Subgroups — #11773452

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂×C₉⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₉⋊#95	C₂	1	1	yes	maximal, characteristic
8	#69421	—	3	1	no	maximal
9	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×Dic₉	C₂²	1	1	yes	characteristic
13	C₂³×Dic₉	C₂²	1	1	yes	characteristic
14	C₂³×Dic₉	C₂²	1	1	yes	characteristic
15	C₂³×Dic₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₉⋊C₄	—	2	2	no	—
17	C₂×Dic₉⋊C₄	—	2	2	no	—
18	C₂×Dic₉⋊C₄	C₄	1	4	yes	complemented
19	C₉×#95	—	2	2	no	—
20	C₉⋊#95	—	2	2	no	—
21	C₉⋊#95	—	2	2	no	—
22	C₉⋊#95	—	2	2	no	—
23	C₉⋊#95	—	2	2	no	—
24	C₉⋊#95	—	2	2	no	—
25	C₂²×Dic₃⋊C₄	—	3	1	no	—
26	C₂×C₃×#95	D₃	1	1	yes	characteristic
27	C₂×C₃⋊#95	—	3	1	no	—
28	C₂×C₃⋊#95	—	3	1	no	—
29	C₂×C₃⋊#95	—	3	1	no	—
30	C₂×C₃⋊#95	—	3	1	no	—
31	C₂×C₃⋊#95	—	3	1	no	—
32	C₂⁴×C₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₉	—	2	1	no	—
34	C₂²×C₄×C₉	—	2	1	no	—
35	C₂²×C₄×C₉	—	2	1	no	—
36	C₂²×C₄×C₉	—	2	1	no	—
37	C₂²×C₄×C₉	—	2	1	no	—
38	C₂²×C₄×C₉	—	2	1	no	—
39	C₂²×C₄×C₉	—	2	1	no	—
40	C₂²×C₄×C₉	—	2	1	no	—
41	C₂²×C₄×C₉	—	2	1	no	—
42	C₂²×C₄×C₉	—	2	1	no	—
43	C₂²×C₄×C₉	—	2	1	no	—
44	C₂²×C₄×C₉	—	2	1	no	—
45	C₂²×C₄×C₉	—	2	1	no	—
46	C₂²×C₄×C₉	—	2	1	no	—
47	C₂²×C₄×C₉	—	2	1	no	—
48	C₂²×C₄×C₉	—	2	1	no	—
49	C₂²×C₄×C₉	—	2	1	no	—
50	C₂²×C₄×C₉	—	2	1	no	—
51	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
52	C₂²×C₄×C₉	D₄	1	2	yes	—
53	C₂²×C₄×C₉	Q₈	1	2	yes	—
54	C₂²×Dic₉	—	2	1	no	—
55	C₂²×Dic₉	—	2	1	no	—
56	C₂²×Dic₉	—	2	1	no	—
57	C₂²×Dic₉	—	2	1	no	—
58	C₂²×Dic₉	—	2	1	no	—
59	C₂²×Dic₉	—	2	1	no	—
60	C₂²×Dic₉	—	2	1	no	—
61	C₂²×Dic₉	—	2	1	no	—
62	C₂²×Dic₉	—	2	1	no	—
63	C₂²×Dic₉	—	2	1	no	—
64	C₂²×Dic₉	—	2	1	no	—
65	C₂²×Dic₉	—	2	1	no	—
66	C₂²×Dic₉	—	2	1	no	—
67	C₂²×Dic₉	—	2	1	no	—
68	C₂²×Dic₉	—	2	1	no	—
69	C₂²×Dic₉	—	2	1	no	—
70	C₂²×Dic₉	—	2	1	no	—
71	C₂²×Dic₉	—	2	1	no	—
72	C₂²×Dic₉	—	2	1	no	—
73	C₂²×Dic₉	—	2	1	no	—
74	C₂²×Dic₉	—	2	1	no	—
75	C₂²×Dic₉	—	2	1	no	—
76	C₂²×Dic₉	C₂×C₄	1	2	yes	—
77	C₂²×Dic₉	C₂×C₄	1	2	yes	—
78	C₂²×Dic₉	D₄	1	2	yes	—
79	C₂²×Dic₉	D₄	1	2	yes	—
80	C₂²×Dic₉	D₄	1	2	yes	—
81	C₂²×Dic₉	Q₈	1	2	yes	—
82	Dic₉⋊C₄	—	2	8	no	—
83	#1445	—	9	1	no	Sylow
84	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
87	C₂³×Dic₃	—	3	1	no	—
88	C₂³×Dic₃	—	3	1	no	—
89	C₂³×Dic₃	—	3	1	no	—
90	C₂³×Dic₃	—	3	1	no	—
