Subgroups — #26034178

Order 11392.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152331	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152302	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152298	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152297	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152291	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152281	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152279	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152277	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152275	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152272	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152247	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152237	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152235	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152235	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152230	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152218	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152198	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152194	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152190	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152181	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152180	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152125	C₂	1	1	yes	maximal, characteristic, complemented
24	#19152125	C₂	1	1	yes	maximal, characteristic, complemented
25	#19152106	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#15667995	C₂	1	1	yes	maximal, characteristic, complemented
27	#123×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
28	#19152077	C₂	1	1	yes	maximal, characteristic, complemented
29	#19152070	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
31	#525×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13083573	C₂²	1	1	yes	characteristic
33	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
39	#15668010	C₂²	1	1	yes	characteristic, complemented
40	#15668008	C₂²	1	1	yes	characteristic
41	#15668007	C₂²	1	1	yes	characteristic, complemented
42	#15668007	C₂²	1	1	yes	characteristic, complemented
43	#15668007	C₂²	1	1	yes	characteristic, complemented
44	#15668007	C₂²	1	1	yes	characteristic, complemented
45	#15668006	C₂²	1	1	yes	characteristic, complemented
46	#15668006	C₂²	1	1	yes	characteristic, complemented
47	#15668005	C₂²	1	1	yes	characteristic, complemented
48	#15668005	C₂²	1	1	yes	characteristic, complemented
49	#15668005	C₂²	1	1	yes	characteristic, complemented
50	#15668005	C₂²	1	1	yes	characteristic, complemented
51	#15668004	C₂²	1	1	yes	characteristic, complemented
52	#15668002	C₂²	1	1	yes	characteristic, complemented
53	#15668002	C₂²	1	1	yes	characteristic, complemented
54	#15668002	C₂²	1	1	yes	characteristic, complemented
55	#15668002	C₂²	1	1	yes	characteristic, complemented
56	#15668001	C₂²	1	1	yes	characteristic, complemented
57	#15668000	C₂²	1	1	yes	characteristic, complemented
58	#15667999	C₂²	1	1	yes	characteristic, complemented
59	#15667998	C₂²	1	1	yes	characteristic, complemented
60	#15667998	C₂²	1	1	yes	characteristic, complemented
61	#15667998	C₂²	1	1	yes	characteristic, complemented
62	#15667998	C₂²	1	1	yes	characteristic, complemented
63	#15667997	C₂²	1	1	yes	characteristic, complemented
64	#15667997	C₂²	1	1	yes	characteristic, complemented
65	#15667997	C₂²	1	1	yes	characteristic, complemented
66	#15667997	C₂²	1	1	yes	characteristic, complemented
67	#15667996	C₂²	1	1	yes	characteristic
68	#15667996	C₂²	1	1	yes	characteristic, complemented
69	#15667995	C₂²	1	1	yes	characteristic
70	#15667995	C₂²	1	1	yes	characteristic
71	#15667995	C₂²	1	1	yes	characteristic, complemented
72	#15667995	C₂²	1	1	yes	characteristic, complemented
73	#15667995	C₂²	1	1	yes	characteristic, complemented
74	#15667995	C₂²	1	1	yes	characteristic, complemented
75	#15667995	C₂²	1	1	yes	characteristic, complemented
76	#15667995	C₂²	1	1	yes	characteristic, complemented
