Subgroups — #26034864

Order 11392.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152351	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152351	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152350	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152349	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152317	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152316	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152306	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152305	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152288	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152285	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152284	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152281	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152279	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152274	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152274	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152227	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152224	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152213	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152212	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152210	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152208	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152205	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152205	C₂	1	1	yes	maximal, characteristic, complemented
24	#19152192	C₂	1	1	yes	maximal, characteristic, complemented
25	#19152191	C₂	1	1	yes	maximal, characteristic, complemented
26	#19152190	C₂	1	1	yes	maximal, characteristic, complemented
27	#19152183	C₂	1	1	yes	maximal, characteristic
28	#19152151	C₂	1	1	yes	maximal, characteristic, complemented
29	#19152125	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#15668005	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
32	#15668012	C₂²	1	1	yes	characteristic, complemented
33	#15668011	C₂²	1	1	yes	characteristic, complemented
34	#15668011	C₂²	1	1	yes	characteristic, complemented
35	#15668011	C₂²	1	1	yes	characteristic, complemented
36	#15668011	C₂²	1	1	yes	characteristic, complemented
37	#15668011	C₂²	1	1	yes	characteristic, complemented
38	#15668010	C₂²	1	1	yes	characteristic, complemented
39	#15668010	C₂²	1	1	yes	characteristic, complemented
40	#15668007	C₂²	1	1	yes	characteristic, complemented
41	#15668007	C₂²	1	1	yes	characteristic, complemented
42	#15668006	C₂²	1	1	yes	characteristic, complemented
43	#15668006	C₂²	1	1	yes	characteristic, complemented
44	#15668005	C₂²	1	1	yes	characteristic
45	#15668005	C₂²	1	1	yes	characteristic
46	#15668005	C₂²	1	1	yes	characteristic
47	#15668005	C₂²	1	1	yes	characteristic
48	#15668005	C₂²	1	1	yes	characteristic
49	#15668005	C₂²	1	1	yes	characteristic
50	#15668005	C₂²	1	1	yes	characteristic
51	#15668005	C₂²	1	1	yes	characteristic
52	#15668005	C₂²	1	1	yes	characteristic
53	#15668005	C₂²	1	1	yes	characteristic
54	#15668005	C₂²	1	1	yes	characteristic
55	#15668005	C₂²	1	1	yes	characteristic
56	#15668005	C₂²	1	1	yes	characteristic
57	#15668005	C₂²	1	1	yes	characteristic
58	#15668005	C₂²	1	1	yes	characteristic
59	#15668005	C₂²	1	1	yes	characteristic
60	#15668005	C₂²	1	1	yes	characteristic, complemented
61	#15668005	C₂²	1	1	yes	characteristic, complemented
62	#15668005	C₂²	1	1	yes	characteristic, complemented
63	#15668005	C₂²	1	1	yes	characteristic, complemented
64	#15668004	C₂²	1	1	yes	characteristic, complemented
