Subgroups — #18088107

Order 4864.

1370 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597333	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597273	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10597267	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
6	#14561864	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597333	—	2	2	no	—
11	C₂×#10597333	—	2	2	no	—
12	C₂×#10597333	—	2	2	no	—
13	C₂×#10597333	—	2	2	no	—
14	C₂×#10597333	—	2	2	no	—
15	C₂×#10597333	C₄	1	4	yes	complemented
16	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₉⋊C₄	—	2	1	no	—
18	C₂²×C₄×Dic₁₉	—	2	1	no	—
19	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×#10597273	—	2	2	no	—
21	C₂×#10597273	—	2	2	no	—
22	C₂×#10597273	C₄	1	4	yes	complemented
23	C₂×#10597267	—	2	2	no	—
24	C₂×#10597267	—	2	2	no	—
25	C₂×#10597267	C₄	1	4	yes	complemented
26	C₂×C₁₉⋊#95	—	2	1	no	—
27	C₂×C₁₉⋊#95	—	2	1	no	—
28	#11926306	—	2	2	no	—
29	#11926298	—	2	2	no	—
30	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#340	—	2	2	no	—
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×Dic₁₉	—	2	1	no	—
38	C₂³×Dic₁₉	—	2	1	no	—
39	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
40	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
41	C₂²×Dic₃₈	—	2	1	no	—
42	C₂²×Dic₃₈	—	2	1	no	—
43	C₂²×Dic₃₈	—	2	1	no	—
44	C₂²×Dic₃₈	—	2	1	no	—
45	C₂²×Dic₃₈	—	2	1	no	—
46	C₂²×Dic₃₈	—	2	1	no	—
47	C₂²×Dic₃₈	—	2	1	no	—
48	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
49	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
50	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
51	C₂²×Dic₃₈	D₄	1	2	yes	—
52	C₂²×Dic₃₈	D₄	1	2	yes	—
53	C₂²×Dic₃₈	D₄	1	2	yes	—
54	C₂²×Dic₃₈	Q₈	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
74	C₂×C₄⋊Dic₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
80	C₂×Dic₁₉⋊C₄	—	2	4	no	—
81	C₂×Dic₁₉⋊C₄	—	2	4	no	—
82	C₂×Dic₁₉⋊C₄	—	2	4	no	—
83	C₂×C₄×Dic₁₉	—	2	4	no	—
84	C₂×C₄×Dic₁₉	—	2	4	no	—
85	C₂×C₄×Dic₁₉	—	2	1	no	—
86	C₂×C₄×Dic₁₉	—	2	1	no	—
87	C₂×C₄×Dic₁₉	—	2	1	no	—
88	C₂×C₄×Dic₁₉	—	2	1	no	—
89	C₂×C₄×Dic₁₉	—	2	4	no	—
90	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
91	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
92	C₂²×C₁₉⋊C₈	—	2	1	no	—
93	C₂²×C₁₉⋊C₈	—	2	1	no	—
94	C₂²×C₁₉⋊C₈	—	2	1	no	—
95	C₂²×C₁₉⋊C₈	—	2	1	no	—
96	C₂²×C₁₉⋊C₈	—	2	1	no	—
97	C₂²×C₁₉⋊C₈	—	2	1	no	—
98	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
99	#10597333	—	2	8	no	—
100	#10597333	—	2	8	no	—
101	#10597333	—	2	8	no	—
102	#10597333	—	2	8	no	—
103	C₁₉⋊#95	—	4	2	no	—
104	C₁₉⋊#95	—	4	2	no	—
105	#10597273	—	2	8	no	—
106	#10597267	—	2	8	no	—
