Subgroups — #18088086

Order 4864.

1394 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927019	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926549	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563368	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926301	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	#11927019	—	2	2	no	—
10	#11927019	—	2	2	no	—
11	#11927019	—	2	2	no	—
12	#11927019	C₄	1	4	yes	complemented
13	C₂×D₄×Dic₁₉	—	2	2	no	—
14	C₂×D₄×Dic₁₉	—	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	C₂²×C₂²⋊Dic₁₉	—	2	2	no	—
19	#11926549	—	2	2	no	—
20	#11926549	C₄	1	4	yes	complemented
21	C₂×#10597289	—	2	2	no	—
22	#11926315	—	2	2	no	—
23	#11926311	—	2	2	no	—
24	#11926303	—	2	2	no	—
25	#11926301	—	2	2	no	—
26	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₁₉×#418	—	2	2	no	—
30	C₁₉×#418	—	2	2	no	—
31	C₂×C₁₉×#102	C₄	1	4	yes	complemented
32	C₂⁵×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	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂²×D₄×C₁₉	D₄	1	2	yes	—
45	C₂²×D₄×C₁₉	D₄	1	2	yes	—
46	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×Dic₁₉	—	2	4	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	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄²×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
64	C₂×C₂²⋊Dic₁₉	—	2	8	no	—
65	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
66	C₂×C₂²⋊Dic₁₉	—	2	8	no	—
67	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
68	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
69	D₄×Dic₁₉	—	2	8	no	—
70	D₄×Dic₁₉	—	2	8	no	—
71	D₄×Dic₁₉	—	2	8	no	—
72	D₄×Dic₁₉	—	2	8	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	C₂×C₄	1	2	yes	—
81	#10597372	C₂×C₄	1	2	yes	—
82	#10597372	C₂×C₄	1	2	yes	complemented
83	#10597372	D₄	1	2	yes	—
84	#10597372	D₄	1	2	yes	—
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	1	no	—
90	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
91	C₂×#64520	—	2	1	no	—
92	C₂×#64520	—	2	1	no	—
93	C₂×#64520	—	2	1	no	—
94	C₂×#64520	—	2	1	no	—
95	C₂×#64520	—	2	1	no	—
96	C₂×#64520	C₂×C₄	1	2	yes	complemented
97	C₂²×C₁₉⋊C₈	—	2	1	no	—
98	C₁₉×#102	—	2	8	no	—
99	#10597289	—	2	8	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	2	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	8	4	no	—
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	C₄²	1	4	yes	—
131	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
132	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
133	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
134	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
135	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
136	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
152	C₂²×Dic₁₉	—	2	2	no	—
153	C₂²×Dic₁₉	—	2	2	no	—
154	C₂²×Dic₁₉	—	2	16	no	—
155	C₂²×Dic₁₉	—	4	1	no	—
156	C₂²×Dic₁₉	—	8	8	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	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	4	1	no	—
167	C₂²⋊C₄×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	4	1	no	—
169	C₄²×C₁₉	—	4	1	no	—
170	C₂²⋊Dic₁₉	—	2	16	no	—
171	C₂²⋊Dic₁₉	—	2	2	no	—
172	C₂²⋊Dic₁₉	—	2	2	no	—
173	C₂²⋊Dic₁₉	—	2	2	no	—
174	C₂²⋊Dic₁₉	—	2	2	no	—
175	C₂²⋊Dic₁₉	—	4	1	no	—
176	C₂²⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
177	C₄⋊Dic₁₉	—	2	2	no	—
178	C₄⋊Dic₁₉	—	2	2	no	—
179	C₄⋊Dic₁₉	—	2	2	no	—
180	C₄⋊Dic₁₉	—	2	2	no	—
