Subgroups — #18088468

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597279	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926502	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	#14563355	C₂	1	1	yes	maximal, characteristic
6	#14563354	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597279	—	2	2	no	—
13	C₂×#10597279	—	2	2	no	—
14	C₂×#10597279	C₄	1	4	yes	complemented
15	C₂×#10597265	—	2	2	no	—
16	C₂×#10597265	—	2	1	no	—
17	C₂×#10597265	—	2	1	no	—
18	C₂×#10597265	C₄	1	4	yes	complemented
19	#11926502	—	2	2	no	—
20	#11926502	C₄	1	4	yes	complemented
21	C₂×#10597272	—	2	1	no	—
22	C₂×C₈×Dic₁₉	—	2	1	no	—
23	#11926312	—	2	2	no	—
24	#11926307	—	2	2	no	—
25	#11926306	—	2	2	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#343	—	2	2	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	C₂×C₄	1	2	yes	—
57	#10597372	Q₈	1	2	yes	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×#64520	—	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	C₂×C₄	1	2	yes	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
76	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
77	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
78	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
79	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
81	#10597279	—	2	8	no	—
82	#10597272	—	2	4	no	—
83	C₈×Dic₁₉	—	2	4	no	—
84	#10597265	—	2	4	no	—
85	#10597265	—	2	4	no	—
86	C₂⁴×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	8	2	no	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×Dic₁₉	—	2	2	no	—
106	C₂²×Dic₁₉	—	2	2	no	—
107	C₂²×Dic₁₉	—	4	1	no	—
108	C₂²×Dic₁₉	—	4	1	no	—
109	C₂²×Dic₁₉	—	8	2	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	2	2	no	—
112	M₁₆×C₁₉	—	2	2	no	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊Dic₁₉	—	2	2	no	—
129	C₂²⋊Dic₁₉	—	2	2	no	—
130	C₄⋊Dic₁₉	—	2	2	no	—
131	C₄⋊Dic₁₉	—	2	2	no	—
132	C₄⋊Dic₁₉	—	2	2	no	—
133	C₄⋊Dic₁₉	—	4	1	no	—
134	C₄⋊Dic₁₉	—	4	1	no	—
135	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	2	2	no	—
138	#64520	—	2	2	no	—
139	#64520	—	2	2	no	—
140	#64520	—	4	1	no	—
141	#64520	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
146	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
149	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
150	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
151	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
152	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
153	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
154	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
155	#10869	—	19	1	no	maximal, Sylow
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	#117	1	1	yes	characteristic
159	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
161	C₂³×C₁₉	#121	1	1	yes	characteristic
162	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	#124	1	1	yes	characteristic
164	C₂³×C₁₉	#125	1	1	yes	characteristic
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	8	2	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
197	C₂×Dic₁₉	—	2	4	no	—
198	C₂×Dic₁₉	—	4	2	no	—
199	C₂×Dic₁₉	—	4	2	no	—
200	C₂×Dic₁₉	—	4	2	no	—
201	C₂×Dic₁₉	—	8	2	no	—
202	C₂×Dic₁₉	—	8	2	no	—
203	C₂×Dic₁₉	—	8	2	no	—
204	C₈×C₁₉	—	2	4	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₁₉⋊C₈	—	4	2	no	—
207	C₁₉⋊C₈	#95	1	4	yes	—
208	C₁₉⋊C₈	#95	1	4	yes	—
209	C₂²×#108	—	19	1	no	—
210	C₂²×#106	—	19	1	no	—
211	C₂×#405	—	19	1	no	—
212	C₂×#343	—	19	1	no	—
213	C₂×#343	D₁₉	1	1	yes	characteristic
214	#1736	—	19	1	no	—
