Subgroups — #18088014

Order 4864.

1230 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597353	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926546	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926543	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926308	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂×#10597353	—	2	2	no	—
10	C₂×#10597353	—	2	2	no	—
11	C₂×#10597353	—	2	2	no	—
12	C₂×#10597353	—	2	2	no	—
13	C₂×#10597353	—	2	2	no	—
14	C₂×#10597353	C₄	1	4	yes	complemented
15	C₂²×#64520	C₂²	1	1	yes	characteristic
16	C₂²×#64515	—	2	1	no	—
17	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₁₉	—	2	1	no	—
19	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926546	—	2	2	no	—
21	#11926546	C₄	1	4	yes	complemented
22	#11926543	—	2	2	no	—
23	#11926543	C₄	1	4	yes	complemented
24	C₂×#10597273	—	2	1	no	—
25	C₂×#10597267	—	2	1	no	—
26	C₂×#10597278	—	2	1	no	—
27	C₂×#10597266	—	2	1	no	—
28	#11926312	—	2	2	no	—
29	#11926308	—	2	2	no	—
30	#11926306	—	2	1	no	—
31	#11926306	—	2	1	no	—
32	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#343	—	2	2	no	—
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₂²⋊D₁₉	—	2	1	no	—
39	C₂³×Dic₁₉	—	2	1	no	—
40	C₂×#64541	—	2	1	no	—
41	C₂×#64541	—	2	1	no	—
42	C₂×#64541	—	2	1	no	—
43	C₂×#64541	—	2	1	no	—
44	C₂×#64541	—	2	1	no	—
45	C₂×#64541	—	2	1	no	—
46	C₂×#64541	C₂×C₄	1	2	yes	—
47	C₂×#64541	C₂×C₄	1	2	yes	—
48	C₂×#64541	C₂×C₄	1	2	yes	—
49	C₂×#64541	D₄	1	2	yes	—
50	C₂×#64541	D₄	1	2	yes	—
51	C₂×#64541	Q₈	1	2	yes	—
52	C₂²×D₇₆	D₄	1	1	yes	characteristic
53	C₂²×C₄×D₁₉	—	2	1	no	—
54	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊Dic₁₉	—	2	1	no	—
76	C₂×C₄⋊Dic₁₉	—	2	1	no	—
77	C₂×C₄⋊Dic₁₉	—	2	1	no	—
78	C₂×C₄⋊Dic₁₉	—	2	1	no	—
79	C₂×C₄⋊Dic₁₉	—	2	1	no	—
80	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	C₂×C₄	1	2	yes	—
87	C₂²×C₁₉⋊C₈	—	2	1	no	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	C₂²×C₁₉⋊C₈	—	2	1	no	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₂²×C₁₉⋊C₈	—	2	1	no	—
92	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
93	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
94	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
95	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
96	#10597353	—	2	8	no	—
97	#10597353	—	2	8	no	—
98	#10597353	—	2	8	no	—
99	#10597353	—	2	8	no	—
100	C₂×#64515	—	2	4	no	—
101	C₂×#64515	—	2	4	no	—
102	C₂×#64515	—	2	4	no	—
103	C₂×C₈×D₁₉	—	2	4	no	—
104	C₂×C₈×D₁₉	—	2	4	no	—
105	C₂×C₈×D₁₉	—	2	4	no	—
106	#10597278	—	2	4	no	—
107	#10597273	—	2	4	no	—
108	#10597267	—	2	4	no	—
109	#10597266	—	2	4	no	—
110	C₂⁴×C₁₉	#41	1	1	yes	characteristic
111	C₂³×D₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	8	1	no	—
116	C₂²×C₄×C₁₉	—	8	1	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₉	—	2	2	no	—
132	C₂×C₂²⋊D₁₉	—	2	2	no	—
133	C₂×C₂²⋊D₁₉	—	2	2	no	—
134	C₂×C₂²⋊D₁₉	—	2	2	no	—
135	C₂×C₂²⋊D₁₉	—	2	2	no	—
