Subgroups — #18088303

Order 4864.

642 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926502	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926316	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926308	C₂	1	1	yes	maximal, characteristic
4	#14563351	C₂	1	1	yes	maximal, characteristic
5	#14563346	C₂	1	1	yes	maximal, characteristic
6	#14563345	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#344	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	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926502	—	2	2	no	—
13	#11926502	C₄	1	4	yes	complemented
14	C₂×#10597272	—	2	1	no	—
15	C₂×C₈×Dic₁₉	—	2	1	no	—
16	#11926316	C₄	1	4	yes	complemented
17	#11926308	—	2	1	no	—
18	#11926308	—	2	1	no	—
19	#11926306	—	2	2	no	—
20	#11926305	—	2	2	no	—
21	#11926304	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#344	C₄	1	4	yes	complemented
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	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	C₂×C₄	1	2	yes	—
36	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
49	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
50	#10597372	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	C₂×C₄	1	2	yes	—
56	#10597372	C₂×C₄	1	2	yes	—
57	#10597372	D₄	1	2	yes	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	C₂×C₄	1	2	yes	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
76	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
77	#10597272	—	2	4	no	—
78	C₈×Dic₁₉	—	2	4	no	—
79	C₂⁴×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×Dic₁₉	—	2	2	no	—
96	C₂²×Dic₁₉	—	4	1	no	—
97	M₁₆×C₁₉	—	2	2	no	—
98	M₁₆×C₁₉	—	2	2	no	—
99	M₁₆×C₁₉	—	2	2	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	M₁₆×C₁₉	—	2	2	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	C₄²	1	4	yes	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	4	1	no	—
117	C₂²⋊Dic₁₉	—	2	2	no	—
118	C₂²⋊Dic₁₉	—	2	2	no	—
119	C₂²⋊Dic₁₉	—	2	2	no	—
120	C₂²⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	2	2	no	—
122	C₄⋊Dic₁₉	—	2	2	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
125	C₄×Dic₁₉	—	2	2	no	—
126	C₄×Dic₁₉	—	2	2	no	—
127	C₄×Dic₁₉	—	2	2	no	—
128	C₄×Dic₁₉	—	4	1	no	—
129	#64520	—	2	2	no	—
130	#64520	—	2	2	no	—
131	#64520	—	4	1	no	—
132	#64520	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	2	1	no	—
137	C₂×C₁₉⋊C₈	—	2	1	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	2	1	no	—
140	C₂×C₁₉⋊C₈	—	2	1	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
146	#10828	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	#117	1	1	yes	characteristic
149	C₂³×C₁₉	#117	1	1	yes	characteristic
150	C₂³×C₁₉	#117	1	1	yes	characteristic
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₁₉	#126	1	1	yes	characteristic
154	C₂³×C₁₉	#126	1	1	yes	characteristic
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
185	C₂×Dic₁₉	—	2	4	no	—
186	C₂×Dic₁₉	—	4	4	no	—
187	C₂×Dic₁₉	—	4	2	no	—
188	C₂×Dic₁₉	—	8	2	no	—
189	C₈×C₁₉	—	2	4	no	—
190	C₈×C₁₉	—	4	2	no	—
191	C₁₉⋊C₈	—	2	2	no	—
192	C₁₉⋊C₈	—	2	2	no	—
193	C₁₉⋊C₈	—	4	2	no	—
194	C₂×#405	—	19	1	no	—
195	C₂×#344	—	19	1	no	—
196	C₂×#344	D₁₉	1	1	yes	characteristic
197	C₂×#341	—	19	1	no	—
198	#1735	—	19	1	no	—
199	#1733	—	19	1	no	—
200	#1733	—	19	1	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	#376	1	1	yes	characteristic
209	C₂²×C₁₉	#380	1	1	yes	characteristic
210	C₂²×C₁₉	#383	1	1	yes	characteristic
211	C₂²×C₁₉	#387	1	1	yes	characteristic
212	C₂²×C₁₉	#387	1	1	yes	characteristic
