Subgroups — C₂×#135×D₁₉ #14578359

Order 2432.

1504 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₉	C₂	1	2	yes	maximal, complemented
2	C₂×#10597365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597350	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597362	C₂	1	2	yes	maximal, complemented
5	C₂×#10597396	C₂	1	2	yes	maximal, complemented
6	C₂×#10597358	C₂	1	1	yes	maximal, characteristic, complemented
7	#135×D₁₉	C₂	1	16	yes	maximal, direct product factor
8	C₂×Q₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×SD₁₆×D₁₉	C₂	1	2	yes	maximal, complemented
10	C₂×D₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
14	#41×D₁₉	—	2	8	no	—
15	#41×D₁₉	C₂²	1	16	yes	complemented
16	C₂×#64545	C₂²	1	2	yes	complemented
17	C₂×Q₈×D₁₉	C₂²	1	2	yes	—
18	C₂×#64543	—	2	2	no	—
19	C₂×#64543	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₉	—	2	2	no	—
21	C₂×D₄×D₁₉	C₂²	1	2	yes	—
22	C₂×#64541	—	2	2	no	—
23	C₂×#64541	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₁₉	—	2	2	no	—
25	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#135	C₂²	1	8	yes	complemented
27	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
29	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	#10597396	C₂²	1	16	yes	complemented
32	C₂×#64528	C₂²	1	2	yes	complemented
33	C₂×#64527	C₂²	1	2	yes	complemented
34	C₂×#64526	C₂²	1	2	yes	complemented
35	C₂×#64525	C₂²	1	2	yes	complemented
36	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	#10597365	C₂²	1	8	yes	complemented
38	Q₁₆×D₁₉	C₂²	1	8	yes	complemented
39	#10597362	C₂²	1	16	yes	complemented
40	SD₁₆×D₁₉	C₂²	1	16	yes	complemented
41	#10597358	C₂²	1	8	yes	complemented
42	D₈×D₁₉	C₂²	1	8	yes	complemented
43	C₂×Dic₇₆	C₂²	1	1	yes	characteristic, complemented
44	#10597350	C₂²	1	8	yes	complemented
45	C₂×D₁₅₂	C₂²	1	1	yes	characteristic, complemented
46	C₂×#64516	C₂²	1	2	yes	complemented
47	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
48	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₈×D₁₉	C₂²	1	8	yes	complemented
50	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
52	C₂³×D₁₉	—	2	2	no	—
53	C₂³×D₁₉	D₄	1	1	yes	characteristic
54	#41×C₁₉	—	2	4	no	—
55	#41×C₁₉	C₂³	1	8	yes	complemented
56	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊D₁₉	—	2	2	no	—
62	C₂×C₂²⋊D₁₉	—	2	2	no	—
63	C₂×C₂²⋊D₁₉	—	2	2	no	—
64	C₂²×Dic₁₉	—	2	2	no	—
65	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
66	#64545	—	2	4	no	—
67	#64545	C₂³	1	8	yes	complemented
68	Q₈×D₁₉	—	2	4	no	—
69	Q₈×D₁₉	C₂³	1	8	yes	—
70	#64543	—	2	16	no	—
71	#64543	—	2	4	no	—
72	#64543	C₂³	1	8	yes	complemented
73	D₄×D₁₉	—	2	16	no	—
74	D₄×D₁₉	—	2	4	no	—
75	D₄×D₁₉	C₂³	1	8	yes	—
76	#64541	—	2	4	no	—
77	#64541	—	2	16	no	—
78	#64541	C₂³	1	8	yes	complemented
79	C₂×D₇₆	—	2	2	no	—
80	C₂×D₇₆	C₂³	1	2	yes	—
81	C₂×C₄×D₁₉	—	2	2	no	—
82	C₂×C₄×D₁₉	—	2	2	no	—
83	C₂×C₄×D₁₉	—	2	2	no	—
84	C₂×C₄×D₁₉	—	2	16	no	—
85	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄×D₁₉	D₄	1	4	yes	—
