Subgroups — #14577303

Order 2432.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927213	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927206	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927201	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927191	C₂	1	3	yes	maximal, complemented
7	#11927190	C₂	1	3	yes	maximal, complemented
8	#11927179	C₂	1	3	yes	maximal, complemented
9	#11927178	C₂	1	3	yes	maximal, complemented
10	#11927123	C₂	1	3	yes	maximal, complemented
11	#11927107	C₂	1	3	yes	maximal, complemented
12	#11927053	C₂	1	3	yes	maximal, complemented
13	#121×D₁₉	C₂	1	3	yes	maximal, complemented
14	#11927026	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	#10597435	—	2	8	no	—
19	#41×D₁₉	—	2	8	no	—
20	C₂×#64545	C₂²	1	1	yes	characteristic
21	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#64543	C₂²	1	3	yes	complemented
24	C₂×D₄×D₁₉	C₂²	1	3	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₉	C₂²	1	3	yes	complemented
27	C₂×D₄×D₁₉	C₂²	1	6	yes	complemented
28	C₂×#64541	C₂²	1	3	yes	complemented
29	C₂×#64541	C₂²	1	3	yes	complemented
30	C₂²×D₇₆	C₂²	1	3	yes	complemented
31	C₂²×C₄×D₁₉	C₂²	1	3	yes	complemented
32	C₁₉×#127	C₂²	1	3	yes	complemented
33	C₁₉×#121	C₂²	1	3	yes	complemented
34	C₁₉×#121	C₂²	1	3	yes	complemented
35	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₉	C₂²	1	3	yes	complemented
37	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597386	C₂²	1	3	yes	complemented
39	#10597385	C₂²	1	3	yes	complemented
40	#10597385	C₂²	1	6	yes	complemented
41	#10597384	C₂²	1	6	yes	complemented
42	#10597384	C₂²	1	3	yes	complemented
43	#10597384	C₂²	1	3	yes	complemented
44	#10597383	C₂²	1	3	yes	complemented
45	#10597383	C₂²	1	6	yes	complemented
46	#10597383	C₂²	1	6	yes	complemented
47	#10597382	C₂²	1	3	yes	complemented
48	#10597376	C₂²	1	3	yes	complemented
49	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
50	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
51	#10597370	C₂²	1	3	yes	complemented
52	#10597343	C₂²	1	3	yes	complemented
53	#10597342	C₂²	1	1	yes	characteristic, complemented
54	#10597341	C₂²	1	3	yes	complemented
55	#10597340	C₂²	1	3	yes	complemented
56	#10597339	C₂²	1	3	yes	complemented
57	C₄⋊C₄×D₁₉	C₂²	1	3	yes	complemented
58	#10597330	C₂²	1	3	yes	complemented
59	#10597330	C₂²	1	6	yes	complemented
60	#10597329	C₂²	1	3	yes	complemented
61	#10597328	C₂²	1	3	yes	complemented
62	C₂²⋊C₄×D₁₉	C₂²	1	6	yes	complemented
63	#10597324	C₂²	1	3	yes	complemented
64	#10597321	C₂²	1	3	yes	complemented
65	C₄×D₇₆	C₂²	1	3	yes	complemented
66	C₄×D₇₆	C₂²	1	3	yes	complemented
67	#10597318	C₂²	1	3	yes	complemented
68	C₂³×D₁₉	C₂³	1	3	yes	—
69	C₂³×D₁₉	C₂³	1	6	yes	—
70	#41×C₁₉	—	2	4	no	—
71	#41×C₁₉	—	2	4	no	—
72	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₁₉	C₂³	1	3	yes	—
74	C₂×D₄×C₁₉	C₂³	1	3	yes	—
75	C₂×D₄×C₁₉	C₂³	1	3	yes	—
76	C₂×D₄×C₁₉	C₂³	1	6	yes	—