77	#15667995	C₂²	1	1	yes	characteristic, complemented
78	#15667995	C₂²	1	1	yes	characteristic, complemented
79	#15667994	C₂²	1	1	yes	characteristic, complemented
80	#15667994	C₂²	1	1	yes	characteristic, complemented
81	#15667994	C₂²	1	1	yes	characteristic, complemented
82	#15667994	C₂²	1	1	yes	characteristic, complemented
83	#15667993	C₂²	1	1	yes	characteristic, complemented
84	#15667993	C₂²	1	1	yes	characteristic, complemented
85	#15667993	C₂²	1	1	yes	characteristic, complemented
86	#15667993	C₂²	1	1	yes	characteristic, complemented
87	#15667991	C₂²	1	1	yes	characteristic, complemented
88	#15667990	C₂²	1	1	yes	characteristic, complemented
89	#15667990	C₂²	1	1	yes	characteristic, complemented
90	#15667990	C₂²	1	1	yes	characteristic, complemented
91	#15667990	C₂²	1	1	yes	characteristic, complemented
92	#15667989	C₂²	1	1	yes	characteristic, complemented
93	#15667989	C₂²	1	1	yes	characteristic, complemented
94	#15667989	C₂²	1	1	yes	characteristic, complemented
95	#15667989	C₂²	1	1	yes	characteristic, complemented
96	#15667988	C₂²	1	1	yes	characteristic, complemented
97	#15667988	C₂²	1	1	yes	characteristic, complemented
98	#15667986	C₂²	1	1	yes	characteristic, complemented
99	#15667985	C₂²	1	1	yes	characteristic
100	#15667985	C₂²	1	1	yes	characteristic
101	#15667985	C₂²	1	1	yes	characteristic, complemented
102	#15667985	C₂²	1	1	yes	characteristic, complemented
103	#15667984	C₂²	1	1	yes	characteristic
104	#15667984	C₂²	1	1	yes	characteristic
105	#15667984	C₂²	1	1	yes	characteristic
106	#15667984	C₂²	1	1	yes	characteristic, complemented
107	#15667984	C₂²	1	1	yes	characteristic, complemented
108	#15667984	C₂²	1	1	yes	characteristic, complemented
109	#15667984	C₂²	1	1	yes	characteristic, complemented
110	#15667984	C₂²	1	1	yes	characteristic, complemented
111	#15667983	C₂²	1	1	yes	characteristic, complemented
112	#15667983	C₂²	1	1	yes	characteristic, complemented
113	#15667982	C₂²	1	1	yes	characteristic
114	#15667982	C₂²	1	1	yes	characteristic
115	#15667980	C₂²	1	1	yes	characteristic
116	#15667980	C₂²	1	1	yes	characteristic, complemented
117	#15667980	C₂²	1	1	yes	characteristic, complemented
118	#15667980	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
120	#15667977	C₂²	1	1	yes	characteristic, complemented
121	#15667977	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
123	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
124	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
125	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
126	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
127	#15667974	C₂²	1	1	yes	characteristic, complemented
128	#15667974	C₂²	1	1	yes	characteristic, complemented
129	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
130	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
131	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
137	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
139	#15667972	C₂²	1	1	yes	characteristic
140	#15667972	C₂²	1	1	yes	characteristic
141	#15667972	C₂²	1	1	yes	characteristic
142	#15667972	C₂²	1	1	yes	characteristic, complemented
143	#15667972	C₂²	1	1	yes	characteristic, complemented
144	#15667972	C₂²	1	1	yes	characteristic, complemented
145	#15667972	C₂²	1	1	yes	characteristic, complemented
146	#15667972	C₂²	1	1	yes	characteristic, complemented
147	#15667970	C₂²	1	1	yes	characteristic, complemented
148	#15667970	C₂²	1	1	yes	characteristic, complemented
149	#15667969	C₂²	1	1	yes	characteristic, complemented
150	#15667969	C₂²	1	1	yes	characteristic, complemented
151	#15667968	C₂²	1	1	yes	characteristic, complemented
152	#15667968	C₂²	1	1	yes	characteristic, complemented
153	#15667968	C₂²	1	1	yes	characteristic, complemented
154	#15667968	C₂²	1	1	yes	characteristic, complemented
155	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
156	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
157	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
