Subgroups — C₂×C₈₉×#3271 #36438877

Order 22784.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#550×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#548×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3271	C₂	1	16	yes	maximal, direct product factor
6	C₂×#496×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#465×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#137×C₈₉	—	2	8	no	—
22	C₂×#137×C₈₉	C₂²	1	8	yes	complemented
23	C₂×#135×C₈₉	—	2	8	no	—
24	C₂×#135×C₈₉	C₂²	1	8	yes	complemented
25	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
36	#550×C₈₉	—	2	4	no	—
37	#550×C₈₉	C₂²	1	8	yes	complemented
38	#548×C₈₉	—	2	4	no	—
39	#548×C₈₉	C₂²	1	8	yes	complemented
40	C₂×#127×C₈₉	—	2	1	no	—
41	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#124×C₈₉	—	2	1	no	—
43	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#121×C₈₉	—	2	1	no	—
47	C₂×#121×C₈₉	—	2	1	no	—
48	C₂×#121×C₈₉	—	2	1	no	—
49	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₈₉	—	2	1	no	—
55	C₂×C₄×D₄×C₈₉	—	2	1	no	—
56	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
57	#496×C₈₉	C₂²	1	8	yes	complemented
58	#469×C₈₉	C₂²	1	8	yes	complemented
59	#465×C₈₉	C₂²	1	8	yes	complemented
60	#464×C₈₉	C₂²	1	8	yes	complemented
61	#460×C₈₉	C₂²	1	8	yes	complemented
62	#452×C₈₉	C₂²	1	8	yes	complemented
63	#449×C₈₉	C₂²	1	8	yes	complemented
64	#449×C₈₉	C₂²	1	8	yes	complemented
65	#448×C₈₉	C₂²	1	8	yes	complemented
66	#441×C₈₉	C₂²	1	8	yes	complemented
67	#435×C₈₉	C₂²	1	8	yes	complemented
68	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
71	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
73	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
74	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
78	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
79	C₂×#41×C₈₉	—	2	2	no	—
80	C₂×#41×C₈₉	—	2	2	no	—
81	C₂×#41×C₈₉	—	2	2	no	—
82	C₂×#41×C₈₉	—	2	4	no	—
83	C₂×#41×C₈₉	—	2	4	no	—
84	C₂×#41×C₈₉	—	2	4	no	—
85	C₂×#41×C₈₉	—	4	2	no	—
86	C₂×#41×C₈₉	—	4	2	no	—
87	C₂×#41×C₈₉	—	4	2	no	—
88	C₂×#41×C₈₉	C₂³	1	4	yes	—
89	C₂×#41×C₈₉	C₂³	1	4	yes	—
90	C₂×#41×C₈₉	C₂³	1	4	yes	—
91	C₂²×Q₈×C₈₉	—	2	1	no	—
92	C₂²×Q₈×C₈₉	—	2	2	no	—
93	C₂²×Q₈×C₈₉	—	2	4	no	—
94	C₂²×Q₈×C₈₉	—	4	2	no	—
95	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
97	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	—	2	1	no	—
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	—	2	1	no	—
105	C₂²×D₄×C₈₉	—	2	1	no	—
106	C₂²×D₄×C₈₉	—	2	1	no	—
107	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	—	2	1	no	—
112	C₂³×C₄×C₈₉	—	2	1	no	—
113	C₂³×C₄×C₈₉	—	2	1	no	—
114	C₂³×C₄×C₈₉	—	2	1	no	—
115	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	#137×C₈₉	—	2	32	no	—
118	#135×C₈₉	—	2	32	no	—
119	C₂×Q₁₆×C₈₉	—	2	4	no	—
120	C₂×Q₁₆×C₈₉	D₄	1	8	yes	complemented
121	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
122	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
123	C₂×SD₁₆×C₈₉	—	2	4	no	—
124	C₂×SD₁₆×C₈₉	—	2	4	no	—
125	C₂×SD₁₆×C₈₉	—	2	4	no	—
126	C₂×SD₁₆×C₈₉	—	2	4	no	—
127	C₂×SD₁₆×C₈₉	—	4	2	no	—
128	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
133	C₂×D₈×C₈₉	—	2	4	no	—
134	C₂×D₈×C₈₉	—	4	2	no	—
