	C₂³×C₈₉	1	12	yes	—
595	C₄×D₄	C₂³×C₈₉	1	24	yes	—
596	C₄×D₄	C₂³×C₈₉	1	24	yes	—
597	C₄×D₄	C₂³×C₈₉	1	12	yes	—
598	#117	C₂³×C₈₉	1	6	yes	—
599	#117	C₂³×C₈₉	1	3	yes	—
600	#117	C₂³×C₈₉	1	6	yes	—
601	#117	C₂³×C₈₉	1	6	yes	—
602	#117	C₂³×C₈₉	1	12	yes	—
603	#117	C₂³×C₈₉	1	24	yes	—
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
607	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
608	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
609	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
610	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
611	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
612	#41	—	2	16	no	—
613	#41	—	2	8	no	—
614	#41	—	2	4	no	—
615	#41	—	4	12	no	—
616	#41	—	4	6	no	—
617	#41	—	4	6	no	—
618	#41	—	4	24	no	—
619	#41	—	4	12	no	—
620	#41	—	8	12	no	—
621	C₂×Q₈	—	2	8	no	—
622	C₂×Q₈	—	4	6	no	—
623	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
624	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
625	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
627	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
629	C₂×D₄	—	4	12	no	—
630	C₂×D₄	—	4	24	no	—
631	C₂×D₄	—	4	12	no	—
632	C₂×D₄	—	4	12	no	—
633	C₂×D₄	—	4	6	no	—
634	C₂×D₄	—	8	24	no	—
635	C₂×D₄	—	8	24	no	—
636	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
637	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
638	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
639	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
640	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
641	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
642	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
643	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
644	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
645	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
646	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
647	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
648	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
649	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
650	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
651	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
652	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
653	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
654	C₂²×C₄	—	4	12	no	—
655	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
656	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
657	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
658	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
659	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
660	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
661	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
662	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
663	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
664	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
666	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
667	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
668	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
670	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
672	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
677	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
678	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
679	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
680	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
681	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
682	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
683	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
684	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
685	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
686	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
687	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
688	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
689	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