158	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
161	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
162	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
163	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
164	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
166	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
171	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
173	C₂³×C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
174	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
177	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
178	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
179	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#120×C₈₉	C₂²	1	1	yes	characteristic
181	#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₈₉	C₂³	1	1	yes	characteristic
188	C₂³×D₈₉	C₂³	1	1	yes	characteristic
189	C₂³×D₈₉	C₂³	1	1	yes	characteristic
190	#13083573	—	2	4	no	—
191	#13083573	—	4	2	no	—
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×D₃₅₆	C₂³	1	1	yes	characteristic
196	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
197	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₈₉	—	2	4	no	—
199	C₂×C₂²⋊D₈₉	—	4	2	no	—
200	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
214	D₄×D₈₉	—	2	4	no	—
215	D₄×D₈₉	—	4	2	no	—
216	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
217	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
218	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
219	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
221	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
222	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
223	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
224	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₈₉	—	4	2	no	—
226	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₈₉	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	#13083553	C₂³	1	1	yes	characteristic
265	#13083553	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	#13083551	C₂³	1	1	yes	characteristic
281	#13083551	C₂³	1	1	yes	characteristic
282	#13083551	C₂³	1	1	yes	characteristic
283	#13083551	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	#13083551	C₂³	1	1	yes	characteristic
293	#13083551	C₂³	1	1	yes	characteristic
294	#13083551	C₂³	1	1	yes	characteristic
295	#13083551	C₂³	1	1	yes	characteristic
296	#13083551	C₂³	1	1	yes	characteristic
297	#13083551	C₂³	1	1	yes	characteristic
298	#13083551	C₂³	1	1	yes	characteristic
299	#13083551	C₂³	1	1	yes	characteristic
300	#13083551	C₂³	1	1	yes	characteristic
301	#13083551	C₂³	1	1	yes	characteristic
302	#13083551	C₂³	1	1	yes	characteristic
303	#13083551	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	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
308	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
309	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
310	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
311	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
313	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
314	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
315	#41×C₈₉	—	4	2	no	—
316	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	—	4	2	no	—
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	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₄²×C₈₉	C₂³	1	1	yes	characteristic
350	C₄²×C₈₉	C₂³	1	1	yes	characteristic
351	C₂³×C₈₉	—	2	2	no	—
352	C₂³×C₈₉	—	2	2	no	—
353	C₂³×C₈₉	—	4	1	no	—
354	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
355	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
356	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂²×D₈₉	—	2	2	no	—
360	C₂²×D₈₉	—	2	2	no	—
361	C₂²×D₈₉	—	2	2	no	—
362	C₂²×D₈₉	—	2	2	no	—
363	C₂²×D₈₉	—	4	1	no	—
364	C₂²×D₈₉	—	4	1	no	—
365	C₂²×D₈₉	—	4	1	no	—
366	C₂²×D₈₉	—	4	1	no	—
367	C₂²×D₈₉	—	4	1	no	—
368	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
369	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
371	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