135	C₂×D₈×C₈₉	C₂³	1	4	yes	—
136	C₂×D₈×C₈₉	C₂³	1	4	yes	—
137	C₂×M₁₆×C₈₉	—	2	4	no	—
138	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
139	C₂²×C₈×C₈₉	—	2	4	no	—
140	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
144	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	#127×C₈₉	—	2	8	no	—
146	#127×C₈₉	—	2	2	no	—
147	#127×C₈₉	C₂³	1	4	yes	—
148	#124×C₈₉	—	2	8	no	—
149	#124×C₈₉	—	2	2	no	—
150	#124×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₈₉	—	2	2	no	—
152	C₂²⋊Q₈×C₈₉	—	2	8	no	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
154	#121×C₈₉	—	2	8	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	8	no	—
159	#121×C₈₉	—	2	8	no	—
160	#121×C₈₉	C₂³	1	4	yes	—
161	#121×C₈₉	C₂³	1	4	yes	—
162	#121×C₈₉	C₂³	1	4	yes	—
163	C₄×Q₈×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
167	C₄×D₄×C₈₉	—	2	8	no	—
168	C₄×D₄×C₈₉	—	2	8	no	—
169	C₄×D₄×C₈₉	D₄	1	4	yes	—
170	C₄×D₄×C₈₉	C₂³	1	4	yes	—
171	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	—	2	1	no	—
186	C₂×C₄²×C₈₉	—	2	1	no	—
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	#106×C₈₉	C₂³	1	4	yes	—
189	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
190	#103×C₈₉	C₂³	1	4	yes	—
191	#103×C₈₉	C₂³	1	4	yes	—
192	#103×C₈₉	C₂³	1	4	yes	—
193	#102×C₈₉	C₂³	1	4	yes	—
194	#102×C₈₉	C₂³	1	4	yes	—
195	#102×C₈₉	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
198	#97×C₈₉	C₂³	1	4	yes	—
199	C₂⁴×C₈₉	—	2	1	no	—
200	C₂⁴×C₈₉	—	2	1	no	—
201	C₂⁴×C₈₉	—	2	1	no	—
202	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
204	#41×C₈₉	—	2	8	no	—
205	#41×C₈₉	—	2	8	no	—
206	#41×C₈₉	—	2	8	no	—
207	#41×C₈₉	—	4	4	no	—
208	#41×C₈₉	—	4	4	no	—
209	#41×C₈₉	—	4	4	no	—
210	#41×C₈₉	—	4	8	no	—
211	#41×C₈₉	—	4	8	no	—
212	#41×C₈₉	—	4	8	no	—
213	C₂×Q₈×C₈₉	—	2	1	no	—
214	C₂×Q₈×C₈₉	—	2	1	no	—
215	C₂×Q₈×C₈₉	—	2	4	no	—
216	C₂×Q₈×C₈₉	—	2	1	no	—
217	C₂×Q₈×C₈₉	—	2	2	no	—
218	C₂×Q₈×C₈₉	—	2	2	no	—
219	C₂×Q₈×C₈₉	—	2	8	no	—
220	C₂×Q₈×C₈₉	—	2	2	no	—
221	C₂×Q₈×C₈₉	—	2	2	no	—
222	C₂×Q₈×C₈₉	—	4	4	no	—
223	C₂×Q₈×C₈₉	—	4	4	no	—
224	C₂×Q₈×C₈₉	—	4	8	no	—
225	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
226	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
227	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
230	C₂×D₄×C₈₉	—	2	4	no	—
231	C₂×D₄×C₈₉	—	2	4	no	—
232	C₂×D₄×C₈₉	—	2	4	no	—
233	C₂×D₄×C₈₉	—	2	4	no	—
234	C₂×D₄×C₈₉	—	2	4	no	—
235	C₂×D₄×C₈₉	—	2	4	no	—
236	C₂×D₄×C₈₉	—	2	2	no	—
237	C₂×D₄×C₈₉	—	2	2	no	—
238	C₂×D₄×C₈₉	—	2	2	no	—
239	C₂×D₄×C₈₉	—	2	4	no	—
240	C₂×D₄×C₈₉	—	2	1	no	—
241	C₂×D₄×C₈₉	—	2	1	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	4	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	4	2	no	—
248	C₂×D₄×C₈₉	—	4	4	no	—
249	C₂×D₄×C₈₉	—	4	4	no	—
250	C₂×D₄×C₈₉	—	4	4	no	—
251	C₂×D₄×C₈₉	—	4	4	no	—
252	C₂×D₄×C₈₉	—	4	4	no	—
253	C₂×D₄×C₈₉	—	8	2	no	—
254	C₂×D₄×C₈₉	—	8	2	no	—
255	C₂×D₄×C₈₉	—	8	2	no	—
256	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₈₉	—	2	1	no	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	2	no	—
264	C₂²×C₄×C₈₉	—	2	2	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	4	no	—
267	C₂²×C₄×C₈₉	—	2	1	no	—
268	C₂²×C₄×C₈₉	—	2	1	no	—
269	C₂²×C₄×C₈₉	—	2	1	no	—