136	C₂×C₂²⋊D₁₉	—	2	2	no	—
137	C₂²×Dic₁₉	—	2	1	no	—
138	C₂²×Dic₁₉	—	2	2	no	—
139	C₂²×Dic₁₉	—	4	1	no	—
140	C₂²×Dic₁₉	—	4	1	no	—
141	C₂²×Dic₁₉	—	8	1	no	—
142	C₂²×Dic₁₉	—	8	1	no	—
143	#64541	—	2	2	no	—
144	#64541	—	2	2	no	—
145	#64541	—	2	2	no	—
146	#64541	—	2	2	no	—
147	#64541	—	2	2	no	—
148	#64541	—	2	2	no	—
149	#64541	—	2	2	no	—
150	#64541	—	2	2	no	—
151	#64541	—	2	2	no	—
152	#64541	—	2	2	no	—
153	#64541	—	2	2	no	—
154	#64541	—	2	2	no	—
155	#64541	C₄²	1	4	yes	—
156	#64541	C₂²⋊C₄	1	4	yes	—
157	#64541	C₄⋊C₄	1	4	yes	—
158	#64541	C₄⋊C₄	1	4	yes	—
159	C₂×D₇₆	—	2	1	no	—
160	C₂×D₇₆	—	2	1	no	—
161	C₂×D₇₆	—	2	1	no	—
162	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
163	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
164	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
165	C₂×C₄×D₁₉	—	2	2	no	—
166	C₂×C₄×D₁₉	—	2	2	no	—
167	C₂×C₄×D₁₉	—	2	2	no	—
168	C₂×C₄×D₁₉	—	2	2	no	—
169	C₂×C₄×D₁₉	—	2	2	no	—
170	C₂×C₄×D₁₉	—	2	2	no	—
171	C₂×Dic₃₈	—	2	1	no	—
172	C₂×Dic₃₈	—	2	1	no	—
173	C₂×Dic₃₈	—	2	1	no	—
174	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
175	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
176	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
177	M₁₆×C₁₉	—	2	2	no	—
178	M₁₆×C₁₉	—	2	2	no	—
179	M₁₆×C₁₉	—	2	2	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	2	2	no	—
182	M₁₆×C₁₉	—	4	1	no	—
183	M₁₆×C₁₉	—	4	1	no	—
184	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	4	1	no	—
190	C₂×C₈×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	—	4	1	no	—
195	C₄⋊Dic₁₉	—	2	2	no	—
196	C₄⋊Dic₁₉	—	2	2	no	—
197	C₄⋊Dic₁₉	—	4	1	no	—
198	C₄⋊Dic₁₉	—	4	1	no	—
199	#64520	—	2	2	no	—
200	#64520	—	2	2	no	—
201	#64520	—	4	1	no	—
202	#64520	—	4	1	no	—
203	C₂×C₁₉⋊C₈	—	2	2	no	—
204	C₂×C₁₉⋊C₈	—	2	2	no	—
205	C₂×C₁₉⋊C₈	—	2	1	no	—
206	C₂×C₁₉⋊C₈	—	2	1	no	—
207	C₂×C₁₉⋊C₈	—	2	1	no	—
208	C₂×C₁₉⋊C₈	—	2	1	no	—
209	C₂×C₁₉⋊C₈	—	2	2	no	—
210	C₂×C₁₉⋊C₈	—	2	2	no	—
211	C₂×C₁₉⋊C₈	—	2	2	no	—
212	C₂×C₁₉⋊C₈	—	4	1	no	—
213	C₂×C₁₉⋊C₈	—	4	1	no	—
214	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
215	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
216	#64515	—	2	16	no	—
217	C₈×D₁₉	—	2	16	no	—
218	#10774	—	19	1	no	maximal, Sylow
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	1	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	#117	1	1	yes	characteristic
224	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
225	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₁₉	#121	1	1	yes	characteristic
227	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂³×C₁₉	#123	1	1	yes	characteristic
229	C₂³×C₁₉	#123	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	2	2	no	—
233	C₂²×D₁₉	—	4	1	no	—
234	C₂²×D₁₉	—	4	1	no	—
235	C₂²×D₁₉	—	4	1	no	—
236	C₂²×D₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	8	1	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
270	C₂²⋊D₁₉	—	2	4	no	—
271	C₂²⋊D₁₉	—	2	4	no	—
272	C₂²⋊D₁₉	—	2	4	no	—
