Subgroups — C₁₉×#20609 #18026568

Order 4864.

4122 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2308	C₂	1	3	yes	maximal, complemented
4	C₁₉×#1790	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
6	C₂×C₁₉×H(5,𝔽₂)	—	2	6	no	—
7	C₂×C₁₉×H(5,𝔽₂)	C₄	1	8	yes	complemented
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
9	C₂²×#41×C₁₉	—	2	3	no	—
10	C₂³×D₄×C₁₉	—	2	3	no	—
11	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
14	C₂×C₁₉×#99	—	2	12	no	—
15	C₂×C₁₉×#99	C₂²	1	12	yes	complemented
16	C₁₉×#386	—	2	6	no	—
17	C₁₉×#386	C₂²	1	12	yes	complemented
18	C₁₉×#381	—	2	3	no	—
19	C₁₉×#379	—	2	3	no	—
20	C₂⁵×C₁₉	—	2	1	no	—
21	C₂⁵×C₁₉	D₄	1	3	yes	—
22	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
23	C₁₉×H(5,𝔽₂)	—	2	48	no	—
24	C₁₉×H(5,𝔽₂)	—	2	48	no	—
25	C₁₉×H(5,𝔽₂)	—	2	24	no	—
26	C₁₉×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
27	C₂×#41×C₁₉	—	2	12	no	—
28	C₂×#41×C₁₉	—	2	24	no	—
29	C₂×#41×C₁₉	—	2	24	no	—
30	C₂×#41×C₁₉	—	2	12	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	3	no	—
33	C₂²×D₄×C₁₉	—	2	12	no	—
34	C₂²×D₄×C₁₉	—	2	24	no	—
35	C₂²×D₄×C₁₉	—	2	24	no	—
36	C₂²×D₄×C₁₉	—	2	6	no	—
37	C₂²×D₄×C₁₉	—	2	12	no	—
38	C₂²×D₄×C₁₉	—	2	12	no	—
39	C₂²×D₄×C₁₉	—	2	6	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	12	yes	—
41	C₂²×D₄×C₁₉	D₄	1	12	yes	—
42	C₂²×D₄×C₁₉	D₄	1	6	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
44	C₂³×C₄×C₁₉	—	2	3	no	—
45	C₂³×C₄×C₁₉	—	2	3	no	—
46	C₂³×C₄×C₁₉	D₄	1	3	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	complemented
48	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
53	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	complemented
54	C₁₉×#99	—	2	24	no	—
55	C₁₉×#95	—	2	12	no	—
56	C₂⁴×C₁₉	—	2	4	no	—
57	C₂⁴×C₁₉	—	2	8	no	—
58	C₂⁴×C₁₉	—	2	3	no	—
59	C₂⁴×C₁₉	—	2	3	no	—
60	C₂⁴×C₁₉	—	2	6	no	—
61	C₂⁴×C₁₉	—	8	2	no	—
62	C₂⁴×C₁₉	—	8	6	no	—
63	C₂⁴×C₁₉	—	8	4	no	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	12	yes	complemented
65	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
66	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
67	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
68	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
69	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
70	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
71	#41×C₁₉	—	2	48	no	—
72	#41×C₁₉	—	2	96	no	—
73	#41×C₁₉	—	2	48	no	—
74	C₂×Q₈×C₁₉	—	2	4	no	—
75	C₂×Q₈×C₁₉	—	2	8	no	—
76	C₂×D₄×C₁₉	—	2	12	no	—
77	C₂×D₄×C₁₉	—	2	24	no	—
78	C₂×D₄×C₁₉	—	2	48	no	—
79	C₂×D₄×C₁₉	—	2	96	no	—
80	C₂×D₄×C₁₉	—	2	24	no	—
81	C₂×D₄×C₁₉	—	2	48	no	—
82	C₂×D₄×C₁₉	—	2	24	no	—
83	C₂×D₄×C₁₉	—	2	12	no	—
84	C₂×D₄×C₁₉	—	2	24	no	—
85	C₂×D₄×C₁₉	—	2	12	no	—
86	C₂×D₄×C₁₉	—	2	24	no	—
87	C₂×D₄×C₁₉	—	2	12	no	—
88	C₂×D₄×C₁₉	—	2	12	no	—
89	C₂×D₄×C₁₉	C₂²⋊C₄	1	24	yes	complemented
90	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
91	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
92	C₂²×C₄×C₁₉	—	2	12	no	—
93	C₂²×C₄×C₁₉	—	2	24	no	—
94	C₂²×C₄×C₁₉	—	2	3	no	—
95	C₂²×C₄×C₁₉	—	2	6	no	—
96	C₂²×C₄×C₁₉	—	2	3	no	—
97	C₂²×C₄×C₁₉	—	2	6	no	—
98	C₂²×C₄×C₁₉	—	2	6	no	—
99	C₂²×C₄×C₁₉	—	4	6	no	—
100	C₂²×C₄×C₁₉	—	8	2	no	—