270	C₂²×C₄×C₈₉	—	2	4	no	—
271	C₂²×C₄×C₈₉	—	2	4	no	—
272	C₂²×C₄×C₈₉	—	2	4	no	—
273	C₂²×C₄×C₈₉	—	4	4	no	—
274	C₂²×C₄×C₈₉	—	4	4	no	—
275	C₂²×C₄×C₈₉	—	4	4	no	—
276	C₂²×C₄×C₈₉	—	4	4	no	—
277	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
286	Q₁₆×C₈₉	—	2	8	no	—
287	Q₁₆×C₈₉	C₂×D₄	1	16	yes	complemented
288	SD₁₆×C₈₉	—	2	8	no	—
289	SD₁₆×C₈₉	—	2	8	no	—
290	SD₁₆×C₈₉	—	2	8	no	—
291	SD₁₆×C₈₉	—	2	8	no	—
292	SD₁₆×C₈₉	—	4	4	no	—
293	D₈×C₈₉	—	2	8	no	—
294	D₈×C₈₉	—	4	4	no	—
295	M₁₆×C₈₉	—	2	8	no	—
296	C₂×C₈×C₈₉	—	2	2	no	—
297	C₂×C₈×C₈₉	—	2	2	no	—
298	C₂×C₈×C₈₉	—	2	2	no	—
299	C₂×C₈×C₈₉	—	2	8	no	—
300	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
301	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
302	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
303	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
304	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₈₉	—	2	4	no	—
306	C₄⋊C₄×C₈₉	—	2	4	no	—
307	C₄⋊C₄×C₈₉	—	2	4	no	—
308	C₄⋊C₄×C₈₉	—	2	1	no	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
311	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	4	no	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
321	C₄²×C₈₉	—	2	4	no	—
322	C₄²×C₈₉	—	2	4	no	—
323	C₄²×C₈₉	C₂×D₄	1	2	yes	—
324	C₄²×C₈₉	C₂⁴	1	2	yes	—
325	C₂³×C₈₉	—	2	2	no	—
326	C₂³×C₈₉	—	2	2	no	—
327	C₂³×C₈₉	—	2	2	no	—
328	C₂³×C₈₉	—	2	2	no	—
329	C₂³×C₈₉	—	2	2	no	—
330	C₂³×C₈₉	—	2	2	no	—
331	C₂³×C₈₉	—	2	2	no	—
332	C₂³×C₈₉	—	2	2	no	—
333	C₂³×C₈₉	—	2	2	no	—
334	C₂³×C₈₉	—	4	2	no	—
335	C₂³×C₈₉	—	4	2	no	—
336	C₂³×C₈₉	—	4	2	no	—
337	C₂³×C₈₉	—	4	2	no	—
338	C₂³×C₈₉	—	4	2	no	—
339	C₂³×C₈₉	—	4	2	no	—
340	C₂³×C₈₉	—	4	2	no	—
341	C₂³×C₈₉	—	4	2	no	—
342	C₂³×C₈₉	—	4	2	no	—
343	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
345	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₈₉	—	2	4	no	—
347	Q₈×C₈₉	—	2	4	no	—
348	Q₈×C₈₉	—	2	2	no	—
349	Q₈×C₈₉	—	2	2	no	—
350	Q₈×C₈₉	—	2	2	no	—
351	Q₈×C₈₉	—	2	2	no	—
352	Q₈×C₈₉	—	4	8	no	—
353	Q₈×C₈₉	—	4	2	no	—
354	Q₈×C₈₉	C₂²×D₄	1	4	yes	—
355	Q₈×C₈₉	C₂²×D₄	1	4	yes	—
356	D₄×C₈₉	—	2	2	no	—
357	D₄×C₈₉	—	2	2	no	—
358	D₄×C₈₉	—	2	2	no	—
359	D₄×C₈₉	—	2	2	no	—
360	D₄×C₈₉	—	2	2	no	—
361	D₄×C₈₉	—	2	2	no	—
362	D₄×C₈₉	—	4	4	no	—
363	D₄×C₈₉	—	4	8	no	—
364	D₄×C₈₉	—	4	8	no	—
365	D₄×C₈₉	—	4	8	no	—
366	D₄×C₈₉	—	4	8	no	—
367	D₄×C₈₉	—	4	8	no	—
368	D₄×C₈₉	—	4	2	no	—
369	D₄×C₈₉	—	4	2	no	—
370	D₄×C₈₉	—	4	2	no	—
371	D₄×C₈₉	—	8	4	no	—
372	D₄×C₈₉	—	8	4	no	—
373	D₄×C₈₉	—	8	4	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	4	no	—
377	C₂×C₄×C₈₉	—	2	4	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	4	no	—
383	C₂×C₄×C₈₉	—	2	4	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	4	8	no	—
392	C₂×C₄×C₈₉	—	4	8	no	—
393	C₂×C₄×C₈₉	—	4	8	no	—
394	C₂×C₄×C₈₉	—	4	8	no	—
395	C₂×C₄×C₈₉	—	4	2	no	—
396	C₂×C₄×C₈₉	—	4	2	no	—
397	C₂×C₄×C₈₉	—	4	2	no	—
398	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
406	C₈×C₈₉	—	2	2	no	—
407	C₈×C₈₉	—	2	2	no	—
408	C₈×C₈₉	—	2	2	no	—
409	C₈×C₈₉	C₂²×D₄	1	4	yes	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	2	2	no	—
414	C₂²×C₈₉	—	2	2	no	—
415	C₂²×C₈₉	—	2	2	no	—
416	C₂²×C₈₉	—	4	4	no	—
