Subgroups — #18088115

Order 4864.

1426 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597294	C₂	1	2	yes	maximal
2	C₂×#11926303	C₂	1	2	yes	maximal, complemented
3	#14563329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₁₉	C₂²	1	2	yes	—
8	C₂×#10597294	—	2	4	no	—
9	C₂×#10597294	—	2	4	no	—
10	C₂×#10597294	C₄	1	8	yes	complemented
11	C₂×C₁₉⋊#95	—	2	2	no	—
12	#11926303	—	2	4	no	—
13	#11926299	—	2	1	no	—
14	#11926299	—	2	1	no	—
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₉	—	2	4	no	—
17	C₄×#41×C₁₉	—	2	4	no	—
18	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	complemented
19	C₂×C₄×D₄×C₁₉	—	2	2	no	—
20	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	complemented
21	C₂×C₁₉×#117	—	2	1	no	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	—	2	1	no	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	1	no	—
28	C₂×#41×C₁₉	—	2	1	no	—
29	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
30	C₂×#41×C₁₉	D₄	1	4	yes	—
31	C₂×#41×C₁₉	D₄	1	2	yes	—
32	C₂×#41×C₁₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	—	2	2	no	—
38	C₂³×C₄×C₁₉	D₄	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×Dic₁₉	—	2	2	no	—
41	C₄×Q₈×C₁₉	—	2	4	no	—
42	C₄×Q₈×C₁₉	—	2	4	no	—
43	C₄×D₄×C₁₉	—	2	16	no	—
44	C₄×D₄×C₁₉	—	2	4	no	—
45	C₄×D₄×C₁₉	—	2	4	no	—
46	C₁₉×#117	—	2	8	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	D₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄²×C₁₉	—	2	8	no	—
54	C₂×C₄²×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	2	2	no	—
58	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₉	—	2	2	no	—
62	C₂×C₄×Dic₁₉	—	2	2	no	—
63	C₂×C₄×Dic₁₉	—	2	2	no	—
64	C₂×C₄×Dic₁₉	—	2	2	no	—
65	C₂×C₄×Dic₁₉	—	2	2	no	—
66	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	complemented
67	C₂×#64520	—	2	2	no	—
68	C₂×#64520	—	2	2	no	—
69	C₂×#64520	—	2	2	no	—
70	C₂×#64520	—	2	2	no	—
71	C₂×#64520	—	2	2	no	—
72	C₂×#64520	C₂×C₄	1	4	yes	complemented
73	C₂²×C₁₉⋊C₈	—	2	2	no	—
74	#10597294	—	2	16	no	—
75	C₁₉⋊#95	—	2	8	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	C₂²⋊C₄	1	8	yes	—
85	#41×C₁₉	C₄⋊C₄	1	8	yes	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
90	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	2	4	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	C₄²	1	2	yes	—
100	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	#41	1	2	yes	—
126	C₂²×Dic₁₉	—	2	8	no	—
127	C₂²×Dic₁₉	—	2	4	no	—
128	C₂²×Dic₁₉	—	4	4	no	—
129	C₂²×Dic₁₉	—	4	2	no	—
130	C₂²×Dic₁₉	—	4	2	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
134	C₂²⋊C₄×C₁₉	—	2	8	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	8	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	4	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄×Dic₁₉	—	2	4	no	—
143	C₄×Dic₁₉	—	2	4	no	—
144	C₄×Dic₁₉	—	4	2	no	—
145	C₄×Dic₁₉	—	4	2	no	—
146	#64520	—	2	4	no	—
147	#64520	—	2	4	no	—
148	#64520	—	4	2	no	—
149	#64520	—	4	2	no	—
150	C₂×C₁₉⋊C₈	—	2	4	no	—
151	C₂×C₁₉⋊C₈	—	4	2	no	—
152	C₂×C₁₉⋊C₈	—	4	2	no	—
153	#10790	—	19	1	no	maximal, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₄×D₄	1	2	yes	—
163	C₂³×C₁₉	#120	1	2	yes	—
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	2	no	—
167	Q₈×C₁₉	—	2	2	no	—
168	Q₈×C₁₉	—	2	2	no	—
169	Q₈×C₁₉	#95	1	4	yes	complemented
170	D₄×C₁₉	—	2	8	no	—
171	D₄×C₁₉	—	2	8	no	—
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	#95	1	4	yes	complemented
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	4	16	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	#104	1	4	yes	complemented
192	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₁₉	#120	1	2	yes	—
204	C₂×C₄×C₁₉	#121	1	2	yes	—
205	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#123	1	2	yes	—
209	C₂×C₄×C₁₉	#123	1	2	yes	—