181	C₄⋊Dic₁₉	—	2	2	no	—
182	C₄⋊Dic₁₉	—	4	1	no	—
183	C₄×Dic₁₉	—	2	2	no	—
184	C₄×Dic₁₉	—	2	2	no	—
185	C₄×Dic₁₉	—	2	2	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	4	1	no	—
188	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
189	#64520	—	2	2	no	—
190	#64520	—	2	2	no	—
191	#64520	—	4	1	no	—
192	#64520	—	4	1	no	—
193	C₂×C₁₉⋊C₈	—	2	2	no	—
194	C₂×C₁₉⋊C₈	—	4	1	no	—
195	C₂×C₁₉⋊C₈	—	4	1	no	—
196	#10785	—	19	1	no	maximal, Sylow
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	2	4	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	8	no	—
206	C₂³×C₁₉	—	8	4	no	—
207	C₂³×C₁₉	—	8	4	no	—
208	C₂³×C₁₉	—	8	4	no	—
209	C₂³×C₁₉	—	8	4	no	—
210	C₂³×C₁₉	—	8	4	no	—
211	C₂³×C₁₉	—	8	4	no	—
212	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₉	#120	1	1	yes	characteristic
216	C₂³×C₁₉	#120	1	1	yes	characteristic
217	C₂³×C₁₉	#121	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	2	4	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	4	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	#95	1	8	yes	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	8	2	no	—
229	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
257	C₂×Dic₁₉	—	2	4	no	—
258	C₂×Dic₁₉	—	2	4	no	—
259	C₂×Dic₁₉	—	4	4	no	—
260	C₂×Dic₁₉	—	4	4	no	—
261	C₂×Dic₁₉	—	4	2	no	—
262	C₂×Dic₁₉	—	8	16	no	—
263	C₂×Dic₁₉	—	8	2	no	—
264	C₈×C₁₉	—	4	2	no	—
265	C₁₉⋊C₈	—	4	2	no	—
266	C₂×#518	—	19	1	no	—
267	C₂×#418	—	19	1	no	—
268	C₂×#418	D₁₉	1	1	yes	characteristic
269	C₂×#344	—	19	1	no	—
270	#1740	—	19	1	no	—
271	#1733	—	19	1	no	—
272	C₂×H(3,ℤ/4)	—	19	1	no	—
273	C₂²×C₁₉	—	2	2	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	8	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	8	no	—
282	C₂²×C₁₉	—	4	8	no	—
283	C₂²×C₁₉	—	4	8	no	—
284	C₂²×C₁₉	—	8	4	no	—
285	C₂²×C₁₉	—	8	4	no	—
286	C₂²×C₁₉	—	8	4	no	—
287	C₂²×C₁₉	—	8	4	no	—
288	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₁₉	#379	1	1	yes	characteristic
290	C₂²×C₁₉	#380	1	1	yes	characteristic
291	C₂²×C₁₉	#385	1	1	yes	characteristic
292	C₂²×C₁₉	#385	1	1	yes	characteristic
293	C₂²×C₁₉	#386	1	1	yes	characteristic
294	C₂²×C₁₉	#386	1	1	yes	characteristic
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
297	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₄×C₁₉	#380	1	1	yes	characteristic
299	C₄×C₁₉	#381	1	1	yes	characteristic
300	C₄×C₁₉	#385	1	1	yes	characteristic
301	C₄×C₁₉	#385	1	1	yes	characteristic
302	C₄×C₁₉	#386	1	1	yes	characteristic
303	C₄×C₁₉	#386	1	1	yes	characteristic
304	Dic₁₉	—	4	4	no	—
305	Dic₁₉	—	4	4	no	—
306	Dic₁₉	—	8	2	no	—
307	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
308	C₂²×M₁₆	—	19	1	no	—
309	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
310	#518	—	19	4	no	—
311	#518	—	38	2	no	—
312	#518	—	38	2	no	—
313	#518	—	38	2	no	—
314	C₂×C₄×D₄	—	38	2	no	—
315	C₂×C₄×D₄	—	38	2	no	—
316	C₂×#117	—	19	1	no	—
317	C₂×#117	—	19	1	no	—
318	C₂×#117	—	19	1	no	—
319	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	—	38	2	no	—
321	#418	—	2	2	no	—
322	#418	—	2	2	no	—
323	#418	—	19	4	no	—
324	#418	—	38	2	no	—
325	C₂×#102	—	38	2	no	—
326	C₂×#102	Dic₁₉	1	4	yes	complemented
327	#344	—	38	2	no	—
328	#342	—	38	2	no	—
329	#339	—	38	2	no	—
330	H(3,ℤ/4)	—	38	2	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	4	8	no	—
338	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
339	C₂×C₁₉	#1904	1	2	yes	—