77	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
78	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
82	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
84	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
85	C₂²×Dic₁₉	C₂³	1	3	yes	—
86	#64545	—	2	4	no	—
87	#64545	D₄	1	8	yes	complemented
88	Q₈×D₁₉	—	2	4	no	—
89	#64543	—	2	12	no	—
90	D₄×D₁₉	—	2	12	no	—
91	D₄×D₁₉	—	2	12	no	—
92	D₄×D₁₉	—	2	12	no	—
93	D₄×D₁₉	—	4	12	no	—
94	#64541	—	2	12	no	—
95	#64541	—	2	12	no	—
96	C₂×D₇₆	—	2	12	no	—
97	C₂×D₇₆	C₂³	1	3	yes	—
98	C₂×D₇₆	C₂³	1	3	yes	—
99	C₂×D₇₆	C₂³	1	3	yes	—
100	C₂×D₇₆	C₂³	1	3	yes	—
101	C₂×C₄×D₁₉	—	2	12	no	—
102	C₂×C₄×D₁₉	C₂³	1	3	yes	—
103	C₂×C₄×D₁₉	C₂³	1	3	yes	—
104	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₉	C₂³	1	3	yes	—
106	C₂×C₄×D₁₉	C₂³	1	6	yes	—
107	C₂×C₄×D₁₉	C₂³	1	3	yes	—
108	C₂×Dic₃₈	C₂³	1	3	yes	—
109	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
112	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
113	C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
114	C₄²×C₁₉	C₂³	1	3	yes	—
115	C₂²⋊Dic₁₉	C₂³	1	3	yes	—
116	C₂²⋊Dic₁₉	C₂³	1	6	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	3	yes	—
118	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
121	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
123	(C₂×D₁₉)⋊C₄	C₂³	1	6	yes	—
124	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
125	C₄⋊Dic₁₉	C₂³	1	3	yes	—
126	C₄⋊Dic₁₉	C₂³	1	3	yes	—
127	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
128	Dic₁₉⋊C₄	C₂³	1	3	yes	—
129	Dic₁₉⋊C₄	C₂³	1	3	yes	—
130	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₉	C₂³	1	3	yes	—
132	C₂³×C₁₉	C₂⁴	1	3	yes	—
133	C₂³×C₁₉	C₂⁴	1	3	yes	—
134	C₂²×D₁₉	—	2	6	no	—
135	C₂²×D₁₉	—	2	6	no	—
136	C₂²×D₁₉	—	2	12	no	—
137	C₂²×D₁₉	—	4	3	no	—
138	C₂²×D₁₉	—	4	6	no	—
139	C₂²×D₁₉	—	4	6	no	—
140	C₂²×D₁₉	C₂⁴	1	3	yes	—
141	C₂²×D₁₉	C₂⁴	1	3	yes	—
142	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
143	Q₈×C₁₉	C₂×D₄	1	4	yes	complemented
144	D₄×C₁₉	—	2	6	no	—
145	D₄×C₁₉	—	2	6	no	—
146	D₄×C₁₉	—	4	6	no	—
147	D₄×C₁₉	—	4	3	no	—
148	C₂×C₄×C₁₉	—	2	6	no	—
149	C₂×C₄×C₁₉	—	2	6	no	—
150	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
152	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
155	C₂²⋊D₁₉	—	2	6	no	—
156	C₂²⋊D₁₉	—	2	12	no	—
157	C₂²⋊D₁₉	—	2	6	no	—
158	C₂²⋊D₁₉	—	2	6	no	—
159	C₂²⋊D₁₉	—	4	6	no	—
160	C₂²⋊D₁₉	—	4	3	no	—
161	C₂×Dic₁₉	—	2	6	no	—
162	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₁₉	C₂⁴	1	3	yes	—
164	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×Dic₁₉	C₂⁴	1	3	yes	—
166	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
167	D₇₆	—	2	6	no	—
168	D₇₆	—	2	6	no	—
169	D₇₆	—	2	6	no	—
170	D₇₆	C₂×D₄	1	12	yes	complemented
171	C₄×D₁₉	—	2	6	no	—
172	C₄×D₁₉	—	2	6	no	—
173	C₄×D₁₉	—	2	6	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	4	6	no	—
176	C₄×D₁₉	C₂×D₄	1	12	yes	complemented
177	Dic₃₈	—	2	6	no	—
178	Dic₃₈	—	2	2	no	—
179	#3488	—	19	1	no	maximal, Sylow