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²×C₄	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×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×Dic₁₉	—	2	2	no	—
137	C₂²×Dic₁₉	—	2	2	no	—
138	C₂²×Dic₁₉	—	2	2	no	—
139	C₂²×Dic₁₉	—	2	2	no	—
140	C₂²×Dic₁₉	—	2	2	no	—
141	C₂²×Dic₁₉	—	2	1	no	—
142	C₂²×Dic₁₉	—	2	1	no	—
143	C₂²×Dic₁₉	—	2	2	no	—
144	C₂²×Dic₁₉	—	2	2	no	—
145	C₂²×Dic₁₉	—	2	1	no	—
146	C₂²×Dic₁₉	—	2	1	no	—
147	C₂²×Dic₁₉	—	2	1	no	—
148	C₂²×Dic₁₉	—	2	1	no	—
149	C₂²×Dic₁₉	—	2	1	no	—
150	C₂²×Dic₁₉	—	2	1	no	—
151	C₂²×Dic₁₉	—	2	1	no	—
152	C₂²×Dic₁₉	—	2	1	no	—
153	C₂²×Dic₁₉	—	2	2	no	—
154	C₂²×Dic₁₉	—	4	1	no	—
155	C₂²×Dic₁₉	—	4	1	no	—
156	C₂²×Dic₁₉	—	4	1	no	—
157	C₂²×Dic₁₉	—	4	1	no	—
158	C₂²×Dic₁₉	—	4	1	no	—
159	C₂²×Dic₁₉	—	4	1	no	—
160	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
161	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
162	C₂²×Dic₁₉	SD₁₆	1	2	yes	—
163	C₂²×Dic₁₉	Q₁₆	1	2	yes	—
164	C₂×Dic₃₈	—	2	2	no	—
165	C₂×Dic₃₈	—	2	2	no	—
166	C₂×Dic₃₈	—	2	2	no	—
167	C₂×Dic₃₈	—	2	2	no	—
168	C₂×Dic₃₈	—	2	2	no	—
169	C₂×Dic₃₈	—	2	2	no	—
170	C₂×Dic₃₈	—	2	2	no	—
171	C₂×Dic₃₈	—	2	2	no	—
172	C₂×Dic₃₈	—	2	2	no	—
173	C₂×Dic₃₈	—	2	2	no	—
174	C₂×Dic₃₈	—	2	2	no	—
175	C₂×Dic₃₈	—	2	2	no	—
176	C₂×Dic₃₈	—	2	2	no	—
177	C₂×Dic₃₈	—	2	2	no	—
178	C₂×Dic₃₈	—	2	2	no	—
179	C₂×Dic₃₈	—	2	2	no	—
180	C₂×Dic₃₈	—	2	2	no	—
181	C₂×Dic₃₈	—	2	2	no	—
182	C₂×Dic₃₈	—	2	2	no	—
183	C₂×Dic₃₈	—	2	2	no	—
184	C₂×Dic₃₈	—	2	2	no	—
185	C₂×Dic₃₈	C₄²	1	4	yes	—
186	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
187	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
188	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
189	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
190	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
191	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
192	C₂×C₈×C₁₉	—	2	2	no	—
193	C₂×C₈×C₁₉	—	2	2	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₂×C₈×C₁₉	—	4	1	no	—
196	C₂×C₈×C₁₉	—	4	1	no	—
197	C₂×C₈×C₁₉	—	4	1	no	—
198	C₂×C₈×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	2	no	—
203	C₄⋊C₄×C₁₉	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	—	4	1	no	—
206	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
207	C₄⋊Dic₁₉	—	2	2	no	—
208	C₄⋊Dic₁₉	—	2	2	no	—
209	C₄⋊Dic₁₉	—	4	1	no	—
210	C₄⋊Dic₁₉	—	4	1	no	—
211	Dic₁₉⋊C₄	—	2	16	no	—
212	C₄×Dic₁₉	—	2	16	no	—
213	C₄×Dic₁₉	—	2	2	no	—
214	C₄×Dic₁₉	—	2	2	no	—
215	C₄×Dic₁₉	—	2	2	no	—
216	C₄×Dic₁₉	—	2	2	no	—
217	C₂×C₁₉⋊C₈	—	2	2	no	—
218	C₂×C₁₉⋊C₈	—	2	2	no	—
219	C₂×C₁₉⋊C₈	—	2	2	no	—
220	C₂×C₁₉⋊C₈	—	4	1	no	—
221	C₂×C₁₉⋊C₈	—	4	1	no	—
222	C₂×C₁₉⋊C₈	—	4	1	no	—