101	C₂²×C₄×C₁₉	—	8	6	no	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	12	yes	complemented
103	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
104	C₂²⋊C₄×C₁₉	—	2	12	no	—
105	C₂²⋊C₄×C₁₉	—	4	6	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	3	no	—
108	C₂²⋊C₄×C₁₉	—	8	12	no	—
109	#20609	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	—	2	16	no	—
111	C₂³×C₁₉	—	2	6	no	—
112	C₂³×C₁₉	—	2	12	no	—
113	C₂³×C₁₉	—	2	6	no	—
114	C₂³×C₁₉	—	2	12	no	—
115	C₂³×C₁₉	—	4	6	no	—
116	C₂³×C₁₉	—	4	2	no	—
117	C₂³×C₁₉	—	4	6	no	—
118	C₂³×C₁₉	—	4	12	no	—
119	C₂³×C₁₉	—	4	12	no	—
120	C₂³×C₁₉	—	8	6	no	—
121	C₂³×C₁₉	—	8	2	no	—
122	C₂³×C₁₉	—	8	6	no	—
123	C₂³×C₁₉	—	8	12	no	—
124	C₂³×C₁₉	—	8	12	no	—
125	C₂³×C₁₉	—	8	16	no	—
126	C₂³×C₁₉	—	8	8	no	—
127	C₂³×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
128	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
130	C₂³×C₁₉	#120	1	1	yes	characteristic
131	C₂³×C₁₉	#120	1	3	yes	—
132	C₂³×C₁₉	#120	1	6	yes	—
133	C₂³×C₁₉	#120	1	6	yes	—
134	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
135	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
136	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
137	Q₈×C₁₉	—	2	16	no	—
138	D₄×C₁₉	—	2	48	no	—
139	D₄×C₁₉	—	2	24	no	—
140	D₄×C₁₉	—	2	24	no	—
141	D₄×C₁₉	—	2	48	no	—
142	C₂×C₄×C₁₉	—	2	48	no	—
143	C₂×C₄×C₁₉	—	2	6	no	—
144	C₂×C₄×C₁₉	—	2	6	no	—
145	C₂×C₄×C₁₉	—	2	12	no	—
146	C₂×C₄×C₁₉	—	2	12	no	—
147	C₂×C₄×C₁₉	—	4	12	no	—
148	C₂×C₄×C₁₉	—	4	12	no	—
149	C₂×C₄×C₁₉	—	4	6	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	8	12	no	—
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
153	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
154	C₂²×#99	C₂×C₁₉	1	3	yes	complemented
155	#2308	C₂×C₁₉	1	3	yes	complemented
156	#1790	C₂×C₁₉	1	8	yes	complemented
157	C₂²×C₁₉	—	2	6	no	—
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	—	2	6	no	—
160	C₂²×C₁₉	—	2	12	no	—
161	C₂²×C₁₉	—	4	6	no	—
162	C₂²×C₁₉	—	4	6	no	—
163	C₂²×C₁₉	—	4	6	no	—
164	C₂²×C₁₉	—	4	6	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	—	4	3	no	—
167	C₂²×C₁₉	—	4	12	no	—
168	C₂²×C₁₉	—	4	24	no	—
169	C₂²×C₁₉	—	4	12	no	—
170	C₂²×C₁₉	—	8	6	no	—
171	C₂²×C₁₉	—	8	12	no	—
172	C₂²×C₁₉	—	8	16	no	—
173	C₂²×C₁₉	#379	1	2	yes	—
174	C₂²×C₁₉	#379	1	6	yes	—
175	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	3	yes	—
176	C₂²×C₁₉	C₂×#120	1	3	yes	—
177	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
178	C₄×C₁₉	—	2	12	no	—
179	C₄×C₁₉	—	8	6	no	—
180	C₄×C₁₉	—	8	2	no	—
181	C₂×H(5,𝔽₂)	—	2	12	no	—
182	C₂×H(5,𝔽₂)	—	2	6	no	—
183	C₂×H(5,𝔽₂)	C₄×C₁₉	1	8	yes	complemented
184	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
185	C₂²×#41	—	2	3	no	—
186	C₂³×D₄	—	2	3	no	—
187	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
189	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
190	C₂×#99	—	2	12	no	—
191	C₂×#99	C₂²×C₁₉	1	12	yes	complemented
192	#386	—	2	6	no	—
193	#386	C₂²×C₁₉	1	12	yes	complemented
194	#381	—	2	3	no	—
195	#379	—	2	3	no	—
196	C₂×C₁₉	—	2	3	no	—
197	C₂×C₁₉	—	2	2	no	—
198	C₂×C₁₉	—	2	3	no	—
199	C₂×C₁₉	—	2	6	no	—
200	C₂×C₁₉	—	4	12	no	—
201	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
