Subgroups — #18090798

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926414	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926307	C₂	1	2	yes	maximal
3	C₂×#11926307	C₂	1	2	yes	maximal
4	#14561865	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
8	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926414	—	2	4	no	—
12	C₂×C₁₉⋊#95	—	2	1	no	—
13	C₂×C₁₉⋊#95	—	2	1	no	—
14	#11926307	—	2	4	no	—
15	#11926307	—	2	4	no	—
16	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#336	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×Dic₁₉	—	2	1	no	—
23	C₂³×Dic₁₉	—	2	1	no	—
24	C₂³×Dic₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂²×C₈×C₁₉	—	2	2	no	—
29	C₂²×C₈×C₁₉	—	2	2	no	—
30	C₂²×C₈×C₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	2	no	—
38	C₂×C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₄⋊Dic₁₉	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	—	2	2	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
44	C₂×C₄⋊Dic₁₉	—	2	4	no	—
45	C₂×C₄⋊Dic₁₉	—	2	4	no	—
46	C₂×C₄⋊Dic₁₉	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	4	2	no	—
50	C₂×C₄⋊Dic₁₉	—	4	2	no	—
51	C₂×C₄⋊Dic₁₉	—	4	2	no	—
52	C₂×C₄⋊Dic₁₉	—	4	2	no	—
53	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
54	C₂×C₄⋊Dic₁₉	D₄	1	4	yes	—
55	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
56	C₁₉⋊#95	—	4	2	no	—
57	C₁₉⋊#95	—	4	2	no	—
58	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	D₈	1	2	yes	—
70	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	2	yes	—
79	C₂²×C₄×C₁₉	#41	1	2	yes	—
80	C₂²×C₄×C₁₉	#41	1	2	yes	—
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
83	C₂²×Dic₁₉	—	2	4	no	—
84	C₂²×Dic₁₉	—	2	2	no	—
85	C₂²×Dic₁₉	—	2	2	no	—
86	C₂²×Dic₁₉	—	4	1	no	—
87	C₂²×Dic₁₉	—	4	2	no	—
88	C₂²×Dic₁₉	—	4	1	no	—
89	C₂²×Dic₁₉	—	4	1	no	—
90	C₂²×Dic₁₉	—	4	2	no	—
91	C₂²×Dic₁₉	—	4	1	no	—
92	C₂²×Dic₁₉	—	4	1	no	—
93	C₂²×Dic₁₉	—	4	1	no	—
94	C₂²×Dic₁₉	—	4	2	no	—
95	C₂²×Dic₁₉	—	4	1	no	—
96	C₂²×Dic₁₉	—	4	1	no	—
97	C₂²×Dic₁₉	—	4	2	no	—
98	C₂²×Dic₁₉	—	4	1	no	—
99	C₂²×Dic₁₉	—	4	1	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₂²×Dic₁₉	—	4	2	no	—
102	C₂²×Dic₁₉	—	4	1	no	—
103	C₂²×Dic₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₂×C₈×C₁₉	—	2	4	no	—
106	C₂×C₈×C₁₉	—	2	4	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₂×C₈×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	4	2	no	—
110	C₂×C₈×C₁₉	—	4	2	no	—
111	C₄²×C₁₉	—	2	4	no	—
112	C₄²×C₁₉	—	2	4	no	—
113	C₄⋊Dic₁₉	—	2	4	no	—
114	C₄⋊Dic₁₉	—	2	4	no	—
115	C₄⋊Dic₁₉	—	2	4	no	—
116	C₄⋊Dic₁₉	—	2	4	no	—
117	C₄⋊Dic₁₉	—	4	8	no	—
118	C₄⋊Dic₁₉	—	4	8	no	—
119	C₄⋊Dic₁₉	—	4	2	no	—
120	C₄⋊Dic₁₉	—	4	2	no	—
121	C₄⋊Dic₁₉	—	4	2	no	—
122	C₄⋊Dic₁₉	—	4	2	no	—
123	#11267	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₉	#120	1	1	yes	characteristic
