Subgroups — #18088961

Order 4864.

1018 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926549	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597290	C₂	1	1	yes	maximal, characteristic
3	#14572053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926314	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563345	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×#64520	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926549	—	2	2	no	—
13	#11926549	—	2	2	no	—
14	C₂×#10597289	C₄	1	4	yes	complemented
15	C₂×#10597290	—	2	2	no	—
16	C₂×#10597290	—	2	2	no	—
17	C₂×#10597290	C₄	1	4	yes	complemented
18	#11926502	—	2	2	no	—
19	#11926499	—	2	2	no	—
20	M₁₆×Dic₁₉	—	2	2	no	—
21	#11926314	—	2	2	no	—
22	#11926304	—	2	2	no	—
23	C₁₉⋊#338	—	2	2	no	—
24	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₁₉×#418	—	2	2	no	—
28	C₁₉×#418	C₄	1	4	yes	complemented
29	C₂×C₁₉×#102	—	2	2	no	—
30	C₂⁵×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	1	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
52	C₂²×C₈×C₁₉	D₄	1	2	yes	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄²×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
61	#10597372	—	2	1	no	—
62	#10597372	—	2	1	no	—
63	#10597372	D₄	1	2	yes	—
64	#10597372	D₄	1	2	yes	—
65	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	—	2	1	no	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	C₂×C₄	1	2	yes	—
82	C₂×#64520	C₂×C₄	1	2	yes	—
83	C₂×#64520	D₄	1	2	yes	—
84	C₂×#64520	D₄	1	2	yes	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₉×#102	—	2	8	no	—
89	#10597290	—	2	8	no	—
90	#10597289	—	2	8	no	—
91	#10597272	—	2	4	no	—
92	C₈×Dic₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	4	1	no	—
97	C₂⁴×C₁₉	—	4	1	no	—
98	C₂⁴×C₁₉	—	4	1	no	—
99	C₂⁴×C₁₉	—	4	1	no	—
100	C₂⁴×C₁₉	—	8	4	no	—
101	C₂⁴×C₁₉	#41	1	1	yes	characteristic
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	C₄²	1	4	yes	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
145	C₂²×Dic₁₉	—	2	2	no	—
146	M₁₆×C₁₉	—	2	2	no	—
147	M₁₆×C₁₉	—	2	2	no	—
148	M₁₆×C₁₉	—	2	2	no	—
149	M₁₆×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	C₂²⋊Dic₁₉	—	2	2	no	—
160	C₂²⋊Dic₁₉	—	2	2	no	—
161	C₄⋊Dic₁₉	—	2	2	no	—
162	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
163	C₄×Dic₁₉	—	2	2	no	—
164	C₄×Dic₁₉	—	2	2	no	—
165	#64520	—	2	2	no	—
166	#64520	—	2	2	no	—
167	#64520	—	2	2	no	—
168	#64520	—	2	2	no	—
169	#64520	—	2	2	no	—
170	#64520	—	4	1	no	—
171	#64520	—	4	1	no	—
172	#64520	—	4	1	no	—
173	#64520	—	4	1	no	—
174	#64520	—	4	1	no	—
175	#64520	—	4	1	no	—
176	#64520	C₂²⋊C₄	1	4	yes	—
177	C₂×C₁₉⋊C₈	—	2	2	no	—
178	C₂×C₁₉⋊C₈	—	2	2	no	—
179	C₂×C₁₉⋊C₈	—	2	2	no	—
180	C₂×C₁₉⋊C₈	—	2	2	no	—
181	C₂×C₁₉⋊C₈	—	2	2	no	—
182	C₂×C₁₉⋊C₈	—	2	2	no	—
183	C₂×C₁₉⋊C₈	—	2	2	no	—
184	C₂×C₁₉⋊C₈	—	4	1	no	—
185	C₂×C₁₉⋊C₈	—	4	1	no	—
186	#10953	—	19	1	no	maximal, Sylow
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	8	4	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	4	no	—
198	C₂³×C₁₉	—	8	4	no	—
199	C₂³×C₁₉	—	8	4	no	—
200	C₂³×C₁₉	—	8	4	no	—
201	C₂³×C₁₉	—	8	4	no	—
202	C₂³×C₁₉	#117	1	1	yes	characteristic
203	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
205	C₂³×C₁₉	#121	1	1	yes	characteristic
206	C₂³×C₁₉	#123	1	1	yes	characteristic
207	C₂³×C₁₉	#124	1	1	yes	characteristic
208	C₂³×C₁₉	#126	1	1	yes	characteristic
209	D₄×C₁₉	—	2	4	no	—
210	D₄×C₁₉	—	2	4	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
247	C₂×Dic₁₉	—	2	4	no	—
248	C₂×Dic₁₉	—	8	2	no	—
249	C₈×C₁₉	—	2	4	no	—
250	C₁₉⋊C₈	—	2	4	no	—
251	C₁₉⋊C₈	—	4	2	no	—
252	C₁₉⋊C₈	—	4	2	no	—
253	C₂×#418	—	19	1	no	—
254	C₂×#418	D₁₉	1	1	yes	characteristic
255	C₂²×#100	—	19	1	no	—
256	#2873	—	19	1	no	—
257	C₂×#344	—	19	1	no	—
258	#1733	—	19	1	no	—
259	C₂×#338	—	19	1	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	8	4	no	—
269	C₂²×C₁₉	—	8	4	no	—
270	C₂²×C₁₉	—	8	4	no	—
271	C₂²×C₁₉	—	8	4	no	—
272	C₂²×C₁₉	—	8	4	no	—
273	C₂²×C₁₉	—	8	4	no	—
274	C₂²×C₁₉	—	8	4	no	—
275	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₁₉	#386	1	1	yes	characteristic
