Subgroups — C₂×C₈₉×#3551 #36440587

Order 22784.

7354 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3551	C₂	direct (N × H)
2. C₂×#563×C₈₉	C₂	semidirect
3. C₂×#560×C₈₉	C₂	semidirect
4. C₂×#555×C₈₉	C₂	semidirect
5. C₂×#553×C₈₉	C₂	semidirect
6. C₂×#552×C₈₉	C₂	semidirect
7. C₂×#551×C₈₉	C₂	semidirect
8. C₂×#548×C₈₉	C₂	semidirect
9. C₂×#546×C₈₉	C₂	semidirect
10. C₂×#540×C₈₉	C₂	semidirect
11. C₂×#538×C₈₉	C₂	semidirect
12. C₂×#537×C₈₉	C₂	semidirect
13. C₂×#536×C₈₉	C₂	semidirect
14. C₂×#535×C₈₉	C₂	semidirect
15. C₂×#532×C₈₉	C₂	semidirect
16. C₂×#529×C₈₉	C₂	semidirect
19. C₂²×#41×C₈₉	C₂²	semidirect
20. C₂³×Q₈×C₈₉	C₂²	semidirect
22. #563×C₈₉	C₂²	semidirect
23. #560×C₈₉	C₂²	semidirect
24. #555×C₈₉	C₂²	semidirect
25. #553×C₈₉	C₂²	semidirect
26. #552×C₈₉	C₂²	semidirect
27. #551×C₈₉	C₂²	semidirect
28. #548×C₈₉	C₂²	semidirect
29. #546×C₈₉	C₂²	semidirect
30. #540×C₈₉	C₂²	semidirect
31. #538×C₈₉	C₂²	semidirect
32. #537×C₈₉	C₂²	semidirect
33. #536×C₈₉	C₂²	semidirect
34. #535×C₈₉	C₂²	semidirect
35. #532×C₈₉	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
37. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
40. #529×C₈₉	C₂²	semidirect
42. C₂×#126×C₈₉	C₂²	semidirect
43. C₂×#126×C₈₉	C₂²	semidirect
44. C₂×#125×C₈₉	C₂²	semidirect
45. C₂×#125×C₈₉	C₂²	semidirect
50. C₂×#124×C₈₉	C₂²	semidirect
51. C₂×#124×C₈₉	C₂²	semidirect
55. C₂×#123×C₈₉	C₂²	semidirect
56. C₂×#123×C₈₉	C₂²	semidirect
57. C₂×#123×C₈₉	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
68. C₂×#121×C₈₉	C₂²	semidirect
69. C₂×#121×C₈₉	C₂²	semidirect
70. C₂×#121×C₈₉	C₂²	semidirect
71. C₂×#121×C₈₉	C₂²	semidirect
72. C₂×#121×C₈₉	C₂²	semidirect
73. C₂×#121×C₈₉	C₂²	semidirect
77. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
80. C₂×C₄×D₄×C₈₉	C₂²	semidirect
81. C₂×C₄×D₄×C₈₉	C₂²	semidirect
82. C₂×C₄×D₄×C₈₉	C₂²	semidirect
83. C₂×C₄×D₄×C₈₉	C₂²	semidirect
85. C₂×#117×C₈₉	C₂²	semidirect
86. C₂×#117×C₈₉	C₂²	semidirect
87. C₂×#117×C₈₉	C₂²	semidirect
88. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
90. C₂²×C₄²×C₈₉	C₂²	semidirect
97. C₂×#41×C₈₉	C₂³	semidirect
103. C₂²×Q₈×C₈₉	C₂³	semidirect
128. C₄⋊Q₈×C₈₉	C₂³	semidirect
129. C₄⋊Q₈×C₈₉	C₂³	semidirect
133. #126×C₈₉	C₂³	semidirect
134. #126×C₈₉	C₂³	semidirect
135. #125×C₈₉	C₂³	semidirect