223	C₂×C₁₉⋊C₈	—	4	1	no	—
224	#10789	—	19	1	no	maximal, Sylow
225	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
227	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₁₉	#120	1	1	yes	characteristic
229	C₂³×C₁₉	#120	1	1	yes	characteristic
230	C₂³×C₁₉	#121	1	1	yes	characteristic
231	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
233	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
234	C₂³×C₁₉	#135	1	1	yes	characteristic
235	C₂³×C₁₉	#135	1	1	yes	characteristic
236	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂³×C₁₉	#137	1	1	yes	characteristic
238	C₂³×C₁₉	#137	1	1	yes	characteristic
239	C₂³×C₁₉	#137	1	1	yes	characteristic
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	8	1	no	—
251	C₂×C₄×C₁₉	—	8	1	no	—
252	C₂×C₄×C₁₉	—	8	1	no	—
253	C₂×C₄×C₁₉	—	8	1	no	—
254	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
279	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
280	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
282	C₂×Dic₁₉	—	2	4	no	—
283	C₂×Dic₁₉	—	2	2	no	—
284	C₂×Dic₁₉	—	2	4	no	—
285	C₂×Dic₁₉	—	2	4	no	—
286	C₂×Dic₁₉	—	2	4	no	—
287	C₂×Dic₁₉	—	2	4	no	—
288	C₂×Dic₁₉	—	2	4	no	—
289	C₂×Dic₁₉	—	2	4	no	—
290	C₂×Dic₁₉	—	2	2	no	—
291	C₂×Dic₁₉	—	2	2	no	—
292	C₂×Dic₁₉	—	2	2	no	—
293	C₂×Dic₁₉	—	2	2	no	—
294	C₂×Dic₁₉	—	2	2	no	—
295	C₂×Dic₁₉	—	2	2	no	—
296	C₂×Dic₁₉	—	2	2	no	—
297	C₂×Dic₁₉	—	2	2	no	—
298	C₂×Dic₁₉	—	4	1	no	—
299	C₂×Dic₁₉	—	4	1	no	—
300	C₂×Dic₁₉	—	4	1	no	—
301	C₂×Dic₁₉	—	4	1	no	—
302	C₂×Dic₁₉	—	4	2	no	—
303	C₂×Dic₁₉	—	4	2	no	—
304	C₂×Dic₁₉	—	4	2	no	—
305	C₂×Dic₁₉	—	8	1	no	—
306	C₂×Dic₁₉	—	8	1	no	—
307	C₂×Dic₁₉	—	8	1	no	—
308	C₂×Dic₁₉	—	8	1	no	—
309	C₂×Dic₁₉	#103	1	4	yes	complemented
310	Dic₃₈	—	2	4	no	—
311	Dic₃₈	—	2	4	no	—
312	Dic₃₈	—	2	4	no	—
313	Dic₃₈	—	2	4	no	—
314	Dic₃₈	—	2	4	no	—
315	Dic₃₈	—	2	4	no	—
316	Dic₃₈	—	2	4	no	—
317	Dic₃₈	#95	1	8	yes	complemented
318	C₈×C₁₉	—	4	2	no	—
319	C₁₉⋊C₈	—	4	2	no	—
320	C₂²×C₄×Q₈	—	19	1	no	—
321	C₂²×#103	—	19	1	no	—
322	C₂²×#103	—	19	1	no	—
323	C₂×#340	—	19	1	no	—
324	C₂×#340	D₁₉	1	1	yes	characteristic
325	C₂×#336	—	19	1	no	—
326	C₄⋊#95	—	19	1	no	—
327	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
328	C₂²×C₁₉	#379	1	1	yes	characteristic
329	C₂²×C₁₉	#380	1	1	yes	characteristic
330	C₂²×C₁₉	#385	1	1	yes	characteristic
331	C₂²×C₁₉	#385	1	1	yes	characteristic
332	C₂²×C₁₉	#386	1	1	yes	characteristic
333	C₂²×C₁₉	#386	1	1	yes	characteristic
334	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
335	C₂²×C₁₉	#416	1	1	yes	characteristic
336	C₂²×C₁₉	#417	1	1	yes	characteristic
337	C₂²×C₁₉	#419	1	1	yes	characteristic