690	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
691	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
692	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
693	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
695	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
696	C₄²	C₂⁴×C₈₉	1	2	yes	—
697	C₄²	C₂⁴×C₈₉	1	6	yes	—
698	C₄²	C₂⁴×C₈₉	1	6	yes	—
699	C₄²	C₂⁴×C₈₉	1	12	yes	—
700	C₄²	C₂⁴×C₈₉	1	3	yes	—
701	C₄²	C₂⁴×C₈₉	1	12	yes	—
702	C₂³	—	4	6	no	—
703	C₂³	—	4	12	no	—
704	C₂³	—	4	6	no	—
705	C₂³	—	4	12	no	—
706	C₂³	—	4	24	no	—
707	C₂³	—	4	12	no	—
708	C₂³	C₂⁵×C₈₉	1	6	yes	—
709	C₂³	C₂⁵×C₈₉	1	2	yes	—
710	C₂³	C₂⁵×C₈₉	1	12	yes	—
711	C₂³	C₂⁵×C₈₉	1	3	yes	—
712	Q₈	—	2	12	no	—
713	Q₈	—	4	3	no	—
714	Q₈	—	4	2	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	6	no	—
717	Q₈	H(5,𝔽₂)×C₈₉	1	4	yes	—
718	D₄	—	2	12	no	—
719	D₄	—	2	24	no	—
720	D₄	—	2	6	no	—
721	D₄	—	4	12	no	—
722	D₄	—	4	6	no	—
723	D₄	—	4	6	no	—
724	D₄	—	4	3	no	—
725	D₄	—	4	12	no	—
726	D₄	—	4	12	no	—
727	D₄	—	4	12	no	—
728	D₄	—	4	12	no	—
729	D₄	—	4	12	no	—
730	D₄	—	4	24	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	24	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	6	no	—
735	D₄	—	4	6	no	—
736	C₂×C₄	—	2	12	no	—
737	C₂×C₄	—	2	24	no	—
738	C₂×C₄	—	2	12	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	12	no	—
742	C₂×C₄	—	4	12	no	—
743	C₂×C₄	—	4	24	no	—
744	C₂×C₄	—	4	6	no	—
745	C₂×C₄	—	4	6	no	—
746	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
747	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
749	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
750	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
751	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
752	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
753	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
754	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	3	no	—
757	C₂²	—	2	12	no	—
758	C₂²	—	2	6	no	—
759	C₂²	—	2	12	no	—
760	C₂²	—	2	6	no	—
761	C₂²	—	2	12	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	12	no	—
764	C₂²	—	8	12	no	—
765	C₂²	—	16	12	no	—
766	C₂²	—	16	6	no	—
767	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	6	no	—
772	C₄	—	2	6	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	12	no	—
775	C₄	—	2	2	no	—
776	C₄	C₂×H(5,𝔽₂)×C₈₉	1	6	yes	—
777	C₂	—	4	2	no	—
778	C₂	—	4	12	no	—
779	C₂	—	4	3	no	—
780	C₂	—	4	6	no	—
781	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
782	C₂	C₈₉×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3558	C₂	semidirect
2. C₈₉×#3551	C₂	semidirect
3. C₈₉×#3549	C₂	semidirect
4. C₈₉×#3543	C₂	semidirect
5. C₈₉×#3542	C₂	semidirect
6. C₈₉×#3537	C₂	semidirect
7. C₈₉×#3529	C₂	semidirect
8. C₈₉×#3524	C₂	semidirect
9. C₈₉×#3517	C₂	semidirect
10. C₈₉×#3500	C₂	semidirect
11. C₈₉×#3498	C₂	semidirect
12. C₈₉×#3488	C₂	semidirect
13. C₈₉×#3487	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
15. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
17. C₂²×#41×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
19. #563×C₈₉	C₂²	semidirect
20. #562×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. H(3,𝔽₄)×C₈₉	C₂²	semidirect
24. #560×C₈₉	C₂²	semidirect
25. #560×C₈₉	C₂²	semidirect
26. #560×C₈₉	C₂²	semidirect
27. #560×C₈₉	C₂²	semidirect
28. #559×C₈₉	C₂²	semidirect
29. #557×C₈₉	C₂²	semidirect
30. #555×C₈₉	C₂²	semidirect
31. #555×C₈₉	C₂²	semidirect
32. #553×C₈₉	C₂²	semidirect
33. #553×C₈₉	C₂²	semidirect
34. #552×C₈₉	C₂²	semidirect
35. #551×C₈₉	C₂²	semidirect
36. #550×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
38. #550×C₈₉	C₂²	semidirect
39. #550×C₈₉	C₂²	semidirect
40. #550×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
43. #548×C₈₉	C₂²	semidirect
44. #547×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #546×C₈₉	C₂²	semidirect
47. #546×C₈₉	C₂²	semidirect
48. #546×C₈₉	C₂²	semidirect
49. D₄²×C₈₉	C₂²	semidirect
50. D₄²×C₈₉	C₂²	semidirect
51. D₄²×C₈₉	C₂²	semidirect
52. D₄²×C₈₉	C₂²	semidirect
53. D₄²×C₈₉	C₂²	semidirect
54. D₄²×C₈₉	C₂²	semidirect
