Subgroups — #18088424

Order 4864.

822 conjugacy classes of subgroups.

The subgroup lattice has 470 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	C₂×#11926580	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	#14563331	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	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	#11926580	—	2	2	no	—
16	#11926580	—	2	2	no	—
17	C₂×#10597264	C₄	1	2	yes	complemented
18	C₂×#10597265	C₄	1	2	yes	complemented
19	C₂×C₈×Dic₁₉	—	2	2	no	—
20	C₂×C₈×Dic₁₉	—	2	2	no	—
21	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
22	#11926305	—	2	2	no	—
23	#11926303	—	2	2	no	—
24	#11926298	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
28	C₁₉×#336	—	2	2	no	—
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×Dic₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	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	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₉	D₄	1	2	yes	—
44	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	—	2	1	no	—
48	C₁₉×#117	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	C₂×C₄	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	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
64	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
65	C₂×#64520	—	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	C₂×C₄	1	2	yes	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
78	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
80	#10597279	—	2	8	no	—
81	C₈×Dic₁₉	—	2	8	no	—
82	#10597265	—	2	4	no	—
83	#10597264	—	2	4	no	—
84	C₂⁴×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×Dic₁₉	—	2	8	no	—
101	C₂²×Dic₁₉	—	2	2	no	—
102	C₂²×Dic₁₉	—	2	2	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₂²⋊C₄×C₁₉	—	4	1	no	—
122	C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₂²⋊Dic₁₉	—	4	1	no	—
126	C₂²⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	2	2	no	—
128	C₄⋊Dic₁₉	—	2	2	no	—
129	C₄×Dic₁₉	—	2	2	no	—
130	C₄×Dic₁₉	—	2	2	no	—
131	C₄×Dic₁₉	—	2	2	no	—
132	C₄×Dic₁₉	—	4	1	no	—
133	C₄×Dic₁₉	—	4	1	no	—
134	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
135	#64520	—	2	2	no	—
136	#64520	—	2	2	no	—
137	#64520	—	4	1	no	—
138	#64520	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
143	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
144	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
146	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
147	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
148	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
149	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
150	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
151	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
152	#10859	—	19	1	no	maximal, Sylow
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	#117	1	1	yes	characteristic
155	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
156	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂³×C₁₉	#124	1	1	yes	characteristic
160	C₂³×C₁₉	#125	1	1	yes	characteristic
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
191	C₂×Dic₁₉	—	2	8	no	—
192	C₂×Dic₁₉	—	2	8	no	—
193	C₂×Dic₁₉	—	2	8	no	—
194	C₂×Dic₁₉	—	2	4	no	—
195	C₂×Dic₁₉	—	4	2	no	—
196	C₂×Dic₁₉	—	4	4	no	—
197	C₈×C₁₉	—	2	4	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₁₉⋊C₈	—	4	2	no	—
200	C₁₉⋊C₈	#95	1	4	yes	—
201	C₁₉⋊C₈	#95	1	4	yes	—
202	C₂²×#108	—	19	1	no	—
203	C₂×#427	—	19	1	no	—
204	C₂²×C₄×C₈	—	19	1	no	—
205	C₂×#339	—	19	1	no	—
206	C₂×#339	—	19	1	no	—
