Subgroups — #18088475

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597275	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926499	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926312	C₂	1	2	yes	maximal
4	#14563355	C₂	1	2	yes	maximal
5	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	1	yes	characteristic
7	C₂×#10597372	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	C₂×#10597275	—	2	1	no	—
10	C₂×#10597275	—	2	1	no	—
11	C₂×#10597275	—	2	2	no	—
12	C₂×#10597275	C₄	1	4	yes	complemented
13	#11926499	—	2	2	no	—
14	#11926499	C₄	1	4	yes	complemented
15	C₂×#10597272	—	2	1	no	—
16	C₂×C₈×Dic₁₉	—	2	1	no	—
17	#11926312	—	2	4	no	—
18	#11926307	—	2	4	no	—
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#108	—	2	2	no	—
22	C₂×C₁₉×#108	—	2	2	no	—
23	C₂×C₁₉×#108	C₄	1	4	yes	complemented
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₉	—	2	2	no	—
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂×M₁₆×C₁₉	—	2	2	no	—
28	C₂×M₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	D₄	1	2	yes	—
39	C₂²×C₈×C₁₉	D₄	1	2	yes	—
40	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
41	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
42	#10597372	—	2	1	no	—
43	#10597372	—	2	1	no	—
44	#10597372	C₂×C₄	1	2	yes	—
45	#10597372	Q₈	1	2	yes	—
46	C₂×C₄⋊Dic₁₉	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	2	no	—
48	C₂×C₄⋊Dic₁₉	—	2	2	no	—
49	C₂×C₄⋊Dic₁₉	—	2	2	no	—
50	C₂×C₄⋊Dic₁₉	—	2	2	no	—
51	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×#64520	—	2	1	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	C₂×C₄	1	2	yes	—
58	C₂×#64520	D₄	1	2	yes	—
59	C₂×#64520	Q₈	1	2	yes	—
60	C₂²×C₁₉⋊C₈	—	2	1	no	—
61	C₁₉×#108	—	2	8	no	—
62	#10597275	—	2	4	no	—
63	#10597275	—	2	4	no	—
64	#10597272	—	2	4	no	—
65	C₈×Dic₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	#41	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂²×Dic₁₉	—	2	2	no	—
82	C₂²×Dic₁₉	—	2	4	no	—
83	C₂²×Dic₁₉	—	4	2	no	—
84	C₂²×Dic₁₉	—	4	2	no	—
85	C₂²×Dic₁₉	—	8	4	no	—
86	M₁₆×C₁₉	—	2	4	no	—
87	M₁₆×C₁₉	—	2	4	no	—
88	M₁₆×C₁₉	—	4	2	no	—
89	M₁₆×C₁₉	—	4	2	no	—
90	C₂×C₈×C₁₉	—	2	4	no	—
91	C₂×C₈×C₁₉	—	4	2	no	—
92	C₂×C₈×C₁₉	—	4	2	no	—
93	C₂×C₈×C₁₉	C₄²	1	4	yes	—
94	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
103	C₂²⋊Dic₁₉	—	2	2	no	—
104	C₂²⋊Dic₁₉	—	2	2	no	—
105	C₄⋊Dic₁₉	—	2	2	no	—
106	C₄⋊Dic₁₉	—	2	4	no	—
107	C₄⋊Dic₁₉	—	2	4	no	—
108	C₄⋊Dic₁₉	—	4	2	no	—
109	C₄⋊Dic₁₉	—	4	2	no	—
110	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
111	C₄×Dic₁₉	—	2	2	no	—
112	C₄×Dic₁₉	—	2	2	no	—
113	#64520	—	2	2	no	—
114	#64520	—	2	2	no	—
115	#64520	—	2	2	no	—
116	#64520	C₄⋊C₄	1	4	yes	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	#10870	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	#117	1	1	yes	characteristic
124	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
125	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
126	C₂³×C₁₉	#121	1	1	yes	characteristic
127	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₁₉	#124	1	1	yes	characteristic
129	C₂³×C₁₉	#125	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₁₉	—	2	4	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	4	2	no	—
161	C₂×Dic₁₉	—	4	4	no	—
162	C₂×Dic₁₉	—	8	4	no	—
163	C₂×Dic₁₉	—	8	4	no	—
164	C₂×Dic₁₉	—	8	4	no	—
165	C₈×C₁₉	—	4	4	no	—
166	C₈×C₁₉	#95	1	4	yes	—
167	C₈×C₁₉	#95	1	4	yes	—
168	C₁₉⋊C₈	—	2	4	no	—
169	C₂²×#108	D₁₉	1	1	yes	characteristic
170	C₂²×#107	—	19	1	no	—
171	C₂×#405	—	19	1	no	—
172	C₂×#343	—	19	2	no	—
173	#1736	—	19	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₉	#380	1	1	yes	characteristic