91	C₂×Dic₃⋊C₄	—	3	4	no	—
92	C₂×Dic₃⋊C₄	—	6	2	no	—
93	C₂×Dic₃⋊C₄	—	6	2	no	—
94	C₃×#95	—	2	2	no	—
95	C₃⋊#95	—	6	2	no	—
96	C₃⋊#95	—	6	2	no	—
97	C₃⋊#95	—	6	2	no	—
98	C₃⋊#95	—	6	2	no	—
99	C₃⋊#95	—	6	2	no	—
100	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
101	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
102	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
103	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
104	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
105	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
106	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
107	C₂³×C₉	#41	1	1	yes	characteristic
108	C₂³×C₉	#41	1	1	yes	characteristic
109	C₂³×C₉	#41	1	1	yes	characteristic
110	C₂³×C₉	#41	1	1	yes	characteristic
111	C₂³×C₉	#41	1	1	yes	characteristic
112	C₂³×C₉	#41	1	1	yes	characteristic
113	C₂³×C₉	#41	1	1	yes	characteristic
114	C₂³×C₉	#41	1	1	yes	characteristic
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	4	1	no	—
125	C₂×C₄×C₉	—	4	1	no	—
126	C₂×C₄×C₉	—	4	1	no	—
127	C₂×C₄×C₉	—	4	1	no	—
128	C₂×C₄×C₉	—	4	1	no	—
129	C₂×C₄×C₉	—	4	1	no	—
130	C₂×C₄×C₉	—	4	1	no	—
131	C₂×C₄×C₉	—	4	1	no	—
132	C₂×C₄×C₉	—	4	1	no	—
133	C₂×C₄×C₉	—	4	1	no	—
134	C₂×C₄×C₉	—	4	1	no	—
135	C₂×C₄×C₉	—	4	1	no	—
136	C₂×Dic₉	—	2	2	no	—
137	C₂×Dic₉	—	2	2	no	—
138	C₂×Dic₉	—	2	2	no	—
139	C₂×Dic₉	—	2	2	no	—
140	C₂×Dic₉	—	2	2	no	—
141	C₂×Dic₉	—	2	2	no	—
142	C₂×Dic₉	—	2	2	no	—
143	C₂×Dic₉	—	2	2	no	—
144	C₂×Dic₉	—	2	2	no	—
145	C₂×Dic₉	—	2	2	no	—
146	C₂×Dic₉	—	2	2	no	—
147	C₂×Dic₉	—	2	2	no	—
148	C₂×Dic₉	—	2	2	no	—
149	C₂×Dic₉	—	2	2	no	—
150	C₂×Dic₉	—	2	2	no	—
151	C₂×Dic₉	—	4	1	no	—
152	C₂×Dic₉	—	4	1	no	—
153	C₂×Dic₉	—	4	1	no	—
154	C₂×Dic₉	—	4	1	no	—
155	C₂×Dic₉	—	4	1	no	—
156	C₂×Dic₉	—	4	1	no	—
157	C₂×Dic₉	—	4	1	no	—
158	C₂×Dic₉	—	4	1	no	—
159	C₂×Dic₉	—	4	1	no	—
160	C₂×Dic₉	—	4	1	no	—
161	C₂×Dic₉	—	4	1	no	—
162	C₂×Dic₉	—	4	1	no	—
163	C₂×Dic₉	C₂²⋊C₄	1	4	yes	—
164	C₂²×C₄⋊C₄	—	9	1	no	—
165	C₂×#95	—	9	1	no	—
166	C₂×#95	—	9	1	no	—
167	C₂×#95	—	9	1	no	—
168	C₂×#95	—	9	1	no	—
169	C₂×#95	—	9	1	no	—
170	C₂×#95	D₉	1	1	yes	characteristic
171	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	2	1	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	Dic₆	1	2	yes	—
191	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
192	C₂²×C₃×C₄	#67	1	2	yes	—