417	C₂²×C₈₉	—	4	4	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	—	4	2	no	—
420	C₂²×C₈₉	—	4	2	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	2	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	2	no	—
426	C₂²×C₈₉	—	4	2	no	—
427	C₂²×C₈₉	—	8	4	no	—
428	C₂²×C₈₉	—	8	4	no	—
429	C₂²×C₈₉	—	8	4	no	—
430	C₂²×C₈₉	D₄²	1	2	yes	—
431	C₂²×C₈₉	#575	1	2	yes	—
432	C₂²×C₈₉	#577	1	2	yes	—
433	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₈₉	—	2	2	no	—
435	C₄×C₈₉	—	2	2	no	—
436	C₄×C₈₉	—	2	4	no	—
437	C₄×C₈₉	—	2	4	no	—
438	C₄×C₈₉	—	2	2	no	—
439	C₄×C₈₉	—	2	2	no	—
440	C₄×C₈₉	—	4	2	no	—
441	C₄×C₈₉	—	4	2	no	—
442	C₄×C₈₉	—	4	2	no	—
443	C₄×C₈₉	D₄²	1	2	yes	—
444	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×#3271	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂×C₈₉	—	4	2	no	—
448	C₂×C₈₉	—	4	2	no	—
449	C₂×C₈₉	—	8	2	no	—
450	C₂×C₈₉	—	8	2	no	—
451	C₂×C₈₉	—	8	2	no	—
452	C₂×C₈₉	#3271	1	4	yes	direct product factor
453	C₂×C₈₉	C₂×D₄²	1	1	yes	characteristic
454	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
455	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
456	C₂²×#137	C₂×C₈₉	1	1	yes	characteristic, complemented
457	C₂²×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
458	C₂×#550	C₂×C₈₉	1	1	yes	characteristic, complemented
459	C₂×#548	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#3271	C₂×C₈₉	1	16	yes	direct product factor
461	C₂×#496	C₂×C₈₉	1	1	yes	characteristic, complemented
462	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
463	C₂×#465	C₂×C₈₉	1	1	yes	characteristic, complemented
464	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
466	C₂×#452	C₂×C₈₉	1	1	yes	characteristic, complemented
467	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
468	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
469	C₂×#448	C₂×C₈₉	1	1	yes	characteristic, complemented
470	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
471	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
472	C₈₉	C₂×#3271	1	1	yes	characteristic, direct product factor, Sylow
473	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
475	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
476	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×#137	—	2	8	no	—
478	C₂×#137	C₂²×C₈₉	1	8	yes	complemented
479	C₂×#135	—	2	8	no	—
480	C₂×#135	C₂²×C₈₉	1	8	yes	complemented
481	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
482	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
483	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
484	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
485	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
486	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
487	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
488	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
489	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
490	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
491	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
492	#550	—	2	4	no	—
493	#550	C₂²×C₈₉	1	8	yes	complemented
494	#548	—	2	4	no	—
495	#548	C₂²×C₈₉	1	8	yes	complemented
496	C₂×#127	—	2	1	no	—