210	C₂×Dic₁₉	—	2	8	no	—
211	C₂×Dic₁₉	—	4	8	no	—
212	C₂×Dic₁₉	—	4	4	no	—
213	C₂×Dic₁₉	—	4	8	no	—
214	C₂×Dic₁₉	—	4	4	no	—
215	C₁₉⋊C₈	—	4	4	no	—
216	C₂×C₄×#41	D₁₉	1	1	yes	characteristic
217	C₂²×#104	—	19	2	no	—
218	C₂×#339	—	19	2	no	—
219	#1728	—	19	1	no	—
220	C₄×#95	—	19	1	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	4	no	—
231	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₁₉	#379	1	1	yes	characteristic
233	C₂²×C₁₉	#380	1	1	yes	characteristic
234	C₂²×C₁₉	#385	1	2	yes	—
235	C₂²×C₁₉	#386	1	2	yes	—
236	C₂²×C₁₉	C₂×#104	1	2	yes	—
237	C₂²×C₁₉	#421	1	2	yes	—
238	C₄×C₁₉	—	2	4	no	—
239	C₄×C₁₉	—	2	4	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
243	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
244	C₄×C₁₉	#380	1	1	yes	characteristic
245	C₄×C₁₉	#381	1	1	yes	characteristic
246	C₄×C₁₉	#385	1	2	yes	—
247	C₄×C₁₉	#386	1	2	yes	—
248	Dic₁₉	—	4	8	no	—
249	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
250	C₂²×M₁₆	—	19	2	no	—
251	C₄×#41	—	2	4	no	—
252	C₄×#41	—	2	4	no	—
253	C₂×C₄×Q₈	Dic₁₉	1	2	yes	complemented
254	C₂×C₄×D₄	—	2	2	no	—
255	C₂×C₄×D₄	Dic₁₉	1	2	yes	complemented
256	C₂×#117	—	2	1	no	—
257	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
258	C₂²×C₄²	—	2	1	no	—
259	C₂²×C₄²	—	19	2	no	—
260	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
261	C₂×#104	—	19	8	no	—
262	C₂×#104	—	38	4	no	—
263	C₂×#104	—	38	4	no	—
264	C₂×#95	—	38	2	no	—
265	#339	—	38	4	no	—
266	#336	—	38	1	no	—
267	#336	—	38	1	no	—
268	C₂×C₁₉	—	2	2	no	—
269	C₂×C₁₉	—	2	2	no	—
270	C₂×C₁₉	—	4	4	no	—
271	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
272	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
273	C₂×C₁₉	#1759	1	1	yes	characteristic
274	C₂×C₁₉	#1789	1	2	yes	—
275	C₂×C₁₉	#1806	1	2	yes	—
276	C₂×#41	—	2	1	no	—
277	C₂×#41	—	2	1	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	Dic₃₈	1	2	yes	—
281	C₂×#41	C₄×D₁₉	1	4	yes	—
282	C₂×#41	D₇₆	1	2	yes	—
283	C₂×#41	C₂²⋊D₁₉	1	4	yes	—
284	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	38	2	no	—
290	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
291	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
292	C₂×M₁₆	—	19	4	no	—
293	C₂×M₁₆	—	38	2	no	—
294	C₂×M₁₆	—	38	2	no	—
295	C₂×M₁₆	—	38	2	no	—
296	C₂×M₁₆	—	38	2	no	—
297	C₂×M₁₆	—	38	2	no	—
298	C₂²×C₈	—	38	2	no	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×D₄	—	2	16	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	#117	—	2	8	no	—
305	#117	—	2	2	no	—
306	#117	C₂²⋊D₁₉	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	8	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	19	4	no	—
317	C₂×C₄²	—	38	2	no	—
318	C₂×C₄²	—	38	2	no	—
319	C₂×C₄²	—	38	2	no	—
320	C₂×C₄²	—	38	2	no	—
321	C₂×C₄²	—	38	2	no	—
322	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
323	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
324	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
325	#104	—	38	16	no	—
326	#95	—	38	8	no	—
327	C₁₉	#10790	1	1	yes	characteristic, complemented, Sylow
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	Dic₁₉⋊C₄	1	8	yes	—
337	#41	(C₂×D₁₉)⋊C₄	1	8	yes	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
342	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
343	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
352	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
353	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	38	8	no	—
367	C₂²×C₄	—	38	4	no	—
368	C₂²×C₄	—	76	4	no	—
369	C₂²×C₄	—	76	2	no	—
370	C₂²×C₄	—	76	2	no	—
371	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
372	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
373	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
375	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