193	C₂²×Dic₃	—	3	2	no	—
194	C₂²×Dic₃	—	3	2	no	—
195	C₂²×Dic₃	—	3	2	no	—
196	C₂²×Dic₃	—	3	2	no	—
197	C₂²×Dic₃	—	3	2	no	—
198	C₂²×Dic₃	—	3	2	no	—
199	C₂²×Dic₃	—	6	1	no	—
200	C₂²×Dic₃	—	6	1	no	—
201	C₂²×Dic₃	—	6	1	no	—
202	C₂²×Dic₃	—	6	1	no	—
203	C₂²×Dic₃	—	6	1	no	—
204	C₂²×Dic₃	—	6	1	no	—
205	C₂²×Dic₃	—	6	1	no	—
206	C₂²×Dic₃	—	6	1	no	—
207	C₂²×Dic₃	—	6	1	no	—
208	C₂²×Dic₃	—	6	1	no	—
209	C₂²×Dic₃	—	6	1	no	—
210	C₂²×Dic₃	—	6	1	no	—
211	C₂²×Dic₃	—	6	1	no	—
212	C₂²×Dic₃	—	6	1	no	—
213	C₂²×Dic₃	—	6	1	no	—
214	C₂²×Dic₃	—	6	1	no	—
215	C₂²×Dic₃	—	6	1	no	—
216	C₂²×Dic₃	—	6	1	no	—
217	C₂²×Dic₃	—	6	1	no	—
218	C₂²×Dic₃	—	6	1	no	—
219	C₂²×Dic₃	—	6	1	no	—
220	C₂²×Dic₃	—	6	1	no	—
221	Dic₃⋊C₄	—	6	8	no	—
222	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₉	#117	1	1	yes	characteristic
224	C₂²×C₉	#117	1	1	yes	characteristic
225	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
226	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
227	C₂²×C₉	C₄×Q₈	1	1	yes	characteristic
228	C₂²×C₉	C₄×Q₈	1	1	yes	characteristic
229	C₂²×C₉	#121	1	1	yes	characteristic
230	C₂²×C₉	#121	1	1	yes	characteristic
231	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂²×C₉	#123	1	1	yes	characteristic
238	C₂²×C₉	#123	1	1	yes	characteristic
239	C₂²×C₉	#123	1	1	yes	characteristic
240	C₂²×C₉	#123	1	1	yes	characteristic
241	C₂²×C₉	#123	1	1	yes	characteristic
242	C₂²×C₉	#123	1	1	yes	characteristic
243	C₂²×C₉	#123	1	1	yes	characteristic
244	C₂²×C₉	#123	1	1	yes	characteristic
245	C₂²×C₉	#124	1	1	yes	characteristic
246	C₂²×C₉	#124	1	1	yes	characteristic
247	C₂²×C₉	#125	1	1	yes	characteristic
248	C₂²×C₉	#125	1	1	yes	characteristic
249	C₂²×C₉	#125	1	1	yes	characteristic
250	C₂²×C₉	#125	1	1	yes	characteristic
251	C₂²×C₉	#126	1	1	yes	characteristic
252	C₂²×C₉	#126	1	1	yes	characteristic
253	C₂²×C₉	#126	1	1	yes	characteristic
254	C₂²×C₉	#126	1	1	yes	characteristic
255	C₂²×C₉	#127	1	1	yes	characteristic
256	C₂²×C₉	C₄⋊Q₈	1	1	yes	characteristic
257	C₄×C₉	—	4	2	no	—
258	C₄×C₉	—	4	2	no	—
259	C₄×C₉	—	4	2	no	—
260	Dic₉	—	2	4	no	—
261	Dic₉	—	4	2	no	—
262	Dic₉	—	4	2	no	—
263	Dic₉	—	4	2	no	—
264	C₂³×C₄	—	9	1	no	—
265	C₂³×C₄	—	9	1	no	—
266	C₂³×C₄	—	9	1	no	—
267	C₂³×C₄	—	9	1	no	—
268	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
269	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