273	C₂²⋊D₁₉	—	2	4	no	—
274	C₂×Dic₁₉	—	2	2	no	—
275	C₂×Dic₁₉	—	2	2	no	—
276	C₂×Dic₁₉	—	2	2	no	—
277	C₂×Dic₁₉	—	4	2	no	—
278	C₂×Dic₁₉	—	8	2	no	—
279	C₂×Dic₁₉	—	8	1	no	—
280	C₂×Dic₁₉	—	8	1	no	—
281	C₂×Dic₁₉	—	8	2	no	—
282	D₇₆	—	2	2	no	—
283	D₇₆	—	2	2	no	—
284	D₇₆	—	2	2	no	—
285	D₇₆	#95	1	4	yes	—
286	C₄×D₁₉	—	2	4	no	—
287	C₄×D₁₉	—	2	4	no	—
288	C₄×D₁₉	—	2	4	no	—
289	C₄×D₁₉	—	2	4	no	—
290	Dic₃₈	—	2	2	no	—
291	Dic₃₈	—	2	2	no	—
292	Dic₃₈	—	2	2	no	—
293	Dic₃₈	#95	1	4	yes	—
294	C₈×C₁₉	—	2	4	no	—
295	C₈×C₁₉	—	4	2	no	—
296	C₁₉⋊C₈	—	2	2	no	—
297	C₁₉⋊C₈	—	2	2	no	—
298	C₁₉⋊C₈	—	4	2	no	—
299	C₂²×#131	—	19	1	no	—
300	C₂×#417	—	19	1	no	—
301	C₂×#417	—	19	1	no	—
302	C₂×#343	—	19	1	no	—
303	C₂×#343	D₁₉	1	1	yes	characteristic, complemented
304	C₂×#341	—	19	1	no	—
305	C₂×#340	—	19	1	no	—
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₁₉	#380	1	1	yes	characteristic
320	C₂²×C₁₉	#381	1	1	yes	characteristic
321	C₂²×C₁₉	#385	1	1	yes	characteristic
322	C₂²×C₁₉	#385	1	1	yes	characteristic
323	C₂²×C₁₉	#386	1	1	yes	characteristic
324	C₂²×C₁₉	#386	1	1	yes	characteristic
325	C₂²×C₁₉	#471	1	1	yes	characteristic
326	C₂²×C₁₉	#471	1	1	yes	characteristic
327	C₂²×C₁₉	#472	1	1	yes	characteristic
328	C₂²×C₁₉	#473	1	1	yes	characteristic
329	C₂×D₁₉	—	2	4	no	—
330	C₂×D₁₉	—	4	2	no	—
331	C₂×D₁₉	—	4	2	no	—
332	C₂×D₁₉	—	4	2	no	—
333	C₂×D₁₉	—	4	2	no	—
334	C₂×D₁₉	—	4	2	no	—
335	C₂×D₁₉	—	4	2	no	—
336	C₄×C₁₉	—	8	2	no	—
337	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
338	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
339	C₄×C₁₉	#379	1	1	yes	characteristic
340	C₄×C₁₉	#380	1	1	yes	characteristic
341	C₄×C₁₉	#385	1	1	yes	characteristic
342	C₄×C₁₉	#385	1	1	yes	characteristic
343	C₄×C₁₉	#386	1	1	yes	characteristic
344	C₄×C₁₉	#386	1	1	yes	characteristic
345	Dic₁₉	—	2	4	no	—
346	Dic₁₉	—	8	2	no	—
347	C₂²×#41	—	19	1	no	—
348	C₂×#131	—	19	4	no	—
349	C₂×#131	—	38	2	no	—
350	C₂×#131	—	38	2	no	—
351	C₂×#131	—	38	2	no	—
352	C₂×#131	—	38	2	no	—
353	C₂×#131	—	38	2	no	—
354	C₂²×M₁₆	—	19	1	no	—
355	C₂²×M₁₆	—	38	1	no	—
356	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
357	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
358	C₂³×C₈	—	19	1	no	—
359	C₂³×C₈	—	38	1	no	—
360	C₂²×C₄⋊C₄	—	19	1	no	—
361	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
362	#417	—	19	4	no	—
363	#417	—	19	4	no	—
364	#417	—	38	2	no	—
365	#417	—	38	2	no	—
366	C₂×#103	—	38	1	no	—
367	C₂×#103	—	38	1	no	—
368	C₂×#102	—	38	1	no	—
369	C₂×#102	—	38	1	no	—
370	#343	—	2	2	no	—
371	#343	—	38	2	no	—
372	#341	—	38	2	no	—
373	#340	—	38	1	no	—
374	#340	—	38	1	no	—
375	C₂×C₁₉	—	2	1	no	—
376	C₂×C₁₉	—	2	1	no	—
377	C₂×C₁₉	—	2	1	no	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
380	C₂×C₁₉	#1815	1	1	yes	characteristic
381	C₂×C₁₉	#1816	1	1	yes	characteristic
382	C₂×C₁₉	#1907	1	1	yes	characteristic
383	C₂×C₁₉	#1907	1	1	yes	characteristic
384	C₂×C₁₉	#1908	1	1	yes	characteristic