372	Q₈×C₈₉	—	4	1	no	—
373	D₄×C₈₉	—	2	2	no	—
374	D₄×C₈₉	—	2	2	no	—
375	D₄×C₈₉	—	2	2	no	—
376	D₄×C₈₉	—	2	2	no	—
377	D₄×C₈₉	—	4	1	no	—
378	D₄×C₈₉	—	4	1	no	—
379	D₄×C₈₉	—	4	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	4	1	no	—
383	C₂×C₄×C₈₉	—	4	1	no	—
384	C₂×C₄×C₈₉	—	4	1	no	—
385	C₂×C₄×C₈₉	—	4	1	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	1	no	—
388	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
398	C₂²⋊D₈₉	—	2	2	no	—
399	C₂²⋊D₈₉	—	2	2	no	—
400	C₂²⋊D₈₉	—	2	2	no	—
401	C₂²⋊D₈₉	—	2	2	no	—
402	C₂²⋊D₈₉	—	2	2	no	—
403	C₂²⋊D₈₉	—	2	2	no	—
404	C₂²⋊D₈₉	—	2	2	no	—
405	C₂²⋊D₈₉	—	4	1	no	—
406	C₂²⋊D₈₉	—	4	1	no	—
407	C₂²⋊D₈₉	—	4	1	no	—
408	C₂²⋊D₈₉	—	4	1	no	—
409	C₂²⋊D₈₉	—	4	1	no	—
410	C₂²⋊D₈₉	—	4	1	no	—
411	C₂²⋊D₈₉	#41	1	4	yes	complemented
412	C₂×Dic₈₉	—	2	2	no	—
413	C₂×Dic₈₉	—	2	2	no	—
414	C₂×Dic₈₉	—	2	2	no	—
415	C₂×Dic₈₉	—	2	2	no	—
416	C₂×Dic₈₉	—	4	1	no	—
417	C₂×Dic₈₉	—	4	1	no	—
418	C₂×Dic₈₉	—	4	1	no	—
419	C₂×Dic₈₉	—	4	1	no	—
420	C₂×Dic₈₉	—	4	1	no	—
421	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
433	D₃₅₆	—	2	2	no	—
434	D₃₅₆	—	4	1	no	—
435	D₃₅₆	—	4	1	no	—
436	C₄×D₈₉	—	2	2	no	—
437	C₄×D₈₉	—	2	2	no	—
438	C₄×D₈₉	—	4	1	no	—
439	C₄×D₈₉	—	4	1	no	—
440	C₄×D₈₉	—	4	1	no	—
441	C₄×D₈₉	—	4	1	no	—
442	C₄×D₈₉	—	4	1	no	—
443	C₄×D₈₉	—	4	1	no	—
444	C₄×D₈₉	—	4	1	no	—
445	C₄×D₈₉	—	4	1	no	—
446	Dic₁₇₈	—	2	2	no	—
447	Dic₁₇₈	—	4	1	no	—
448	Dic₁₇₈	—	4	1	no	—
449	C₂²×C₈₉	—	2	1	no	—
450	C₂²×C₈₉	—	2	1	no	—
451	C₂²×C₈₉	—	2	1	no	—
452	C₂²×C₈₉	—	2	1	no	—
453	C₂²×C₈₉	—	2	1	no	—
454	C₂²×C₈₉	—	2	1	no	—
455	C₂²×C₈₉	—	2	1	no	—
456	C₂²×C₈₉	—	2	1	no	—
457	C₂²×C₈₉	—	2	1	no	—
458	C₂²×C₈₉	—	2	1	no	—
459	C₂²×C₈₉	—	2	1	no	—
460	C₂²×C₈₉	—	2	1	no	—
461	C₂²×C₈₉	—	2	1	no	—
462	C₂²×C₈₉	—	4	4	no	—
463	C₂²×C₈₉	C₂×#41	1	2	yes	—
464	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
465	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
466	C₂×D₈₉	—	2	1	no	—
467	C₂×D₈₉	—	2	1	no	—
468	C₂×D₈₉	—	2	1	no	—
469	C₂×D₈₉	—	2	1	no	—
470	C₂×D₈₉	—	2	1	no	—
471	C₂×D₈₉	—	2	1	no	—
472	C₂×D₈₉	—	2	1	no	—
473	C₂×D₈₉	—	2	1	no	—
474	C₂×D₈₉	—	2	1	no	—
475	C₂×D₈₉	—	2	1	no	—
476	C₂×D₈₉	—	2	1	no	—
477	C₂×D₈₉	—	4	4	no	—
478	C₂×D₈₉	—	8	2	no	—
479	C₂×D₈₉	—	8	2	no	—
480	C₂×D₈₉	C₂×#41	1	2	yes	—
481	C₄×C₈₉	—	2	1	no	—
482	C₄×C₈₉	—	2	1	no	—
483	C₄×C₈₉	—	2	1	no	—
484	C₄×C₈₉	—	2	1	no	—
485	C₄×C₈₉	—	2	1	no	—
486	C₄×C₈₉	—	2	1	no	—
487	C₄×C₈₉	—	2	1	no	—
488	C₄×C₈₉	—	2	1	no	—
489	C₄×C₈₉	—	2	1	no	—
490	C₄×C₈₉	—	2	1	no	—
491	Dic₈₉	—	2	1	no	—
492	Dic₈₉	—	2	1	no	—
493	Dic₈₉	—	2	1	no	—
494	Dic₈₉	—	2	1	no	—
495	Dic₈₉	—	2	1	no	—
496	Dic₈₉	—	2	1	no	—
497	Dic₈₉	—	2	1	no	—
498	Dic₈₉	—	2	1	no	—
499	Dic₈₉	—	2	1	no	—
500	Dic₈₉	—	2	1	no	—
501	Dic₈₉	—	2	1	no	—
502	Dic₈₉	C₂×#41	1	2	yes	—
503	C₂×C₈₉	—	2	2	no	—
504	C₂×C₈₉	—	2	2	no	—
505	C₂×C₈₉	—	4	1	no	—
506	C₂×C₈₉	—	4	1	no	—
507	C₂×C₈₉	—	4	1	no	—
508	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
509	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂×C₈₉	#585	1	1	yes	characteristic
511	D₈₉	—	2	2	no	—
512	D₈₉	—	4	1	no	—
513	D₈₉	—	4	1	no	—
514	D₈₉	—	4	1	no	—
515	#3513	—	89	1	no	maximal, Sylow
516	C₈₉	#3513	1	1	yes	characteristic, complemented, Sylow
517	#559	—	89	1	no	—
518	#554	—	89	1	no	—
519	#553	—	89	1	no	—
520	#553	—	89	1	no	—
521	#553	—	89	1	no	—
522	#552	—	89	1	no	—
523	#551	—	89	1	no	—
524	#551	—	89	1	no	—
525	#551	—	89	1	no	—
526	#551	—	89	1	no	—
527	#547	—	89	1	no	—
528	#546	—	89	1	no	—
529	#546	—	89	1	no	—
530	#546	—	89	1	no	—
531	#546	—	89	1	no	—
532	D₄²	—	89	1	no	—
533	#542	—	89	1	no	—
534	#540	—	89	1	no	—
535	#539	—	89	1	no	—
536	#539	—	89	1	no	—
537	#538	—	89	1	no	—
538	#538	—	89	1	no	—
539	#529	—	89	1	no	—
540	#529	—	89	1	no	—
541	#525	—	89	1	no	—
542	#525	D₈₉	1	1	yes	characteristic, complemented
543	C₂×#123	—	89	1	no	—
544	C₂×#123	—	89	1	no	—
545	#520	—	89	1	no	—
546	#518	—	89	1	no	—
547	C₂×C₄×D₄	—	89	1	no	—
548	C₂×#41	—	89	1	no	—
549	C₂×#41	—	89	1	no	—
550	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
551	C₂²×D₄	—	89	1	no	—