55. #542×C₈₉	C₂²	semidirect
56. #540×C₈₉	C₂²	semidirect
57. #540×C₈₉	C₂²	semidirect
58. #540×C₈₉	C₂²	semidirect
59. #538×C₈₉	C₂²	semidirect
60. #538×C₈₉	C₂²	semidirect
61. #537×C₈₉	C₂²	semidirect
62. #536×C₈₉	C₂²	semidirect
63. #535×C₈₉	C₂²	semidirect
64. #535×C₈₉	C₂²	semidirect
65. #535×C₈₉	C₂²	semidirect
66. #535×C₈₉	C₂²	semidirect
67. #535×C₈₉	C₂²	semidirect
68. #535×C₈₉	C₂²	semidirect
69. #535×C₈₉	C₂²	semidirect
70. #534×C₈₉	C₂²	semidirect
71. #534×C₈₉	C₂²	semidirect
72. #532×C₈₉	C₂²	semidirect
73. #532×C₈₉	C₂²	semidirect
74. #532×C₈₉	C₂²	semidirect
75. C₂×#127×C₈₉	C₂²	semidirect
76. #529×C₈₉	C₂²	semidirect
77. #529×C₈₉	C₂²	semidirect
78. #529×C₈₉	C₂²	semidirect
79. C₂×#124×C₈₉	C₂²	semidirect
80. #525×C₈₉	C₂²	semidirect
81. #525×C₈₉	C₂²	semidirect
82. #525×C₈₉	C₂²	semidirect
83. C₂×#121×C₈₉	C₂²	semidirect
84. #520×C₈₉	C₂²	semidirect
85. #519×C₈₉	C₂²	semidirect
86. C₄×#41×C₈₉	C₂²	semidirect
87. C₄×#41×C₈₉	C₂²	semidirect
385. #63066	C₈₉	direct (N × H)
392. #3558	C₂×C₈₉	semidirect
393. #3551	C₂×C₈₉	semidirect
394. #3549	C₂×C₈₉	semidirect
395. #3543	C₂×C₈₉	semidirect
396. #3542	C₂×C₈₉	semidirect
397. #3537	C₂×C₈₉	semidirect
398. #3529	C₂×C₈₉	semidirect
399. #3524	C₂×C₈₉	semidirect
400. #3517	C₂×C₈₉	semidirect
401. #3500	C₂×C₈₉	semidirect
402. #3498	C₂×C₈₉	semidirect
403. #3488	C₂×C₈₉	semidirect
404. #3487	C₂×C₈₉	semidirect
405. C₈₉	#63066	direct (N × H)
406. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
407. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
408. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
409. C₂²×#41	C₂²×C₈₉	semidirect
410. #563	C₂²×C₈₉	semidirect
411. #563	C₂²×C₈₉	semidirect
412. #562	C₂²×C₈₉	semidirect
413. #562	C₂²×C₈₉	semidirect
414. H(3,𝔽₄)	C₂²×C₈₉	semidirect
415. H(3,𝔽₄)	C₂²×C₈₉	semidirect
416. #560	C₂²×C₈₉	semidirect
417. #560	C₂²×C₈₉	semidirect
418. #560	C₂²×C₈₉	semidirect
419. #560	C₂²×C₈₉	semidirect
420. #559	C₂²×C₈₉	semidirect
421. #557	C₂²×C₈₉	semidirect
422. #555	C₂²×C₈₉	semidirect
423. #555	C₂²×C₈₉	semidirect
424. #553	C₂²×C₈₉	semidirect
425. #553	C₂²×C₈₉	semidirect
426. #552	C₂²×C₈₉	semidirect
427. #551	C₂²×C₈₉	semidirect
428. #550	C₂²×C₈₉	semidirect
429. #550	C₂²×C₈₉	semidirect
430. #550	C₂²×C₈₉	semidirect
431. #550	C₂²×C₈₉	semidirect
432. #550	C₂²×C₈₉	semidirect
433. #548	C₂²×C₈₉	semidirect
434. #548	C₂²×C₈₉	semidirect
435. #548	C₂²×C₈₉	semidirect
436. #547	C₂²×C₈₉	semidirect
437. #546	C₂²×C₈₉	semidirect
438. #546	C₂²×C₈₉	semidirect
439. #546	C₂²×C₈₉	semidirect
440. #546	C₂²×C₈₉	semidirect
441. D₄²	C₂²×C₈₉	semidirect
442. D₄²	C₂²×C₈₉	semidirect
443. D₄²	C₂²×C₈₉	semidirect
444. D₄²	C₂²×C₈₉	semidirect
445. D₄²	C₂²×C₈₉	semidirect
446. D₄²	C₂²×C₈₉	semidirect
447. #542	C₂²×C₈₉	semidirect
448. #540	C₂²×C₈₉	semidirect
449. #540	C₂²×C₈₉	semidirect
450. #540	C₂²×C₈₉	semidirect
451. #538	C₂²×C₈₉	semidirect
452. #538	C₂²×C₈₉	semidirect
453. #537	C₂²×C₈₉	semidirect
454. #536	C₂²×C₈₉	semidirect
455. #535	C₂²×C₈₉	semidirect
456. #535	C₂²×C₈₉	semidirect
457. #535	C₂²×C₈₉	semidirect
458. #535	C₂²×C₈₉	semidirect
459. #535	C₂²×C₈₉	semidirect
460. #535	C₂²×C₈₉	semidirect
461. #535	C₂²×C₈₉	semidirect
462. #534	C₂²×C₈₉	semidirect
463. #534	C₂²×C₈₉	semidirect
464. #532	C₂²×C₈₉	semidirect
465. #532	C₂²×C₈₉	semidirect
466. #532	C₂²×C₈₉	semidirect
467. C₂×#127	C₂²×C₈₉	semidirect
468. #529	C₂²×C₈₉	semidirect
469. #529	C₂²×C₈₉	semidirect
470. #529	C₂²×C₈₉	semidirect
471. C₂×#124	C₂²×C₈₉	semidirect
472. #525	C₂²×C₈₉	semidirect
473. #525	C₂²×C₈₉	semidirect
474. #525	C₂²×C₈₉	semidirect
475. C₂×#121	C₂²×C₈₉	semidirect
476. #520	C₂²×C₈₉	semidirect
477. #519	C₂²×C₈₉	semidirect
478. C₄×#41	C₂²×C₈₉	semidirect
479. C₄×#41	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3558	2
C₈₉×#3551	2
C₈₉×#3549	2
C₈₉×#3543	2
C₈₉×#3542	2
C₈₉×#3537	2
C₈₉×#3529	2
C₈₉×#3524	2
C₈₉×#3517	2
C₈₉×#3500	2
C₈₉×#3498	2
C₈₉×#3488	2
C₈₉×#3487	2
#63066	89

Subgroups — C89×#63066 #36440914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63066 #36440914