Subgroups — #18088088

Order 4864.

1178 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927021	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926554	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926554	C₂	1	1	yes	maximal, characteristic
4	#14563367	C₂	1	1	yes	maximal, characteristic
5	#14563346	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926301	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₃₈	C₂²	1	1	yes	characteristic
9	#11927021	—	2	2	no	—
10	#11927021	—	2	2	no	—
11	#11927021	—	2	2	no	—
12	#11927021	C₄	1	4	yes	complemented
13	C₂×C₄×Dic₃₈	—	2	2	no	—
14	C₂×#10597333	—	2	2	no	—
15	C₂×#10597372	C₂²	1	1	yes	characteristic
16	C₂×#10597372	C₂²	1	1	yes	characteristic
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂×#10597323	—	2	2	no	—
19	#11926554	—	2	2	no	—
20	#11926554	—	2	2	no	—
21	#11926554	—	2	2	no	—
22	#11926554	C₄	1	4	yes	complemented
23	C₂×#10597273	—	2	2	no	—
24	C₂×#10597273	C₄	1	4	yes	complemented
25	#11926310	—	2	2	no	—
26	#11926305	—	2	2	no	—
27	#11926301	—	2	2	no	—
28	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₁₉×#344	—	2	2	no	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂³×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₃₈	—	2	1	no	—
35	C₂²×Dic₃₈	—	2	1	no	—
36	C₂²×Dic₃₈	—	2	1	no	—
37	C₂²×Dic₃₈	—	2	1	no	—
38	C₂²×Dic₃₈	—	2	1	no	—
39	C₂²×Dic₃₈	—	2	1	no	—
40	C₂²×Dic₃₈	—	2	1	no	—
41	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
42	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
43	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
44	C₂²×Dic₃₈	D₄	1	2	yes	—
45	C₂²×Dic₃₈	D₄	1	2	yes	—
46	C₂²×Dic₃₈	D₄	1	2	yes	—
47	C₂²×Dic₃₈	Q₈	1	2	yes	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	C₂×C₄	1	2	yes	—
65	C₁₉×#117	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
70	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
71	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
72	#10597372	—	2	1	no	—
73	#10597372	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	—	2	1	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	C₂×C₄	1	2	yes	—
82	#10597372	C₂×C₄	1	2	yes	—
83	#10597372	D₄	1	2	yes	—
84	C₂×C₄⋊Dic₁₉	—	2	1	no	—
85	C₂×C₄⋊Dic₁₉	—	2	1	no	—
86	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
87	C₂×Dic₁₉⋊C₄	—	2	4	no	—
88	C₂×C₄×Dic₁₉	—	2	4	no	—
89	C₂×C₄×Dic₁₉	—	2	1	no	—
90	C₂×C₄×Dic₁₉	—	2	1	no	—
91	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
92	#10597333	—	2	8	no	—
93	#10597333	—	2	8	no	—
94	#10597323	—	2	8	no	—
95	#10597323	—	2	8	no	—
96	C₄×Dic₃₈	—	2	8	no	—
97	C₄×Dic₃₈	—	2	8	no	—
98	#10597273	—	2	8	no	—
99	#10597273	—	2	8	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	C₂²×Dic₁₉	—	2	2	no	—
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	2	2	no	—
119	C₂²×Dic₁₉	—	2	2	no	—
120	C₂²×Dic₁₉	—	2	2	no	—
121	C₂²×Dic₁₉	—	2	2	no	—