270	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	9	4	no	—
272	C₂×C₄⋊C₄	—	18	2	no	—
273	C₂×C₄⋊C₄	—	18	2	no	—
274	#95	—	2	2	no	—
275	#95	—	18	2	no	—
276	#95	—	18	2	no	—
277	#95	—	18	2	no	—
278	#95	—	18	2	no	—
279	#95	—	18	2	no	—
280	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
281	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂³×C₃	#235	1	1	yes	characteristic
283	C₂³×C₃	#235	1	1	yes	characteristic
284	C₂³×C₃	#235	1	1	yes	characteristic
285	C₂³×C₃	#235	1	1	yes	characteristic
286	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
287	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
288	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
289	C₂³×C₃	#237	1	1	yes	characteristic
290	C₂³×C₃	#237	1	1	yes	characteristic
291	C₂³×C₃	#237	1	1	yes	characteristic
292	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
293	C₂³×C₃	#239	1	1	yes	characteristic
294	C₂³×C₃	C₂×#67	1	1	yes	characteristic
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	4	1	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	—	4	1	no	—
311	C₂×C₃×C₄	—	4	1	no	—
312	C₂×C₃×C₄	—	4	1	no	—
313	C₂×C₃×C₄	—	4	1	no	—
314	C₂×C₃×C₄	—	4	1	no	—
315	C₂×C₃×C₄	—	4	1	no	—
316	C₂×Dic₃	—	3	4	no	—
317	C₂×Dic₃	—	6	2	no	—
318	C₂×Dic₃	—	6	2	no	—
319	C₂×Dic₃	—	6	2	no	—
320	C₂×Dic₃	—	6	2	no	—
321	C₂×Dic₃	—	6	2	no	—
322	C₂×Dic₃	—	6	2	no	—
323	C₂×Dic₃	—	6	2	no	—
324	C₂×Dic₃	—	6	2	no	—
325	C₂×Dic₃	—	6	2	no	—
326	C₂×Dic₃	—	6	2	no	—
327	C₂×Dic₃	—	6	2	no	—
328	C₂×Dic₃	—	6	2	no	—
329	C₂×Dic₃	—	6	2	no	—
330	C₂×Dic₃	—	6	2	no	—
331	C₂×Dic₃	—	6	2	no	—
332	C₂×Dic₃	—	12	1	no	—
333	C₂×Dic₃	—	12	1	no	—
334	C₂×Dic₃	—	12	1	no	—
335	C₂×Dic₃	—	12	1	no	—
336	C₂×Dic₃	—	12	1	no	—
337	C₂×Dic₃	—	12	1	no	—
338	C₂×Dic₃	—	12	1	no	—
339	C₂×Dic₃	—	12	1	no	—
340	C₂×Dic₃	—	12	1	no	—
341	C₂×Dic₃	—	12	1	no	—
342	C₂×Dic₃	—	12	1	no	—
343	C₂×Dic₃	—	12	1	no	—
344	C₂×C₉	#381	1	1	yes	characteristic
345	C₂×C₉	#387	1	1	yes	characteristic
346	C₂×C₉	#387	1	1	yes	characteristic
347	C₂×C₉	#387	1	1	yes	characteristic
348	C₂×C₉	#387	1	1	yes	characteristic
349	C₂×C₉	#390	1	1	yes	characteristic
350	C₂×C₉	#391	1	1	yes	characteristic
351	C₂×C₉	#397	1	1	yes	characteristic
352	C₂×C₉	#397	1	1	yes	characteristic
353	C₂×C₉	#398	1	1	yes	characteristic
354	C₂×C₉	#398	1	1	yes	characteristic