184	C₂²×C₁₉	#382	1	1	yes	characteristic
185	C₂²×C₁₉	#389	1	1	yes	characteristic
186	C₂²×C₁₉	#389	1	1	yes	characteristic
187	C₂²×C₁₉	#390	1	1	yes	characteristic
188	C₂²×C₁₉	#391	1	1	yes	characteristic
189	C₂²×C₁₉	#472	1	2	yes	—
190	C₂²×C₁₉	#473	1	2	yes	—
191	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
192	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₄×C₁₉	#380	1	1	yes	characteristic
194	C₄×C₁₉	#384	1	1	yes	characteristic
195	C₄×C₁₉	#389	1	1	yes	characteristic
196	C₄×C₁₉	#389	1	1	yes	characteristic
197	C₄×C₁₉	#390	1	1	yes	characteristic
198	C₄×C₁₉	#391	1	1	yes	characteristic
199	Dic₁₉	—	4	4	no	—
200	Dic₁₉	—	8	4	no	—
201	C₂²×M₁₆	—	19	1	no	—
202	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
203	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
204	C₂×#117	—	19	1	no	—
205	C₂²×C₄⋊C₄	—	19	2	no	—
206	C₂×#108	—	2	2	no	—
207	C₂×#108	—	2	2	no	—
208	C₂×#108	Dic₁₉	1	4	yes	complemented
209	C₂×#107	—	19	4	no	—
210	C₂×#107	—	38	1	no	—
211	C₂×#107	—	38	1	no	—
212	C₂×#107	—	38	2	no	—
213	#405	—	19	4	no	—
214	#405	—	38	2	no	—
215	C₂×#97	—	38	1	no	—
216	C₂×C₄×C₈	—	38	1	no	—
217	#343	—	38	4	no	—
218	#340	—	38	4	no	—
219	C₂×C₁₉	—	2	1	no	—
220	C₂×C₁₉	—	2	1	no	—
221	C₂×C₁₉	—	2	1	no	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
224	C₂×C₁₉	#1816	1	2	yes	—
225	C₂×C₁₉	#1952	1	2	yes	—
226	C₂×C₁₉	#1978	1	1	yes	characteristic
227	C₂×C₁₉	#1979	1	1	yes	characteristic
228	C₂³×C₄	—	38	2	no	—
229	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	19	2	no	—
236	C₂×M₁₆	—	19	2	no	—
237	C₂×M₁₆	—	19	2	no	—
238	C₂×M₁₆	—	38	1	no	—
239	C₂×M₁₆	—	38	1	no	—
240	C₂×M₁₆	—	38	1	no	—
241	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	38	1	no	—
244	C₂²×C₈	Dic₃₈	1	2	yes	—
245	C₂²×C₈	C₄×D₁₉	1	2	yes	—
246	C₂²×C₈	C₄×D₁₉	1	2	yes	—
247	C₂²×C₈	D₇₆	1	1	yes	characteristic
248	C₂²×C₈	D₇₆	1	1	yes	characteristic
249	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
250	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
251	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
252	#117	—	19	2	no	—
253	#117	—	19	2	no	—
254	#117	—	38	1	no	—
255	#117	—	38	1	no	—
256	C₂×C₄⋊C₄	—	19	2	no	—
257	C₂×C₄⋊C₄	—	19	4	no	—
258	C₂×C₄⋊C₄	—	38	2	no	—
259	C₂×C₄⋊C₄	—	38	2	no	—
260	C₂×C₄⋊C₄	—	38	2	no	—
261	C₂×C₄⋊C₄	—	38	2	no	—
262	C₂×C₄⋊C₄	—	38	2	no	—
263	C₂×C₂²⋊C₄	—	38	1	no	—
264	C₂×C₄²	—	38	1	no	—
265	#108	—	2	8	no	—
266	#107	—	38	4	no	—
267	#107	—	38	4	no	—
268	#97	—	38	4	no	—
269	C₄×C₈	—	38	4	no	—
270	C₁₉	#10870	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	#64545	1	1	yes	characteristic
272	C₂²×C₄	—	38	2	no	—
273	C₂²×C₄	—	38	4	no	—
274	C₂²×C₄	—	76	2	no	—
275	C₂²×C₄	—	76	2	no	—
276	C₂²×C₄	—	152	4	no	—
277	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
281	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
282	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
283	C₂²×C₄	#64543	1	1	yes	characteristic
284	C₂²×C₄	#64543	1	1	yes	characteristic
285	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	#64545	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
291	M₁₆	—	2	4	no	—
292	M₁₆	—	2	4	no	—
293	M₁₆	—	4	2	no	—
294	M₁₆	—	4	2	no	—
295	M₁₆	—	19	4	no	—
296	M₁₆	—	38	2	no	—
297	M₁₆	—	38	2	no	—
298	M₁₆	—	38	2	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	38	2	no	—
303	C₂×C₈	—	38	2	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
306	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
307	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
308	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
309	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