122	C₂²×Dic₁₉	—	2	2	no	—
123	C₂²×Dic₁₉	—	2	2	no	—
124	C₂²×Dic₁₉	—	2	2	no	—
125	C₂²×Dic₁₉	—	4	1	no	—
126	C₂×Dic₃₈	—	2	2	no	—
127	C₂×Dic₃₈	—	2	2	no	—
128	C₂×Dic₃₈	—	2	2	no	—
129	C₂×Dic₃₈	—	2	2	no	—
130	C₂×Dic₃₈	—	2	2	no	—
131	C₂×Dic₃₈	—	2	2	no	—
132	C₂×Dic₃₈	—	2	2	no	—
133	C₂×Dic₃₈	—	2	2	no	—
134	C₂×Dic₃₈	—	2	2	no	—
135	C₂×Dic₃₈	—	2	2	no	—
136	C₂×Dic₃₈	—	2	2	no	—
137	C₂×Dic₃₈	—	2	2	no	—
138	C₂×Dic₃₈	—	2	2	no	—
139	C₂×Dic₃₈	—	2	2	no	—
140	C₂×Dic₃₈	—	2	2	no	—
141	C₂×Dic₃₈	—	2	2	no	—
142	C₂×Dic₃₈	—	2	2	no	—
143	C₂×Dic₃₈	—	2	2	no	—
144	C₂×Dic₃₈	—	2	2	no	—
145	C₂×Dic₃₈	—	2	2	no	—
146	C₂×Dic₃₈	—	2	2	no	—
147	C₂×Dic₃₈	C₄²	1	4	yes	—
148	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
149	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
150	C₂×Dic₃₈	C₂²⋊C₄	1	4	yes	—
151	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
152	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
153	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	4	1	no	—
157	M₁₆×C₁₉	—	4	1	no	—
158	M₁₆×C₁₉	—	4	1	no	—
159	M₁₆×C₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	4	1	no	—
161	M₁₆×C₁₉	—	4	1	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₂²⋊Dic₁₉	—	2	2	no	—
175	C₂²⋊Dic₁₉	—	2	2	no	—
176	C₂²⋊Dic₁₉	—	2	2	no	—
177	C₂²⋊Dic₁₉	—	4	1	no	—
178	C₂²⋊Dic₁₉	—	4	1	no	—
179	C₂²⋊Dic₁₉	—	4	1	no	—
180	C₄⋊Dic₁₉	—	2	2	no	—
181	C₄⋊Dic₁₉	—	2	2	no	—
182	C₄⋊Dic₁₉	—	2	2	no	—
183	C₄⋊Dic₁₉	—	2	2	no	—
184	C₄⋊Dic₁₉	—	2	2	no	—
185	C₄⋊Dic₁₉	—	4	1	no	—
186	Dic₁₉⋊C₄	—	2	16	no	—
187	C₄×Dic₁₉	—	2	16	no	—
188	C₄×Dic₁₉	—	2	2	no	—
189	C₄×Dic₁₉	—	2	2	no	—
190	C₄×Dic₁₉	—	4	1	no	—
191	C₄×Dic₁₉	—	4	1	no	—
192	C₄×Dic₁₉	—	4	1	no	—
193	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
194	#10786	—	19	1	no	maximal, Sylow
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
198	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₁₉	#120	1	1	yes	characteristic
200	C₂³×C₁₉	#120	1	1	yes	characteristic
201	C₂³×C₁₉	#121	1	1	yes	characteristic
202	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
233	C₂×Dic₁₉	—	2	4	no	—
234	C₂×Dic₁₉	—	2	4	no	—
235	C₂×Dic₁₉	—	2	4	no	—
236	C₂×Dic₁₉	—	2	4	no	—
237	C₂×Dic₁₉	—	2	4	no	—
238	C₂×Dic₁₉	—	2	4	no	—
239	C₂×Dic₁₉	—	2	4	no	—
240	C₂×Dic₁₉	—	2	4	no	—
241	C₂×Dic₁₉	—	4	4	no	—
242	C₂×Dic₁₉	—	4	2	no	—
243	C₂×Dic₁₉	—	4	2	no	—
244	C₂×Dic₁₉	—	8	2	no	—
245	C₂×Dic₁₉	—	8	2	no	—
246	Dic₃₈	—	2	4	no	—
247	Dic₃₈	—	2	4	no	—
248	Dic₃₈	—	2	4	no	—
249	Dic₃₈	—	2	4	no	—
250	Dic₃₈	—	2	4	no	—
251	Dic₃₈	—	2	4	no	—
252	Dic₃₈	—	2	4	no	—
253	Dic₃₈	#95	1	8	yes	—
254	C₈×C₁₉	—	4	2	no	—
255	C₈×C₁₉	—	4	2	no	—
256	C₂×#519	—	19	1	no	—
257	C₂×#419	—	19	1	no	—
258	C₂×#419	—	19	1	no	—
259	C₂×#344	D₁₉	1	1	yes	characteristic
260	#1740	—	19	1	no	—
261	#1733	—	19	1	no	—
262	C₂×H(3,ℤ/4)	—	19	1	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₁₉	#379	1	1	yes	characteristic