136. #125×C₈₉	C₂³	semidirect
141. #124×C₈₉	C₂³	semidirect
142. #124×C₈₉	C₂³	semidirect
146. #123×C₈₉	C₂³	semidirect
147. #123×C₈₉	C₂³	semidirect
148. #123×C₈₉	C₂³	semidirect
150. C₂²⋊Q₈×C₈₉	C₂³	semidirect
151. C₂²⋊Q₈×C₈₉	C₂³	semidirect
152. C₂²⋊Q₈×C₈₉	C₂³	semidirect
153. C₂²⋊Q₈×C₈₉	C₂³	semidirect
159. #121×C₈₉	C₂³	semidirect
160. #121×C₈₉	C₂³	semidirect
161. #121×C₈₉	C₂³	semidirect
162. #121×C₈₉	C₂³	semidirect
163. #121×C₈₉	C₂³	semidirect
164. #121×C₈₉	C₂³	semidirect
168. C₄×Q₈×C₈₉	C₂³	semidirect
171. C₄×D₄×C₈₉	C₂³	semidirect
172. C₄×D₄×C₈₉	C₂³	semidirect
173. C₄×D₄×C₈₉	C₂³	semidirect
174. C₄×D₄×C₈₉	C₂³	semidirect
176. #117×C₈₉	C₂³	semidirect
177. #117×C₈₉	C₂³	semidirect
178. #117×C₈₉	C₂³	semidirect
190. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
213. C₂×C₄²×C₈₉	C₂³	semidirect
419. C₂×#3551	C₈₉	direct (N × H)
425. C₂×C₈₉	#3551	direct (N × H)
428. #3551	C₂×C₈₉	direct (N × H)
429. C₂×#563	C₂×C₈₉	semidirect
430. C₂×#560	C₂×C₈₉	semidirect
431. C₂×#555	C₂×C₈₉	semidirect
432. C₂×#553	C₂×C₈₉	semidirect
433. C₂×#552	C₂×C₈₉	semidirect
434. C₂×#551	C₂×C₈₉	semidirect
435. C₂×#548	C₂×C₈₉	semidirect
436. C₂×#546	C₂×C₈₉	semidirect
437. C₂×#540	C₂×C₈₉	semidirect
438. C₂×#538	C₂×C₈₉	semidirect
439. C₂×#537	C₂×C₈₉	semidirect
440. C₂×#536	C₂×C₈₉	semidirect
441. C₂×#535	C₂×C₈₉	semidirect
442. C₂×#532	C₂×C₈₉	semidirect
443. C₂×#529	C₂×C₈₉	semidirect
444. C₈₉	C₂×#3551	direct (N × H)
447. C₂²×#41	C₂²×C₈₉	semidirect
448. C₂³×Q₈	C₂²×C₈₉	semidirect
450. #563	C₂²×C₈₉	semidirect
451. #560	C₂²×C₈₉	semidirect
452. #555	C₂²×C₈₉	semidirect
453. #553	C₂²×C₈₉	semidirect
454. #552	C₂²×C₈₉	semidirect
455. #551	C₂²×C₈₉	semidirect
456. #548	C₂²×C₈₉	semidirect
457. #546	C₂²×C₈₉	semidirect
458. #540	C₂²×C₈₉	semidirect
459. #538	C₂²×C₈₉	semidirect
460. #537	C₂²×C₈₉	semidirect
461. #536	C₂²×C₈₉	semidirect
462. #535	C₂²×C₈₉	semidirect
463. #532	C₂²×C₈₉	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
465. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
468. #529	C₂²×C₈₉	semidirect
470. C₂×#126	C₂²×C₈₉	semidirect
471. C₂×#126	C₂²×C₈₉	semidirect
472. C₂×#125	C₂²×C₈₉	semidirect
473. C₂×#125	C₂²×C₈₉	semidirect
478. C₂×#124	C₂²×C₈₉	semidirect
479. C₂×#124	C₂²×C₈₉	semidirect
483. C₂×#123	C₂²×C₈₉	semidirect