277	C₂²×C₁₉	#388	1	1	yes	characteristic
278	C₂²×C₁₉	#388	1	1	yes	characteristic
279	C₂²×C₁₉	#388	1	1	yes	characteristic
280	C₂²×C₁₉	#388	1	1	yes	characteristic
281	C₂²×C₁₉	#390	1	1	yes	characteristic
282	C₄×C₁₉	—	8	2	no	—
283	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
284	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₁₉	#386	1	1	yes	characteristic
286	C₄×C₁₉	#386	1	1	yes	characteristic
287	C₄×C₁₉	#388	1	1	yes	characteristic
288	C₄×C₁₉	#388	1	1	yes	characteristic
289	C₄×C₁₉	#390	1	1	yes	characteristic
290	C₄×C₁₉	#390	1	1	yes	characteristic
291	Dic₁₉	—	4	4	no	—
292	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
293	C₂²×M₁₆	—	19	1	no	—
294	C₂²×M₁₆	—	19	1	no	—
295	C₂²×M₁₆	—	19	1	no	—
296	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
297	C₂×#117	—	19	1	no	—
298	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
299	#418	—	2	2	no	—
300	#418	—	38	2	no	—
301	#418	—	38	2	no	—
302	#418	Dic₁₉	1	4	yes	complemented
303	C₂×#102	—	2	2	no	—
304	C₂×#102	—	19	4	no	—
305	C₂×#100	—	19	4	no	—
306	C₂×#100	—	38	2	no	—
307	C₂×#100	—	38	2	no	—
308	#405	—	38	2	no	—
309	#405	—	38	2	no	—
310	C₄×M₁₆	—	38	2	no	—
311	#344	—	38	2	no	—
312	#339	—	38	2	no	—
313	#338	—	38	2	no	—
314	C₂×C₁₉	—	2	1	no	—
315	C₂×C₁₉	—	2	1	no	—
316	C₂×C₁₉	—	2	1	no	—
317	C₂×C₁₉	—	2	1	no	—
318	C₂×C₁₉	—	2	1	no	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	8	4	no	—
321	C₂×C₁₉	#1437	1	1	yes	characteristic
322	C₂×C₁₉	#1903	1	2	yes	—
323	C₂⁵	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₄×D₁₉	1	2	yes	—
336	C₂²×D₄	C₄×D₁₉	1	2	yes	—
337	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
338	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	19	2	no	—
344	C₂×M₁₆	—	19	2	no	—
345	C₂×M₁₆	—	19	2	no	—
346	C₂×M₁₆	—	19	2	no	—
347	C₂×M₁₆	—	38	1	no	—
348	C₂×M₁₆	—	38	1	no	—
349	C₂×M₁₆	—	38	1	no	—
350	C₂×M₁₆	—	38	1	no	—
351	C₂×M₁₆	—	38	1	no	—
352	C₂×M₁₆	—	38	1	no	—
353	C₂×M₁₆	—	38	1	no	—
354	C₂×M₁₆	—	38	1	no	—
355	C₂×M₁₆	—	38	1	no	—
356	C₂×M₁₆	—	38	1	no	—
357	C₂×M₁₆	—	38	1	no	—
358	C₂×M₁₆	—	38	1	no	—
359	C₂×M₁₆	—	38	1	no	—
360	C₂×M₁₆	—	38	1	no	—
361	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
362	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
363	C₂²×C₈	—	19	2	no	—
364	C₂²×C₈	—	38	1	no	—
365	C₂²×C₈	—	38	1	no	—
366	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	19	2	no	—
371	#117	—	19	2	no	—
372	#117	—	38	1	no	—
373	#117	—	38	1	no	—
374	#117	C₂×Dic₁₉	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	19	2	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	38	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	38	1	no	—
381	#102	—	2	8	no	—
382	#102	—	38	8	no	—
383	#100	—	38	8	no	—
384	#97	—	38	4	no	—
385	C₄×C₈	—	38	4	no	—
386	C₁₉	#10953	1	1	yes	characteristic, complemented, Sylow
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	4	1	no	—
391	C₂⁴	—	4	1	no	—
392	C₂⁴	—	4	1	no	—
393	C₂⁴	—	4	1	no	—
394	C₂⁴	—	8	4	no	—
395	C₂⁴	#64543	1	1	yes	characteristic
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	C₄×Dic₁₉	1	4	yes	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	38	2	no	—
426	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
428	C₂²×C₄	#64541	1	1	yes	characteristic
429	C₂²×C₄	#64541	1	1	yes	characteristic
430	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
431	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
432	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
433	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
434	C₂²×C₄	#64543	1	1	yes	characteristic
435	C₂²×C₄	#64543	1	1	yes	characteristic
436	C₂²×C₄	#64543	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	19	4	no	—
445	M₁₆	—	38	2	no	—
446	M₁₆	—	38	2	no	—
447	M₁₆	—	38	2	no	—
448	M₁₆	—	38	2	no	—
449	M₁₆	—	38	2	no	—
450	M₁₆	—	76	1	no	—
451	M₁₆	—	76	1	no	—
452	M₁₆	—	76	1	no	—
453	M₁₆	—	76	1	no	—
454	M₁₆	—	76	1	no	—
455	M₁₆	—	76	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	38	2	no	—
459	C₂×C₈	—	38	2	no	—
460	C₂×C₈	—	38	2	no	—