338	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
339	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
340	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
341	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
342	C₂²×C₁₉	#440	1	1	yes	characteristic
343	C₂²×C₁₉	#440	1	1	yes	characteristic
344	C₂²×C₁₉	#441	1	1	yes	characteristic
345	C₂²×C₁₉	#441	1	1	yes	characteristic
346	C₂²×C₁₉	#448	1	1	yes	characteristic
347	C₂²×C₁₉	#448	1	1	yes	characteristic
348	C₂²×C₁₉	#449	1	1	yes	characteristic
349	C₂²×C₁₉	#449	1	1	yes	characteristic
350	C₂²×C₁₉	#451	1	1	yes	characteristic
351	C₂²×C₁₉	#451	1	1	yes	characteristic
352	C₂²×C₁₉	#452	1	1	yes	characteristic
353	C₂²×C₁₉	#452	1	1	yes	characteristic
354	C₂²×C₁₉	#460	1	1	yes	characteristic
355	C₂²×C₁₉	#462	1	1	yes	characteristic
356	C₂²×C₁₉	#464	1	1	yes	characteristic
357	C₂²×C₁₉	#464	1	1	yes	characteristic
358	C₂²×C₁₉	#475	1	1	yes	characteristic
359	C₂²×C₁₉	#477	1	1	yes	characteristic
360	C₂²×C₁₉	#479	1	1	yes	characteristic
361	C₂²×C₁₉	#479	1	1	yes	characteristic
362	C₄×C₁₉	—	4	4	no	—
363	C₄×C₁₉	—	8	2	no	—
364	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
365	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
366	C₄×C₁₉	#380	1	1	yes	characteristic
367	C₄×C₁₉	#381	1	1	yes	characteristic
368	C₄×C₁₉	#385	1	1	yes	characteristic
369	C₄×C₁₉	#385	1	1	yes	characteristic
370	C₄×C₁₉	#386	1	1	yes	characteristic
371	C₄×C₁₉	#386	1	1	yes	characteristic
372	Dic₁₉	—	2	8	no	—
373	Dic₁₉	—	2	4	no	—
374	Dic₁₉	—	4	2	no	—
375	Dic₁₉	—	8	2	no	—
376	C₂³×Q₈	—	19	1	no	—
377	C₂³×C₈	—	19	1	no	—
378	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
379	C₂×C₄×Q₈	—	19	4	no	—
380	C₂×C₄×Q₈	—	38	2	no	—
381	C₂×C₄×Q₈	—	38	2	no	—
382	C₂×C₄×Q₈	—	38	2	no	—
383	C₂×C₄×Q₈	—	38	2	no	—
384	C₂×C₄×Q₈	—	38	2	no	—
385	C₂²×C₄⋊C₄	—	19	1	no	—
386	C₂²×C₄⋊C₄	—	38	1	no	—
387	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
389	C₂²×C₄²	—	19	1	no	—
390	C₂²×C₄²	—	38	1	no	—
391	C₂×#103	—	19	4	no	—
392	C₂×#103	—	19	4	no	—
393	C₂×#103	—	38	2	no	—
394	C₂×#103	—	38	2	no	—
395	C₂×#103	—	38	2	no	—
396	C₂×#103	—	38	2	no	—
397	C₂×#95	—	38	1	no	—
398	C₂×#95	—	38	1	no	—
399	#340	—	2	2	no	—
400	#340	—	38	2	no	—
401	#336	—	38	2	no	—
402	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
403	C₂×C₁₉	C₄×#103	1	1	yes	characteristic
404	C₂×C₁₉	#1763	1	1	yes	characteristic
405	C₂×C₁₉	#1787	1	1	yes	characteristic
406	C₂×C₁₉	#1788	1	1	yes	characteristic
407	C₂×C₁₉	#1803	1	1	yes	characteristic
408	C₂×C₁₉	#1805	1	1	yes	characteristic
409	C₂×C₁₉	#1863	1	1	yes	characteristic
410	C₂×C₁₉	#1863	1	1	yes	characteristic
411	C₂×C₁₉	#1865	1	1	yes	characteristic