180	C₂²×C₁₉	—	2	3	no	—
181	C₂²×C₁₉	—	2	3	no	—
182	C₂²×C₁₉	—	2	3	no	—
183	C₂²×C₁₉	—	2	3	no	—
184	C₂²×C₁₉	—	2	3	no	—
185	C₂²×C₁₉	—	2	3	no	—
186	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
187	C₂×D₁₉	—	2	1	no	—
188	C₂×D₁₉	—	2	3	no	—
189	C₂×D₁₉	—	2	1	no	—
190	C₂×D₁₉	—	2	3	no	—
191	C₂×D₁₉	—	2	3	no	—
192	C₂×D₁₉	—	2	3	no	—
193	C₂×D₁₉	—	2	3	no	—
194	C₂×D₁₉	—	4	12	no	—
195	C₂×D₁₉	—	8	12	no	—
196	C₂×D₁₉	C₂²×D₄	1	6	yes	—
197	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	complemented
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	3	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	C₂²×D₄	1	6	yes	—
203	Dic₁₉	—	2	3	no	—
204	Dic₁₉	—	2	1	no	—
205	Dic₁₉	—	2	3	no	—
206	Dic₁₉	—	2	1	no	—
207	Dic₁₉	C₂²×D₄	1	2	yes	—
208	C₂×H(5,𝔽₂)	—	19	1	no	—
209	C₂²×#41	—	19	1	no	—
210	#550	—	19	1	no	—
211	#550	D₁₉	1	1	yes	characteristic, complemented
212	#548	—	19	1	no	—
213	#548	—	19	1	no	—
214	#546	—	19	3	no	—
215	#546	—	19	3	no	—
216	D₄²	—	19	3	no	—
217	D₄²	—	19	3	no	—
218	#537	—	19	3	no	—
219	#535	—	19	3	no	—
220	#525	—	19	3	no	—
221	C₂×#121	—	19	3	no	—
222	#520	—	19	1	no	—
223	C₂×C₁₉	—	4	3	no	—
224	C₂×C₁₉	—	4	3	no	—
225	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
226	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₁₉	#585	1	1	yes	characteristic
228	D₁₉	—	2	2	no	—
229	D₁₉	—	2	6	no	—
230	D₁₉	—	4	3	no	—
231	H(5,𝔽₂)	—	38	8	no	—
232	C₂×#41	—	19	1	no	—
233	C₂×#41	—	19	1	no	—
234	C₂×#41	—	19	3	no	—
235	C₂×#41	—	19	3	no	—
236	C₂×#41	—	19	3	no	—
237	C₂×#41	—	38	8	no	—
238	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
239	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
240	C₂²×Q₈	—	19	1	no	—
241	C₂²×D₄	—	19	3	no	—
242	C₂²×D₄	—	19	3	no	—
243	C₂²×D₄	—	19	3	no	—
244	C₂²×D₄	—	19	6	no	—
245	C₂²×D₄	—	19	3	no	—
246	C₂³×C₄	—	19	3	no	—
247	#127	—	19	3	no	—
248	#127	C₂×D₁₉	1	3	yes	complemented
249	#124	—	19	3	no	—
250	#124	—	19	3	no	—
251	#123	—	19	3	no	—
252	#123	—	19	3	no	—
253	C₂²⋊Q₈	—	19	3	no	—
254	C₂²⋊Q₈	—	19	1	no	—
255	C₂²⋊Q₈	—	19	3	no	—
256	C₂²⋊Q₈	—	19	3	no	—
257	#121	—	19	3	no	—
258	#121	—	19	6	no	—
259	#121	—	19	3	no	—
260	#121	—	19	6	no	—
261	#121	—	19	3	no	—
262	#121	—	19	3	no	—
263	#121	—	19	3	no	—
264	#121	—	19	3	no	—
265	#121	—	19	6	no	—
266	#121	C₂×D₁₉	1	3	yes	complemented
267	#121	C₂×D₁₉	1	3	yes	complemented
268	#120	—	19	3	no	—
269	#120	—	19	6	no	—
270	#120	—	19	6	no	—
271	#120	—	19	3	no	—
272	C₄×Q₈	—	19	1	no	—
273	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
274	C₄×D₄	—	19	3	no	—
275	C₄×D₄	—	19	3	no	—
276	C₄×D₄	—	19	3	no	—
277	C₄×D₄	—	19	3	no	—
278	C₄×D₄	—	19	3	no	—
279	C₄×D₄	C₂×D₁₉	1	3	yes	complemented
280	#117	—	19	3	no	—
281	C₂×C₄⋊C₄	—	19	3	no	—
282	C₂×C₂²⋊C₄	—	19	6	no	—
283	C₁₉	#3488	1	1	yes	characteristic, complemented, Sylow
284	C₂⁴	—	19	3	no	—
285	C₂⁴	—	19	6	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	19	8	no	—
289	#41	—	38	12	no	—