126	C₂³×C₁₉	#121	1	1	yes	characteristic
127	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₁₉	#123	1	1	yes	characteristic
129	C₂³×C₁₉	#124	1	1	yes	characteristic
130	C₂³×C₁₉	#124	1	1	yes	characteristic
131	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
134	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
135	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂³×C₁₉	#137	1	1	yes	characteristic
138	C₂³×C₁₉	#137	1	1	yes	characteristic
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	#106	1	4	yes	—
152	C₂×C₄×C₁₉	#107	1	4	yes	—
153	C₂×C₄×C₁₉	#117	1	2	yes	—
154	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
160	C₂×C₄×C₁₉	#123	1	2	yes	—
161	C₂×C₄×C₁₉	#123	1	2	yes	—
162	C₂×C₄×C₁₉	#124	1	2	yes	—
163	C₂×C₄×C₁₉	#125	1	2	yes	—
164	C₂×C₄×C₁₉	#125	1	2	yes	—
165	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#126	1	2	yes	—
167	C₂×C₄×C₁₉	#126	1	2	yes	—
168	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
169	C₂×Dic₁₉	—	4	2	no	—
170	C₂×Dic₁₉	—	4	4	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	4	4	no	—
173	C₂×Dic₁₉	—	4	4	no	—
174	C₂×Dic₁₉	—	4	2	no	—
175	C₂×Dic₁₉	—	4	2	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	—	4	2	no	—
178	C₂×Dic₁₉	—	8	1	no	—
179	C₂×Dic₁₉	—	8	1	no	—
180	C₂×Dic₁₉	—	8	2	no	—
181	C₂×Dic₁₉	—	8	2	no	—
182	C₂×Dic₁₉	—	8	1	no	—
183	C₂×Dic₁₉	—	8	1	no	—
184	C₂×Dic₁₉	—	8	1	no	—
185	C₂×Dic₁₉	—	8	1	no	—
186	C₂×Dic₁₉	—	8	2	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	C₂×Dic₁₉	—	8	1	no	—
189	C₂×Dic₁₉	—	8	2	no	—
190	C₈×C₁₉	—	4	4	no	—
191	C₂×#384	—	19	1	no	—
192	C₂×#340	—	19	2	no	—
193	C₂×#340	—	19	2	no	—
194	C₂×#336	D₁₉	1	1	yes	characteristic
195	C₄⋊#95	—	19	1	no	—
196	C₂²×C₁₉	#382	1	1	yes	characteristic
197	C₂²×C₁₉	#385	1	1	yes	characteristic
198	C₂²×C₁₉	#389	1	1	yes	characteristic
199	C₂²×C₁₉	#393	1	1	yes	characteristic
200	C₂²×C₁₉	#394	1	1	yes	characteristic
201	C₂²×C₁₉	#397	1	1	yes	characteristic
202	C₂²×C₁₉	#400	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
205	C₂²×C₁₉	#428	1	1	yes	characteristic
206	C₂²×C₁₉	#428	1	1	yes	characteristic
207	C₂²×C₁₉	#447	1	1	yes	characteristic
208	C₂²×C₁₉	#448	1	1	yes	characteristic
209	C₂²×C₁₉	#450	1	1	yes	characteristic
210	C₂²×C₁₉	#451	1	1	yes	characteristic
211	C₂²×C₁₉	#459	1	1	yes	characteristic
212	C₂²×C₁₉	#460	1	1	yes	characteristic
213	C₂²×C₁₉	#461	1	1	yes	characteristic
214	C₂²×C₁₉	#462	1	1	yes	characteristic
215	C₂²×C₁₉	#474	1	1	yes	characteristic
216	C₂²×C₁₉	#475	1	1	yes	characteristic
217	C₂²×C₁₉	#476	1	1	yes	characteristic
218	C₂²×C₁₉	#477	1	1	yes	characteristic
219	C₂²×C₁₉	#480	1	1	yes	characteristic
220	C₂²×C₁₉	#481	1	1	yes	characteristic
221	C₂²×C₁₉	#483	1	1	yes	characteristic
222	C₂²×C₁₉	#484	1	1	yes	characteristic
223	C₂²×C₁₉	#486	1	1	yes	characteristic