412	C₂×C₁₉	#1865	1	1	yes	characteristic
413	C₂×C₁₉	#1878	1	1	yes	characteristic
414	C₂×C₁₉	#1878	1	1	yes	characteristic
415	C₂×C₁₉	#1880	1	1	yes	characteristic
416	C₂×C₁₉	#1880	1	1	yes	characteristic
417	C₂²×Q₈	—	19	2	no	—
418	C₂²×Q₈	—	19	2	no	—
419	C₂²×Q₈	—	19	2	no	—
420	C₂²×Q₈	—	19	2	no	—
421	C₂²×Q₈	—	19	2	no	—
422	C₂²×Q₈	—	19	2	no	—
423	C₂²×Q₈	—	19	2	no	—
424	C₂²×Q₈	—	38	1	no	—
425	C₂²×Q₈	—	38	1	no	—
426	C₂²×Q₈	—	38	1	no	—
427	C₂²×Q₈	—	38	1	no	—
428	C₂²×Q₈	—	38	1	no	—
429	C₂²×Q₈	—	38	1	no	—
430	C₂²×Q₈	—	38	1	no	—
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	—	19	1	no	—
434	C₂³×C₄	—	19	1	no	—
435	C₂³×C₄	—	38	1	no	—
436	C₂³×C₄	—	38	1	no	—
437	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	—	2	1	no	—
441	C₂²×C₈	—	2	1	no	—
442	C₂²×C₈	—	2	1	no	—
443	C₂²×C₈	—	2	1	no	—
444	C₂²×C₈	—	19	2	no	—
445	C₂²×C₈	—	38	1	no	—
446	C₂²×C₈	—	38	1	no	—
447	C₂²×C₈	—	38	1	no	—
448	C₂²×C₈	—	38	1	no	—
449	C₂²×C₈	—	38	1	no	—
450	C₂²×C₈	—	38	1	no	—
451	C₂²×C₈	C₄×D₁₉	1	2	yes	—
452	C₄×Q₈	—	38	8	no	—
453	C₄×Q₈	—	38	8	no	—
454	C₄×Q₈	—	38	8	no	—
455	C₄×Q₈	—	38	8	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	19	2	no	—
465	C₂×C₄⋊C₄	—	38	4	no	—
466	C₂×C₄⋊C₄	—	38	4	no	—
467	C₂×C₄⋊C₄	—	38	4	no	—
468	C₂×C₄⋊C₄	—	38	1	no	—
469	C₂×C₄⋊C₄	—	38	1	no	—
470	C₂×C₄⋊C₄	—	38	1	no	—
471	C₂×C₄⋊C₄	—	38	1	no	—
472	C₂×C₄⋊C₄	—	38	1	no	—
473	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
475	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
476	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
477	C₂×C₄²	—	19	2	no	—
478	C₂×C₄²	—	19	2	no	—
479	C₂×C₄²	—	38	4	no	—
480	C₂×C₄²	—	38	4	no	—
481	C₂×C₄²	—	38	4	no	—
482	C₂×C₄²	—	38	1	no	—
483	C₂×C₄²	—	38	1	no	—
484	C₂×C₄²	—	38	1	no	—
485	C₂×C₄²	—	38	1	no	—
486	#103	—	38	8	no	—
487	#103	—	38	8	no	—
488	#95	—	76	2	no	—
489	#95	—	76	2	no	—
490	C₁₉	#10789	1	1	yes	characteristic, complemented, Sylow
491	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
492	C₂×Q₈	—	19	4	no	—
493	C₂×Q₈	—	19	4	no	—
494	C₂×Q₈	—	19	4	no	—
495	C₂×Q₈	—	19	4	no	—
496	C₂×Q₈	—	19	4	no	—
497	C₂×Q₈	—	19	4	no	—
498	C₂×Q₈	—	19	4	no	—
499	C₂×Q₈	—	38	2	no	—
500	C₂×Q₈	—	38	2	no	—
501	C₂×Q₈	—	38	2	no	—
502	C₂×Q₈	—	38	2	no	—
503	C₂×Q₈	—	38	2	no	—
504	C₂×Q₈	—	38	2	no	—
505	C₂×Q₈	—	38	2	no	—
506	C₂×Q₈	—	38	2	no	—
507	C₂×Q₈	—	38	2	no	—
508	C₂×Q₈	—	38	2	no	—
509	C₂×Q₈	—	38	2	no	—
510	C₂×Q₈	—	38	2	no	—
511	C₂×Q₈	—	38	2	no	—
512	C₂×Q₈	—	38	2	no	—
513	C₂×Q₈	—	38	2	no	—
514	C₂×Q₈	—	38	2	no	—
515	C₂×Q₈	—	38	2	no	—
516	C₂×Q₈	—	38	2	no	—
517	C₂×Q₈	—	38	2	no	—
518	C₂×Q₈	—	38	2	no	—
519	C₂×Q₈	—	38	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	19	2	no	—