207	#1729	—	19	1	no	—
208	#1729	D₁₉	1	1	yes	characteristic
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₉	#380	1	1	yes	characteristic
217	C₂²×C₁₉	#382	1	1	yes	characteristic
218	C₂²×C₁₉	#389	1	1	yes	characteristic
219	C₂²×C₁₉	#389	1	1	yes	characteristic
220	C₂²×C₁₉	#390	1	1	yes	characteristic
221	C₂²×C₁₉	#391	1	1	yes	characteristic
222	C₂²×C₁₉	#443	1	4	yes	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
225	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₁₉	#380	1	1	yes	characteristic
227	C₄×C₁₉	#384	1	1	yes	characteristic
228	C₄×C₁₉	#389	1	1	yes	characteristic
229	C₄×C₁₉	#389	1	1	yes	characteristic
230	C₄×C₁₉	#390	1	1	yes	characteristic
231	C₄×C₁₉	#391	1	1	yes	characteristic
232	Dic₁₉	—	2	8	no	—
233	Dic₁₉	—	8	2	no	—
234	C₂²×M₁₆	—	19	1	no	—
235	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
236	C₂³×C₈	—	19	1	no	—
237	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
238	C₂×#117	—	19	1	no	—
239	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
240	C₂²×C₄²	—	19	1	no	—
241	C₂×#108	—	19	4	no	—
242	C₂×#108	—	38	2	no	—
243	C₂×#108	—	38	2	no	—
244	#427	—	38	2	no	—
245	#427	—	38	2	no	—
246	C₂×#107	—	19	2	no	—
247	C₂×#106	—	19	2	no	—
248	C₂×C₄×C₈	—	19	4	no	—
249	C₂×C₄×C₈	—	38	2	no	—
250	C₂×C₄×C₈	—	38	2	no	—
251	#339	—	38	2	no	—
252	#339	—	38	2	no	—
253	#336	—	2	2	no	—
254	#336	—	38	2	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
260	C₂×C₁₉	#1772	1	2	yes	—
261	C₂×C₁₉	#1945	1	2	yes	—
262	C₂×C₁₉	#1974	1	2	yes	—
263	C₂³×C₄	—	38	1	no	—
264	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	19	2	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂×M₁₆	—	38	1	no	—
273	C₂×M₁₆	—	38	1	no	—
274	C₂×M₁₆	—	38	1	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	19	2	no	—
283	C₂²×C₈	—	19	1	no	—
284	C₂²×C₈	—	19	1	no	—
285	C₂²×C₈	—	19	2	no	—
286	C₂²×C₈	—	19	2	no	—
287	C₂²×C₈	—	19	2	no	—
288	C₂²×C₈	—	19	2	no	—
289	C₂²×C₈	—	19	2	no	—
290	C₂²×C₈	—	38	1	no	—
291	C₂²×C₈	Dic₃₈	1	2	yes	—
292	C₂²×C₈	C₄×D₁₉	1	2	yes	—
293	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	—	38	1	no	—
299	#117	—	38	1	no	—
300	#117	—	38	1	no	—
301	#117	—	38	1	no	—
302	C₂×C₄⋊C₄	—	19	2	no	—
303	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	38	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	19	2	no	—
308	C₂×C₄²	—	19	2	no	—
309	C₂×C₄²	—	19	2	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₂×C₄²	—	38	1	no	—
312	C₂×C₄²	—	38	1	no	—
313	C₂×C₄²	—	38	1	no	—
314	#108	—	38	8	no	—
315	#107	—	38	4	no	—
316	#106	—	38	4	no	—
317	C₄×C₈	—	38	8	no	—
318	C₁₉	#10859	1	1	yes	characteristic, complemented, Sylow
319	C₂⁴	#64541	1	1	yes	characteristic
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	38	8	no	—
322	C₂²×C₄	—	38	2	no	—
323	C₂²×C₄	—	38	2	no	—
324	C₂²×C₄	—	38	2	no	—
325	C₂²×C₄	—	38	2	no	—
326	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	#64541	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	#64543	1	1	yes	characteristic
336	C₂²×C₄	#64543	1	1	yes	characteristic
337	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
338	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	38	2	no	—
345	M₁₆	—	38	2	no	—
346	M₁₆	—	76	1	no	—
347	M₁₆	—	76	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	19	2	no	—
358	C₂×C₈	—	19	2	no	—
359	C₂×C₈	—	19	4	no	—
360	C₂×C₈	—	19	2	no	—
361	C₂×C₈	—	19	2	no	—
362	C₂×C₈	—	19	4	no	—
363	C₂×C₈	—	19	4	no	—
364	C₂×C₈	—	19	4	no	—
365	C₂×C₈	—	19	2	no	—
366	C₂×C₈	—	19	2	no	—
367	C₂×C₈	—	38	2	no	—
368	C₂×C₈	—	76	1	no	—
369	C₂×C₈	—	76	1	no	—