497	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×#124	—	2	1	no	—
499	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
500	C₂×C₂²⋊Q₈	—	2	1	no	—
501	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
502	C₂×#121	—	2	1	no	—
503	C₂×#121	—	2	1	no	—
504	C₂×#121	—	2	1	no	—
505	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
508	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×C₄×D₄	—	2	1	no	—
511	C₂×C₄×D₄	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
513	#496	C₂²×C₈₉	1	8	yes	complemented
514	#469	C₂²×C₈₉	1	8	yes	complemented
515	#465	C₂²×C₈₉	1	8	yes	complemented
516	#464	C₂²×C₈₉	1	8	yes	complemented
517	#460	C₂²×C₈₉	1	8	yes	complemented
518	#452	C₂²×C₈₉	1	8	yes	complemented
519	#449	C₂²×C₈₉	1	8	yes	complemented
520	#449	C₂²×C₈₉	1	8	yes	complemented
521	#448	C₂²×C₈₉	1	8	yes	complemented
522	#441	C₂²×C₈₉	1	8	yes	complemented
523	#435	C₂²×C₈₉	1	8	yes	complemented
524	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
525	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
526	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
527	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
528	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
529	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
530	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
531	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	4	no	—
539	C₂×#41	—	2	4	no	—
540	C₂×#41	—	2	4	no	—
541	C₂×#41	—	4	2	no	—
542	C₂×#41	—	4	2	no	—
543	C₂×#41	—	4	2	no	—
544	C₂×#41	C₂³×C₈₉	1	4	yes	—
545	C₂×#41	C₂³×C₈₉	1	4	yes	—
546	C₂×#41	C₂³×C₈₉	1	4	yes	—
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×Q₈	—	2	2	no	—
549	C₂²×Q₈	—	2	4	no	—
550	C₂²×Q₈	—	4	2	no	—
551	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
553	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
567	C₂³×C₄	—	2	1	no	—
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
573	#137	—	2	32	no	—
574	#135	—	2	32	no	—
575	C₂×Q₁₆	—	2	4	no	—
576	C₂×Q₁₆	D₄×C₈₉	1	8	yes	complemented
577	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
578	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
579	C₂×SD₁₆	—	2	4	no	—
580	C₂×SD₁₆	—	2	4	no	—
581	C₂×SD₁₆	—	2	4	no	—
582	C₂×SD₁₆	—	2	4	no	—
583	C₂×SD₁₆	—	4	2	no	—
584	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
587	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
589	C₂×D₈	—	2	4	no	—
590	C₂×D₈	—	4	2	no	—
591	C₂×D₈	C₂³×C₈₉	1	4	yes	—
592	C₂×D₈	C₂³×C₈₉	1	4	yes	—
593	C₂×M₁₆	—	2	4	no	—
594	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
595	C₂²×C₈	—	2	4	no	—
596	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
598	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
601	#127	—	2	8	no	—
602	#127	—	2	2	no	—
603	#127	C₂³×C₈₉	1	4	yes	—
604	#124	—	2	8	no	—
605	#124	—	2	2	no	—
606	#124	C₂³×C₈₉	1	4	yes	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	8	no	—
609	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
610	#121	—	2	8	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	8	no	—
615	#121	—	2	8	no	—
616	#121	C₂³×C₈₉	1	4	yes	—
617	#121	C₂³×C₈₉	1	4	yes	—
618	#121	C₂³×C₈₉	1	4	yes	—
619	C₄×Q₈	—	2	2	no	—
620	C₄×Q₈	—	2	2	no	—