535	C₂²×C₄	—	19	2	no	—
536	C₂²×C₄	—	19	2	no	—
537	C₂²×C₄	—	19	2	no	—
538	C₂²×C₄	—	38	1	no	—
539	C₂²×C₄	—	38	2	no	—
540	C₂²×C₄	—	38	2	no	—
541	C₂²×C₄	—	38	2	no	—
542	C₂²×C₄	—	38	1	no	—
543	C₂²×C₄	—	38	2	no	—
544	C₂²×C₄	—	38	2	no	—
545	C₂²×C₄	—	38	2	no	—
546	C₂²×C₄	—	38	2	no	—
547	C₂²×C₄	—	38	1	no	—
548	C₂²×C₄	—	38	1	no	—
549	C₂²×C₄	—	38	1	no	—
550	C₂²×C₄	—	38	1	no	—
551	C₂²×C₄	—	38	1	no	—
552	C₂²×C₄	—	38	1	no	—
553	C₂²×C₄	—	38	1	no	—
554	C₂²×C₄	—	38	1	no	—
555	C₂²×C₄	—	38	2	no	—
556	C₂²×C₄	—	76	1	no	—
557	C₂²×C₄	—	76	1	no	—
558	C₂²×C₄	—	76	1	no	—
559	C₂²×C₄	—	76	1	no	—
560	C₂²×C₄	—	76	1	no	—
561	C₂²×C₄	—	76	1	no	—
562	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
566	C₂²×C₄	#64541	1	1	yes	characteristic
567	C₂²×C₄	#64541	1	1	yes	characteristic
568	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
569	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
570	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
571	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
572	C₂²×C₄	#64543	1	1	yes	characteristic
573	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
574	C₂²×C₄	#64545	1	1	yes	characteristic
575	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
576	C₂×C₈	—	2	2	no	—
577	C₂×C₈	—	2	2	no	—
578	C₂×C₈	—	2	2	no	—
579	C₂×C₈	—	4	1	no	—
580	C₂×C₈	—	4	1	no	—
581	C₂×C₈	—	4	1	no	—
582	C₂×C₈	—	4	1	no	—
583	C₂×C₈	—	38	2	no	—
584	C₂×C₈	—	38	2	no	—
585	C₂×C₈	—	38	2	no	—
586	C₂×C₈	—	76	1	no	—
587	C₂×C₈	—	76	1	no	—
588	C₂×C₈	—	76	1	no	—
589	C₂×C₈	—	76	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	—	38	16	no	—
598	C₄⋊C₄	—	38	2	no	—
599	C₄⋊C₄	—	38	2	no	—
600	C₄⋊C₄	—	76	1	no	—
601	C₄⋊C₄	—	76	1	no	—
602	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
603	C₄²	—	38	16	no	—
604	C₄²	—	38	2	no	—
605	C₄²	—	38	2	no	—
606	C₄²	—	38	2	no	—
607	C₄²	—	38	2	no	—
608	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
609	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
610	C₂³	#10597328	1	1	yes	characteristic
611	C₂³	#10597330	1	1	yes	characteristic
612	C₂³	#10597339	1	1	yes	characteristic
613	C₂³	#10597342	1	1	yes	characteristic
614	C₂³	#10597357	1	1	yes	characteristic
615	C₂³	#10597358	1	1	yes	characteristic
616	C₂³	SD₁₆×D₁₉	1	1	yes	characteristic
617	C₂³	#10597361	1	1	yes	characteristic
618	C₂³	#10597361	1	1	yes	characteristic
619	C₂³	#10597362	1	1	yes	characteristic
620	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
621	C₂³	#10597364	1	1	yes	characteristic
622	C₂³	#10597383	1	1	yes	characteristic
623	Q₈	—	19	8	no	—
624	Q₈	—	38	4	no	—
625	Q₈	—	38	4	no	—
626	Q₈	—	38	4	no	—