272	C₂²×C₁₉	#380	1	1	yes	characteristic
273	C₂²×C₁₉	#385	1	1	yes	characteristic
274	C₂²×C₁₉	#385	1	1	yes	characteristic
275	C₂²×C₁₉	#386	1	1	yes	characteristic
276	C₂²×C₁₉	#386	1	1	yes	characteristic
277	C₄×C₁₉	—	4	4	no	—
278	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
279	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
280	C₄×C₁₉	#380	1	1	yes	characteristic
281	C₄×C₁₉	#381	1	1	yes	characteristic
282	C₄×C₁₉	#385	1	1	yes	characteristic
283	C₄×C₁₉	#385	1	1	yes	characteristic
284	C₄×C₁₉	#386	1	1	yes	characteristic
285	C₄×C₁₉	#386	1	1	yes	characteristic
286	Dic₁₉	—	2	8	no	—
287	Dic₁₉	—	4	4	no	—
288	Dic₁₉	—	8	2	no	—
289	Dic₁₉	—	8	2	no	—
290	C₂³×Q₈	—	19	1	no	—
291	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
292	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
293	#519	—	19	4	no	—
294	#519	—	38	2	no	—
295	#519	—	38	2	no	—
296	#519	—	38	2	no	—
297	C₂×C₄×Q₈	—	38	2	no	—
298	C₂×C₄×Q₈	—	38	2	no	—
299	C₂×#117	—	19	1	no	—
300	C₂×#117	—	19	1	no	—
301	C₂×#117	—	19	1	no	—
302	C₂×#117	—	38	2	no	—
303	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
304	#419	—	19	4	no	—
305	#419	—	38	2	no	—
306	#419	—	38	2	no	—
307	#419	—	38	2	no	—
308	C₂×#103	—	19	4	no	—
309	C₂×#103	—	38	2	no	—
310	#344	—	2	2	no	—
311	#342	—	38	2	no	—
312	#339	—	38	2	no	—
313	H(3,ℤ/4)	—	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	C₂²⋊#95	1	1	yes	characteristic
321	C₂×C₁₉	#1905	1	2	yes	—
322	C₂²×Q₈	—	19	2	no	—
323	C₂²×Q₈	—	19	2	no	—
324	C₂²×Q₈	—	19	2	no	—
325	C₂²×Q₈	—	19	2	no	—
326	C₂²×Q₈	—	19	2	no	—
327	C₂²×Q₈	—	19	2	no	—
328	C₂²×Q₈	—	19	2	no	—
329	C₂²×Q₈	—	38	1	no	—
330	C₂²×Q₈	—	38	1	no	—
331	C₂²×Q₈	—	38	1	no	—
332	C₂²×Q₈	—	38	1	no	—
333	C₂²×Q₈	—	38	1	no	—
334	C₂²×Q₈	—	38	1	no	—
335	C₂²×Q₈	—	38	1	no	—
336	C₂³×C₄	—	38	1	no	—
337	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
338	C₂×M₁₆	—	2	1	no	—
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	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	C₄×D₁₉	1	2	yes	—
352	C₄×Q₈	—	38	8	no	—
353	C₄×Q₈	—	38	8	no	—
354	C₄×Q₈	—	38	8	no	—
355	C₄×Q₈	—	38	8	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	—	19	2	no	—
359	#117	—	19	2	no	—
360	#117	—	19	2	no	—
361	#117	—	38	8	no	—
362	#117	—	38	1	no	—
363	#117	—	38	1	no	—
364	#117	—	38	8	no	—
365	#117	—	38	1	no	—
366	#117	—	38	1	no	—
367	#117	—	38	1	no	—
368	#117	—	38	1	no	—
369	#117	—	38	1	no	—
370	#117	—	38	1	no	—
371	#117	—	38	1	no	—
372	#117	C₄×D₁₉	1	2	yes	—
373	#117	C₂²⋊D₁₉	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	19	2	no	—
376	C₂×C₄⋊C₄	—	38	4	no	—
377	C₂×C₄⋊C₄	—	38	1	no	—
378	C₂×C₄⋊C₄	—	38	1	no	—
379	C₂×C₂²⋊C₄	—	38	1	no	—
380	C₂×C₂²⋊C₄	—	38	1	no	—
381	C₂×C₂²⋊C₄	—	38	1	no	—
382	C₂×C₂²⋊C₄	D₇₆	1	2	yes	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	19	2	no	—
385	C₂×C₄²	—	38	4	no	—
386	C₂×C₄²	—	38	1	no	—
