Subgroups — #18088352

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926567	C₂	1	1	yes	maximal, characteristic
2	#14566038	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926390	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926567	—	2	2	no	—
13	#11926567	C₄	1	4	yes	complemented
14	C₂×Dic₁₉⋊C₈	—	2	2	no	—
15	#11926413	C₄	1	2	yes	complemented
16	#11926409	C₄	1	2	yes	complemented
17	#11926402	—	2	2	no	—
18	C₄×Dic₁₉⋊C₄	—	2	2	no	—
19	#11926390	—	2	2	no	—
20	#11926390	C₄	1	4	yes	complemented
21	C₂×C₁₉⋊#95	—	2	2	no	—
22	#11926305	—	2	2	no	—
23	#11926304	—	2	2	no	—
24	#11926303	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#339	—	2	2	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	D₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×#117	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₉	D₄	1	2	yes	—
52	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
53	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	#10597372	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
59	C₂×Dic₁₉⋊C₄	—	2	4	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	—	2	1	no	—
64	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
70	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
71	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
72	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
73	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	C₂×C₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	—	2	1	no	—
81	C₁₉⋊#95	—	2	8	no	—
82	C₁₉⋊#95	—	2	4	no	—
83	Dic₁₉⋊C₈	—	2	8	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	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×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	2	2	no	—
106	C₂²×Dic₁₉	—	2	2	no	—
107	C₂²×Dic₁₉	—	2	2	no	—
108	C₂²×Dic₁₉	—	4	4	no	—
109	C₂²×Dic₁₉	—	4	4	no	—
110	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
111	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
113	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	M₁₆×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₄²×C₁₉	C₄⋊C₄	1	4	yes	complemented
131	C₂²⋊Dic₁₉	—	4	1	no	—
132	C₂²⋊Dic₁₉	—	4	1	no	—
133	C₄⋊Dic₁₉	—	2	2	no	—
134	C₄⋊Dic₁₉	—	2	2	no	—
135	Dic₁₉⋊C₄	—	4	8	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	2	2	no	—
138	C₄×Dic₁₉	—	2	2	no	—
139	C₄×Dic₁₉	—	4	1	no	—
140	C₄×Dic₁₉	—	4	1	no	—
141	C₄×Dic₁₉	C₄²	1	2	yes	—
142	C₄×Dic₁₉	C₄²	1	2	yes	—
143	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
144	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
145	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
146	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
147	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	complemented
148	#64520	—	2	2	no	—
149	#64520	—	2	2	no	—
150	#64520	—	4	1	no	—
151	#64520	—	4	1	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	#10840	—	19	1	no	maximal, Sylow
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂³×C₁₉	#121	1	1	yes	characteristic
161	C₂³×C₁₉	#121	1	1	yes	characteristic
162	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×C₄⋊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	#117	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	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	C₄×Q₈	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	#124	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	#125	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#127	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×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
198	C₂×Dic₁₉	—	2	4	no	—
199	C₂×Dic₁₉	—	2	4	no	—
200	C₂×Dic₁₉	—	2	4	no	—
201	C₂×Dic₁₉	—	4	4	no	—
202	C₂×Dic₁₉	—	4	4	no	—
203	C₂×Dic₁₉	—	4	4	no	—
204	C₂×Dic₁₉	—	4	4	no	—
205	C₂×Dic₁₉	—	4	4	no	—
206	C₂×Dic₁₉	—	4	2	no	—
207	C₂×Dic₁₉	—	4	4	no	—
208	C₂×Dic₁₉	#95	1	4	yes	—