552	C₂²×D₄	—	89	1	no	—
553	C₂²×D₄	—	89	1	no	—
554	C₂²×D₄	—	89	1	no	—
555	C₂³×C₄	—	89	1	no	—
556	C₂³×C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
557	C₄⋊Q₈	—	89	1	no	—
558	#127	—	89	1	no	—
559	#126	—	89	1	no	—
560	#126	—	89	1	no	—
561	#126	—	89	1	no	—
562	#126	—	89	1	no	—
563	#126	—	89	1	no	—
564	#126	—	89	1	no	—
565	#126	—	89	1	no	—
566	#126	—	89	1	no	—
567	#126	—	89	1	no	—
568	#126	—	89	1	no	—
569	#125	—	89	1	no	—
570	#125	—	89	1	no	—
571	#125	—	89	1	no	—
572	#125	—	89	1	no	—
573	#125	—	89	1	no	—
574	#124	—	89	1	no	—
575	#124	—	89	1	no	—
576	#124	—	89	1	no	—
577	#124	—	89	1	no	—
578	#124	—	89	1	no	—
579	#124	—	89	1	no	—
580	#124	—	89	1	no	—
581	#123	—	89	1	no	—
582	#123	—	89	1	no	—
583	#123	—	89	1	no	—
584	#123	—	89	1	no	—
585	#123	—	89	1	no	—
586	#123	—	89	1	no	—
587	#123	—	89	1	no	—
588	#123	—	89	1	no	—
589	#123	—	89	1	no	—
590	#123	—	89	1	no	—
591	#123	—	89	1	no	—
592	#123	—	89	1	no	—
593	#123	—	89	1	no	—
594	#123	—	89	1	no	—
595	#123	—	89	1	no	—
596	#123	—	89	1	no	—
597	#123	—	89	1	no	—
598	#123	—	89	1	no	—
599	#123	—	89	1	no	—
600	#123	—	89	1	no	—
601	#123	—	89	1	no	—
602	#123	—	89	1	no	—
603	#123	—	89	1	no	—
604	#123	—	89	1	no	—
605	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
606	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
607	C₂²⋊Q₈	—	89	1	no	—
608	C₂²⋊Q₈	—	89	1	no	—
609	C₂²⋊Q₈	—	89	1	no	—
610	C₂²⋊Q₈	—	89	1	no	—
611	C₂²⋊Q₈	—	89	1	no	—
612	C₂²⋊Q₈	—	89	1	no	—
613	C₂²⋊Q₈	—	89	1	no	—
614	C₂²⋊Q₈	—	89	1	no	—
615	C₂²⋊Q₈	—	89	1	no	—
616	C₂²⋊Q₈	—	89	1	no	—
617	C₂²⋊Q₈	—	89	1	no	—
618	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
619	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
620	#121	—	89	1	no	—
621	#121	—	89	1	no	—
622	#121	—	89	1	no	—
623	#121	—	89	1	no	—
624	#121	—	89	1	no	—
625	#121	—	89	1	no	—
626	#121	—	89	1	no	—
627	#121	—	89	1	no	—
628	#121	—	89	1	no	—
629	#121	—	89	1	no	—
630	#121	—	89	1	no	—
631	#121	—	89	1	no	—
632	#121	—	89	1	no	—
633	#121	—	89	1	no	—
634	#121	—	89	1	no	—
635	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
636	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
637	#120	—	89	1	no	—
638	#120	—	89	1	no	—
639	#120	—	89	1	no	—
640	#120	—	89	1	no	—
641	#120	—	89	1	no	—
642	#120	—	89	1	no	—
643	#120	C₂×D₈₉	1	1	yes	characteristic
644	#120	C₂×D₈₉	1	1	yes	characteristic, complemented
645	C₄×Q₈	—	89	1	no	—
646	C₄×Q₈	—	89	1	no	—
647	C₄×Q₈	—	89	1	no	—
648	C₄×D₄	—	89	1	no	—
649	C₄×D₄	—	89	1	no	—
650	C₄×D₄	—	89	1	no	—
651	C₄×D₄	—	89	1	no	—
652	C₄×D₄	—	89	1	no	—
653	C₄×D₄	—	89	1	no	—
654	C₄×D₄	—	89	1	no	—
655	C₄×D₄	—	89	1	no	—
656	C₄×D₄	—	89	1	no	—
657	C₄×D₄	—	89	1	no	—
658	C₄×D₄	—	89	1	no	—
659	C₄×D₄	—	89	1	no	—
660	C₄×D₄	—	89	1	no	—
661	C₄×D₄	—	89	1	no	—
662	C₄×D₄	—	89	1	no	—
663	C₄×D₄	—	89	1	no	—
664	C₄×D₄	—	89	1	no	—
665	C₄×D₄	—	89	1	no	—
666	C₄×D₄	—	89	1	no	—
667	C₄×D₄	—	89	1	no	—
668	C₄×D₄	—	89	1	no	—
669	C₄×D₄	—	89	1	no	—
670	C₄×D₄	—	89	1	no	—
671	C₄×D₄	—	89	1	no	—
672	C₄×D₄	—	89	1	no	—
673	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
674	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
675	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
676	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
677	#117	—	89	1	no	—
678	#117	—	89	1	no	—
679	#117	—	89	1	no	—
680	#117	—	89	1	no	—
681	#117	—	89	1	no	—
682	#117	—	89	1	no	—
683	#117	—	89	1	no	—
684	#117	—	89	1	no	—
685	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
686	C₂×C₄⋊C₄	—	89	1	no	—
687	C₂×C₄⋊C₄	—	89	1	no	—
688	C₂×C₄⋊C₄	—	89	1	no	—
689	C₂×C₄⋊C₄	—	89	1	no	—
690	C₂×C₄⋊C₄	—	89	1	no	—
691	C₂×C₄⋊C₄	—	89	1	no	—
692	C₂×C₂²⋊C₄	—	89	1	no	—
693	C₂×C₂²⋊C₄	—	89	1	no	—
694	C₂×C₂²⋊C₄	—	89	1	no	—
695	C₂×C₂²⋊C₄	—	89	1	no	—
696	C₂×C₂²⋊C₄	—	89	1	no	—
697	C₂×C₂²⋊C₄	—	89	1	no	—
698	C₂×C₂²⋊C₄	—	89	1	no	—
699	C₂×C₂²⋊C₄	—	89	1	no	—
700	C₂×C₂²⋊C₄	—	89	1	no	—
701	C₂×C₂²⋊C₄	—	89	1	no	—
702	C₂×C₄²	—	89	1	no	—
703	C₂⁴	—	89	1	no	—
704	C₂⁴	—	89	1	no	—
705	C₂⁴	—	89	1	no	—
706	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