385	C₂×C₁₉	#1908	1	1	yes	characteristic
386	D₁₉	—	4	4	no	—
387	C₂×#41	—	19	2	no	—
388	C₂×#41	—	19	2	no	—
389	C₂×#41	—	19	2	no	—
390	C₂×#41	—	19	2	no	—
391	C₂×#41	—	19	2	no	—
392	C₂×#41	—	19	2	no	—
393	C₂×#41	—	38	1	no	—
394	C₂×#41	—	38	1	no	—
395	C₂×#41	—	38	1	no	—
396	C₂×#41	—	38	1	no	—
397	C₂×#41	—	38	1	no	—
398	C₂×#41	—	38	1	no	—
399	C₂²×Q₈	—	19	1	no	—
400	C₂²×D₄	—	19	1	no	—
401	C₂²×D₄	—	38	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	38	1	no	—
404	C₂³×C₄	—	38	1	no	—
405	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
406	#131	—	38	8	no	—
407	#131	—	38	8	no	—
408	#131	—	38	8	no	—
409	#131	—	38	8	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	19	2	no	—
419	C₂×M₁₆	—	38	4	no	—
420	C₂×M₁₆	—	38	4	no	—
421	C₂×M₁₆	—	38	4	no	—
422	C₂×M₁₆	—	38	1	no	—
423	C₂×M₁₆	—	38	1	no	—
424	C₂×M₁₆	—	38	1	no	—
425	C₂×M₁₆	—	38	1	no	—
426	C₂×M₁₆	—	38	1	no	—
427	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
428	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
429	C₂×M₁₆	D₇₆	1	2	yes	—
430	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
431	C₂²×C₈	—	2	1	no	—
432	C₂²×C₈	—	2	1	no	—
433	C₂²×C₈	—	19	2	no	—
434	C₂²×C₈	—	19	1	no	—
435	C₂²×C₈	—	19	1	no	—
436	C₂²×C₈	—	19	2	no	—
437	C₂²×C₈	—	38	4	no	—
438	C₂²×C₈	—	38	4	no	—
439	C₂²×C₈	—	38	4	no	—
440	C₂²×C₈	—	38	1	no	—
441	C₂²×C₈	—	38	1	no	—
442	C₂²×C₈	—	38	1	no	—
443	C₂²×C₈	—	38	1	no	—
444	C₂²×C₈	—	38	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	19	2	no	—
451	C₂×C₄⋊C₄	—	38	1	no	—
452	C₂×C₄⋊C₄	—	38	1	no	—
453	C₂×C₄⋊C₄	—	38	1	no	—
454	C₂×C₄⋊C₄	—	38	1	no	—
455	C₂×C₄⋊C₄	—	38	1	no	—
456	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
457	#103	—	38	4	no	—
458	#103	—	38	4	no	—
459	#102	—	38	4	no	—
460	#102	—	38	4	no	—
461	C₁₉	#10774	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	—	38	1	no	—
463	C₂⁴	#64541	1	1	yes	characteristic
464	#41	—	19	4	no	—
465	#41	—	19	4	no	—
466	#41	—	19	4	no	—
467	#41	—	19	4	no	—
468	#41	—	38	2	no	—
469	#41	—	38	2	no	—
470	#41	—	38	2	no	—
471	#41	—	38	2	no	—
472	#41	—	38	2	no	—
473	#41	—	38	2	no	—
474	#41	—	38	2	no	—
475	#41	—	38	2	no	—
476	#41	—	38	2	no	—
477	#41	—	38	2	no	—
478	#41	—	38	2	no	—
479	#41	—	38	2	no	—
480	C₂×Q₈	—	19	2	no	—
481	C₂×Q₈	—	19	2	no	—
482	C₂×Q₈	—	19	2	no	—
483	C₂×Q₈	—	38	1	no	—
484	C₂×Q₈	—	38	1	no	—
485	C₂×Q₈	—	38	1	no	—
486	C₂×D₄	—	19	2	no	—
487	C₂×D₄	—	19	2	no	—
488	C₂×D₄	—	19	2	no	—
489	C₂×D₄	—	38	2	no	—
490	C₂×D₄	—	38	2	no	—
491	C₂×D₄	—	38	2	no	—
492	C₂×D₄	—	38	2	no	—
493	C₂×D₄	—	38	2	no	—
494	C₂×D₄	—	38	2	no	—
495	C₂×D₄	—	38	1	no	—
496	C₂×D₄	—	38	1	no	—
497	C₂×D₄	—	38	1	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	—	38	1	no	—
504	C₂²×C₄	—	38	2	no	—
505	C₂²×C₄	—	38	2	no	—
506	C₂²×C₄	—	38	2	no	—
507	C₂²×C₄	—	38	2	no	—
508	C₂²×C₄	—	38	2	no	—
509	C₂²×C₄	—	38	2	no	—
510	C₂²×C₄	—	38	2	no	—
511	C₂²×C₄	—	76	1	no	—
512	C₂²×C₄	—	76	1	no	—
513	C₂²×C₄	—	152	1	no	—
514	C₂²×C₄	—	152	1	no	—