213	C₂²×C₁₉	#388	1	1	yes	characteristic
214	C₂²×C₁₉	#388	1	1	yes	characteristic
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
217	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₁₉	#381	1	1	yes	characteristic
219	C₄×C₁₉	#382	1	1	yes	characteristic
220	C₄×C₁₉	#387	1	1	yes	characteristic
221	C₄×C₁₉	#387	1	1	yes	characteristic
222	C₄×C₁₉	#388	1	1	yes	characteristic
223	C₄×C₁₉	#388	1	1	yes	characteristic
224	Dic₁₉	—	4	4	no	—
225	Dic₁₉	—	8	2	no	—
226	C₂²×M₁₆	—	19	1	no	—
227	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
228	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
229	C₂³×C₈	—	19	1	no	—
230	C₂×#117	—	19	1	no	—
231	C₂×#117	—	19	1	no	—
232	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
233	#405	—	19	4	no	—
234	#405	—	38	2	no	—
235	C₂×#97	—	38	1	no	—
236	C₂×C₄×C₈	—	38	1	no	—
237	#344	—	19	4	no	—
238	#344	Dic₁₉	1	4	yes	complemented
239	#341	—	38	1	no	—
240	#341	—	38	1	no	—
241	#340	—	38	2	no	—
242	#339	—	38	2	no	—
243	#339	—	38	2	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	#1434	1	1	yes	characteristic
251	C₂×C₁₉	#1814	1	2	yes	—
252	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	19	2	no	—
262	C₂×M₁₆	—	38	1	no	—
263	C₂×M₁₆	—	38	1	no	—
264	C₂×M₁₆	—	38	1	no	—
265	C₂×M₁₆	—	38	1	no	—
266	C₂×M₁₆	—	38	1	no	—
267	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
268	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
269	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
270	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	19	2	no	—
274	C₂²×C₈	—	19	2	no	—
275	C₂²×C₈	—	19	1	no	—
276	C₂²×C₈	—	19	1	no	—
277	C₂²×C₈	—	38	1	no	—
278	C₂²×C₈	—	38	1	no	—
279	C₂²×C₈	—	38	1	no	—
280	C₂²×C₈	—	38	1	no	—
281	C₂²×C₈	—	38	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	19	2	no	—
286	#117	—	19	2	no	—
287	#117	—	19	2	no	—
288	#117	—	38	1	no	—
289	#117	—	38	1	no	—
290	#117	—	38	1	no	—
291	#117	—	38	1	no	—
292	#117	—	38	1	no	—
293	#117	C₂×Dic₁₉	1	2	yes	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	19	2	no	—
296	C₂×C₄⋊C₄	—	38	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	38	1	no	—
299	C₂×C₂²⋊C₄	—	38	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	38	1	no	—
302	C₂×C₄²	—	38	1	no	—
303	#97	—	38	4	no	—
304	C₄×C₈	—	38	4	no	—
305	C₁₉	#10828	1	1	yes	characteristic, complemented, Sylow
306	C₂⁴	#64541	1	1	yes	characteristic
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	38	2	no	—
309	C₂²×C₄	—	76	1	no	—
310	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	#64541	1	1	yes	characteristic
313	C₂²×C₄	#64541	1	1	yes	characteristic
314	C₂²×C₄	#64541	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
318	C₂²×C₄	#64543	1	1	yes	characteristic
319	C₂²×C₄	#64543	1	1	yes	characteristic
320	C₂²×C₄	#64543	1	1	yes	characteristic
321	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	#64545	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	38	2	no	—
332	M₁₆	—	38	2	no	—
333	M₁₆	—	76	1	no	—
334	M₁₆	—	76	1	no	—
335	M₁₆	C₄×Dic₁₉	1	4	yes	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	19	2	no	—
343	C₂×C₈	—	19	2	no	—
344	C₂×C₈	—	38	2	no	—
345	C₂×C₈	—	38	2	no	—
346	C₂×C₈	—	38	1	no	—
347	C₂×C₈	—	38	1	no	—
348	C₂×C₈	—	38	2	no	—
349	C₂×C₈	—	38	2	no	—
350	C₂×C₈	—	38	1	no	—
351	C₂×C₈	—	38	1	no	—
352	C₂×C₈	—	38	2	no	—
353	C₂×C₈	—	76	1	no	—
354	C₂×C₈	—	76	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	19	4	no	—
358	C₄⋊C₄	—	38	2	no	—
359	C₄⋊C₄	—	38	2	no	—