707	#41	—	4	2	no	—
708	#41	—	356	2	no	—
709	#41	—	178	4	no	—
710	C₂×Q₈	—	89	1	no	—
711	C₂×Q₈	—	89	1	no	—
712	C₂×Q₈	—	89	1	no	—
713	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
714	C₂×D₄	—	89	1	no	—
715	C₂×D₄	—	89	1	no	—
716	C₂×D₄	—	89	1	no	—
717	C₂×D₄	—	89	1	no	—
718	C₂×D₄	—	89	1	no	—
719	C₂×D₄	—	89	1	no	—
720	C₂×D₄	—	89	1	no	—
721	C₂×D₄	—	89	1	no	—
722	C₂×D₄	—	89	1	no	—
723	C₂×D₄	—	89	1	no	—
724	C₂×D₄	—	89	1	no	—
725	C₂×D₄	—	89	1	no	—
726	C₂×D₄	—	89	1	no	—
727	C₂×D₄	—	89	1	no	—
728	C₂×D₄	—	89	1	no	—
729	C₂×D₄	—	89	1	no	—
730	C₂×D₄	—	89	1	no	—
731	C₂×D₄	—	356	2	no	—
732	C₂×D₄	—	356	2	no	—
733	C₂×D₄	—	178	4	no	—
734	C₂×D₄	—	178	4	no	—
735	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
736	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
738	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
739	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
742	C₂²×C₄	—	4	2	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	—	356	2	no	—
763	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
764	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
765	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
766	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
771	C₄⋊C₄	—	89	1	no	—
772	C₄⋊C₄	—	89	1	no	—
773	C₄⋊C₄	—	89	1	no	—
774	C₄⋊C₄	—	89	1	no	—
775	C₄⋊C₄	—	89	1	no	—
776	C₄⋊C₄	—	89	1	no	—
777	C₄⋊C₄	—	89	1	no	—
778	C₄⋊C₄	—	89	1	no	—
779	C₄⋊C₄	—	89	1	no	—
780	C₄⋊C₄	—	89	1	no	—
781	C₄⋊C₄	—	89	1	no	—
782	C₄⋊C₄	—	89	1	no	—
783	C₄⋊C₄	—	89	1	no	—
784	C₄⋊C₄	—	89	1	no	—
785	C₄⋊C₄	—	89	1	no	—
786	C₄⋊C₄	—	89	1	no	—
787	C₄⋊C₄	—	89	1	no	—
788	C₄⋊C₄	—	89	1	no	—
789	C₄⋊C₄	—	89	1	no	—
790	C₄⋊C₄	—	89	1	no	—
791	C₄⋊C₄	—	89	1	no	—
792	C₄⋊C₄	—	89	1	no	—
793	C₄⋊C₄	—	89	1	no	—
794	C₄⋊C₄	—	89	1	no	—
795	C₄⋊C₄	—	89	1	no	—
796	C₄⋊C₄	—	89	1	no	—
797	C₄⋊C₄	—	89	1	no	—
798	C₄⋊C₄	—	89	1	no	—
799	C₄⋊C₄	—	89	1	no	—
800	C₄⋊C₄	—	89	1	no	—
801	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
807	C₂²⋊C₄	—	89	1	no	—
808	C₂²⋊C₄	—	89	1	no	—
809	C₂²⋊C₄	—	89	1	no	—
810	C₂²⋊C₄	—	89	1	no	—
811	C₂²⋊C₄	—	89	1	no	—
812	C₂²⋊C₄	—	89	1	no	—
813	C₂²⋊C₄	—	89	1	no	—
814	C₂²⋊C₄	—	89	1	no	—
815	C₂²⋊C₄	—	89	1	no	—
816	C₂²⋊C₄	—	89	1	no	—
817	C₂²⋊C₄	—	89	1	no	—
818	C₂²⋊C₄	—	89	1	no	—
819	C₂²⋊C₄	—	89	1	no	—
820	C₂²⋊C₄	—	89	1	no	—
821	C₂²⋊C₄	—	89	1	no	—
822	C₂²⋊C₄	—	89	1	no	—
823	C₂²⋊C₄	—	89	1	no	—
824	C₂²⋊C₄	—	89	1	no	—
825	C₂²⋊C₄	—	89	1	no	—
826	C₂²⋊C₄	—	89	1	no	—
827	C₂²⋊C₄	—	89	1	no	—
828	C₂²⋊C₄	—	89	1	no	—
829	C₂²⋊C₄	—	89	1	no	—
830	C₂²⋊C₄	—	89	1	no	—
831	C₂²⋊C₄	—	89	1	no	—
832	C₂²⋊C₄	—	89	1	no	—
833	C₂²⋊C₄	—	89	1	no	—
834	C₂²⋊C₄	—	89	1	no	—
835	C₂²⋊C₄	—	89	1	no	—
836	C₂²⋊C₄	—	89	1	no	—
837	C₂²⋊C₄	—	89	1	no	—
838	C₂²⋊C₄	—	89	1	no	—
839	C₂²⋊C₄	—	89	1	no	—
840	C₂²⋊C₄	—	89	1	no	—
841	C₂²⋊C₄	—	89	1	no	—
842	C₂²⋊C₄	—	89	1	no	—
843	C₂²⋊C₄	—	89	1	no	—
844	C₂²⋊C₄	—	89	1	no	—
845	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
854	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
855	C₄²	—	89	1	no	—
856	C₄²	—	89	1	no	—
857	C₄²	—	89	1	no	—
858	C₄²	—	89	1	no	—
859	C₄²	—	89	1	no	—
860	C₄²	—	89	1	no	—
861	C₄²	—	89	1	no	—
862	C₄²	—	89	1	no	—
863	C₄²	—	89	1	no	—
864	C₄²	—	89	1	no	—
865	C₄²	C₂²×D₈₉	1	1	yes	characteristic
866	C₄²	C₂²×D₈₉	1	1	yes	characteristic
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	89	1	no	—
871	C₂³	—	89	1	no	—
872	C₂³	—	89	1	no	—
873	C₂³	—	89	1	no	—
874	C₂³	—	356	1	no	—
875	C₂³	—	356	1	no	—
876	C₂³	—	356	1	no	—
877	C₂³	—	356	1	no	—
878	C₂³	—	356	1	no	—
879	C₂³	—	178	2	no	—
880	C₂³	—	178	2	no	—
881	C₂³	—	178	2	no	—
882	C₂³	—	178	2	no	—
883	C₂³	C₂³×D₈₉	1	1	yes	characteristic
884	C₂³	C₂³×D₈₉	1	1	yes	characteristic
885	C₂³	C₂³×D₈₉	1	1	yes	characteristic
886	C₂³	C₂³×D₈₉	1	1	yes	characteristic
887	C₂³	C₂³×D₈₉	1	1	yes	characteristic
888	Q₈	—	4	1	no	—
889	Q₈	—	356	1	no	—
890	Q₈	—	356	1	no	—
891	Q₈	—	178	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	4	1	no	—
899	D₄	—	89	4	no	—
900	D₄	—	356	1	no	—
901	D₄	—	356	1	no	—
902	D₄	—	356	1	no	—
903	D₄	—	356	1	no	—