461	C₂×C₈	—	38	2	no	—
462	C₂×C₈	—	38	2	no	—
463	C₂×C₈	—	38	2	no	—
464	C₂×C₈	—	38	2	no	—
465	C₂×C₈	—	76	1	no	—
466	C₂×C₈	—	76	1	no	—
467	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	19	4	no	—
471	C₄⋊C₄	—	38	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	38	2	no	—
475	C₂²⋊C₄	—	38	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	4	1	no	—
478	C₄²	—	38	2	no	—
479	C₄²	—	38	2	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	—	8	4	no	—
494	C₂³	—	8	4	no	—
495	C₂³	#10597323	1	1	yes	characteristic
496	C₂³	#10597325	1	1	yes	characteristic
497	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
498	C₂³	#10597329	1	1	yes	characteristic
499	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
500	C₂³	#10597382	1	1	yes	characteristic
501	C₂³	#10597384	1	1	yes	characteristic
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	38	4	no	—
513	C₂×C₄	—	152	2	no	—
514	C₂×C₄	#10597323	1	1	yes	characteristic
515	C₂×C₄	#10597325	1	1	yes	characteristic
516	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
518	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
519	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
520	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
521	C₂×C₄	#10597329	1	1	yes	characteristic
522	C₂×C₄	#10597330	1	1	yes	characteristic
523	C₂×C₄	#10597330	1	1	yes	characteristic
524	C₂×C₄	#10597331	1	1	yes	characteristic
525	C₂×C₄	#10597331	1	1	yes	characteristic
526	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
527	C₂×C₄	#10597372	1	1	yes	characteristic
528	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
529	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
530	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
531	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
532	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
533	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
534	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
535	C₂×C₄	#10597381	1	1	yes	characteristic
536	C₂×C₄	#10597383	1	1	yes	characteristic
537	C₂×C₄	#10597384	1	1	yes	characteristic
538	C₂×C₄	#10597385	1	1	yes	characteristic
539	C₂×C₄	#10597385	1	1	yes	characteristic
540	C₂×C₄	#10597386	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	38	4	no	—
544	C₈	—	76	2	no	—
545	C₈	—	76	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	8	4	no	—
555	C₂²	—	8	4	no	—
556	C₂²	—	8	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
562	C₂²	#11926420	1	1	yes	characteristic
563	C₂²	#11926432	1	1	yes	characteristic
564	C₂²	#11926437	1	1	yes	characteristic
565	C₂²	#11926438	1	1	yes	characteristic
566	C₂²	#11926438	1	1	yes	characteristic
567	C₂²	#11926447	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	76	4	no	—
570	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
571	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
572	C₄	#11926420	1	1	yes	characteristic
573	C₄	#11926424	1	1	yes	characteristic
574	C₄	#11926432	1	1	yes	characteristic
575	C₄	#11926437	1	1	yes	characteristic
576	C₄	#11926444	1	1	yes	characteristic
577	C₄	#11926444	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	8	4	no	—
585	C₂	#14561872	1	1	yes	characteristic
586	C₂	#14564112	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926420
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#418	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×D₄×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#418	D₁₉
hypocenter	C₁₉	#10953
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#418

Complements

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

N	H ≅ G/N	type
3. #14572053	C₂	semidirect
4. C₂×#11926314	C₂	semidirect
5. #14563345	C₂	semidirect
6. C₂×C₁₉⋊#338	C₂	semidirect
14. C₂×#10597289	C₄	semidirect
17. C₂×#10597290	C₄	semidirect
28. C₁₉×#418	C₄	semidirect
302. #418	Dic₁₉	semidirect
386. C₁₉	#10953	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926549	2
C₂²×#10597290	2
#14572053	2
C₂×#11926314	2
#14563345	2
C₂×C₁₉⋊#338	2
C₂×C₁₉×#418	2
#10953	19