515	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
519	C₂²×C₄	#64541	1	1	yes	characteristic
520	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
521	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
522	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
523	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
524	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
525	C₂²×C₄	#64543	1	1	yes	characteristic
526	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
527	C₂²×C₄	#64545	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
529	M₁₆	—	2	2	no	—
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	4	1	no	—
535	M₁₆	—	4	1	no	—
536	M₁₆	—	38	16	no	—
537	M₁₆	—	38	2	no	—
538	M₁₆	—	38	2	no	—
539	M₁₆	—	76	1	no	—
540	M₁₆	—	76	1	no	—
541	M₁₆	(C₂×D₁₉)⋊C₄	1	4	yes	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	2	2	no	—
546	C₂×C₈	—	4	1	no	—
547	C₂×C₈	—	4	1	no	—
548	C₂×C₈	—	19	2	no	—
549	C₂×C₈	—	19	2	no	—
550	C₂×C₈	—	38	16	no	—
551	C₂×C₈	—	38	1	no	—
552	C₂×C₈	—	38	1	no	—
553	C₂×C₈	—	38	2	no	—
554	C₂×C₈	—	38	2	no	—
555	C₂×C₈	—	38	1	no	—
556	C₂×C₈	—	38	1	no	—
557	C₂×C₈	—	38	2	no	—
558	C₂×C₈	—	38	2	no	—
559	C₂×C₈	—	38	2	no	—
560	C₂×C₈	—	76	1	no	—
561	C₂×C₈	—	76	1	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	4	1	no	—
565	C₄⋊C₄	—	4	1	no	—
566	C₄⋊C₄	—	38	2	no	—
567	C₄⋊C₄	—	38	2	no	—
568	C₄⋊C₄	—	76	1	no	—
569	C₄⋊C₄	—	76	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	38	2	no	—
575	C₂³	—	38	2	no	—
576	C₂³	—	38	2	no	—
577	C₂³	—	76	1	no	—
578	C₂³	—	76	1	no	—
579	C₂³	—	76	1	no	—
580	C₂³	—	76	1	no	—
581	C₂³	#10597318	1	1	yes	characteristic
582	C₂³	C₄×D₇₆	1	1	yes	characteristic
583	C₂³	#10597329	1	1	yes	characteristic
584	C₂³	#10597330	1	1	yes	characteristic
585	C₂³	#10597340	1	1	yes	characteristic
586	C₂³	#10597342	1	1	yes	characteristic
587	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
588	Q₈	—	19	4	no	—
589	Q₈	—	38	2	no	—
590	Q₈	—	38	2	no	—
591	Q₈	—	38	2	no	—
592	D₄	—	19	4	no	—
593	D₄	—	38	4	no	—
594	D₄	—	38	4	no	—
595	D₄	—	38	4	no	—
596	D₄	—	38	4	no	—
597	D₄	—	38	2	no	—
598	D₄	—	38	2	no	—
599	D₄	—	38	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	—	8	1	no	—
603	C₂×C₄	—	8	1	no	—
604	C₂×C₄	—	8	2	no	—
605	C₂×C₄	—	38	2	no	—
606	C₂×C₄	—	38	2	no	—
607	C₂×C₄	—	38	2	no	—
608	C₂×C₄	—	38	4	no	—
609	C₂×C₄	—	38	4	no	—
610	C₂×C₄	—	38	4	no	—
611	C₂×C₄	—	38	4	no	—
612	C₂×C₄	—	76	2	no	—
613	C₂×C₄	—	152	2	no	—
614	C₂×C₄	—	152	1	no	—
615	C₂×C₄	—	152	1	no	—
616	C₂×C₄	—	152	2	no	—
617	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
618	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
619	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
620	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
623	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
624	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
625	C₂×C₄	#10597328	1	1	yes	characteristic
626	C₂×C₄	#10597328	1	1	yes	characteristic