370	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	38	2	no	—
374	C₄⋊C₄	—	38	2	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	76	1	no	—
378	C₂²⋊C₄	—	76	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	—	19	4	no	—
382	C₄²	—	38	2	no	—
383	C₄²	—	38	2	no	—
384	C₄²	—	38	2	no	—
385	C₄²	—	76	1	no	—
386	C₄²	—	76	1	no	—
387	C₂³	—	2	4	no	—
388	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
389	C₂³	#10597318	1	1	yes	characteristic
390	C₂³	#10597330	1	1	yes	characteristic
391	C₂³	#10597331	1	1	yes	characteristic
392	C₂³	#10597335	1	1	yes	characteristic
393	C₂³	#10597342	1	1	yes	characteristic
394	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	38	8	no	—
398	C₂×C₄	—	38	8	no	—
399	C₂×C₄	—	38	8	no	—
400	C₂×C₄	—	38	4	no	—
401	C₂×C₄	—	76	4	no	—
402	C₂×C₄	—	76	2	no	—
403	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
404	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
405	C₂×C₄	#10597323	1	1	yes	characteristic
406	C₂×C₄	#10597324	1	1	yes	characteristic
407	C₂×C₄	#10597324	1	1	yes	characteristic
408	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
409	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
411	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
412	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	#10597330	1	1	yes	characteristic
414	C₂×C₄	#10597331	1	1	yes	characteristic
415	C₂×C₄	#10597333	1	1	yes	characteristic
416	C₂×C₄	#10597333	1	1	yes	characteristic
417	C₂×C₄	#10597334	1	1	yes	characteristic
418	C₂×C₄	#10597334	1	1	yes	characteristic
419	C₂×C₄	#10597335	1	1	yes	characteristic
420	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
421	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
422	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
423	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
424	C₂×C₄	#10597342	1	1	yes	characteristic
425	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
426	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
427	C₂×C₄	#10597385	1	1	yes	characteristic
428	C₂×C₄	#10597385	1	1	yes	characteristic
429	C₂×C₄	#10597386	1	1	yes	characteristic
430	C₂×C₄	#10597390	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	4	2	no	—
433	C₈	—	19	4	no	—
434	C₈	—	19	4	no	—
435	C₈	—	76	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
443	C₂²	#11926403	1	1	yes	characteristic
444	C₂²	#11926408	1	1	yes	characteristic
445	C₂²	#11926439	1	1	yes	characteristic
446	C₂²	#11926441	1	1	yes	characteristic
447	C₂²	#11926444	1	1	yes	characteristic
448	C₂²	#11926448	1	1	yes	characteristic
449	C₂²	#11926659	1	4	yes	—
450	C₄	—	8	2	no	—
451	C₄	—	38	8	no	—
452	C₄	—	152	2	no	—
453	C₄	#95×D₁₉	1	1	yes	characteristic
454	C₄	#11926395	1	1	yes	characteristic
455	C₄	#11926402	1	1	yes	characteristic
456	C₄	#11926413	1	1	yes	characteristic
457	C₄	#11926439	1	1	yes	characteristic
458	C₄	#11926441	1	1	yes	characteristic
459	C₄	#11926444	1	1	yes	characteristic
460	C₄	#11926448	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	1	no	—
465	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
466	C₂	#14563515	1	2	yes	—
467	C₂	#14564380	1	2	yes	—
468	C₂	#14564522	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#10859
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
14. C₂×#10597279	C₄	semidirect
17. C₂×#10597264	C₄	semidirect
18. C₂×#10597265	C₄	semidirect
21. C₂×C₈×Dic₁₉	C₄	semidirect
318. C₁₉	#10859	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
C₂×#11926580	2
C₂²×C₈×Dic₁₉	2
C₂×#11926305	2
C₂×#11926303	2
#14563331	2
C₁₉×#1729	2
#10859	19