340	C₂⁵	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	Dic₃₈	1	2	yes	—
349	C₂²×D₄	C₄×D₁₉	1	2	yes	—
350	C₂²×D₄	C₄×D₁₉	1	2	yes	—
351	C₂²×D₄	D₇₆	1	2	yes	—
352	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
353	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
354	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
355	C₂³×C₄	—	38	4	no	—
356	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	19	2	no	—
364	C₂×M₁₆	—	38	1	no	—
365	C₂×M₁₆	—	38	1	no	—
366	C₂×M₁₆	—	38	1	no	—
367	C₂×M₁₆	—	38	1	no	—
368	C₂×M₁₆	—	38	1	no	—
369	C₂²×C₈	—	38	1	no	—
370	C₂²×C₈	C₂×Dic₁₉	1	2	yes	complemented
371	C₄×D₄	—	38	8	no	—
372	C₄×D₄	—	38	8	no	—
373	C₄×D₄	—	38	8	no	—
374	C₄×D₄	—	38	8	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	19	2	no	—
380	#117	—	19	2	no	—
381	#117	—	19	2	no	—
382	#117	—	19	2	no	—
383	#117	—	19	2	no	—
384	#117	—	38	1	no	—
385	#117	—	38	1	no	—
386	#117	—	38	1	no	—
387	#117	—	38	1	no	—
388	#117	—	38	1	no	—
389	#117	—	38	1	no	—
390	#117	—	38	1	no	—
391	C₂×C₄⋊C₄	—	38	1	no	—
392	C₂×C₄⋊C₄	—	38	1	no	—
393	C₂×C₄⋊C₄	—	38	1	no	—
394	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	complemented
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	19	2	no	—
397	C₂×C₂²⋊C₄	—	38	8	no	—
398	C₂×C₂²⋊C₄	—	38	4	no	—
399	C₂×C₂²⋊C₄	—	38	8	no	—
400	C₂×C₂²⋊C₄	—	38	1	no	—
401	C₂×C₂²⋊C₄	—	38	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	19	2	no	—
404	C₂×C₄²	—	38	1	no	—
405	C₂×C₄²	—	38	1	no	—
406	#102	—	2	8	no	—
407	#102	—	38	8	no	—
408	C₁₉	#10785	1	1	yes	characteristic, complemented, Sylow
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	8	4	no	—
417	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	C₄×Dic₁₉	1	4	yes	—
440	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
441	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
442	C₂×D₄	C₄⋊Dic₁₉	1	4	yes	—
443	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
444	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
445	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	38	2	no	—
448	C₂²×C₄	—	38	2	no	—
449	C₂²×C₄	—	38	16	no	—
450	C₂²×C₄	—	76	1	no	—
451	C₂²×C₄	—	152	8	no	—
452	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
459	C₂²×C₄	#64543	1	1	yes	characteristic
460	C₂²×C₄	#64543	1	1	yes	characteristic
461	C₂²×C₄	#64543	1	1	yes	characteristic
462	C₂²×C₄	#64543	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	38	2	no	—
471	M₁₆	—	38	2	no	—
472	M₁₆	—	76	1	no	—
473	M₁₆	—	76	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	38	2	no	—
478	C₂×C₈	—	76	1	no	—
479	C₂×C₈	—	76	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	38	2	no	—
483	C₄⋊C₄	—	38	2	no	—
484	C₄⋊C₄	—	38	2	no	—
485	C₄⋊C₄	—	38	2	no	—
486	C₄⋊C₄	—	38	2	no	—
487	C₄⋊C₄	—	76	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	19	4	no	—
491	C₂²⋊C₄	—	38	16	no	—
492	C₂²⋊C₄	—	38	2	no	—
493	C₂²⋊C₄	—	38	2	no	—
494	C₂²⋊C₄	—	38	2	no	—
495	C₂²⋊C₄	—	38	2	no	—
496	C₂²⋊C₄	—	76	1	no	—
497	C₄²	—	4	1	no	—
498	C₄²	—	4	1	no	—
499	C₄²	—	19	4	no	—
500	C₄²	—	38	2	no	—
501	C₄²	—	38	2	no	—
502	C₄²	—	38	2	no	—
503	C₄²	—	38	2	no	—
504	C₄²	—	76	1	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	8	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	—	8	4	no	—
518	C₂³	—	8	4	no	—
519	C₂³	—	8	4	no	—
520	C₂³	#10597324	1	1	yes	characteristic
521	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