627	C₂×C₄	#10597329	1	1	yes	characteristic
628	C₂×C₄	#10597330	1	1	yes	characteristic
629	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
630	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
631	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
632	C₂×C₄	#10597338	1	1	yes	characteristic
633	C₂×C₄	#10597339	1	1	yes	characteristic
634	C₂×C₄	#10597339	1	1	yes	characteristic
635	C₂×C₄	#10597340	1	1	yes	characteristic
636	C₂×C₄	#10597341	1	1	yes	characteristic
637	C₂×C₄	#10597342	1	1	yes	characteristic
638	C₂×C₄	#10597343	1	1	yes	characteristic
639	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
640	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
641	C₂×C₄	#10597383	1	1	yes	characteristic
642	C₂×C₄	#10597383	1	1	yes	characteristic
643	C₂×C₄	#10597384	1	1	yes	characteristic
644	C₂×C₄	#10597392	1	1	yes	characteristic
645	C₈	—	2	4	no	—
646	C₈	—	4	2	no	—
647	C₈	—	38	2	no	—
648	C₈	—	38	2	no	—
649	C₈	—	76	2	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	38	4	no	—
663	C₂²	—	76	2	no	—
664	C₂²	—	76	2	no	—
665	C₂²	—	76	2	no	—
666	C₂²	—	76	2	no	—
667	C₂²	—	76	2	no	—
668	C₂²	—	76	2	no	—
669	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
670	C₂²	#11926403	1	1	yes	characteristic
671	C₂²	#11926406	1	1	yes	characteristic
672	C₂²	#11926415	1	1	yes	characteristic
673	C₂²	#11926418	1	1	yes	characteristic
674	C₂²	#11926420	1	1	yes	characteristic
675	C₂²	#11926422	1	1	yes	characteristic
676	C₂²	#11926806	1	1	yes	characteristic
677	C₂²	#11926810	1	1	yes	characteristic
678	C₂²	#11926813	1	1	yes	characteristic
679	C₂²	#11926818	1	1	yes	characteristic
680	C₄	—	8	2	no	—
681	C₄	—	38	4	no	—
682	C₄	—	152	2	no	—
683	C₄	#95×D₁₉	1	1	yes	characteristic
684	C₄	#11926391	1	1	yes	characteristic
685	C₄	#11926399	1	1	yes	characteristic
686	C₄	#11926401	1	1	yes	characteristic
687	C₄	#11926415	1	1	yes	characteristic
688	C₄	#11926418	1	1	yes	characteristic
689	C₄	#11926420	1	1	yes	characteristic
690	C₄	#11926422	1	1	yes	characteristic
691	C₂	—	2	1	no	—
692	C₂	—	2	1	no	—
693	C₂	—	2	1	no	—
694	C₂	—	2	1	no	—
695	C₂	—	76	4	no	—
696	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
697	C₂	#14563693	1	1	yes	characteristic
698	C₂	#14563698	1	1	yes	characteristic
699	C₂	#14564140	1	1	yes	characteristic
700	C₂	#14564144	1	1	yes	characteristic
701	C₂	#14564147	1	1	yes	characteristic
702	C₂	#14564151	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#10774
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
4. C₂×#11926312	C₂	semidirect
5. C₂×#11926308	C₂	semidirect
6. C₂×#11926306	C₂	semidirect
7. C₂×C₁₉×#343	C₂	semidirect
14. C₂×#10597353	C₄	semidirect
21. #11926546	C₄	semidirect
23. #11926543	C₄	semidirect
303. C₂×#343	D₁₉	semidirect
461. C₁₉	#10774	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597353	2
C₂×#11926546	2
C₂×#11926543	2
C₂×#11926312	2
C₂×#11926308	2
C₂×#11926306	2
C₂×C₁₉×#343	2
#10774	19