387	C₂×C₄²	—	38	1	no	—
388	#103	—	38	8	no	—
389	#103	—	38	8	no	—
390	C₁₉	#10786	1	1	yes	characteristic, complemented, Sylow
391	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
392	C₂×Q₈	—	19	4	no	—
393	C₂×Q₈	—	19	4	no	—
394	C₂×Q₈	—	19	4	no	—
395	C₂×Q₈	—	19	4	no	—
396	C₂×Q₈	—	19	4	no	—
397	C₂×Q₈	—	19	4	no	—
398	C₂×Q₈	—	19	4	no	—
399	C₂×Q₈	—	38	2	no	—
400	C₂×Q₈	—	38	2	no	—
401	C₂×Q₈	—	38	2	no	—
402	C₂×Q₈	—	38	2	no	—
403	C₂×Q₈	—	38	2	no	—
404	C₂×Q₈	—	38	2	no	—
405	C₂×Q₈	—	38	2	no	—
406	C₂×Q₈	—	38	2	no	—
407	C₂×Q₈	—	38	2	no	—
408	C₂×Q₈	—	38	2	no	—
409	C₂×Q₈	—	38	2	no	—
410	C₂×Q₈	—	38	2	no	—
411	C₂×Q₈	—	38	2	no	—
412	C₂×Q₈	—	38	2	no	—
413	C₂×Q₈	—	38	2	no	—
414	C₂×Q₈	—	38	2	no	—
415	C₂×Q₈	—	38	2	no	—
416	C₂×Q₈	—	38	2	no	—
417	C₂×Q₈	—	38	2	no	—
418	C₂×Q₈	—	38	2	no	—
419	C₂×Q₈	—	38	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	38	2	no	—
422	C₂²×C₄	—	38	2	no	—
423	C₂²×C₄	—	38	2	no	—
424	C₂²×C₄	—	38	2	no	—
425	C₂²×C₄	—	38	2	no	—
426	C₂²×C₄	—	38	2	no	—
427	C₂²×C₄	—	38	2	no	—
428	C₂²×C₄	—	38	2	no	—
429	C₂²×C₄	—	38	2	no	—
430	C₂²×C₄	—	76	1	no	—
431	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
434	C₂²×C₄	#64541	1	1	yes	characteristic
435	C₂²×C₄	#64541	1	1	yes	characteristic
436	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
437	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
441	C₂²×C₄	#64543	1	1	yes	characteristic
442	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
443	C₂²×C₄	#64545	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	4	1	no	—
449	M₁₆	—	4	1	no	—
450	M₁₆	—	4	1	no	—
451	M₁₆	—	4	1	no	—
452	M₁₆	—	4	1	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	4	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	38	16	no	—
462	C₄⋊C₄	—	38	2	no	—
463	C₄⋊C₄	—	38	2	no	—
464	C₄⋊C₄	—	38	2	no	—
465	C₄⋊C₄	—	38	2	no	—
466	C₄⋊C₄	—	38	2	no	—
467	C₄⋊C₄	—	76	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	38	2	no	—
470	C₂²⋊C₄	—	38	2	no	—
471	C₂²⋊C₄	—	38	2	no	—
472	C₂²⋊C₄	—	76	1	no	—
473	C₂²⋊C₄	—	76	1	no	—
474	C₂²⋊C₄	—	76	1	no	—
475	C₂²⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	19	4	no	—
479	C₄²	—	38	16	no	—
480	C₄²	—	38	2	no	—
481	C₄²	—	38	2	no	—
482	C₄²	—	76	1	no	—
483	C₄²	—	76	1	no	—
484	C₄²	—	76	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	C₄×D₇₆	1	1	yes	characteristic
487	C₂³	C₄×D₇₆	1	1	yes	characteristic
488	C₂³	#10597328	1	1	yes	characteristic
489	C₂³	#10597328	1	1	yes	characteristic
490	C₂³	#10597341	1	1	yes	characteristic
491	C₂³	#10597343	1	1	yes	characteristic
492	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
493	Q₈	—	19	8	no	—
494	Q₈	—	38	4	no	—
495	Q₈	—	38	4	no	—
496	Q₈	—	38	4	no	—
497	Q₈	—	38	4	no	—
498	Q₈	—	38	4	no	—
499	Q₈	—	38	4	no	—
500	Q₈	—	38	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	38	4	no	—
504	C₂×C₄	—	38	4	no	—
505	C₂×C₄	—	38	4	no	—