215	#1736	—	19	1	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
225	C₂²×C₁₉	#380	1	1	yes	characteristic
226	C₂²×C₁₉	#382	1	1	yes	characteristic
227	C₂²×C₁₉	#389	1	1	yes	characteristic
228	C₂²×C₁₉	#389	1	1	yes	characteristic
229	C₂²×C₁₉	#390	1	1	yes	characteristic
230	C₂²×C₁₉	#391	1	1	yes	characteristic
231	C₂²×C₁₉	#471	1	2	yes	—
232	C₂²×C₁₉	#471	1	2	yes	—
233	C₄×C₁₉	—	8	2	no	—
234	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
235	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₄×C₁₉	#380	1	1	yes	characteristic
237	C₄×C₁₉	#384	1	1	yes	characteristic
238	C₄×C₁₉	#389	1	1	yes	characteristic
239	C₄×C₁₉	#389	1	1	yes	characteristic
240	C₄×C₁₉	#390	1	1	yes	characteristic
241	C₄×C₁₉	#391	1	1	yes	characteristic
242	Dic₁₉	—	4	4	no	—
243	Dic₁₉	—	8	2	no	—
244	C₂²×M₁₆	—	19	1	no	—
245	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
246	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
247	C₂³×C₈	—	19	1	no	—
248	C₂×#117	—	19	1	no	—
249	C₂²×C₄⋊C₄	—	19	1	no	—
250	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
251	C₂×#108	—	19	4	no	—
252	C₂×#108	—	38	2	no	—
253	C₂×#108	—	38	2	no	—
254	C₂×#106	—	19	4	no	—
255	C₂×#106	—	38	1	no	—
256	C₂×#106	—	38	1	no	—
257	C₂×#106	—	38	2	no	—
258	#405	—	19	4	no	—
259	#405	—	38	2	no	—
260	C₂×#97	—	38	1	no	—
261	C₂×C₄×C₈	—	38	1	no	—
262	#343	—	2	2	no	—
263	#343	—	38	2	no	—
264	#340	—	38	2	no	—
265	#340	—	38	2	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
271	C₂×C₁₉	#1815	1	2	yes	—
272	C₂×C₁₉	#1951	1	2	yes	—
273	C₂×C₁₉	#1977	1	1	yes	characteristic
274	C₂×C₁₉	#1977	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	38	1	no	—
277	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	19	2	no	—
287	C₂×M₁₆	—	38	1	no	—
288	C₂×M₁₆	—	38	1	no	—
289	C₂×M₁₆	—	38	1	no	—
290	C₂×M₁₆	—	38	1	no	—
291	C₂×M₁₆	—	38	1	no	—
292	C₂×M₁₆	Dic₃₈	1	2	yes	—
293	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
294	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
295	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	19	2	no	—
299	C₂²×C₈	—	19	2	no	—
300	C₂²×C₈	—	19	2	no	—
301	C₂²×C₈	—	19	1	no	—
302	C₂²×C₈	—	19	1	no	—
303	C₂²×C₈	—	19	2	no	—
304	C₂²×C₈	—	19	2	no	—
305	C₂²×C₈	—	19	2	no	—
306	C₂²×C₈	—	38	1	no	—
307	#117	—	19	2	no	—
308	#117	—	19	2	no	—
309	#117	—	38	1	no	—
310	#117	—	38	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	19	2	no	—
317	C₂×C₄⋊C₄	—	19	2	no	—
318	C₂×C₄⋊C₄	—	38	1	no	—
319	C₂×C₄⋊C₄	—	38	1	no	—
320	C₂×C₄⋊C₄	—	38	1	no	—
321	C₂×C₄⋊C₄	—	38	1	no	—
322	C₂×C₄⋊C₄	—	38	1	no	—
323	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
324	C₂×C₂²⋊C₄	—	38	1	no	—
325	C₂×C₄²	—	38	1	no	—
326	#108	—	38	8	no	—
327	#106	—	38	4	no	—
328	#106	—	38	4	no	—
329	#97	—	38	4	no	—
330	C₄×C₈	—	38	4	no	—
331	C₁₉	#10869	1	1	yes	characteristic, complemented, Sylow
332	C₂⁴	#64541	1	1	yes	characteristic
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	—	38	2	no	—
338	C₂²×C₄	—	38	2	no	—
339	C₂²×C₄	—	76	1	no	—
340	C₂²×C₄	—	76	1	no	—
341	C₂²×C₄	—	152	2	no	—
342	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
346	C₂²×C₄	#64541	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	#64543	1	1	yes	characteristic
352	C₂²×C₄	#64543	1	1	yes	characteristic
353	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
354	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	4	1	no	—
362	M₁₆	—	4	1	no	—
363	M₁₆	—	38	2	no	—
364	M₁₆	—	38	2	no	—
365	M₁₆	—	76	1	no	—
366	M₁₆	—	76	1	no	—
367	M₁₆	Dic₁₉⋊C₄	1	4	yes	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	19	4	no	—
375	C₂×C₈	—	19	2	no	—
376	C₂×C₈	—	19	2	no	—