627	Q₈	—	38	4	no	—
628	Q₈	—	38	4	no	—
629	Q₈	—	38	4	no	—
630	Q₈	—	38	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	1	no	—
644	C₂×C₄	—	8	1	no	—
645	C₂×C₄	—	19	4	no	—
646	C₂×C₄	—	38	2	no	—
647	C₂×C₄	—	38	4	no	—
648	C₂×C₄	—	38	2	no	—
649	C₂×C₄	—	38	4	no	—
650	C₂×C₄	—	38	4	no	—
651	C₂×C₄	—	38	4	no	—
652	C₂×C₄	—	38	4	no	—
653	C₂×C₄	—	38	4	no	—
654	C₂×C₄	—	38	4	no	—
655	C₂×C₄	—	38	2	no	—
656	C₂×C₄	—	38	2	no	—
657	C₂×C₄	—	38	2	no	—
658	C₂×C₄	—	38	2	no	—
659	C₂×C₄	—	38	2	no	—
660	C₂×C₄	—	38	2	no	—
661	C₂×C₄	—	38	2	no	—
662	C₂×C₄	—	76	1	no	—
663	C₂×C₄	—	76	1	no	—
664	C₂×C₄	—	76	1	no	—
665	C₂×C₄	—	76	1	no	—
666	C₂×C₄	—	76	2	no	—
667	C₂×C₄	—	76	2	no	—
668	C₂×C₄	—	76	2	no	—
669	C₂×C₄	—	152	1	no	—
670	C₂×C₄	—	152	1	no	—
671	C₂×C₄	—	152	1	no	—
672	C₂×C₄	—	152	1	no	—
673	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
674	C₂×C₄	#10597318	1	1	yes	characteristic
675	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
676	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
677	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
678	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
679	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
680	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
681	C₂×C₄	#10597328	1	1	yes	characteristic
682	C₂×C₄	#10597329	1	1	yes	characteristic
683	C₂×C₄	#10597329	1	1	yes	characteristic
684	C₂×C₄	#10597330	1	1	yes	characteristic
685	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
686	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
687	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
688	C₂×C₄	#10597338	1	1	yes	characteristic
689	C₂×C₄	#10597339	1	1	yes	characteristic
690	C₂×C₄	#10597340	1	1	yes	characteristic
691	C₂×C₄	#10597340	1	1	yes	characteristic
692	C₂×C₄	#10597341	1	1	yes	characteristic
693	C₂×C₄	#10597342	1	1	yes	characteristic
694	C₂×C₄	#10597343	1	1	yes	characteristic
695	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
696	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
697	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
698	C₂×C₄	#10597383	1	1	yes	characteristic
699	C₂×C₄	#10597384	1	1	yes	characteristic
700	C₂×C₄	#10597392	1	1	yes	characteristic
701	C₈	—	4	2	no	—
702	C₈	—	76	2	no	—
703	C₂²	#11926391	1	1	yes	characteristic
704	C₂²	#11926399	1	1	yes	characteristic
705	C₂²	#11926403	1	1	yes	characteristic
706	C₂²	#11926415	1	1	yes	characteristic
707	C₂²	#11926418	1	1	yes	characteristic
708	C₂²	#11926420	1	1	yes	characteristic
709	C₂²	#11926422	1	1	yes	characteristic
710	C₂²	#103×D₁₉	1	1	yes	characteristic
711	C₂²	#11926537	1	1	yes	characteristic