355	C₂×C₉	#399	1	1	yes	characteristic
356	C₂×C₉	#399	1	1	yes	characteristic
357	C₂×C₉	#400	1	1	yes	characteristic
358	C₂×C₉	#400	1	1	yes	characteristic
359	C₂⁴	C₂²×D₉	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	9	2	no	—
379	C₂²×C₄	—	9	2	no	—
380	C₂²×C₄	—	9	2	no	—
381	C₂²×C₄	—	9	2	no	—
382	C₂²×C₄	—	9	2	no	—
383	C₂²×C₄	—	9	2	no	—
384	C₂²×C₄	—	18	1	no	—
385	C₂²×C₄	—	18	1	no	—
386	C₂²×C₄	—	18	1	no	—
387	C₂²×C₄	—	18	1	no	—
388	C₂²×C₄	—	18	1	no	—
389	C₂²×C₄	—	18	1	no	—
390	C₂²×C₄	—	18	1	no	—
391	C₂²×C₄	—	18	1	no	—
392	C₂²×C₄	—	18	1	no	—
393	C₂²×C₄	—	18	1	no	—
394	C₂²×C₄	—	18	1	no	—
395	C₂²×C₄	—	18	1	no	—
396	C₂²×C₄	—	18	1	no	—
397	C₂²×C₄	—	18	1	no	—
398	C₂²×C₄	—	18	1	no	—
399	C₂²×C₄	—	18	1	no	—
400	C₂²×C₄	—	18	1	no	—
401	C₂²×C₄	—	18	1	no	—
402	C₂²×C₄	—	18	1	no	—
403	C₂²×C₄	—	18	1	no	—
404	C₂²×C₄	—	18	1	no	—
405	C₂²×C₄	—	18	1	no	—
406	C₂²×C₄	Dic₁₈	1	2	yes	—
407	C₂²×C₄	C₄×D₉	1	2	yes	—
408	C₂²×C₄	#611	1	2	yes	—
409	C₄⋊C₄	—	18	8	no	—
410	C₂²×C₃	C₄×Dic₆	1	1	yes	characteristic
411	C₂²×C₃	#870	1	1	yes	characteristic
412	C₂²×C₃	#872	1	1	yes	characteristic
413	C₂²×C₃	#876	1	1	yes	characteristic
414	C₂²×C₃	#878	1	1	yes	characteristic
415	C₂²×C₃	#878	1	1	yes	characteristic
416	C₂²×C₃	#879	1	1	yes	characteristic
417	C₂²×C₃	#879	1	1	yes	characteristic
418	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
420	C₂²×C₃	#883	1	1	yes	characteristic
421	C₂²×C₃	#883	1	1	yes	characteristic
422	C₂²×C₃	#883	1	1	yes	characteristic
423	C₂²×C₃	#884	1	1	yes	characteristic
424	C₂²×C₃	#885	1	1	yes	characteristic
425	C₂²×C₃	#885	1	1	yes	characteristic
426	C₂²×C₃	#887	1	1	yes	characteristic
427	C₂²×C₃	#888	1	1	yes	characteristic
428	C₂²×C₃	#889	1	1	yes	characteristic
429	C₂²×C₃	#889	1	1	yes	characteristic
430	C₂²×C₃	#890	1	1	yes	characteristic
431	C₂²×C₃	#892	1	1	yes	characteristic
432	C₂²×C₃	#894	1	1	yes	characteristic
433	C₂²×C₃	#894	1	1	yes	characteristic
434	C₂²×C₃	#894	1	1	yes	characteristic
435	C₂²×C₃	#896	1	1	yes	characteristic
436	C₂²×C₃	#896	1	1	yes	characteristic
437	C₂²×C₃	#898	1	1	yes	characteristic
438	C₂²×C₃	#924	1	1	yes	characteristic
439	C₂²×C₃	C₄×#67	1	1	yes	characteristic
440	C₂²×C₃	#929	1	1	yes	characteristic
441	C₂²×C₃	#935	1	1	yes	characteristic
442	C₂²×C₃	#939	1	1	yes	characteristic
443	C₂²×C₃	#940	1	1	yes	characteristic