65	#15668004	C₂²	1	1	yes	characteristic, complemented
66	#15668003	C₂²	1	1	yes	characteristic, complemented
67	#15668003	C₂²	1	1	yes	characteristic, complemented
68	#15668003	C₂²	1	1	yes	characteristic, complemented
69	#15668003	C₂²	1	1	yes	characteristic, complemented
70	#15668003	C₂²	1	1	yes	characteristic, complemented
71	#15668002	C₂²	1	1	yes	characteristic, complemented
72	#15668002	C₂²	1	1	yes	characteristic, complemented
73	#15668002	C₂²	1	1	yes	characteristic, complemented
74	#15668002	C₂²	1	1	yes	characteristic, complemented
75	#15668002	C₂²	1	1	yes	characteristic, complemented
76	#15668002	C₂²	1	1	yes	characteristic, complemented
77	#15668002	C₂²	1	1	yes	characteristic, complemented
78	#15668002	C₂²	1	1	yes	characteristic, complemented
79	#15668002	C₂²	1	1	yes	characteristic, complemented
80	#15668002	C₂²	1	1	yes	characteristic, complemented
81	#15668002	C₂²	1	1	yes	characteristic, complemented
82	#15668002	C₂²	1	1	yes	characteristic, complemented
83	#15667999	C₂²	1	1	yes	characteristic
84	#15667999	C₂²	1	1	yes	characteristic
85	#15667998	C₂²	1	1	yes	characteristic
86	#15667998	C₂²	1	1	yes	characteristic
87	#15667998	C₂²	1	1	yes	characteristic
88	#15667998	C₂²	1	1	yes	characteristic, complemented
89	#15667996	C₂²	1	1	yes	characteristic
90	#15667996	C₂²	1	1	yes	characteristic
91	#15667995	C₂²	1	1	yes	characteristic
92	#15667995	C₂²	1	1	yes	characteristic
93	#15667995	C₂²	1	1	yes	characteristic, complemented
94	#15667994	C₂²	1	1	yes	characteristic
95	#15667994	C₂²	1	1	yes	characteristic
96	#15667994	C₂²	1	1	yes	characteristic
97	#15667994	C₂²	1	1	yes	characteristic, complemented
98	#15667993	C₂²	1	1	yes	characteristic
99	#15667993	C₂²	1	1	yes	characteristic
100	#15667993	C₂²	1	1	yes	characteristic
101	#15667993	C₂²	1	1	yes	characteristic
102	#15667992	C₂²	1	1	yes	characteristic, complemented
103	#15667992	C₂²	1	1	yes	characteristic, complemented
104	#15667991	C₂²	1	1	yes	characteristic
105	#15667991	C₂²	1	1	yes	characteristic
106	#15667991	C₂²	1	1	yes	characteristic
107	#15667991	C₂²	1	1	yes	characteristic
108	#15667991	C₂²	1	1	yes	characteristic
109	#15667991	C₂²	1	1	yes	characteristic
110	#15667991	C₂²	1	1	yes	characteristic, complemented
111	#15667991	C₂²	1	1	yes	characteristic, complemented
112	#15667990	C₂²	1	1	yes	characteristic, complemented
113	#15667990	C₂²	1	1	yes	characteristic, complemented
114	#15667989	C₂²	1	1	yes	characteristic
115	#15667989	C₂²	1	1	yes	characteristic
116	#15667989	C₂²	1	1	yes	characteristic
117	#15667989	C₂²	1	1	yes	characteristic
118	#15667989	C₂²	1	1	yes	characteristic
119	#15667989	C₂²	1	1	yes	characteristic
120	#15667989	C₂²	1	1	yes	characteristic
121	#15667989	C₂²	1	1	yes	characteristic
122	#15667989	C₂²	1	1	yes	characteristic
123	#15667989	C₂²	1	1	yes	characteristic
124	#15667989	C₂²	1	1	yes	characteristic
125	#15667989	C₂²	1	1	yes	characteristic
126	#15667989	C₂²	1	1	yes	characteristic
127	#15667989	C₂²	1	1	yes	characteristic, complemented
128	#15667989	C₂²	1	1	yes	characteristic, complemented
129	#15667989	C₂²	1	1	yes	characteristic, complemented
130	#15667988	C₂²	1	1	yes	characteristic, complemented
131	#15667984	C₂²	1	1	yes	characteristic
132	#15667984	C₂²	1	1	yes	characteristic
133	#15667983	C₂²	1	1	yes	characteristic
134	#15667981	C₂²	1	1	yes	characteristic
135	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
138	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
139	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
140	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