712	C₂²	#11926542	1	1	yes	characteristic
713	C₂²	#11926551	1	1	yes	characteristic
714	C₂²	#11926631	1	1	yes	characteristic
715	C₂²	#11926635	1	1	yes	characteristic
716	C₂²	#11926636	1	1	yes	characteristic
717	C₂²	#11926638	1	1	yes	characteristic
718	C₂²	#11926641	1	1	yes	characteristic
719	C₂²	#11926643	1	1	yes	characteristic
720	C₂²	#11926648	1	1	yes	characteristic
721	C₂²	#11926650	1	1	yes	characteristic
722	C₂²	#11926681	1	1	yes	characteristic
723	C₂²	#11926684	1	1	yes	characteristic
724	C₂²	#11926686	1	1	yes	characteristic
725	C₂²	#11926690	1	1	yes	characteristic
726	C₂²	#11926698	1	1	yes	characteristic
727	C₂²	#11926701	1	1	yes	characteristic
728	C₂²	#11926703	1	1	yes	characteristic
729	C₂²	#11926707	1	1	yes	characteristic
730	C₂²	#11926743	1	1	yes	characteristic
731	C₂²	#11926753	1	1	yes	characteristic
732	C₂²	#11926765	1	1	yes	characteristic
733	C₂²	#11926769	1	1	yes	characteristic
734	C₂²	#11926828	1	1	yes	characteristic
735	C₂²	#11926838	1	1	yes	characteristic
736	C₂²	#11926850	1	1	yes	characteristic
737	C₂²	#11926854	1	1	yes	characteristic
738	C₄	—	4	4	no	—
739	C₄	—	8	2	no	—
740	C₄	—	38	8	no	—
741	C₄	—	38	4	no	—
742	C₄	—	76	2	no	—
743	C₄	—	152	2	no	—
744	C₄	#95×D₁₉	1	1	yes	characteristic
745	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
746	C₄	#11926401	1	1	yes	characteristic
747	C₄	#11926406	1	1	yes	characteristic
748	C₄	#11926415	1	1	yes	characteristic
749	C₄	#11926418	1	1	yes	characteristic
750	C₄	#11926420	1	1	yes	characteristic
751	C₄	#11926422	1	1	yes	characteristic
752	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
753	C₂	#14563454	1	1	yes	characteristic
754	C₂	#14563464	1	1	yes	characteristic
755	C₂	#14563568	1	1	yes	characteristic
756	C₂	#14563572	1	1	yes	characteristic
757	C₂	#14563639	1	1	yes	characteristic
758	C₂	#14563649	1	1	yes	characteristic
759	C₂	#14563886	1	1	yes	characteristic
760	C₂	#14563890	1	1	yes	characteristic
761	C₂	#14563900	1	1	yes	characteristic
762	C₂	#14563904	1	1	yes	characteristic
763	C₂	#14563973	1	1	yes	characteristic
764	C₂	#14563977	1	1	yes	characteristic
765	C₂	#14563987	1	1	yes	characteristic
766	C₂	#14563991	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	#10789
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
15. C₂×#10597333	C₄	semidirect
22. C₂×#10597273	C₄	semidirect
25. C₂×#10597267	C₄	semidirect
309. C₂×Dic₁₉	#103	semidirect
317. Dic₃₈	#95	semidirect
490. C₁₉	#10789	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597333	2
C₂²×#10597273	2
C₂²×#10597267	2
C₂×#11926306	2
C₂×#11926298	2
#14561864	2
C₂×C₁₉×#340	2
#10789	19