224	C₂²×C₁₉	#486	1	1	yes	characteristic
225	C₂²×C₁₉	#487	1	1	yes	characteristic
226	C₂²×C₁₉	#487	1	1	yes	characteristic
227	C₂²×C₁₉	#489	1	1	yes	characteristic
228	C₂²×C₁₉	#489	1	1	yes	characteristic
229	C₂²×C₁₉	#490	1	1	yes	characteristic
230	C₂²×C₁₉	#491	1	1	yes	characteristic
231	C₄×C₁₉	—	2	4	no	—
232	C₄×C₁₉	—	2	4	no	—
233	C₄×C₁₉	#387	1	2	yes	—
234	C₄×C₁₉	#388	1	2	yes	—
235	C₄×C₁₉	#398	1	2	yes	—
236	C₄×C₁₉	#400	1	2	yes	—
237	Dic₁₉	—	8	2	no	—
238	Dic₁₉	—	8	2	no	—
239	Dic₁₉	—	8	4	no	—
240	C₂³×C₈	C₂×D₁₉	1	2	yes	—
241	C₂²×C₄⋊C₄	—	19	1	no	—
242	C₂²×C₄⋊C₄	—	19	1	no	—
243	C₂²×C₄⋊C₄	—	19	2	no	—
244	C₂²×C₄⋊C₄	—	38	1	no	—
245	C₂²×C₄⋊C₄	—	38	1	no	—
246	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
247	#384	—	38	4	no	—
248	C₂×#95	—	38	1	no	—
249	C₂×#95	—	38	1	no	—
250	#340	—	38	4	no	—
251	#340	—	38	4	no	—
252	#336	Dic₁₉	1	4	yes	complemented
253	C₂×C₁₉	#1442	1	1	yes	characteristic
254	C₂×C₁₉	#1834	1	1	yes	characteristic
255	C₂×C₁₉	#1836	1	1	yes	characteristic
256	C₂×C₁₉	#1852	1	1	yes	characteristic
257	C₂×C₁₉	#1853	1	1	yes	characteristic
258	C₂×C₁₉	#1947	1	1	yes	characteristic
259	C₂×C₁₉	#1948	1	1	yes	characteristic
260	C₂×C₁₉	#2023	1	1	yes	characteristic
261	C₂×C₁₉	#2024	1	1	yes	characteristic
262	C₂×C₁₉	#2041	1	1	yes	characteristic
263	C₂×C₁₉	#2043	1	1	yes	characteristic
264	C₂×C₁₉	#2071	1	1	yes	characteristic
265	C₂×C₁₉	#2072	1	1	yes	characteristic
266	C₂×C₁₉	#2099	1	1	yes	characteristic
267	C₂×C₁₉	#2100	1	1	yes	characteristic
268	C₂³×C₄	—	38	2	no	—
269	C₂³×C₄	—	38	1	no	—
270	C₂³×C₄	—	38	1	no	—
271	C₂³×C₄	D₇₆	1	1	yes	characteristic
272	C₂³×C₄	D₇₆	1	1	yes	characteristic
273	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
281	C₂×C₄⋊C₄	—	19	2	no	—
282	C₂×C₄⋊C₄	—	19	4	no	—
283	C₂×C₄⋊C₄	—	19	2	no	—
284	C₂×C₄⋊C₄	—	38	2	no	—
285	C₂×C₄⋊C₄	—	38	2	no	—
286	C₂×C₄⋊C₄	—	38	2	no	—
287	C₂×C₄⋊C₄	—	38	2	no	—
288	C₂×C₄⋊C₄	—	38	2	no	—
289	C₂×C₄⋊C₄	—	38	2	no	—
290	C₂×C₄⋊C₄	—	38	2	no	—
291	C₂×C₄⋊C₄	—	38	2	no	—
292	C₂×C₄⋊C₄	—	38	4	no	—
293	C₂×C₄⋊C₄	—	38	4	no	—
294	C₂×C₄⋊C₄	—	38	2	no	—
295	C₂×C₄⋊C₄	—	38	1	no	—
296	C₂×C₄⋊C₄	—	38	1	no	—
297	C₂×C₄⋊C₄	—	76	2	no	—
298	C₂×C₄⋊C₄	—	76	2	no	—
299	C₂×C₄⋊C₄	—	76	2	no	—
300	C₂×C₄⋊C₄	—	76	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	Dic₃₈	1	2	yes	—
304	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
305	#95	—	76	2	no	—
306	#95	—	76	2	no	—
307	C₁₉	#11267	1	1	yes	characteristic, complemented, Sylow
308	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	38	4	no	—
318	C₂²×C₄	—	38	2	no	—
319	C₂²×C₄	—	38	2	no	—
320	C₂²×C₄	—	76	1	no	—
321	C₂²×C₄	—	76	2	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	—	76	1	no	—
324	C₂²×C₄	—	76	1	no	—
325	C₂²×C₄	—	76	2	no	—
326	C₂²×C₄	—	76	1	no	—
327	C₂²×C₄	—	76	1	no	—
328	C₂²×C₄	—	76	2	no	—