310	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
311	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
312	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
313	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
314	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
315	C₄⋊C₄	—	19	4	no	—
316	C₄⋊C₄	—	38	2	no	—
317	C₄⋊C₄	—	38	4	no	—
318	C₄⋊C₄	—	38	4	no	—
319	C₄⋊C₄	—	76	2	no	—
320	C₄⋊C₄	—	76	2	no	—
321	C₂²⋊C₄	—	38	2	no	—
322	C₂²⋊C₄	—	38	2	no	—
323	C₄²	—	38	2	no	—
324	C₄²	—	38	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	#10597336	1	1	yes	characteristic
328	C₂³	#10597338	1	1	yes	characteristic
329	C₂³	#10597339	1	1	yes	characteristic
330	C₂³	#10597341	1	1	yes	characteristic
331	C₂³	Q₈×Dic₁₉	1	1	yes	characteristic
332	C₂³	#10597392	1	1	yes	characteristic
333	C₂³	#10597393	1	1	yes	characteristic
334	C₂×C₄	—	38	4	no	—
335	C₂×C₄	—	76	2	no	—
336	C₂×C₄	—	76	2	no	—
337	C₂×C₄	—	76	4	no	—
338	C₂×C₄	—	152	4	no	—
339	C₂×C₄	—	152	4	no	—
340	C₂×C₄	—	152	4	no	—
341	C₂×C₄	#10597333	1	1	yes	characteristic
342	C₂×C₄	#10597333	1	1	yes	characteristic
343	C₂×C₄	#10597334	1	1	yes	characteristic
344	C₂×C₄	#10597334	1	1	yes	characteristic
345	C₂×C₄	#10597336	1	1	yes	characteristic
346	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
347	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
348	C₂×C₄	#10597338	1	1	yes	characteristic
349	C₂×C₄	#10597339	1	1	yes	characteristic
350	C₂×C₄	#10597341	1	1	yes	characteristic
351	C₂×C₄	#10597343	1	1	yes	characteristic
352	C₂×C₄	#10597343	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
357	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
360	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
361	C₂×C₄	#10597382	1	1	yes	characteristic
362	C₂×C₄	#10597384	1	1	yes	characteristic
363	C₂×C₄	#10597384	1	1	yes	characteristic
364	C₂×C₄	#10597386	1	1	yes	characteristic
365	C₂×C₄	#10597390	1	1	yes	characteristic
366	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
367	C₂×C₄	#10597392	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
369	C₈	—	4	4	no	—
370	C₈	—	38	4	no	—
371	C₈	C₁₉⋊#95	1	4	yes	—
372	C₈	C₁₉⋊#95	1	4	yes	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
382	C₂²	#11926401	1	1	yes	characteristic
383	C₂²	#11926409	1	1	yes	characteristic
384	C₂²	#11926440	1	1	yes	characteristic
385	C₂²	#11926443	1	1	yes	characteristic
386	C₂²	#11926445	1	1	yes	characteristic
387	C₂²	#11926451	1	1	yes	characteristic
388	C₂²	#11926815	1	2	yes	—
389	C₂²	#11926820	1	2	yes	—
390	C₄	—	76	4	no	—
391	C₄	—	152	4	no	—
392	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
393	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
394	C₄	#11926401	1	1	yes	characteristic
395	C₄	#11926413	1	1	yes	characteristic
396	C₄	#11926440	1	1	yes	characteristic
397	C₄	#11926443	1	1	yes	characteristic
398	C₄	#11926447	1	1	yes	characteristic
399	C₄	#11926449	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#14561864	1	1	yes	characteristic
405	C₂	#14563696	1	2	yes	—
406	C₂	#14564421	1	2	yes	—
407	C₂	#14564543	1	1	yes	characteristic
408	C₂	#14564548	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#108	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#108	D₁₉
hypocenter	C₁₉	#10870
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
12. C₂×#10597275	C₄	semidirect
14. #11926499	C₄	semidirect
23. C₂×C₁₉×#108	C₄	semidirect
208. C₂×#108	Dic₁₉	semidirect
270. C₁₉	#10870	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597275	2
C₂×#11926499	2
C₂×#11926312	2
#14563355	2
C₂²×C₁₉×#108	2
#10870	19