141	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
142	#15667977	C₂²	1	1	yes	characteristic, complemented
143	#15667977	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
145	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
146	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
149	#15667972	C₂²	1	1	yes	characteristic
150	#15667972	C₂²	1	1	yes	characteristic
151	#15667972	C₂²	1	1	yes	characteristic
152	#15667972	C₂²	1	1	yes	characteristic, complemented
153	#15667971	C₂²	1	1	yes	characteristic
154	#15667971	C₂²	1	1	yes	characteristic
155	#15667970	C₂²	1	1	yes	characteristic, complemented
156	#15667969	C₂²	1	1	yes	characteristic, complemented
157	#15667968	C₂²	1	1	yes	characteristic
158	#15667968	C₂²	1	1	yes	characteristic
159	#15667968	C₂²	1	1	yes	characteristic
160	#15667968	C₂²	1	1	yes	characteristic
161	#15667968	C₂²	1	1	yes	characteristic, complemented
162	#15667968	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
164	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13083553	C₂²	1	1	yes	characteristic
166	C₂×#13083553	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
168	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
169	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
170	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
172	#126×C₈₉	C₂²	1	1	yes	characteristic
173	#126×C₈₉	C₂²	1	1	yes	characteristic
174	#124×C₈₉	C₂²	1	1	yes	characteristic
175	#123×C₈₉	C₂²	1	1	yes	characteristic
176	#123×C₈₉	C₂²	1	1	yes	characteristic
177	#123×C₈₉	C₂²	1	1	yes	characteristic
178	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
180	#120×C₈₉	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
183	#117×C₈₉	C₂²	1	1	yes	characteristic
184	#117×C₈₉	C₂²	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
188	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
189	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
190	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
191	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
192	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
193	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
199	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
206	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
228	#13083553	C₂³	1	1	yes	characteristic
229	#13083553	C₂³	1	1	yes	characteristic
230	#13083553	C₂³	1	1	yes	characteristic
231	#13083553	C₂³	1	1	yes	characteristic
232	#13083553	C₂³	1	1	yes	characteristic
233	#13083553	C₂³	1	1	yes	characteristic
234	#13083553	C₂³	1	1	yes	characteristic
235	#13083553	C₂³	1	1	yes	characteristic
236	#13083553	C₂³	1	1	yes	characteristic
237	#13083553	C₂³	1	1	yes	characteristic
238	#13083553	C₂³	1	1	yes	characteristic
239	#13083553	C₂³	1	1	yes	characteristic
240	#13083553	C₂³	1	1	yes	characteristic
241	#13083553	C₂³	1	1	yes	characteristic
242	#13083553	C₂³	1	1	yes	characteristic
243	#13083553	C₂³	1	1	yes	characteristic
244	#13083553	C₂³	1	1	yes	characteristic
245	#13083553	C₂³	1	1	yes	characteristic
246	#13083553	C₂³	1	1	yes	characteristic
247	#13083553	C₂³	1	1	yes	characteristic
248	#13083553	C₂³	1	1	yes	characteristic
249	#13083553	C₂³	1	1	yes	characteristic
250	#13083553	C₂³	1	1	yes	characteristic
251	#13083553	C₂³	1	1	yes	characteristic
252	#13083553	C₂³	1	1	yes	characteristic
253	#13083553	C₂³	1	1	yes	characteristic
254	#13083553	C₂³	1	1	yes	characteristic
255	#13083553	C₂³	1	1	yes	characteristic
256	#13083553	C₂³	1	1	yes	characteristic
257	#13083553	C₂³	1	1	yes	characteristic