444	C₂²×C₃	#946	1	1	yes	characteristic
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	2	no	—
448	Dic₃	—	6	4	no	—
449	Dic₃	—	12	2	no	—
450	Dic₃	—	12	2	no	—
451	Dic₃	—	12	2	no	—
452	C₉	#1445	1	1	yes	characteristic, complemented, Sylow
453	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
454	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
455	C₂³	#3697	1	1	yes	characteristic
456	C₂³	#3697	1	1	yes	characteristic
457	C₂³	#3697	1	1	yes	characteristic
458	C₂³	#3697	1	1	yes	characteristic
459	C₂³	D₄×D₉	1	1	yes	characteristic
460	C₂³	D₄×D₉	1	1	yes	characteristic
461	C₂³	D₄×D₉	1	1	yes	characteristic
462	C₂³	#3699	1	1	yes	characteristic
463	C₂³	#3699	1	1	yes	characteristic
464	C₂³	#3699	1	1	yes	characteristic
465	C₂³	Q₈×D₉	1	1	yes	characteristic
466	C₂³	#3701	1	1	yes	characteristic
467	C₂³	C₂×#611	1	1	yes	characteristic
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	9	4	no	—
490	C₂×C₄	—	18	2	no	—
491	C₂×C₄	—	18	2	no	—
492	C₂×C₄	—	18	2	no	—
493	C₂×C₄	—	18	2	no	—
494	C₂×C₄	—	18	2	no	—
495	C₂×C₄	—	18	2	no	—
496	C₂×C₄	—	18	2	no	—
497	C₂×C₄	—	18	2	no	—
498	C₂×C₄	—	18	2	no	—
499	C₂×C₄	—	18	2	no	—
500	C₂×C₄	—	18	2	no	—
501	C₂×C₄	—	18	2	no	—
502	C₂×C₄	—	18	2	no	—
503	C₂×C₄	—	18	2	no	—
504	C₂×C₄	—	18	2	no	—
505	C₂×C₄	—	36	1	no	—
506	C₂×C₄	—	36	1	no	—
507	C₂×C₄	—	36	1	no	—
508	C₂×C₄	—	36	1	no	—
509	C₂×C₄	—	36	1	no	—
510	C₂×C₄	—	36	1	no	—
511	C₂×C₄	—	36	1	no	—
512	C₂×C₄	—	36	1	no	—
513	C₂×C₄	—	36	1	no	—
514	C₂×C₄	—	36	1	no	—
515	C₂×C₄	—	36	1	no	—
516	C₂×C₄	—	36	1	no	—
517	C₂×C₃	#4646	1	1	yes	characteristic
518	C₂×C₃	#4652	1	1	yes	characteristic
519	C₂×C₃	#4655	1	1	yes	characteristic
520	C₂×C₃	#4657	1	1	yes	characteristic
521	C₂×C₃	#4658	1	1	yes	characteristic
522	C₂×C₃	#4660	1	1	yes	characteristic
523	C₂×C₃	#4664	1	1	yes	characteristic
524	C₂×C₃	#4675	1	1	yes	characteristic
525	C₂×C₃	#4933	1	1	yes	characteristic
526	C₂×C₃	#4949	1	1	yes	characteristic
527	C₂×C₃	#4952	1	1	yes	characteristic
528	C₂×C₃	#4957	1	1	yes	characteristic
529	C₂×C₃	#4978	1	1	yes	characteristic
530	C₂×C₃	#4982	1	1	yes	characteristic
531	C₂×C₃	#4993	1	1	yes	characteristic
532	C₂²	C₄×Dic₁₈	1	1	yes	characteristic
533	C₂²	#63432	1	1	yes	characteristic
534	C₂²	#63434	1	1	yes	characteristic
535	C₂²	#63438	1	1	yes	characteristic
536	C₂²	#63440	1	1	yes	characteristic