621	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
622	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
623	C₄×D₄	—	2	8	no	—
624	C₄×D₄	—	2	8	no	—
625	C₄×D₄	D₄×C₈₉	1	4	yes	—
626	C₄×D₄	C₂³×C₈₉	1	4	yes	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
644	#106	C₂³×C₈₉	1	4	yes	—
645	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
646	#103	C₂³×C₈₉	1	4	yes	—
647	#103	C₂³×C₈₉	1	4	yes	—
648	#103	C₂³×C₈₉	1	4	yes	—
649	#102	C₂³×C₈₉	1	4	yes	—
650	#102	C₂³×C₈₉	1	4	yes	—
651	#102	C₂³×C₈₉	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
654	#97	C₂³×C₈₉	1	4	yes	—
655	C₂⁴	—	2	1	no	—
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
660	#41	—	2	8	no	—
661	#41	—	2	8	no	—
662	#41	—	2	8	no	—
663	#41	—	4	4	no	—
664	#41	—	4	4	no	—
665	#41	—	4	4	no	—
666	#41	—	4	8	no	—
667	#41	—	4	8	no	—
668	#41	—	4	8	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	8	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	4	no	—
680	C₂×Q₈	—	4	8	no	—
681	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
682	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
683	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	8	2	no	—
710	C₂×D₄	—	8	2	no	—
711	C₂×D₄	—	8	2	no	—
712	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
713	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
714	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
715	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
738	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
742	Q₁₆	—	2	8	no	—
743	Q₁₆	C₂×D₄×C₈₉	1	16	yes	complemented
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	2	8	no	—
746	SD₁₆	—	2	8	no	—
747	SD₁₆	—	2	8	no	—
748	SD₁₆	—	4	4	no	—
749	D₈	—	2	8	no	—
750	D₈	—	4	4	no	—
751	M₁₆	—	2	8	no	—
752	C₂×C₈	—	2	2	no	—
753	C₂×C₈	—	2	2	no	—
754	C₂×C₈	—	2	2	no	—
755	C₂×C₈	—	2	8	no	—
756	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
757	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
758	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
759	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
760	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
767	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
776	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	C₂×D₄×C₈₉	1	2	yes	—
780	C₄²	C₂⁴×C₈₉	1	2	yes	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	4	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
800	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
801	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
802	Q₈	—	2	4	no	—
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	4	8	no	—
809	Q₈	—	4	2	no	—
810	Q₈	C₂²×D₄×C₈₉	1	4	yes	—
811	Q₈	C₂²×D₄×C₈₉	1	4	yes	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	2	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	8	4	no	—
828	D₄	—	8	4	no	—
829	D₄	—	8	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
860	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
861	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
862	C₈	—	2	2	no	—
863	C₈	—	2	2	no	—
864	C₈	—	2	2	no	—
865	C₈	C₂²×D₄×C₈₉	1	4	yes	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	4	no	—