209	C₂×Dic₁₉	#95	1	4	yes	—
210	C₈×C₁₉	—	4	2	no	—
211	C₁₉⋊C₈	—	4	2	no	—
212	C₂×#423	—	19	1	no	—
213	#2285	—	19	1	no	—
214	C₂×#376	—	19	1	no	—
215	C₂×#339	—	19	1	no	—
216	C₂×#339	—	19	1	no	—
217	C₂×#339	—	19	1	no	—
218	C₂×#339	D₁₉	1	1	yes	characteristic
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
226	C₂²×C₁₉	#380	1	1	yes	characteristic
227	C₂²×C₁₉	#380	1	1	yes	characteristic
228	C₂²×C₁₉	#389	1	1	yes	characteristic
229	C₂²×C₁₉	#389	1	1	yes	characteristic
230	C₂²×C₁₉	#390	1	1	yes	characteristic
231	C₂²×C₁₉	#391	1	1	yes	characteristic
232	C₂²×C₁₉	#421	1	4	yes	—
233	C₄×C₁₉	—	4	4	no	—
234	C₄×C₁₉	—	8	2	no	—
235	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₁₉	#382	1	1	yes	characteristic
238	C₄×C₁₉	#384	1	1	yes	characteristic
239	C₄×C₁₉	#389	1	1	yes	characteristic
240	C₄×C₁₉	#389	1	1	yes	characteristic
241	C₄×C₁₉	#390	1	1	yes	characteristic
242	C₄×C₁₉	#391	1	1	yes	characteristic
243	Dic₁₉	—	2	4	no	—
244	Dic₁₉	—	2	4	no	—
245	Dic₁₉	—	4	4	no	—
246	Dic₁₉	—	8	2	no	—
247	C₂²×M₁₆	—	19	1	no	—
248	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
249	C₂×#117	—	19	1	no	—
250	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
251	C₂²×C₄²	—	19	1	no	—
252	C₂²×C₄²	—	19	1	no	—
253	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
254	#423	—	19	4	no	—
255	#423	—	38	2	no	—
256	C₂×C₄⋊C₈	—	38	2	no	—
257	#384	—	19	2	no	—
258	#382	—	19	2	no	—
259	#380	—	38	2	no	—
260	C₄×C₄⋊C₄	—	38	2	no	—
261	#376	—	19	4	no	—
262	#376	—	38	2	no	—
263	C₂×#95	—	38	2	no	—
264	#339	—	2	2	no	—
265	#339	—	38	2	no	—
266	#339	—	38	2	no	—
267	#339	—	38	2	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
273	C₂×C₁₉	#1733	1	2	yes	—
274	C₂×C₁₉	#1963	1	2	yes	—
275	C₂×C₁₉	#1995	1	2	yes	—
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	19	2	no	—
278	C₂³×C₄	—	38	1	no	—
279	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	—	19	2	no	—
286	C₂×M₁₆	—	38	1	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	C₄×D₁₉	1	2	yes	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	38	1	no	—
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	—	38	4	no	—
304	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	38	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	19	2	no	—
312	C₂×C₄²	—	19	1	no	—
313	C₂×C₄²	—	19	1	no	—
314	C₂×C₄²	—	19	2	no	—
315	C₂×C₄²	—	19	2	no	—
316	C₂×C₄²	—	19	2	no	—
317	C₂×C₄²	—	19	2	no	—
318	C₂×C₄²	—	19	2	no	—
319	C₂×C₄²	—	19	2	no	—
320	C₂×C₄²	—	19	2	no	—
321	C₂×C₄²	—	38	1	no	—
322	C₂×C₄²	—	38	1	no	—
323	C₂×C₄²	—	38	1	no	—
324	C₂×C₄²	—	38	1	no	—
325	C₂×C₄²	Dic₃₈	1	2	yes	—
326	C₂×C₄²	C₄×D₁₉	1	2	yes	—
327	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
328	C₄⋊C₈	—	38	8	no	—
329	#95	—	38	8	no	—
330	#95	—	38	4	no	—
331	C₁₉	#10840	1	1	yes	characteristic, complemented, Sylow
332	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	19	2	no	—
339	C₂²×C₄	—	19	2	no	—
340	C₂²×C₄	—	19	4	no	—
341	C₂²×C₄	—	19	4	no	—
342	C₂²×C₄	—	38	2	no	—
343	C₂²×C₄	—	38	2	no	—
344	C₂²×C₄	—	38	2	no	—
345	C₂²×C₄	—	38	2	no	—
346	C₂²×C₄	—	76	4	no	—
347	C₂²×C₄	—	76	4	no	—
348	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	#64541	1	1	yes	characteristic
353	C₂²×C₄	#64541	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
357	C₂²×C₄	#64543	1	1	yes	characteristic
358	C₂²×C₄	#64543	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	1	no	—
365	M₁₆	—	4	1	no	—
366	M₁₆	—	38	2	no	—
367	M₁₆	—	38	2	no	—
368	M₁₆	—	76	1	no	—
369	M₁₆	—	76	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	38	2	no	—
374	C₂×C₈	—	76	1	no	—
375	C₂×C₈	—	76	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	38	2	no	—
379	C₄⋊C₄	—	38	2	no	—
380	C₄⋊C₄	—	76	8	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	76	1	no	—
384	C₂²⋊C₄	—	76	1	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	19	2	no	—