258	#13083553	C₂³	1	1	yes	characteristic
259	#13083553	C₂³	1	1	yes	characteristic
260	#13083553	C₂³	1	1	yes	characteristic
261	#13083553	C₂³	1	1	yes	characteristic
262	#13083553	C₂³	1	1	yes	characteristic
263	#13083553	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
284	#13083551	C₂³	1	1	yes	characteristic
285	#13083551	C₂³	1	1	yes	characteristic
286	#13083551	C₂³	1	1	yes	characteristic
287	#13083551	C₂³	1	1	yes	characteristic
288	#13083551	C₂³	1	1	yes	characteristic
289	#13083551	C₂³	1	1	yes	characteristic
290	#13083551	C₂³	1	1	yes	characteristic
291	#13083551	C₂³	1	1	yes	characteristic
292	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
293	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
294	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
295	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
296	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
297	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
298	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
299	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
300	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
301	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
302	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
303	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
304	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
305	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
306	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
307	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
309	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
311	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
312	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
313	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
325	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₄²×C₈₉	C₂³	1	1	yes	characteristic
340	C₄²×C₈₉	C₂³	1	1	yes	characteristic
341	C₄²×C₈₉	C₂³	1	1	yes	characteristic
342	C₂³×C₈₉	—	2	2	no	—
343	C₂³×C₈₉	—	4	1	no	—
344	C₂³×C₈₉	—	4	1	no	—
345	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
350	Q₈×C₈₉	—	4	1	no	—
351	D₄×C₈₉	—	2	2	no	—
352	D₄×C₈₉	—	4	1	no	—
353	D₄×C₈₉	—	4	1	no	—
354	C₂×C₄×C₈₉	—	2	2	no	—
355	C₂×C₄×C₈₉	—	4	1	no	—
356	C₂×C₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²⋊D₈₉	—	2	2	no	—
371	C₂²⋊D₈₉	—	4	1	no	—
372	C₂²⋊D₈₉	—	4	1	no	—
373	C₂²⋊D₈₉	—	4	1	no	—
374	C₂×Dic₈₉	—	2	2	no	—
375	C₂×Dic₈₉	—	4	1	no	—
376	C₂×Dic₈₉	—	4	1	no	—
377	C₂×Dic₈₉	—	4	1	no	—
378	C₂×Dic₈₉	—	4	1	no	—
379	C₂×Dic₈₉	—	4	1	no	—
380	C₂×Dic₈₉	—	4	1	no	—
381	C₂×Dic₈₉	—	4	1	no	—
382	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
397	C₄×D₈₉	—	4	1	no	—
398	C₄×D₈₉	—	4	1	no	—
399	C₄×D₈₉	—	4	1	no	—
400	Dic₁₇₈	—	4	1	no	—
401	Dic₁₇₈	—	4	1	no	—
402	Dic₁₇₈	—	4	1	no	—
403	Dic₁₇₈	—	4	1	no	—
404	Dic₁₇₈	—	4	1	no	—
405	Dic₁₇₈	—	4	1	no	—
406	Dic₁₇₈	—	4	1	no	—
407	Dic₁₇₈	—	4	1	no	—
408	C₂²×C₈₉	—	2	1	no	—
409	C₂²×C₈₉	—	2	1	no	—
410	C₂²×C₈₉	—	2	1	no	—
411	C₂²×C₈₉	—	2	1	no	—
412	C₂²×C₈₉	—	2	1	no	—
413	C₂²×C₈₉	—	2	1	no	—
414	C₂²×C₈₉	—	2	1	no	—
415	C₂²×C₈₉	—	2	1	no	—
416	C₂²×C₈₉	—	2	1	no	—
417	C₂²×C₈₉	—	2	1	no	—
418	C₂²×C₈₉	—	2	1	no	—
419	C₂²×C₈₉	—	8	2	no	—
420	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
421	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
422	C₂×D₈₉	—	2	1	no	—
423	C₂×D₈₉	—	2	1	no	—
424	C₂×D₈₉	—	2	1	no	—
425	C₄×C₈₉	—	2	1	no	—
426	C₄×C₈₉	—	2	1	no	—
427	C₄×C₈₉	—	2	1	no	—
428	C₄×C₈₉	—	2	1	no	—
429	C₄×C₈₉	—	2	1	no	—
430	C₄×C₈₉	—	2	1	no	—
431	C₄×C₈₉	—	2	1	no	—
432	C₄×C₈₉	—	2	1	no	—