884	C₂²	—	8	4	no	—
885	C₂²	—	8	4	no	—
886	C₂²	D₄²×C₈₉	1	2	yes	—
887	C₂²	#575×C₈₉	1	2	yes	—
888	C₂²	#577×C₈₉	1	2	yes	—
889	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	4	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	D₄²×C₈₉	1	2	yes	—
900	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
901	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
902	C₂	—	4	2	no	—
903	C₂	—	4	2	no	—
904	C₂	—	8	2	no	—
905	C₂	—	8	2	no	—
906	C₂	—	8	2	no	—
907	C₂	C₈₉×#3271	1	4	yes	direct product factor
908	C₂	C₂×D₄²×C₈₉	1	1	yes	characteristic
909	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
910	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₈₉	C₂	semidirect
2. C₂²×#135×C₈₉	C₂	semidirect
3. C₂×#550×C₈₉	C₂	semidirect
4. C₂×#548×C₈₉	C₂	semidirect
5. C₈₉×#3271	C₂	direct (N × H)
6. C₂×#496×C₈₉	C₂	semidirect
7. C₂×#469×C₈₉	C₂	semidirect
8. C₂×#465×C₈₉	C₂	semidirect
9. C₂×#464×C₈₉	C₂	semidirect
10. C₂×#460×C₈₉	C₂	semidirect
11. C₂×#452×C₈₉	C₂	semidirect
12. C₂×#449×C₈₉	C₂	semidirect
13. C₂×#449×C₈₉	C₂	semidirect
14. C₂×#448×C₈₉	C₂	semidirect
15. C₂×#441×C₈₉	C₂	semidirect
16. C₂×#435×C₈₉	C₂	semidirect
22. C₂×#137×C₈₉	C₂²	semidirect
24. C₂×#135×C₈₉	C₂²	semidirect
37. #550×C₈₉	C₂²	semidirect
39. #548×C₈₉	C₂²	semidirect
57. #496×C₈₉	C₂²	semidirect
58. #469×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #460×C₈₉	C₂²	semidirect
62. #452×C₈₉	C₂²	semidirect
63. #449×C₈₉	C₂²	semidirect
64. #449×C₈₉	C₂²	semidirect
65. #448×C₈₉	C₂²	semidirect
66. #441×C₈₉	C₂²	semidirect
67. #435×C₈₉	C₂²	semidirect
120. C₂×Q₁₆×C₈₉	D₄	semidirect
287. Q₁₆×C₈₉	C₂×D₄	semidirect
446. C₂×#3271	C₈₉	direct (N × H)
452. C₂×C₈₉	#3271	direct (N × H)
456. C₂²×#137	C₂×C₈₉	semidirect
457. C₂²×#135	C₂×C₈₉	semidirect
458. C₂×#550	C₂×C₈₉	semidirect
459. C₂×#548	C₂×C₈₉	semidirect
460. #3271	C₂×C₈₉	direct (N × H)
461. C₂×#496	C₂×C₈₉	semidirect
462. C₂×#469	C₂×C₈₉	semidirect
463. C₂×#465	C₂×C₈₉	semidirect
464. C₂×#464	C₂×C₈₉	semidirect
465. C₂×#460	C₂×C₈₉	semidirect
466. C₂×#452	C₂×C₈₉	semidirect
467. C₂×#449	C₂×C₈₉	semidirect
468. C₂×#449	C₂×C₈₉	semidirect
469. C₂×#448	C₂×C₈₉	semidirect
470. C₂×#441	C₂×C₈₉	semidirect
471. C₂×#435	C₂×C₈₉	semidirect
472. C₈₉	C₂×#3271	direct (N × H)
478. C₂×#137	C₂²×C₈₉	semidirect
480. C₂×#135	C₂²×C₈₉	semidirect
493. #550	C₂²×C₈₉	semidirect
495. #548	C₂²×C₈₉	semidirect
513. #496	C₂²×C₈₉	semidirect
514. #469	C₂²×C₈₉	semidirect
515. #465	C₂²×C₈₉	semidirect
516. #464	C₂²×C₈₉	semidirect
517. #460	C₂²×C₈₉	semidirect
518. #452	C₂²×C₈₉	semidirect
519. #449	C₂²×C₈₉	semidirect
520. #449	C₂²×C₈₉	semidirect
521. #448	C₂²×C₈₉	semidirect
522. #441	C₂²×C₈₉	semidirect
523. #435	C₂²×C₈₉	semidirect
576. C₂×Q₁₆	D₄×C₈₉	semidirect
743. Q₁₆	C₂×D₄×C₈₉	semidirect
907. C₂	C₈₉×#3271	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₈₉	2
C₂²×#135×C₈₉	2
C₂×#550×C₈₉	2
C₂×#548×C₈₉	2
C₈₉×#3271	2
C₂×#496×C₈₉	2
C₂×#469×C₈₉	2
C₂×#465×C₈₉	2
C₂×#464×C₈₉	2
C₂×#460×C₈₉	2
C₂×#452×C₈₉	2
C₂×#449×C₈₉	2
C₂×#448×C₈₉	2
C₂×#441×C₈₉	2
C₂×#435×C₈₉	2
C₂×#3271	89

Subgroups — C2×C89×#3271 #36438877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3271 #36438877