360	C₄⋊C₄	—	76	1	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	38	2	no	—
364	C₂²⋊C₄	—	38	2	no	—
365	C₂²⋊C₄	—	38	2	no	—
366	C₂²⋊C₄	—	76	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	38	2	no	—
370	C₄²	—	38	2	no	—
371	C₄²	—	38	2	no	—
372	C₄²	—	76	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	#10597318	1	1	yes	characteristic
375	C₂³	#10597318	1	1	yes	characteristic
376	C₂³	#10597325	1	1	yes	characteristic
377	C₂³	#10597330	1	1	yes	characteristic
378	C₂³	#10597342	1	1	yes	characteristic
379	C₂³	#10597344	1	1	yes	characteristic
380	C₂³	#10597372	1	1	yes	characteristic
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	38	4	no	—
384	C₂×C₄	—	76	4	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	—	152	2	no	—
387	C₂×C₄	#10597318	1	1	yes	characteristic
388	C₂×C₄	#10597318	1	1	yes	characteristic
389	C₂×C₄	#10597323	1	1	yes	characteristic
390	C₂×C₄	#10597325	1	1	yes	characteristic
391	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
392	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	#10597329	1	1	yes	characteristic
395	C₂×C₄	#10597329	1	1	yes	characteristic
396	C₂×C₄	#10597330	1	1	yes	characteristic
397	C₂×C₄	#10597331	1	1	yes	characteristic
398	C₂×C₄	#10597331	1	1	yes	characteristic
399	C₂×C₄	#10597333	1	1	yes	characteristic
400	C₂×C₄	#10597335	1	1	yes	characteristic
401	C₂×C₄	#10597335	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
403	C₂×C₄	#10597338	1	1	yes	characteristic
404	C₂×C₄	#10597339	1	1	yes	characteristic
405	C₂×C₄	#10597340	1	1	yes	characteristic
406	C₂×C₄	#10597340	1	1	yes	characteristic
407	C₂×C₄	#10597342	1	1	yes	characteristic
408	C₂×C₄	#10597344	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
410	C₂×C₄	#10597372	1	1	yes	characteristic
411	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
412	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
413	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
414	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
415	C₈	—	2	4	no	—
416	C₈	—	4	2	no	—
417	C₈	—	38	2	no	—
418	C₈	—	38	2	no	—
419	C₈	—	76	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	#11926390	1	1	yes	characteristic
428	C₂²	#11926403	1	1	yes	characteristic
429	C₂²	#11926411	1	1	yes	characteristic
430	C₂²	#11926426	1	1	yes	characteristic
431	C₂²	#11926430	1	1	yes	characteristic
432	C₂²	#11926433	1	1	yes	characteristic
433	C₂²	#11926437	1	1	yes	characteristic
434	C₄	—	8	2	no	—
435	C₄	—	76	4	no	—
436	C₄	—	152	2	no	—
437	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
438	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
439	C₄	#11926406	1	1	yes	characteristic
440	C₄	#11926408	1	1	yes	characteristic
441	C₄	#11926426	1	1	yes	characteristic
442	C₄	#11926430	1	1	yes	characteristic
443	C₄	#11926433	1	1	yes	characteristic
444	C₄	#11926437	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	#14561860	1	1	yes	characteristic
452	C₂	#14563688	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597330
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#344	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#344	D₁₉
hypocenter	C₁₉	#10828
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
13. #11926502	C₄	semidirect
16. #11926316	C₄	semidirect
25. C₁₉×#344	C₄	semidirect
238. #344	Dic₁₉	semidirect
305. C₁₉	#10828	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926502	2
C₂×#11926316	2
C₂×#11926308	2
#14563351	2
#14563346	2
#14563345	2
C₂×C₁₉×#344	2
#10828	19