433	C₄×C₈₉	—	2	1	no	—
434	C₄×C₈₉	—	2	1	no	—
435	C₄×C₈₉	—	2	1	no	—
436	Dic₈₉	—	2	1	no	—
437	Dic₈₉	—	2	1	no	—
438	Dic₈₉	—	2	1	no	—
439	Dic₈₉	—	2	1	no	—
440	Dic₈₉	—	2	1	no	—
441	Dic₈₉	—	2	1	no	—
442	Dic₈₉	—	2	1	no	—
443	Dic₈₉	—	2	1	no	—
444	Dic₈₉	—	2	1	no	—
445	Dic₈₉	—	2	1	no	—
446	Dic₈₉	—	2	1	no	—
447	Dic₈₉	—	2	1	no	—
448	Dic₈₉	—	2	1	no	—
449	Dic₈₉	—	2	1	no	—
450	Dic₈₉	—	2	1	no	—
451	C₂×C₈₉	—	2	2	no	—
452	C₂×C₈₉	—	4	1	no	—
453	C₂×C₈₉	—	4	1	no	—
454	C₂×C₈₉	—	4	1	no	—
455	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₈₉	#585	1	1	yes	characteristic
457	C₂×C₈₉	#585	1	1	yes	characteristic
458	D₈₉	—	4	1	no	—
459	#3564	—	89	1	no	maximal, Sylow
460	C₈₉	#3564	1	1	yes	characteristic, complemented, Sylow
461	#563	—	89	1	no	—
462	#563	—	89	1	no	—
463	#563	—	89	1	no	—
464	#563	—	89	1	no	—
465	#556	—	89	1	no	—
466	#556	—	89	1	no	—
467	#554	—	89	1	no	—
468	#554	—	89	1	no	—
469	#552	—	89	1	no	—
470	#552	—	89	1	no	—
471	#552	—	89	1	no	—
472	#552	—	89	1	no	—
473	#551	—	89	1	no	—
474	#551	—	89	1	no	—
475	#551	—	89	1	no	—
476	#551	D₈₉	1	1	yes	characteristic, complemented
477	#544	—	89	1	no	—
478	#543	—	89	1	no	—
479	#542	—	89	1	no	—
480	#542	—	89	1	no	—
481	#541	—	89	1	no	—
482	#541	—	89	1	no	—
483	#541	—	89	1	no	—
484	#541	—	89	1	no	—
485	#539	—	89	1	no	—
486	#539	—	89	1	no	—
487	#539	—	89	1	no	—
488	#538	—	89	1	no	—
489	#533	—	89	1	no	—
490	#529	—	89	1	no	—
491	C₂×#126	—	89	1	no	—
492	C₄⋊Q₈	—	89	1	no	—
493	C₄⋊Q₈	—	89	1	no	—
494	C₄⋊Q₈	—	89	1	no	—
495	C₄⋊Q₈	—	89	1	no	—
496	C₄⋊Q₈	—	89	1	no	—
497	C₄⋊Q₈	—	89	1	no	—
498	C₄⋊Q₈	—	89	1	no	—
499	C₄⋊Q₈	—	89	1	no	—
500	#126	—	89	1	no	—
501	#126	—	89	1	no	—
502	#126	—	89	1	no	—
503	#126	—	89	1	no	—
504	#126	—	89	1	no	—
505	#126	—	89	1	no	—
506	#126	—	89	1	no	—
507	#126	—	89	1	no	—
508	#126	—	89	1	no	—
509	#126	—	89	1	no	—
510	#126	—	89	1	no	—
511	#126	—	89	1	no	—
512	#126	—	89	1	no	—
513	#126	—	89	1	no	—
514	#126	—	89	1	no	—
515	#126	—	89	1	no	—
516	#126	—	89	1	no	—
517	#126	—	89	1	no	—
518	#126	—	89	1	no	—
519	#126	—	89	1	no	—
520	#126	—	89	1	no	—
521	#126	—	89	1	no	—
522	#126	—	89	1	no	—
523	#126	—	89	1	no	—
524	#126	C₂×D₈₉	1	1	yes	characteristic
525	#126	C₂×D₈₉	1	1	yes	characteristic
526	#125	—	89	1	no	—
527	#125	—	89	1	no	—
528	#125	—	89	1	no	—
529	#125	—	89	1	no	—
530	#125	—	89	1	no	—
531	#125	—	89	1	no	—
532	#125	—	89	1	no	—
533	#125	—	89	1	no	—
534	#125	—	89	1	no	—
535	#125	—	89	1	no	—
536	#125	—	89	1	no	—
537	#125	—	89	1	no	—
538	#125	—	89	1	no	—
539	#125	—	89	1	no	—
540	#125	—	89	1	no	—
541	#125	—	89	1	no	—
542	#125	—	89	1	no	—
543	#125	—	89	1	no	—
544	#125	—	89	1	no	—
545	#124	—	89	1	no	—
546	#124	—	89	1	no	—
547	#124	—	89	1	no	—
548	#124	—	89	1	no	—
549	#124	—	89	1	no	—
550	#124	—	89	1	no	—
551	#124	C₂×D₈₉	1	1	yes	characteristic
552	#123	—	89	1	no	—
553	#123	—	89	1	no	—
554	#123	—	89	1	no	—
555	#123	—	89	1	no	—
556	#123	—	89	1	no	—
557	#123	—	89	1	no	—
558	#123	—	89	1	no	—
559	#123	—	89	1	no	—
560	#123	—	89	1	no	—
561	#123	—	89	1	no	—
562	#123	—	89	1	no	—
563	#123	—	89	1	no	—
564	#123	—	89	1	no	—
565	#123	C₂×D₈₉	1	1	yes	characteristic
566	#123	C₂×D₈₉	1	1	yes	characteristic
567	#123	C₂×D₈₉	1	1	yes	characteristic
568	C₂²⋊Q₈	—	89	1	no	—
569	C₂²⋊Q₈	—	89	1	no	—
570	C₂²⋊Q₈	—	89	1	no	—
571	C₂²⋊Q₈	—	89	1	no	—
572	C₂²⋊Q₈	—	89	1	no	—
573	C₂²⋊Q₈	—	89	1	no	—
574	C₂²⋊Q₈	—	89	1	no	—
575	C₂²⋊Q₈	—	89	1	no	—
576	C₂²⋊Q₈	—	89	1	no	—
577	C₂²⋊Q₈	—	89	1	no	—
578	C₂²⋊Q₈	—	89	1	no	—
579	C₂²⋊Q₈	—	89	1	no	—
580	C₂²⋊Q₈	—	89	1	no	—
581	C₂²⋊Q₈	—	89	1	no	—
582	C₂²⋊Q₈	—	89	1	no	—
583	C₂²⋊Q₈	—	89	1	no	—