537	C₂²	#63440	1	1	yes	characteristic
538	C₂²	#63441	1	1	yes	characteristic
539	C₂²	#63441	1	1	yes	characteristic
540	C₂²	C₂²⋊C₄×D₉	1	1	yes	characteristic
541	C₂²	#611⋊C₄	1	1	yes	characteristic
542	C₂²	#63445	1	1	yes	characteristic
543	C₂²	#63445	1	1	yes	characteristic
544	C₂²	#63445	1	1	yes	characteristic
545	C₂²	#63446	1	1	yes	characteristic
546	C₂²	#63447	1	1	yes	characteristic
547	C₂²	#63447	1	1	yes	characteristic
548	C₂²	#63449	1	1	yes	characteristic
549	C₂²	#63450	1	1	yes	characteristic
550	C₂²	#63451	1	1	yes	characteristic
551	C₂²	#63451	1	1	yes	characteristic
552	C₂²	#63452	1	1	yes	characteristic
553	C₂²	#63454	1	1	yes	characteristic
554	C₂²	#63456	1	1	yes	characteristic
555	C₂²	#63456	1	1	yes	characteristic
556	C₂²	#63456	1	1	yes	characteristic
557	C₂²	#63458	1	1	yes	characteristic
558	C₂²	#63458	1	1	yes	characteristic
559	C₂²	#63460	1	1	yes	characteristic
560	C₂²	#63486	1	1	yes	characteristic
561	C₂²	C₄×#611	1	1	yes	characteristic
562	C₂²	#63491	1	1	yes	characteristic
563	C₂²	#63497	1	1	yes	characteristic
564	C₂²	#63501	1	1	yes	characteristic
565	C₂²	#63502	1	1	yes	characteristic
566	C₂²	#63508	1	1	yes	characteristic
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	18	4	no	—
571	C₄	—	36	2	no	—
572	C₄	—	36	2	no	—
573	C₄	—	36	2	no	—
574	C₃	#69421	1	1	yes	characteristic
575	C₂	#10588326	1	1	yes	characteristic
576	C₂	#10588332	1	1	yes	characteristic
577	C₂	#10588335	1	1	yes	characteristic
578	C₂	#10588337	1	1	yes	characteristic
579	C₂	#10588338	1	1	yes	characteristic
580	C₂	#10588340	1	1	yes	characteristic
581	C₂	#10588344	1	1	yes	characteristic
582	C₂	#10588355	1	1	yes	characteristic
583	C₂	#10588613	1	1	yes	characteristic
584	C₂	#10588629	1	1	yes	characteristic
585	C₂	#10588632	1	1	yes	characteristic
586	C₂	#10588637	1	1	yes	characteristic
587	C₂	#10588658	1	1	yes	characteristic
588	C₂	#10588662	1	1	yes	characteristic
589	C₂	#10588673	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₉
commutator	C₂³×C₉	C₂²×C₄
Frattini, socle, prime radical	C₂⁴×C₃	C₂²×D₃
Fitting	C₂×C₉×#95	C₂
cosocle	C₂⁴×C₉	C₂³
hypercenter	C₂×#95	D₉
hypocenter	C₉	#1445
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
18. C₂×Dic₉⋊C₄	C₄	semidirect
452. C₉	#1445	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₉⋊C₄	2
C₂×C₉×#95	2
C₂×C₉⋊#95	2
#69421	3