290	#41	—	38	12	no	—
291	#41	—	38	12	no	—
292	#41	—	38	4	no	—
293	C₂×Q₈	—	19	1	no	—
294	C₂×Q₈	—	19	3	no	—
295	C₂×Q₈	—	38	4	no	—
296	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
297	C₂×D₄	—	19	3	no	—
298	C₂×D₄	—	19	6	no	—
299	C₂×D₄	—	19	3	no	—
300	C₂×D₄	—	19	3	no	—
301	C₂×D₄	—	19	3	no	—
302	C₂×D₄	—	19	6	no	—
303	C₂×D₄	—	19	3	no	—
304	C₂×D₄	—	19	3	no	—
305	C₂×D₄	—	19	3	no	—
306	C₂×D₄	—	19	3	no	—
307	C₂×D₄	—	38	12	no	—
308	C₂×D₄	—	38	12	no	—
309	C₂×D₄	—	38	12	no	—
310	C₂×D₄	—	38	12	no	—
311	C₂×D₄	—	76	12	no	—
312	C₂×D₄	C₂²×D₁₉	1	3	yes	—
313	C₂×D₄	C₂²×D₁₉	1	3	yes	—
314	C₂×D₄	C₂²×D₁₉	1	3	yes	—
315	C₂×D₄	C₂²×D₁₉	1	6	yes	—
316	C₂²×C₄	—	19	3	no	—
317	C₂²×C₄	—	19	3	no	—
318	C₂²×C₄	—	19	3	no	—
319	C₂²×C₄	—	19	3	no	—
320	C₂²×C₄	—	19	3	no	—
321	C₂²×C₄	—	19	1	no	—
322	C₂²×C₄	—	19	6	no	—
323	C₂²×C₄	—	38	12	no	—
324	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
325	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
326	C₄⋊C₄	—	19	3	no	—
327	C₄⋊C₄	—	19	1	no	—
328	C₄⋊C₄	—	19	1	no	—
329	C₄⋊C₄	—	19	3	no	—
330	C₄⋊C₄	—	19	3	no	—
331	C₄⋊C₄	—	19	3	no	—
332	C₄⋊C₄	C₂²×D₁₉	1	3	yes	—
333	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
334	C₂²⋊C₄	—	19	6	no	—
335	C₂²⋊C₄	—	19	3	no	—
336	C₂²⋊C₄	—	19	3	no	—
337	C₂²⋊C₄	—	19	3	no	—
338	C₂²⋊C₄	—	19	6	no	—
339	C₂²⋊C₄	—	19	3	no	—
340	C₂²⋊C₄	—	19	3	no	—
341	C₂²⋊C₄	—	19	1	no	—
342	C₂²⋊C₄	—	19	1	no	—
343	C₂²⋊C₄	—	19	3	no	—
344	C₂²⋊C₄	C₂²×D₁₉	1	3	yes	—
345	C₂²⋊C₄	C₂²×D₁₉	1	3	yes	—
346	C₄²	—	19	3	no	—
347	C₄²	C₂²×D₁₉	1	3	yes	—
348	C₂³	—	19	3	no	—
349	C₂³	—	19	1	no	—
350	C₂³	—	19	3	no	—
351	C₂³	—	38	6	no	—
352	C₂³	—	38	6	no	—
353	C₂³	—	38	12	no	—
354	C₂³	—	76	3	no	—
355	C₂³	—	76	6	no	—
356	C₂³	—	76	6	no	—
357	C₂³	C₂³×D₁₉	1	3	yes	—
358	C₂³	C₂³×D₁₉	1	3	yes	—
359	Q₈	—	38	2	no	—
360	Q₈	—	38	6	no	—
361	Q₈	D₄×D₁₉	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	4	6	no	—
365	D₄	—	4	3	no	—
366	D₄	—	19	12	no	—
367	D₄	—	38	6	no	—
368	D₄	—	38	6	no	—
369	D₄	—	38	6	no	—
370	D₄	—	38	6	no	—
371	D₄	—	38	12	no	—
372	D₄	—	38	6	no	—
373	D₄	—	38	6	no	—
374	D₄	—	76	6	no	—
375	D₄	—	76	3	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	19	1	no	—
379	C₂×C₄	—	19	12	no	—
380	C₂×C₄	—	19	1	no	—
381	C₂×C₄	—	19	3	no	—
382	C₂×C₄	—	19	3	no	—
383	C₂×C₄	—	19	1	no	—
384	C₂×C₄	—	38	2	no	—
385	C₂×C₄	—	38	6	no	—
386	C₂×C₄	—	38	6	no	—
387	C₂×C₄	—	38	6	no	—
388	C₂×C₄	—	38	6	no	—
389	C₂×C₄	—	76	6	no	—
390	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₉	1	3	yes	—
392	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₉	1	3	yes	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	19	6	no	—
402	C₂²	—	19	2	no	—
403	C₂²	—	38	1	no	—
404	C₂²	—	38	3	no	—
405	C₂²	—	38	1	no	—
406	C₂²	—	38	3	no	—
407	C₂²	—	38	3	no	—
408	C₂²	—	38	3	no	—
409	C₂²	—	38	3	no	—
410	C₂²	—	76	12	no	—
411	C₂²	—	152	12	no	—
412	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	19	2	no	—
418	C₄	—	38	1	no	—
419	C₄	—	38	3	no	—
420	C₄	—	38	3	no	—