584	C₂²⋊Q₈	—	89	1	no	—
585	C₂²⋊Q₈	—	89	1	no	—
586	C₂²⋊Q₈	—	89	1	no	—
587	C₂²⋊Q₈	—	89	1	no	—
588	C₂²⋊Q₈	—	89	1	no	—
589	C₂²⋊Q₈	—	89	1	no	—
590	C₂²⋊Q₈	—	89	1	no	—
591	C₂²⋊Q₈	—	89	1	no	—
592	C₂²⋊Q₈	—	89	1	no	—
593	C₂²⋊Q₈	—	89	1	no	—
594	C₂²⋊Q₈	—	89	1	no	—
595	C₂²⋊Q₈	—	89	1	no	—
596	C₂²⋊Q₈	—	89	1	no	—
597	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
598	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
599	#121	—	89	1	no	—
600	#121	—	89	1	no	—
601	#121	—	89	1	no	—
602	#120	—	89	1	no	—
603	#120	C₂×D₈₉	1	1	yes	characteristic
604	C₄×Q₈	—	89	1	no	—
605	C₄×Q₈	—	89	1	no	—
606	C₄×Q₈	—	89	1	no	—
607	C₄×Q₈	—	89	1	no	—
608	C₄×Q₈	—	89	1	no	—
609	C₄×Q₈	—	89	1	no	—
610	C₄×Q₈	—	89	1	no	—
611	C₄×Q₈	—	89	1	no	—
612	C₄×Q₈	—	89	1	no	—
613	C₄×D₄	—	89	1	no	—
614	C₄×D₄	—	89	1	no	—
615	C₄×D₄	—	89	1	no	—
616	C₄×D₄	—	89	1	no	—
617	C₄×D₄	—	89	1	no	—
618	C₄×D₄	—	89	1	no	—
619	C₄×D₄	—	89	1	no	—
620	C₄×D₄	—	89	1	no	—
621	C₄×D₄	—	89	1	no	—
622	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
623	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
624	#117	—	89	1	no	—
625	#117	—	89	1	no	—
626	#117	—	89	1	no	—
627	#117	—	89	1	no	—
628	#117	—	89	1	no	—
629	#117	—	89	1	no	—
630	#117	—	89	1	no	—
631	#117	—	89	1	no	—
632	#117	—	89	1	no	—
633	#117	—	89	1	no	—
634	#117	C₂×D₈₉	1	1	yes	characteristic
635	#117	C₂×D₈₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	—	89	1	no	—
637	C₂×C₄⋊C₄	—	89	1	no	—
638	C₂×C₄⋊C₄	—	89	1	no	—
639	C₂×C₄⋊C₄	—	89	1	no	—
640	C₂×C₄⋊C₄	—	89	1	no	—
641	C₂×C₂²⋊C₄	—	89	1	no	—
642	C₂×C₂²⋊C₄	—	89	1	no	—
643	C₂×C₂²⋊C₄	—	89	1	no	—
644	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
646	C₂×C₄²	—	89	1	no	—
647	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
648	C₂×Q₈	—	89	1	no	—
649	C₂×Q₈	—	89	1	no	—
650	C₂×Q₈	—	89	1	no	—
651	C₂×Q₈	—	89	1	no	—
652	C₂×Q₈	—	89	1	no	—
653	C₂×Q₈	—	89	1	no	—
654	C₂×Q₈	—	89	1	no	—
655	C₂×Q₈	—	89	1	no	—
656	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
657	C₂×D₄	—	89	1	no	—
658	C₂×D₄	—	89	1	no	—
659	C₂×D₄	—	89	1	no	—
660	C₂×D₄	—	89	1	no	—
661	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
662	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
663	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
664	C₂²×C₄	—	89	1	no	—
665	C₂²×C₄	—	89	1	no	—
666	C₂²×C₄	—	89	1	no	—
667	C₂²×C₄	—	89	1	no	—
668	C₂²×C₄	—	89	1	no	—
669	C₂²×C₄	—	89	1	no	—
670	C₂²×C₄	—	89	1	no	—
671	C₂²×C₄	—	89	1	no	—
672	C₂²×C₄	—	89	1	no	—
673	C₂²×C₄	—	89	1	no	—
674	C₂²×C₄	—	89	1	no	—
675	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
676	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
677	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
678	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
679	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
680	C₄⋊C₄	—	89	1	no	—
681	C₄⋊C₄	—	89	1	no	—
682	C₄⋊C₄	—	89	1	no	—
683	C₄⋊C₄	—	89	1	no	—
684	C₄⋊C₄	—	89	1	no	—
685	C₄⋊C₄	—	89	1	no	—
686	C₄⋊C₄	—	89	1	no	—
687	C₄⋊C₄	—	89	1	no	—
688	C₄⋊C₄	—	89	1	no	—
689	C₄⋊C₄	—	89	1	no	—
690	C₄⋊C₄	—	89	1	no	—
691	C₄⋊C₄	—	89	1	no	—
692	C₄⋊C₄	—	89	1	no	—
693	C₄⋊C₄	—	89	1	no	—
694	C₄⋊C₄	—	89	1	no	—
695	C₄⋊C₄	—	89	1	no	—
696	C₄⋊C₄	—	89	1	no	—
697	C₄⋊C₄	—	89	1	no	—
698	C₄⋊C₄	—	89	1	no	—
699	C₄⋊C₄	—	89	1	no	—
700	C₄⋊C₄	—	89	1	no	—
701	C₄⋊C₄	—	89	1	no	—
702	C₄⋊C₄	—	89	1	no	—
703	C₄⋊C₄	—	89	1	no	—
704	C₄⋊C₄	—	89	1	no	—
705	C₄⋊C₄	—	89	1	no	—
706	C₄⋊C₄	—	89	1	no	—
707	C₄⋊C₄	—	89	1	no	—
708	C₄⋊C₄	—	89	1	no	—
709	C₄⋊C₄	—	89	1	no	—
710	C₄⋊C₄	—	89	1	no	—
711	C₄⋊C₄	—	89	1	no	—
712	C₄⋊C₄	—	89	1	no	—