329	C₂²×C₄	—	76	1	no	—
330	C₂²×C₄	—	76	1	no	—
331	C₂²×C₄	—	76	2	no	—
332	C₂²×C₄	—	76	2	no	—
333	C₂²×C₄	—	76	2	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	—	76	1	no	—
336	C₂²×C₄	—	76	1	no	—
337	C₂²×C₄	—	76	1	no	—
338	C₂²×C₄	#64516	1	2	yes	—
339	C₂²×C₄	#64516	1	2	yes	—
340	C₂²×C₄	D₁₅₂	1	2	yes	—
341	C₂²×C₄	Dic₇₆	1	2	yes	—
342	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
343	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
344	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
345	C₂²×C₄	#64541	1	2	yes	—
346	C₂²×C₄	#64541	1	2	yes	—
347	C₂²×C₄	D₄×D₁₉	1	2	yes	—
348	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	#64543	1	2	yes	—
350	C₂²×C₄	#64543	1	1	yes	characteristic
351	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	#64545	1	1	yes	characteristic
353	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	4	2	no	—
361	C₄⋊C₄	—	38	4	no	—
362	C₄⋊C₄	—	38	4	no	—
363	C₄⋊C₄	—	38	4	no	—
364	C₄⋊C₄	—	38	4	no	—
365	C₄⋊C₄	—	76	8	no	—
366	C₄⋊C₄	—	76	8	no	—
367	C₄⋊C₄	—	76	2	no	—
368	C₄⋊C₄	—	76	2	no	—
369	C₄⋊C₄	—	76	2	no	—
370	C₄⋊C₄	—	76	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	#10597321	1	1	yes	characteristic
374	C₂³	#10597321	1	1	yes	characteristic
375	C₂³	#10597328	1	1	yes	characteristic
376	C₂³	#10597332	1	1	yes	characteristic
377	C₂³	#10597341	1	1	yes	characteristic
378	C₂³	#10597343	1	1	yes	characteristic
379	C₂³	C₂×#64516	1	1	yes	characteristic
380	C₂³	C₂×#64516	1	1	yes	characteristic
381	C₂³	C₂×D₁₅₂	1	1	yes	characteristic
382	C₂³	C₂×Dic₇₆	1	1	yes	characteristic
383	C₂³	#10597354	1	1	yes	characteristic
384	C₂³	#10597354	1	1	yes	characteristic
385	C₂³	#10597355	1	1	yes	characteristic
386	C₂³	#10597355	1	1	yes	characteristic
387	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	76	2	no	—
401	C₂×C₄	—	76	2	no	—
402	C₂×C₄	—	76	4	no	—
403	C₂×C₄	—	76	4	no	—
404	C₂×C₄	—	76	2	no	—
405	C₂×C₄	—	76	4	no	—
406	C₂×C₄	—	76	2	no	—
407	C₂×C₄	—	76	2	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	152	1	no	—
410	C₂×C₄	—	152	1	no	—
411	C₂×C₄	—	152	2	no	—
412	C₂×C₄	—	152	1	no	—
413	C₂×C₄	—	152	1	no	—
414	C₂×C₄	—	152	1	no	—
415	C₂×C₄	—	152	1	no	—
416	C₂×C₄	—	152	2	no	—
417	C₂×C₄	—	152	1	no	—
418	C₂×C₄	—	152	1	no	—
419	C₂×C₄	—	152	2	no	—
420	C₂×C₄	—	152	2	no	—
421	C₂×C₄	#10597274	1	4	yes	—
422	C₂×C₄	#10597275	1	4	yes	—
423	C₂×C₄	#10597316	1	2	yes	—
424	C₂×C₄	#10597324	1	2	yes	—
425	C₂×C₄	#10597325	1	2	yes	—
426	C₂×C₄	#10597329	1	2	yes	—
427	C₂×C₄	#10597330	1	2	yes	—
428	C₂×C₄	#10597331	1	2	yes	—
429	C₂×C₄	#10597334	1	1	yes	characteristic
430	C₂×C₄	#10597335	1	2	yes	—
431	C₂×C₄	#10597336	1	1	yes	characteristic
432	C₂×C₄	#10597340	1	2	yes	—
433	C₂×C₄	#10597342	1	2	yes	—
434	C₂×C₄	#10597344	1	2	yes	—
435	C₂×C₄	#10597372	1	2	yes	—