391	C₄²	—	19	2	no	—
392	C₄²	—	19	4	no	—
393	C₄²	—	19	4	no	—
394	C₄²	—	19	2	no	—
395	C₄²	—	19	2	no	—
396	C₄²	—	19	4	no	—
397	C₄²	—	38	2	no	—
398	C₄²	—	38	2	no	—
399	C₄²	—	38	2	no	—
400	C₄²	—	76	1	no	—
401	C₄²	—	76	1	no	—
402	C₄²	Dic₁₉⋊C₄	1	4	yes	complemented
403	C₂³	—	2	4	no	—
404	C₂³	#10597324	1	1	yes	characteristic
405	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
406	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
407	C₂³	#10597330	1	1	yes	characteristic
408	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
409	C₂³	#10597342	1	1	yes	characteristic
410	C₂³	#10597385	1	1	yes	characteristic
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	19	4	no	—
418	C₂×C₄	—	19	4	no	—
419	C₂×C₄	—	38	4	no	—
420	C₂×C₄	—	38	4	no	—
421	C₂×C₄	—	38	4	no	—
422	C₂×C₄	—	76	4	no	—
423	C₂×C₄	—	76	4	no	—
424	C₂×C₄	—	76	4	no	—
425	C₂×C₄	—	76	4	no	—
426	C₂×C₄	—	76	4	no	—
427	C₂×C₄	—	76	4	no	—
428	C₂×C₄	—	76	2	no	—
429	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
430	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
431	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
432	C₂×C₄	#10597318	1	1	yes	characteristic
433	C₂×C₄	#10597323	1	1	yes	characteristic
434	C₂×C₄	#10597324	1	1	yes	characteristic
435	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
436	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
437	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
438	C₂×C₄	#10597330	1	1	yes	characteristic
439	C₂×C₄	#10597331	1	1	yes	characteristic
440	C₂×C₄	#10597331	1	1	yes	characteristic
441	C₂×C₄	#10597333	1	1	yes	characteristic
442	C₂×C₄	#10597333	1	1	yes	characteristic
443	C₂×C₄	#10597334	1	1	yes	characteristic
444	C₂×C₄	#10597334	1	1	yes	characteristic
445	C₂×C₄	#10597335	1	1	yes	characteristic
446	C₂×C₄	#10597335	1	1	yes	characteristic
447	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
448	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
449	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
450	C₂×C₄	#10597342	1	1	yes	characteristic
451	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
452	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
453	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
454	C₂×C₄	#10597385	1	1	yes	characteristic
455	C₂×C₄	#10597386	1	1	yes	characteristic
456	C₂×C₄	#10597390	1	1	yes	characteristic
457	C₈	—	4	2	no	—
458	C₈	—	76	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	#95×D₁₉	1	1	yes	characteristic
466	C₂²	#11926402	1	1	yes	characteristic
467	C₂²	#11926403	1	1	yes	characteristic
468	C₂²	#11926439	1	1	yes	characteristic
469	C₂²	#11926441	1	1	yes	characteristic
470	C₂²	#11926444	1	1	yes	characteristic
471	C₂²	#11926448	1	1	yes	characteristic
472	C₂²	#11926559	1	4	yes	—
473	C₄	—	4	4	no	—
474	C₄	—	8	2	no	—
475	C₄	—	38	4	no	—
476	C₄	—	38	4	no	—
477	C₄	—	76	4	no	—
478	C₄	—	152	2	no	—
479	C₄	#11926395	1	1	yes	characteristic
480	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
481	C₄	#11926408	1	1	yes	characteristic
482	C₄	#11926413	1	1	yes	characteristic
483	C₄	#11926439	1	1	yes	characteristic
484	C₄	#11926441	1	1	yes	characteristic
485	C₄	#11926444	1	1	yes	characteristic
486	C₄	#11926448	1	1	yes	characteristic
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
492	C₂	#14563343	1	2	yes	—
493	C₂	#14564465	1	2	yes	—
494	C₂	#14564614	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#10840
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #11926567	C₄	semidirect
15. #11926413	C₄	semidirect
16. #11926409	C₄	semidirect
20. #11926390	C₄	semidirect
130. C₄²×C₁₉	C₄⋊C₄	semidirect
147. C₄×Dic₁₉	C₄⋊C₄	semidirect
331. C₁₉	#10840	semidirect
402. C₄²	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926567	2
#14566038	2
C₂×#11926390	2
C₂×#11926305	2
C₂×#11926304	2
C₂×#11926303	2
C₂×C₁₉×#339	2
#10840	19