484. C₂×#123	C₂²×C₈₉	semidirect
485. C₂×#123	C₂²×C₈₉	semidirect
487. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
489. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
490. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
496. C₂×#121	C₂²×C₈₉	semidirect
497. C₂×#121	C₂²×C₈₉	semidirect
498. C₂×#121	C₂²×C₈₉	semidirect
499. C₂×#121	C₂²×C₈₉	semidirect
500. C₂×#121	C₂²×C₈₉	semidirect
501. C₂×#121	C₂²×C₈₉	semidirect
505. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
508. C₂×C₄×D₄	C₂²×C₈₉	semidirect
509. C₂×C₄×D₄	C₂²×C₈₉	semidirect
510. C₂×C₄×D₄	C₂²×C₈₉	semidirect
511. C₂×C₄×D₄	C₂²×C₈₉	semidirect
513. C₂×#117	C₂²×C₈₉	semidirect
514. C₂×#117	C₂²×C₈₉	semidirect
515. C₂×#117	C₂²×C₈₉	semidirect
516. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
518. C₂²×C₄²	C₂²×C₈₉	semidirect
525. C₂×#41	C₂³×C₈₉	semidirect
531. C₂²×Q₈	C₂³×C₈₉	semidirect
556. C₄⋊Q₈	C₂³×C₈₉	semidirect
557. C₄⋊Q₈	C₂³×C₈₉	semidirect
561. #126	C₂³×C₈₉	semidirect
562. #126	C₂³×C₈₉	semidirect
563. #125	C₂³×C₈₉	semidirect
564. #125	C₂³×C₈₉	semidirect
569. #124	C₂³×C₈₉	semidirect
570. #124	C₂³×C₈₉	semidirect
574. #123	C₂³×C₈₉	semidirect
575. #123	C₂³×C₈₉	semidirect
576. #123	C₂³×C₈₉	semidirect
578. C₂²⋊Q₈	C₂³×C₈₉	semidirect
579. C₂²⋊Q₈	C₂³×C₈₉	semidirect
580. C₂²⋊Q₈	C₂³×C₈₉	semidirect
581. C₂²⋊Q₈	C₂³×C₈₉	semidirect
587. #121	C₂³×C₈₉	semidirect
588. #121	C₂³×C₈₉	semidirect
589. #121	C₂³×C₈₉	semidirect
590. #121	C₂³×C₈₉	semidirect
591. #121	C₂³×C₈₉	semidirect
592. #121	C₂³×C₈₉	semidirect
596. C₄×Q₈	C₂³×C₈₉	semidirect
599. C₄×D₄	C₂³×C₈₉	semidirect
600. C₄×D₄	C₂³×C₈₉	semidirect
601. C₄×D₄	C₂³×C₈₉	semidirect
602. C₄×D₄	C₂³×C₈₉	semidirect
604. #117	C₂³×C₈₉	semidirect
605. #117	C₂³×C₈₉	semidirect
606. #117	C₂³×C₈₉	semidirect
618. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
641. C₂×C₄²	C₂³×C₈₉	semidirect
852. C₂	C₈₉×#3551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3551	2
C₂×#563×C₈₉	2
C₂×#560×C₈₉	2
C₂×#555×C₈₉	2
C₂×#553×C₈₉	2
C₂×#552×C₈₉	2
C₂×#551×C₈₉	2
C₂×#548×C₈₉	2
C₂×#546×C₈₉	2
C₂×#540×C₈₉	2
C₂×#538×C₈₉	2
C₂×#537×C₈₉	2
C₂×#536×C₈₉	2
C₂×#535×C₈₉	2
C₂×#532×C₈₉	2
C₂×#529×C₈₉	2
C₂×#3551	89

Subgroups — C2×C89×#3551 #36440587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3551 #36440587