904	D₄	—	356	1	no	—
905	D₄	—	356	1	no	—
906	D₄	—	356	1	no	—
907	D₄	—	356	1	no	—
908	D₄	—	178	2	no	—
909	D₄	—	178	2	no	—
910	D₄	—	178	2	no	—
911	D₄	—	178	2	no	—
912	D₄	—	178	2	no	—
913	D₄	—	178	2	no	—
914	D₄	—	178	2	no	—
915	D₄	—	178	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	89	1	no	—
925	C₂×C₄	—	89	1	no	—
926	C₂×C₄	—	89	1	no	—
927	C₂×C₄	—	89	1	no	—
928	C₂×C₄	—	89	1	no	—
929	C₂×C₄	—	89	1	no	—
930	C₂×C₄	—	89	1	no	—
931	C₂×C₄	—	89	1	no	—
932	C₂×C₄	—	89	1	no	—
933	C₂×C₄	—	89	1	no	—
934	C₂×C₄	—	89	1	no	—
935	C₂×C₄	—	89	1	no	—
936	C₂×C₄	—	356	1	no	—
937	C₂×C₄	—	356	1	no	—
938	C₂×C₄	—	356	1	no	—
939	C₂×C₄	—	356	1	no	—
940	C₂×C₄	—	356	1	no	—
941	C₂×C₄	—	356	1	no	—
942	C₂×C₄	—	356	1	no	—
943	C₂×C₄	—	356	1	no	—
944	C₂×C₄	—	356	1	no	—
945	C₂×C₄	—	356	1	no	—
946	C₂×C₄	—	356	1	no	—
947	C₂×C₄	—	356	1	no	—
948	C₂×C₄	—	356	1	no	—
949	C₂×C₄	—	178	2	no	—
950	C₂×C₄	—	178	2	no	—
951	C₂×C₄	—	178	2	no	—
952	C₂×C₄	—	178	2	no	—
953	C₂×C₄	—	178	2	no	—
954	C₂×C₄	—	178	2	no	—
955	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	89	2	no	—
980	C₂²	—	356	4	no	—
981	C₂²	—	178	1	no	—
982	C₂²	—	178	1	no	—
983	C₂²	—	178	1	no	—
984	C₂²	—	178	1	no	—
985	C₂²	—	178	1	no	—
986	C₂²	—	178	1	no	—
987	C₂²	—	178	1	no	—
988	C₂²	—	178	1	no	—
989	C₂²	—	178	1	no	—
990	C₂²	—	178	1	no	—
991	C₂²	—	178	1	no	—
992	C₂²	—	712	2	no	—
993	C₂²	—	712	2	no	—
994	C₂²	#41×D₈₉	1	2	yes	—
995	C₂²	#15668057	1	2	yes	—
996	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	89	2	no	—
1008	C₄	—	178	1	no	—
1009	C₄	—	178	1	no	—
1010	C₄	—	178	1	no	—
1011	C₄	—	178	1	no	—
1012	C₄	—	178	1	no	—
1013	C₄	—	178	1	no	—
1014	C₄	—	178	1	no	—
1015	C₄	—	178	1	no	—
1016	C₄	—	178	1	no	—
1017	C₄	—	178	1	no	—
1018	C₄	—	178	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	2	2	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	356	1	no	—
1025	C₂	—	356	1	no	—
1026	C₂	—	356	1	no	—
1027	C₂	—	178	2	no	—
1028	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
1029	C₂	C₂×#15668057	1	1	yes	characteristic
1030	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#525×C₈₉	C₂
hypercenter	#525	D₈₉
hypocenter	C₈₉	#3513
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #19152331	C₂	semidirect
2. #19152302	C₂	semidirect
3. #19152298	C₂	semidirect
4. #19152297	C₂	semidirect
5. #19152291	C₂	semidirect
6. #19152281	C₂	semidirect
7. #19152279	C₂	semidirect
8. #19152277	C₂	semidirect
9. #19152275	C₂	semidirect
10. #19152272	C₂	semidirect
11. #19152247	C₂	semidirect
12. #19152237	C₂	semidirect
13. #19152236	C₂	semidirect
14. #19152235	C₂	semidirect
15. #19152235	C₂	semidirect
16. #19152230	C₂	semidirect
17. #19152218	C₂	semidirect
18. #19152198	C₂	semidirect
19. #19152194	C₂	semidirect
20. #19152190	C₂	semidirect
21. #19152181	C₂	semidirect
22. #19152180	C₂	semidirect
23. #19152125	C₂	semidirect
24. #19152125	C₂	semidirect
25. #19152106	C₂	semidirect
26. C₂×#15667995	C₂	semidirect
27. #123×D₈₉	C₂	semidirect
28. #19152077	C₂	semidirect
29. #19152070	C₂	semidirect
30. C₂×C₄×C₂²⋊D₈₉	C₂	semidirect
31. #525×C₈₉	C₂	semidirect
33. C₂×#13083573	C₂²	semidirect
38. C₂²×C₄×D₈₉	C₂²	semidirect
39. #15668010	C₂²	semidirect
41. #15668007	C₂²	semidirect
42. #15668007	C₂²	semidirect
43. #15668007	C₂²	semidirect
44. #15668007	C₂²	semidirect
45. #15668006	C₂²	semidirect
46. #15668006	C₂²	semidirect
47. #15668005	C₂²	semidirect
48. #15668005	C₂²	semidirect
49. #15668005	C₂²	semidirect
50. #15668005	C₂²	semidirect
51. #15668004	C₂²	semidirect
52. #15668002	C₂²	semidirect
53. #15668002	C₂²	semidirect
54. #15668002	C₂²	semidirect
55. #15668002	C₂²	semidirect
56. #15668001	C₂²	semidirect
57. #15668000	C₂²	semidirect
58. #15667999	C₂²	semidirect
59. #15667998	C₂²	semidirect
60. #15667998	C₂²	semidirect
61. #15667998	C₂²	semidirect
62. #15667998	C₂²	semidirect
63. #15667997	C₂²	semidirect
64. #15667997	C₂²	semidirect
65. #15667997	C₂²	semidirect
66. #15667997	C₂²	semidirect
68. #15667996	C₂²	semidirect
71. #15667995	C₂²	semidirect
72. #15667995	C₂²	semidirect