713	C₄⋊C₄	—	89	1	no	—
714	C₄⋊C₄	—	89	1	no	—
715	C₄⋊C₄	—	89	1	no	—
716	C₄⋊C₄	—	89	1	no	—
717	C₄⋊C₄	—	89	1	no	—
718	C₄⋊C₄	—	89	1	no	—
719	C₄⋊C₄	—	89	1	no	—
720	C₄⋊C₄	—	89	1	no	—
721	C₄⋊C₄	—	89	1	no	—
722	C₄⋊C₄	—	89	1	no	—
723	C₄⋊C₄	—	89	1	no	—
724	C₄⋊C₄	—	89	1	no	—
725	C₄⋊C₄	—	89	1	no	—
726	C₄⋊C₄	—	89	1	no	—
727	C₄⋊C₄	—	89	1	no	—
728	C₄⋊C₄	—	89	1	no	—
729	C₄⋊C₄	—	89	1	no	—
730	C₄⋊C₄	—	89	1	no	—
731	C₄⋊C₄	—	89	1	no	—
732	C₄⋊C₄	—	89	1	no	—
733	C₄⋊C₄	—	89	1	no	—
734	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
742	C₂²⋊C₄	—	89	1	no	—
743	C₂²⋊C₄	—	89	1	no	—
744	C₂²⋊C₄	—	89	1	no	—
745	C₂²⋊C₄	—	89	1	no	—
746	C₂²⋊C₄	—	89	1	no	—
747	C₂²⋊C₄	—	89	1	no	—
748	C₂²⋊C₄	—	89	1	no	—
749	C₂²⋊C₄	—	89	1	no	—
750	C₂²⋊C₄	—	89	1	no	—
751	C₂²⋊C₄	—	89	1	no	—
752	C₂²⋊C₄	—	89	1	no	—
753	C₂²⋊C₄	—	89	1	no	—
754	C₂²⋊C₄	—	89	1	no	—
755	C₂²⋊C₄	—	89	1	no	—
756	C₂²⋊C₄	—	89	1	no	—
757	C₂²⋊C₄	—	89	1	no	—
758	C₂²⋊C₄	—	89	1	no	—
759	C₂²⋊C₄	—	89	1	no	—
760	C₂²⋊C₄	—	89	1	no	—
761	C₂²⋊C₄	—	89	1	no	—
762	C₂²⋊C₄	—	89	1	no	—
763	C₂²⋊C₄	—	89	1	no	—
764	C₂²⋊C₄	—	89	1	no	—
765	C₂²⋊C₄	—	89	1	no	—
766	C₂²⋊C₄	—	89	1	no	—
767	C₂²⋊C₄	—	89	1	no	—
768	C₂²⋊C₄	—	89	1	no	—
769	C₂²⋊C₄	—	89	1	no	—
770	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
777	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
778	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
784	C₄²	—	89	1	no	—
785	C₄²	—	89	1	no	—
786	C₄²	—	89	1	no	—
787	C₄²	—	89	1	no	—
788	C₄²	—	89	1	no	—
789	C₄²	—	89	1	no	—
790	C₄²	—	89	1	no	—
791	C₄²	—	89	1	no	—
792	C₄²	—	89	1	no	—
793	C₄²	—	89	1	no	—
794	C₄²	—	89	1	no	—
795	C₄²	—	89	1	no	—
796	C₄²	—	89	1	no	—
797	C₄²	—	89	1	no	—
798	C₄²	—	89	1	no	—
799	C₄²	C₂²×D₈₉	1	1	yes	characteristic
800	C₄²	C₂²×D₈₉	1	1	yes	characteristic
801	C₄²	C₂²×D₈₉	1	1	yes	characteristic
802	C₂³	—	2	2	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	89	1	no	—
806	C₂³	C₂³×D₈₉	1	1	yes	characteristic
807	C₂³	C₂³×D₈₉	1	1	yes	characteristic
808	C₂³	C₂³×D₈₉	1	1	yes	characteristic
809	C₂³	C₂³×D₈₉	1	1	yes	characteristic
810	Q₈	—	4	1	no	—
811	Q₈	—	356	1	no	—
812	Q₈	—	356	1	no	—
813	Q₈	—	356	1	no	—
814	Q₈	—	356	1	no	—
815	Q₈	—	356	1	no	—
816	Q₈	—	356	1	no	—
817	Q₈	—	356	1	no	—
818	Q₈	—	356	1	no	—
819	D₄	—	2	2	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	356	1	no	—
823	D₄	—	356	1	no	—
824	D₄	—	356	1	no	—
825	D₄	—	178	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	89	1	no	—
832	C₂×C₄	—	89	1	no	—
833	C₂×C₄	—	89	1	no	—
834	C₂×C₄	—	89	1	no	—
835	C₂×C₄	—	89	1	no	—
836	C₂×C₄	—	89	1	no	—
837	C₂×C₄	—	89	1	no	—
838	C₂×C₄	—	89	1	no	—
839	C₂×C₄	—	89	1	no	—
840	C₂×C₄	—	89	1	no	—
841	C₂×C₄	—	89	1	no	—
842	C₂×C₄	—	89	1	no	—
843	C₂×C₄	—	89	1	no	—
844	C₂×C₄	—	89	1	no	—
845	C₂×C₄	—	89	1	no	—
846	C₂×C₄	—	356	1	no	—
847	C₂×C₄	—	356	1	no	—
848	C₂×C₄	—	356	1	no	—
849	C₂×C₄	—	356	1	no	—
850	C₂×C₄	—	356	1	no	—
851	C₂×C₄	—	356	1	no	—
852	C₂×C₄	—	356	1	no	—
853	C₂×C₄	—	356	1	no	—
854	C₂×C₄	—	356	1	no	—
855	C₂×C₄	—	356	1	no	—
856	C₂×C₄	—	178	2	no	—
857	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	8	2	no	—
880	C₂²	—	178	1	no	—
881	C₂²	—	178	1	no	—
882	C₂²	—	178	1	no	—
883	C₂²	#15668059	1	2	yes	—
884	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	178	1	no	—
897	C₄	—	178	1	no	—
898	C₄	—	178	1	no	—
899	C₄	—	178	1	no	—
900	C₄	—	178	1	no	—
901	C₄	—	178	1	no	—
902	C₄	—	178	1	no	—
903	C₄	—	178	1	no	—
904	C₄	—	178	1	no	—
905	C₄	—	178	1	no	—
906	C₄	—	178	1	no	—
907	C₄	—	178	1	no	—
908	C₄	—	178	1	no	—
909	C₄	—	178	1	no	—
910	C₄	—	178	1	no	—
911	C₂	—	2	2	no	—
912	C₂	—	4	1	no	—