377	C₂×C₈	—	19	2	no	—
378	C₂×C₈	—	19	2	no	—
379	C₂×C₈	—	19	4	no	—
380	C₂×C₈	—	19	4	no	—
381	C₂×C₈	—	19	2	no	—
382	C₂×C₈	—	19	2	no	—
383	C₂×C₈	—	19	4	no	—
384	C₂×C₈	—	38	2	no	—
385	C₂×C₈	—	76	1	no	—
386	C₂×C₈	—	76	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	19	4	no	—
392	C₄⋊C₄	—	38	2	no	—
393	C₄⋊C₄	—	38	2	no	—
394	C₄⋊C₄	—	38	2	no	—
395	C₄⋊C₄	—	76	1	no	—
396	C₄⋊C₄	—	76	1	no	—
397	C₂²⋊C₄	—	38	2	no	—
398	C₂²⋊C₄	—	38	2	no	—
399	C₄²	—	38	2	no	—
400	C₄²	—	38	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
404	C₂³	#10597318	1	1	yes	characteristic
405	C₂³	#10597330	1	1	yes	characteristic
406	C₂³	#10597331	1	1	yes	characteristic
407	C₂³	#10597335	1	1	yes	characteristic
408	C₂³	#10597342	1	1	yes	characteristic
409	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	38	4	no	—
415	C₂×C₄	—	76	2	no	—
416	C₂×C₄	—	76	2	no	—
417	C₂×C₄	—	76	2	no	—
418	C₂×C₄	—	152	2	no	—
419	C₂×C₄	—	152	2	no	—
420	C₂×C₄	—	152	2	no	—
421	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
422	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
423	C₂×C₄	#10597323	1	1	yes	characteristic
424	C₂×C₄	#10597324	1	1	yes	characteristic
425	C₂×C₄	#10597324	1	1	yes	characteristic
426	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
429	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
430	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
431	C₂×C₄	#10597330	1	1	yes	characteristic
432	C₂×C₄	#10597331	1	1	yes	characteristic
433	C₂×C₄	#10597333	1	1	yes	characteristic
434	C₂×C₄	#10597333	1	1	yes	characteristic
435	C₂×C₄	#10597334	1	1	yes	characteristic
436	C₂×C₄	#10597334	1	1	yes	characteristic
437	C₂×C₄	#10597335	1	1	yes	characteristic
438	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
439	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
440	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
441	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
442	C₂×C₄	#10597342	1	1	yes	characteristic
443	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
445	C₂×C₄	#10597385	1	1	yes	characteristic
446	C₂×C₄	#10597385	1	1	yes	characteristic
447	C₂×C₄	#10597386	1	1	yes	characteristic
448	C₂×C₄	#10597390	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₈	—	19	4	no	—
452	C₈	—	19	4	no	—
453	C₈	—	76	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
463	C₂²	#11926403	1	1	yes	characteristic
464	C₂²	#11926408	1	1	yes	characteristic
465	C₂²	#11926439	1	1	yes	characteristic
466	C₂²	#11926441	1	1	yes	characteristic
467	C₂²	#11926444	1	1	yes	characteristic
468	C₂²	#11926448	1	1	yes	characteristic
469	C₂²	#11926806	1	2	yes	—
470	C₂²	#11926810	1	2	yes	—
471	C₄	—	8	2	no	—
472	C₄	—	76	4	no	—
473	C₄	—	152	2	no	—
474	C₄	#95×D₁₉	1	1	yes	characteristic
475	C₄	#11926395	1	1	yes	characteristic
476	C₄	#11926402	1	1	yes	characteristic
477	C₄	#11926413	1	1	yes	characteristic
478	C₄	#11926439	1	1	yes	characteristic
479	C₄	#11926441	1	1	yes	characteristic
480	C₄	#11926444	1	1	yes	characteristic
481	C₄	#11926448	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
487	C₂	#14563693	1	2	yes	—
488	C₂	#14564414	1	2	yes	—
489	C₂	#14564535	1	1	yes	characteristic
490	C₂	#14564539	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#10869
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
14. C₂×#10597279	C₄	semidirect
18. C₂×#10597265	C₄	semidirect
20. #11926502	C₄	semidirect
331. C₁₉	#10869	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597279	2
C₂²×#10597265	2
C₂×#11926502	2
C₂×#11926312	2
#14563355	2
#14563354	2
C₂×C₁₉×#343	2
#10869	19