202	C₂×C₁₉	#3026	1	2	yes	—
203	C₂⁵	—	2	1	no	—
204	C₂⁵	D₄×C₁₉	1	3	yes	—
205	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
206	H(5,𝔽₂)	—	2	48	no	—
207	H(5,𝔽₂)	—	2	48	no	—
208	H(5,𝔽₂)	—	2	24	no	—
209	H(5,𝔽₂)	C₂×C₄×C₁₉	1	16	yes	complemented
210	C₂×#41	—	2	24	no	—
211	C₂×#41	—	2	12	no	—
212	C₂×#41	—	2	24	no	—
213	C₂×#41	—	2	12	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	3	no	—
216	C₂²×D₄	—	2	24	no	—
217	C₂²×D₄	—	2	12	no	—
218	C₂²×D₄	—	2	24	no	—
219	C₂²×D₄	—	2	6	no	—
220	C₂²×D₄	—	2	12	no	—
221	C₂²×D₄	—	2	12	no	—
222	C₂²×D₄	—	2	6	no	—
223	C₂²×D₄	C₂×C₄×C₁₉	1	12	yes	—
224	C₂²×D₄	D₄×C₁₉	1	12	yes	—
225	C₂²×D₄	D₄×C₁₉	1	6	yes	—
226	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
227	C₂³×C₄	—	2	3	no	—
228	C₂³×C₄	—	2	3	no	—
229	C₂³×C₄	D₄×C₁₉	1	3	yes	—
230	C₂³×C₄	C₂³×C₁₉	1	2	yes	complemented
231	C₂×C₂²⋊C₄	—	2	12	no	—
232	C₂×C₂²⋊C₄	—	2	3	no	—
233	C₂×C₂²⋊C₄	—	2	3	no	—
234	C₂×C₂²⋊C₄	—	2	3	no	—
235	C₂×C₂²⋊C₄	—	2	12	no	—
236	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	complemented
237	#99	—	2	24	no	—
238	#95	—	2	12	no	—
239	C₁₉	#20609	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	—	2	8	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	3	no	—
243	C₂⁴	—	2	6	no	—
244	C₂⁴	—	2	3	no	—
245	C₂⁴	—	8	2	no	—
246	C₂⁴	—	8	6	no	—
247	C₂⁴	—	8	4	no	—
248	C₂⁴	C₂²⋊C₄×C₁₉	1	12	yes	complemented
249	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
250	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
251	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
252	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
253	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
254	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
255	#41	—	2	96	no	—
256	#41	—	2	48	no	—
257	#41	—	2	48	no	—
258	C₂×Q₈	—	2	8	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×D₄	—	2	24	no	—
261	C₂×D₄	—	2	12	no	—
262	C₂×D₄	—	2	96	no	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	—	2	24	no	—
265	C₂×D₄	—	2	48	no	—
266	C₂×D₄	—	2	24	no	—
267	C₂×D₄	—	2	24	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	—	2	12	no	—
271	C₂×D₄	—	2	12	no	—
272	C₂×D₄	—	2	12	no	—
273	C₂×D₄	C₂²⋊C₄×C₁₉	1	24	yes	complemented
274	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
275	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
276	C₂²×C₄	—	2	24	no	—
277	C₂²×C₄	—	2	12	no	—
278	C₂²×C₄	—	2	3	no	—
279	C₂²×C₄	—	2	6	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	6	no	—
282	C₂²×C₄	—	2	6	no	—
283	C₂²×C₄	—	4	6	no	—
284	C₂²×C₄	—	8	2	no	—
285	C₂²×C₄	—	8	6	no	—
286	C₂²×C₄	C₂²⋊C₄×C₁₉	1	12	yes	complemented
287	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
288	C₂²⋊C₄	—	2	12	no	—
289	C₂²⋊C₄	—	4	6	no	—
290	C₂²⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	3	no	—
292	C₂²⋊C₄	—	8	12	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	12	no	—
295	C₂³	—	2	6	no	—
296	C₂³	—	2	12	no	—
297	C₂³	—	2	6	no	—
298	C₂³	—	4	6	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	6	no	—
301	C₂³	—	4	12	no	—
302	C₂³	—	4	12	no	—
303	C₂³	—	8	6	no	—
304	C₂³	—	8	2	no	—
305	C₂³	—	8	6	no	—
306	C₂³	—	8	12	no	—
307	C₂³	—	8	12	no	—
308	C₂³	—	8	16	no	—
309	C₂³	—	8	8	no	—