913	C₂	—	4	1	no	—
914	C₂	—	4	1	no	—
915	C₂	—	356	1	no	—
916	C₂	C₂×#15668059	1	1	yes	characteristic
917	C₂	#19152433	1	1	yes	characteristic
918	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#551×C₈₉	C₂
prime radical	#19152183	C₂
hypercenter	#551	D₈₉
hypocenter	C₈₉	#3564
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #19152351	C₂	semidirect
2. #19152351	C₂	semidirect
3. #19152350	C₂	semidirect
4. #19152349	C₂	semidirect
5. #19152317	C₂	semidirect
6. #19152316	C₂	semidirect
7. #19152306	C₂	semidirect
8. #19152305	C₂	semidirect
9. #19152288	C₂	semidirect
10. #19152285	C₂	semidirect
11. #19152284	C₂	semidirect
12. #19152281	C₂	semidirect
13. #19152279	C₂	semidirect
14. #19152274	C₂	semidirect
15. #19152274	C₂	semidirect
16. #19152227	C₂	semidirect
17. #19152224	C₂	semidirect
18. #19152213	C₂	semidirect
19. #19152212	C₂	semidirect
20. #19152210	C₂	semidirect
21. #19152208	C₂	semidirect
22. #19152205	C₂	semidirect
23. #19152205	C₂	semidirect
24. #19152192	C₂	semidirect
25. #19152191	C₂	semidirect
26. #19152190	C₂	semidirect
28. #19152151	C₂	semidirect
29. #19152125	C₂	semidirect
30. C₂×#15668005	C₂	semidirect
31. #551×C₈₉	C₂	semidirect
32. #15668012	C₂²	semidirect
33. #15668011	C₂²	semidirect
34. #15668011	C₂²	semidirect
35. #15668011	C₂²	semidirect
36. #15668011	C₂²	semidirect
37. #15668011	C₂²	semidirect
38. #15668010	C₂²	semidirect
39. #15668010	C₂²	semidirect
40. #15668007	C₂²	semidirect
41. #15668007	C₂²	semidirect
42. #15668006	C₂²	semidirect
43. #15668006	C₂²	semidirect
60. #15668005	C₂²	semidirect
61. #15668005	C₂²	semidirect
62. #15668005	C₂²	semidirect
63. #15668005	C₂²	semidirect
64. #15668004	C₂²	semidirect
65. #15668004	C₂²	semidirect
66. #15668003	C₂²	semidirect
67. #15668003	C₂²	semidirect
68. #15668003	C₂²	semidirect
69. #15668003	C₂²	semidirect
70. #15668003	C₂²	semidirect
71. #15668002	C₂²	semidirect
72. #15668002	C₂²	semidirect
73. #15668002	C₂²	semidirect
74. #15668002	C₂²	semidirect
75. #15668002	C₂²	semidirect
76. #15668002	C₂²	semidirect
77. #15668002	C₂²	semidirect
78. #15668002	C₂²	semidirect
79. #15668002	C₂²	semidirect
80. #15668002	C₂²	semidirect
81. #15668002	C₂²	semidirect
82. #15668002	C₂²	semidirect
88. #15667998	C₂²	semidirect
93. #15667995	C₂²	semidirect
97. #15667994	C₂²	semidirect
102. #15667992	C₂²	semidirect
103. #15667992	C₂²	semidirect
110. #15667991	C₂²	semidirect
111. #15667991	C₂²	semidirect
112. #15667990	C₂²	semidirect
113. #15667990	C₂²	semidirect
127. #15667989	C₂²	semidirect
128. #15667989	C₂²	semidirect
129. #15667989	C₂²	semidirect
130. #15667988	C₂²	semidirect
135. Q₈×Dic₈₉	C₂²	semidirect
136. C₄×Dic₁₇₈	C₂²	semidirect
137. C₄×Dic₁₇₈	C₂²	semidirect
138. C₄×Dic₁₇₈	C₂²	semidirect
139. C₄×Dic₁₇₈	C₂²	semidirect
140. C₄×Dic₁₇₈	C₂²	semidirect
141. C₄×Dic₁₇₈	C₂²	semidirect
142. #15667977	C₂²	semidirect
143. #15667977	C₂²	semidirect
152. #15667972	C₂²	semidirect
155. #15667970	C₂²	semidirect
156. #15667969	C₂²	semidirect
161. #15667968	C₂²	semidirect
162. #15667968	C₂²	semidirect
164. C₂×C₄⋊Dic₈₉	C₂²	semidirect
167. C₄⋊C₄×D₈₉	C₂²	semidirect
460. C₈₉	#3564	semidirect
476. #551	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152351	2
#19152350	2
#19152349	2
#19152317	2
#19152316	2
#19152306	2
#19152305	2
#19152288	2
#19152285	2
#19152284	2
#19152281	2
#19152279	2
#19152274	2
#19152227	2
#19152224	2
#19152213	2
#19152212	2
#19152210	2
#19152208	2
#19152205	2
#19152192	2
#19152191	2
#19152190	2
#19152183	2
#19152151	2
#19152125	2
C₂×#15668005	2
#551×C₈₉	2
#3564	89