73. #15667995	C₂²	semidirect
74. #15667995	C₂²	semidirect
75. #15667995	C₂²	semidirect
76. #15667995	C₂²	semidirect
77. #15667995	C₂²	semidirect
78. #15667995	C₂²	semidirect
79. #15667994	C₂²	semidirect
80. #15667994	C₂²	semidirect
81. #15667994	C₂²	semidirect
82. #15667994	C₂²	semidirect
83. #15667993	C₂²	semidirect
84. #15667993	C₂²	semidirect
85. #15667993	C₂²	semidirect
86. #15667993	C₂²	semidirect
87. #15667991	C₂²	semidirect
88. #15667990	C₂²	semidirect
89. #15667990	C₂²	semidirect
90. #15667990	C₂²	semidirect
91. #15667990	C₂²	semidirect
92. #15667989	C₂²	semidirect
93. #15667989	C₂²	semidirect
94. #15667989	C₂²	semidirect
95. #15667989	C₂²	semidirect
96. #15667988	C₂²	semidirect
97. #15667988	C₂²	semidirect
98. #15667986	C₂²	semidirect
101. #15667985	C₂²	semidirect
102. #15667985	C₂²	semidirect
106. #15667984	C₂²	semidirect
107. #15667984	C₂²	semidirect
108. #15667984	C₂²	semidirect
109. #15667984	C₂²	semidirect
110. #15667984	C₂²	semidirect
111. #15667983	C₂²	semidirect
112. #15667983	C₂²	semidirect
116. #15667980	C₂²	semidirect
117. #15667980	C₂²	semidirect
118. #15667980	C₂²	semidirect
119. C₄×Dic₁₇₈	C₂²	semidirect
120. #15667977	C₂²	semidirect
121. #15667977	C₂²	semidirect
122. C₄×D₃₅₆	C₂²	semidirect
123. D₄×Dic₈₉	C₂²	semidirect
124. D₄×Dic₈₉	C₂²	semidirect
125. D₄×Dic₈₉	C₂²	semidirect
126. D₄×Dic₈₉	C₂²	semidirect
127. #15667974	C₂²	semidirect
128. #15667974	C₂²	semidirect
131. C₄×C₂²⋊D₈₉	C₂²	semidirect
132. C₄×C₂²⋊D₈₉	C₂²	semidirect
133. C₄×C₂²⋊D₈₉	C₂²	semidirect
134. C₄×C₂²⋊D₈₉	C₂²	semidirect
135. C₄×C₂²⋊D₈₉	C₂²	semidirect
136. C₄×C₂²⋊D₈₉	C₂²	semidirect
137. C₄×C₂²⋊D₈₉	C₂²	semidirect
138. C₄×C₂²⋊D₈₉	C₂²	semidirect
142. #15667972	C₂²	semidirect
143. #15667972	C₂²	semidirect
144. #15667972	C₂²	semidirect
145. #15667972	C₂²	semidirect
146. #15667972	C₂²	semidirect
147. #15667970	C₂²	semidirect
148. #15667970	C₂²	semidirect
149. #15667969	C₂²	semidirect
150. #15667969	C₂²	semidirect
151. #15667968	C₂²	semidirect
152. #15667968	C₂²	semidirect
153. #15667968	C₂²	semidirect
154. #15667968	C₂²	semidirect
155. C₂×#13083553	C₂²	semidirect
156. C₂×#13083553	C₂²	semidirect
157. C₂×#13083553	C₂²	semidirect
158. C₂×#13083553	C₂²	semidirect
159. C₄⋊C₄×D₈₉	C₂²	semidirect
160. C₄⋊C₄×D₈₉	C₂²	semidirect
161. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
162. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
163. C₂×#13083551	C₂²	semidirect
164. C₂×#13083551	C₂²	semidirect
165. C₂×#13083551	C₂²	semidirect
166. C₂×#13083551	C₂²	semidirect
167. C₂²⋊C₄×D₈₉	C₂²	semidirect
168. C₂²⋊C₄×D₈₉	C₂²	semidirect
169. C₂²⋊C₄×D₈₉	C₂²	semidirect
170. C₂²⋊C₄×D₈₉	C₂²	semidirect
171. C₂×C₄×Dic₈₉	C₂²	semidirect
172. C₂×#41×C₈₉	C₂²	semidirect
173. C₂³×C₄×C₈₉	C₂²	semidirect
174. #123×C₈₉	C₂²	semidirect
175. #123×C₈₉	C₂²	semidirect
176. C₂²⋊Q₈×C₈₉	C₂²	semidirect
177. C₂²⋊Q₈×C₈₉	C₂²	semidirect
178. #121×C₈₉	C₂²	semidirect
179. #121×C₈₉	C₂²	semidirect
181. #120×C₈₉	C₂²	semidirect
182. C₄×D₄×C₈₉	C₂²	semidirect
183. C₄×D₄×C₈₉	C₂²	semidirect
184. C₄×D₄×C₈₉	C₂²	semidirect
185. C₄×D₄×C₈₉	C₂²	semidirect
186. #117×C₈₉	C₂²	semidirect
411. C₂²⋊D₈₉	#41	semidirect
516. C₈₉	#3513	semidirect
542. #525	D₈₉	semidirect
550. C₂×#41	C₂×D₈₉	semidirect
556. C₂³×C₄	C₂×D₈₉	semidirect
605. #123	C₂×D₈₉	semidirect
606. #123	C₂×D₈₉	semidirect
618. C₂²⋊Q₈	C₂×D₈₉	semidirect
619. C₂²⋊Q₈	C₂×D₈₉	semidirect
635. #121	C₂×D₈₉	semidirect
636. #121	C₂×D₈₉	semidirect
644. #120	C₂×D₈₉	semidirect
673. C₄×D₄	C₂×D₈₉	semidirect
674. C₄×D₄	C₂×D₈₉	semidirect
675. C₄×D₄	C₂×D₈₉	semidirect
676. C₄×D₄	C₂×D₈₉	semidirect
685. #117	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152331	2
#19152302	2
#19152298	2
#19152297	2
#19152291	2
#19152281	2
#19152279	2
#19152277	2
#19152275	2
#19152272	2
#19152247	2
#19152237	2
#19152236	2
#19152235	2
#19152230	2
#19152218	2
#19152198	2
#19152194	2
#19152190	2
#19152181	2
#19152180	2
#19152125	2
#19152106	2
C₂×#15667995	2
#123×D₈₉	2
#19152077	2
#19152070	2
C₂×C₄×C₂²⋊D₈₉	2
#525×C₈₉	2
#3513	89