506	C₂×C₄	—	38	4	no	—
507	C₂×C₄	—	38	4	no	—
508	C₂×C₄	—	38	4	no	—
509	C₂×C₄	—	38	4	no	—
510	C₂×C₄	—	38	4	no	—
511	C₂×C₄	—	76	4	no	—
512	C₂×C₄	—	76	2	no	—
513	C₂×C₄	—	76	2	no	—
514	C₂×C₄	—	152	2	no	—
515	C₂×C₄	—	152	2	no	—
516	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
517	C₂×C₄	#10597318	1	1	yes	characteristic
518	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
522	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
523	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	#10597329	1	1	yes	characteristic
525	C₂×C₄	#10597329	1	1	yes	characteristic
526	C₂×C₄	#10597330	1	1	yes	characteristic
527	C₂×C₄	#10597330	1	1	yes	characteristic
528	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
529	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
530	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
531	C₂×C₄	#10597338	1	1	yes	characteristic
532	C₂×C₄	#10597339	1	1	yes	characteristic
533	C₂×C₄	#10597339	1	1	yes	characteristic
534	C₂×C₄	#10597340	1	1	yes	characteristic
535	C₂×C₄	#10597340	1	1	yes	characteristic
536	C₂×C₄	#10597342	1	1	yes	characteristic
537	C₂×C₄	#10597342	1	1	yes	characteristic
538	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
539	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
540	C₂×C₄	#10597383	1	1	yes	characteristic
541	C₂×C₄	#10597383	1	1	yes	characteristic
542	C₂×C₄	#10597384	1	1	yes	characteristic
543	C₂×C₄	#10597392	1	1	yes	characteristic
544	C₈	—	4	2	no	—
545	C₈	—	4	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	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
554	C₂²	#11926399	1	1	yes	characteristic
555	C₂²	#11926401	1	1	yes	characteristic
556	C₂²	#11926418	1	1	yes	characteristic
557	C₂²	#11926418	1	1	yes	characteristic
558	C₂²	#11926422	1	1	yes	characteristic
559	C₂²	#11926422	1	1	yes	characteristic
560	C₄	—	4	4	no	—
561	C₄	—	38	8	no	—
562	C₄	—	76	4	no	—
563	C₄	—	152	2	no	—
564	C₄	—	152	2	no	—
565	C₄	#95×D₁₉	1	1	yes	characteristic
566	C₄	#11926391	1	1	yes	characteristic
567	C₄	#11926403	1	1	yes	characteristic
568	C₄	#11926406	1	1	yes	characteristic
569	C₄	#11926415	1	1	yes	characteristic
570	C₄	#11926415	1	1	yes	characteristic
571	C₄	#11926420	1	1	yes	characteristic
572	C₄	#11926420	1	1	yes	characteristic
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
580	C₂	#14564128	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926422
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#344	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#344	D₁₉
hypocenter	C₁₉	#10786
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
12. #11927021	C₄	semidirect
22. #11926554	C₄	semidirect
24. C₂×#10597273	C₄	semidirect
390. C₁₉	#10786	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927021	2
C₂×#11926554	2
#14563367	2
#14563346	2
C₂×#11926301	2
C₂×C₁₉×#344	2
#10786	19