421	C₄	—	38	1	no	—
422	C₄	C₂×D₄×D₁₉	1	6	yes	—
423	C₂	—	4	3	no	—
424	C₂	—	4	3	no	—
425	C₂	—	38	2	no	—
426	C₂	—	38	6	no	—
427	C₂	—	76	3	no	—
428	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic
429	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
430	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#550	C₂
hypercenter	#550	D₁₉
hypocenter	C₁₉	#3488
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. C₂×#10597435	C₂	semidirect
2. C₂×#41×D₁₉	C₂	semidirect
3. #11927213	C₂	semidirect
4. #11927206	C₂	semidirect
5. #11927201	C₂	semidirect
6. #11927191	C₂	semidirect
7. #11927190	C₂	semidirect
8. #11927179	C₂	semidirect
9. #11927178	C₂	semidirect
10. #11927123	C₂	semidirect
11. #11927107	C₂	semidirect
12. #11927053	C₂	semidirect
13. #121×D₁₉	C₂	semidirect
14. #11927026	C₂	semidirect
15. C₁₉×#550	C₂	semidirect
16. C₂×#41×C₁₉	C₂²	semidirect
17. C₂×#41×C₁₉	C₂²	semidirect
21. C₂×#64545	C₂²	semidirect
22. C₂×Q₈×D₁₉	C₂²	semidirect
23. C₂×#64543	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×D₄×D₁₉	C₂²	semidirect
27. C₂×D₄×D₁₉	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
30. C₂²×D₇₆	C₂²	semidirect
31. C₂²×C₄×D₁₉	C₂²	semidirect
32. C₁₉×#127	C₂²	semidirect
33. C₁₉×#121	C₂²	semidirect
34. C₁₉×#121	C₂²	semidirect
35. C₄×Q₈×C₁₉	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
37. Q₈×Dic₁₉	C₂²	semidirect
38. #10597386	C₂²	semidirect
39. #10597385	C₂²	semidirect
40. #10597385	C₂²	semidirect
41. #10597384	C₂²	semidirect
42. #10597384	C₂²	semidirect
43. #10597384	C₂²	semidirect
44. #10597383	C₂²	semidirect
45. #10597383	C₂²	semidirect
46. #10597383	C₂²	semidirect
47. #10597382	C₂²	semidirect
48. #10597376	C₂²	semidirect
49. C₄×C₂²⋊D₁₉	C₂²	semidirect
50. C₄×C₂²⋊D₁₉	C₂²	semidirect
51. #10597370	C₂²	semidirect
52. #10597343	C₂²	semidirect
53. #10597342	C₂²	semidirect
54. #10597341	C₂²	semidirect
55. #10597340	C₂²	semidirect
56. #10597339	C₂²	semidirect
57. C₄⋊C₄×D₁₉	C₂²	semidirect
58. #10597330	C₂²	semidirect
59. #10597330	C₂²	semidirect
60. #10597329	C₂²	semidirect
61. #10597328	C₂²	semidirect
62. C₂²⋊C₄×D₁₉	C₂²	semidirect
63. #10597324	C₂²	semidirect
64. #10597321	C₂²	semidirect
65. C₄×D₇₆	C₂²	semidirect
66. C₄×D₇₆	C₂²	semidirect
67. #10597318	C₂²	semidirect
87. #64545	D₄	semidirect
143. Q₈×C₁₉	C₂×D₄	semidirect
170. D₇₆	C₂×D₄	semidirect
176. C₄×D₁₉	C₂×D₄	semidirect
197. C₂×D₁₉	H(5,𝔽₂)	semidirect
211. #550	D₁₉	semidirect
238. C₂×#41	C₂×D₁₉	semidirect
239. C₂×#41	C₂×D₁₉	semidirect
248. #127	C₂×D₁₉	semidirect
266. #121	C₂×D₁₉	semidirect
267. #121	C₂×D₁₉	semidirect
273. C₄×Q₈	C₂×D₁₉	semidirect
279. C₄×D₄	C₂×D₁₉	semidirect
283. C₁₉	#3488	semidirect
361. Q₈	D₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597435	2
C₂×#41×D₁₉	2
#11927213	2
#11927206	2
#11927201	2
#11927191	2
#11927190	2
#11927179	2
#11927178	2
#11927123	2
#11927107	2
#11927053	2
#121×D₁₉	2
#11927026	2
C₁₉×#550	2
#3488	19