310	C₂³	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
311	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
312	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
313	C₂³	C₁₉×#120	1	1	yes	characteristic
314	C₂³	C₁₉×#120	1	3	yes	—
315	C₂³	C₁₉×#120	1	6	yes	—
316	C₂³	C₁₉×#120	1	6	yes	—
317	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
318	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
319	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
320	Q₈	—	2	16	no	—
321	D₄	—	2	48	no	—
322	D₄	—	2	48	no	—
323	D₄	—	2	24	no	—
324	D₄	—	2	24	no	—
325	C₂×C₄	—	2	48	no	—
326	C₂×C₄	—	2	12	no	—
327	C₂×C₄	—	2	12	no	—
328	C₂×C₄	—	2	6	no	—
329	C₂×C₄	—	2	6	no	—
330	C₂×C₄	—	4	12	no	—
331	C₂×C₄	—	4	12	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	12	no	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
336	C₂²	—	2	6	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	6	no	—
339	C₂²	—	2	12	no	—
340	C₂²	—	4	6	no	—
341	C₂²	—	4	6	no	—
342	C₂²	—	4	6	no	—
343	C₂²	—	4	6	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	3	no	—
346	C₂²	—	4	12	no	—
347	C₂²	—	4	24	no	—
348	C₂²	—	4	12	no	—
349	C₂²	—	8	6	no	—
350	C₂²	—	8	12	no	—
351	C₂²	—	8	16	no	—
352	C₂²	C₁₉×#379	1	2	yes	—
353	C₂²	C₁₉×#379	1	6	yes	—
354	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	3	yes	—
355	C₂²	C₂×C₁₉×#120	1	3	yes	—
356	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
357	C₄	—	2	12	no	—
358	C₄	—	8	6	no	—
359	C₄	—	8	2	no	—
360	C₂	—	2	3	no	—
361	C₂	—	2	2	no	—
362	C₂	—	2	3	no	—
363	C₂	—	2	6	no	—
364	C₂	—	4	12	no	—
365	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
366	C₂	C₁₉×#3026	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#99	C₂	semidirect
3. C₁₉×#2308	C₂	semidirect
4. C₁₉×#1790	C₂	semidirect
7. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
12. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
13. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
15. C₂×C₁₉×#99	C₂²	semidirect
17. C₁₉×#386	C₂²	semidirect
26. C₁₉×H(5,𝔽₂)	C₂×C₄	semidirect
47. C₂³×C₄×C₁₉	C₂³	semidirect
53. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
64. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
89. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
102. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
109. #20609	C₁₉	direct (N × H)
154. C₂²×#99	C₂×C₁₉	semidirect
155. #2308	C₂×C₁₉	semidirect
156. #1790	C₂×C₁₉	semidirect
183. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
188. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
189. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
191. C₂×#99	C₂²×C₁₉	semidirect
193. #386	C₂²×C₁₉	semidirect
209. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
230. C₂³×C₄	C₂³×C₁₉	semidirect
236. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
239. C₁₉	#20609	direct (N × H)
248. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
273. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
286. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×H(5,𝔽₂)	2
C₂²×C₁₉×#99	2
C₁₉×#2308	2
C₁₉×#1790	2
#20609	19

Subgroups — C19×#20609 #18026568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20609 #18026568