436	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
437	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
438	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
439	C₈	—	4	4	no	—
440	C₂²	#11926410	1	1	yes	characteristic
441	C₂²	#11926419	1	1	yes	characteristic
442	C₂²	#11926443	1	1	yes	characteristic
443	C₂²	#11926457	1	1	yes	characteristic
444	C₂²	#11926462	1	1	yes	characteristic
445	C₂²	#11926471	1	1	yes	characteristic
446	C₂²	#11926484	1	1	yes	characteristic
447	C₂²	C₂×#10597274	1	1	yes	characteristic
448	C₂²	C₂×#10597275	1	1	yes	characteristic
449	C₂²	#11926586	1	1	yes	characteristic
450	C₂²	#11926586	1	1	yes	characteristic
451	C₂²	#11926680	1	1	yes	characteristic
452	C₂²	#11926685	1	1	yes	characteristic
453	C₂²	#11926697	1	1	yes	characteristic
454	C₂²	#11926702	1	1	yes	characteristic
455	C₂²	#11926740	1	1	yes	characteristic
456	C₂²	#11926745	1	1	yes	characteristic
457	C₂²	#11926750	1	1	yes	characteristic
458	C₂²	#11926755	1	1	yes	characteristic
459	C₂²	#11926825	1	1	yes	characteristic
460	C₂²	#11926830	1	1	yes	characteristic
461	C₂²	#11926835	1	1	yes	characteristic
462	C₂²	#11926840	1	1	yes	characteristic
463	C₂²	#11926858	1	1	yes	characteristic
464	C₂²	#11926863	1	1	yes	characteristic
465	C₂²	#11926875	1	1	yes	characteristic
466	C₂²	#11926880	1	1	yes	characteristic
467	C₂²	#11926891	1	1	yes	characteristic
468	C₂²	#11926891	1	1	yes	characteristic
469	C₂²	#11926895	1	1	yes	characteristic
470	C₂²	#11926895	1	1	yes	characteristic
471	C₂²	#11926904	1	1	yes	characteristic
472	C₂²	#11926904	1	1	yes	characteristic
473	C₂²	#11926909	1	1	yes	characteristic
474	C₂²	#11926913	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	152	4	no	—
478	C₄	—	152	2	no	—
479	C₄	—	152	2	no	—
480	C₄	#11926430	1	2	yes	—
481	C₄	#11926437	1	2	yes	—
482	C₄	#11926478	1	2	yes	—
483	C₄	#11926486	1	2	yes	—
484	C₂	#14561892	1	1	yes	characteristic
485	C₂	#14563763	1	1	yes	characteristic
486	C₂	#14563769	1	1	yes	characteristic
487	C₂	#14563825	1	1	yes	characteristic
488	C₂	#14563830	1	1	yes	characteristic
489	C₂	#14564394	1	1	yes	characteristic
490	C₂	#14564399	1	1	yes	characteristic
491	C₂	#14564772	1	1	yes	characteristic
492	C₂	#14564777	1	1	yes	characteristic
493	C₂	#14564870	1	1	yes	characteristic
494	C₂	#14564882	1	1	yes	characteristic
495	C₂	#14565040	1	1	yes	characteristic
496	C₂	#14565045	1	1	yes	characteristic
497	C₂	#14565194	1	1	yes	characteristic
498	C₂	#14565199	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#336	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#11267
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
18. C₁₉×#336	C₄	semidirect
252. #336	Dic₁₉	semidirect
307. C₁₉	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926414	2
C₂×#11926307	2
#14561865	2
C₂×C₁₉×#336	2
#11267	19