376	C₂²×C₄	#64541	1	2	yes	—
377	C₂²×C₄	#64541	1	1	yes	characteristic
378	C₂²×C₄	#64541	1	1	yes	characteristic
379	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
381	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
382	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
383	M₁₆	—	38	4	no	—
384	M₁₆	—	38	4	no	—
385	M₁₆	—	76	2	no	—
386	M₁₆	—	76	2	no	—
387	C₂×C₈	—	38	4	no	—
388	C₂×C₈	—	76	2	no	—
389	C₂×C₈	—	76	2	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₄²	—	2	8	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	38	4	no	—
402	C₄²	—	38	4	no	—
403	C₄²	—	76	2	no	—
404	C₄²	—	76	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	#10597370	1	1	yes	characteristic
413	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
414	C₂³	#10597376	1	1	yes	characteristic
415	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
416	C₂³	#10597399	1	2	yes	—
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	C₁₉⋊#95	1	4	yes	complemented
421	D₄	—	2	8	no	—
422	D₄	—	2	8	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	C₁₉⋊#95	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	16	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	38	8	no	—
443	C₂×C₄	—	76	8	no	—
444	C₂×C₄	—	76	4	no	—
445	C₂×C₄	—	76	8	no	—
446	C₂×C₄	—	76	4	no	—
447	C₂×C₄	#10597294	1	4	yes	complemented
448	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
450	C₂×C₄	#10597370	1	2	yes	—
451	C₂×C₄	#10597370	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
453	C₂×C₄	#10597372	1	1	yes	characteristic
454	C₂×C₄	#10597372	1	1	yes	characteristic
455	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
456	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
457	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
458	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
459	C₂×C₄	#10597375	1	2	yes	—
460	C₂×C₄	#10597375	1	2	yes	—
461	C₂×C₄	#10597376	1	2	yes	—
462	C₂×C₄	#10597376	1	1	yes	characteristic
463	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
465	C₂×C₄	#10597399	1	2	yes	—
466	C₈	—	76	4	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
478	C₂²	#11926400	1	1	yes	characteristic
479	C₂²	#11926404	1	1	yes	characteristic
480	C₂²	#11926417	1	2	yes	—
481	C₂²	#11926423	1	2	yes	—
482	C₂²	C₂×#10597294	1	2	yes	—
483	C₂²	#11926561	1	2	yes	—
484	C₄	—	2	4	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	76	8	no	—
489	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
490	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
491	C₄	#11926404	1	1	yes	characteristic
492	C₄	#11926407	1	1	yes	characteristic
493	C₄	#11926417	1	2	yes	—
494	C₄	#11926423	1	2	yes	—
495	C₂	—	2	2	no	—
496	C₂	—	2	2	no	—
497	C₂	—	4	4	no	—
498	C₂	#14561858	1	1	yes	characteristic
499	C₂	C₄×#10597294	1	1	yes	characteristic
500	C₂	#14563445	1	1	yes	characteristic
501	C₂	#14563579	1	2	yes	—
502	C₂	#14563655	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×#41×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×#41	D₁₉
hypocenter	C₁₉	#10790
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₂×#11926303	C₂	semidirect
3. #14563329	C₂	semidirect
4. C₄×C₁₉⋊#95	C₂	semidirect
10. C₂×#10597294	C₄	semidirect
18. C₂×C₄×Q₈×C₁₉	C₄	semidirect
20. C₂×C₄×D₄×C₁₉	C₄	semidirect
66. C₂×C₄×Dic₁₉	C₂×C₄	semidirect
72. C₂×#64520	C₂×C₄	semidirect
169. Q₈×C₁₉	#95	semidirect
175. D₄×C₁₉	#95	semidirect
191. C₂×C₄×C₁₉	#104	semidirect
253. C₂×C₄×Q₈	Dic₁₉	semidirect
255. C₂×C₄×D₄	Dic₁₉	semidirect
327. C₁₉	#10790	semidirect
420. Q₈	C₁₉⋊#95	semidirect
426. D₄	C₁₉⋊#95	semidirect
447. C₂×C₄	#10597294	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597294	2
C₂×#11926303	2
#14563329	2
C₄×C₁₉⋊#95	2
C₂×C₄×#41×C₁₉	2
#10790	19