522	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
523	C₂³	#10597328	1	1	yes	characteristic
524	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
525	C₂³	#10597383	1	1	yes	characteristic
526	C₂³	#10597385	1	1	yes	characteristic
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	C₁₉⋊#95	1	8	yes	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	—	38	4	no	—
538	C₂×C₄	—	38	4	no	—
539	C₂×C₄	—	76	4	no	—
540	C₂×C₄	—	76	4	no	—
541	C₂×C₄	—	76	2	no	—
542	C₂×C₄	—	152	16	no	—
543	C₂×C₄	—	152	2	no	—
544	C₂×C₄	#10597323	1	1	yes	characteristic
545	C₂×C₄	#10597323	1	1	yes	characteristic
546	C₂×C₄	#10597324	1	1	yes	characteristic
547	C₂×C₄	#10597324	1	1	yes	characteristic
548	C₂×C₄	#10597324	1	1	yes	characteristic
549	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
550	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	#10597328	1	1	yes	characteristic
554	C₂×C₄	#10597332	1	1	yes	characteristic
555	C₂×C₄	#10597332	1	1	yes	characteristic
556	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
560	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
562	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
563	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
564	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
565	C₂×C₄	#10597381	1	1	yes	characteristic
566	C₂×C₄	#10597381	1	1	yes	characteristic
567	C₂×C₄	#10597383	1	1	yes	characteristic
568	C₂×C₄	#10597385	1	1	yes	characteristic
569	C₂×C₄	#10597385	1	1	yes	characteristic
570	C₂×C₄	#10597385	1	1	yes	characteristic
571	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	76	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	8	no	—
585	C₂²	—	8	4	no	—
586	C₂²	—	8	4	no	—
587	C₂²	—	8	4	no	—
588	C₂²	—	8	4	no	—
589	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
590	C₂²	#11926399	1	1	yes	characteristic
591	C₂²	#11926402	1	1	yes	characteristic
592	C₂²	#11926416	1	1	yes	characteristic
593	C₂²	#11926419	1	1	yes	characteristic
594	C₂²	#11926421	1	1	yes	characteristic
595	C₂²	#11926424	1	1	yes	characteristic
596	C₄	—	8	2	no	—
597	C₄	—	76	4	no	—
598	C₄	—	76	4	no	—
599	C₄	—	152	2	no	—
600	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
601	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
602	C₄	#11926402	1	1	yes	characteristic
603	C₄	#11926405	1	1	yes	characteristic
604	C₄	#11926416	1	1	yes	characteristic
605	C₄	#11926419	1	1	yes	characteristic
606	C₄	#11926421	1	1	yes	characteristic
607	C₄	#11926424	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	4	8	no	—
615	C₂	#14561857	1	1	yes	characteristic
616	C₂	#14564124	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926424
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	#10785
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. C₂×#11926315	C₂	semidirect
4. #14563368	C₂	semidirect
5. #14563344	C₂	semidirect
6. C₂×#11926301	C₂	semidirect
12. #11927019	C₄	semidirect
20. #11926549	C₄	semidirect
31. C₂×C₁₉×#102	C₄	semidirect
55. C₂²×C₈×C₁₉	C₂×C₄	semidirect
60. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
82. #10597372	C₂×C₄	semidirect
96. C₂×#64520	C₂×C₄	semidirect
326. C₂×#102	Dic₁₉	semidirect
370. C₂²×C₈	C₂×Dic₁₉	semidirect
394. C₂×C₄⋊C₄	C₂×Dic₁₉	semidirect
408. C₁₉	#10785	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927019	2
C₂×#11926549	2
C₂×#11926315	2
#14563368	2
#14563344	2
C₂×#11926301	2
C₂×C₁₉×#418	2
#10785	19