88	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₁₉	C₂³	1	4	yes	—
91	C₂×Dic₃₈	—	2	2	no	—
92	C₂×Dic₃₈	C₂³	1	2	yes	—
93	Q₁₆×C₁₉	C₂³	1	4	yes	complemented
94	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
95	D₈×C₁₉	C₂³	1	4	yes	complemented
96	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₁₉	C₂³	1	4	yes	complemented
99	#64528	C₂³	1	8	yes	complemented
100	#64527	C₂³	1	8	yes	complemented
101	#64526	C₂³	1	8	yes	complemented
102	#64525	C₂³	1	8	yes	complemented
103	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	4	yes	complemented
106	Dic₇₆	C₂³	1	4	yes	complemented
107	D₁₅₂	C₂³	1	4	yes	complemented
108	#64516	C₂³	1	8	yes	complemented
109	C₈×D₁₉	C₂³	1	4	yes	—
110	C₈×D₁₉	C₂³	1	4	yes	—
111	C₈×D₁₉	C₂³	1	4	yes	complemented
112	C₈×D₁₉	C₂³	1	4	yes	complemented
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×D₁₉	—	2	4	no	—
116	C₂²×D₁₉	—	2	2	no	—
117	C₂²×D₁₉	—	2	8	no	—
118	C₂²×D₁₉	—	4	8	no	—
119	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×D₁₉	C₂×D₄	1	4	yes	—
121	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	2	no	—
123	Q₈×C₁₉	C₂⁴	1	4	yes	—
124	D₄×C₁₉	—	2	8	no	—
125	D₄×C₁₉	—	2	2	no	—
126	D₄×C₁₉	C₂⁴	1	4	yes	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	8	no	—
129	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
133	C₂²⋊D₁₉	—	2	8	no	—
134	C₂²⋊D₁₉	—	2	8	no	—
135	C₂²⋊D₁₉	—	2	8	no	—
136	C₂×Dic₁₉	—	2	2	no	—
137	C₂×Dic₁₉	—	2	8	no	—
138	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
141	D₇₆	—	2	8	no	—
142	D₇₆	—	2	2	no	—
143	D₇₆	C₂⁴	1	4	yes	—
144	C₄×D₁₉	—	2	8	no	—
145	C₄×D₁₉	—	2	8	no	—
146	C₄×D₁₉	—	2	8	no	—
147	C₄×D₁₉	C₂×D₄	1	4	yes	—
148	C₄×D₁₉	C₂×D₄	1	4	yes	—
149	C₄×D₁₉	C₂×D₄	1	2	yes	—
150	C₄×D₁₉	C₂×D₄	1	2	yes	—
151	C₄×D₁₉	C₂⁴	1	2	yes	—
152	C₄×D₁₉	C₂⁴	1	2	yes	—
153	Dic₃₈	—	2	2	no	—
154	Dic₃₈	—	2	8	no	—
155	Dic₃₈	C₂⁴	1	4	yes	—
156	C₈×C₁₉	C₂⁴	1	2	yes	—
157	C₈×C₁₉	C₂⁴	1	2	yes	—
158	C₁₉⋊C₈	C₂⁴	1	2	yes	—
159	C₁₉⋊C₈	C₂⁴	1	2	yes	—
160	C₂²×#135	—	19	1	no	maximal, Sylow
161	C₂²×C₁₉	—	2	2	no	—
162	C₂²×C₁₉	—	2	4	no	—
163	C₂²×C₁₉	—	4	4	no	—
164	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
165	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×D₁₉	—	2	2	no	—
167	C₂×D₁₉	—	2	8	no	—
168	C₂×D₁₉	—	2	4	no	—
169	C₂×D₁₉	—	4	4	no	—
170	C₂×D₁₉	—	4	16	no	—
171	C₂×D₁₉	#135	1	4	yes	direct product factor
172	C₂×D₁₉	C₂²×D₄	1	2	yes	—
173	C₂×D₁₉	C₂²×D₄	1	2	yes	—
174	C₄×C₁₉	—	2	4	no	—
175	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₄×C₁₉	C₂²×D₄	1	2	yes	—
177	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
178	Dic₁₉	—	2	4	no	—
179	Dic₁₉	C₂²×D₄	1	2	yes	—
180	Dic₁₉	C₂²×D₄	1	2	yes	—
181	C₂²×#41	—	19	2	no	—
182	C₂×#135	—	19	2	no	—
183	C₂×#135	—	19	16	no	—
184	C₂×#135	—	19	1	no	—
185	C₂×#135	—	19	2	no	—
186	C₂×#135	—	19	1	no	—
187	C₂×#135	—	19	1	no	—
188	C₂×#135	D₁₉	1	1	yes	characteristic, direct product factor
189	C₂²×Q₁₆	—	19	1	no	—
190	C₂²×SD₁₆	—	19	2	no	—
191	C₂²×D₈	—	19	1	no	—
192	C₂³×C₈	—	19	1	no	—
193	C₂×C₁₉	—	2	2	no	—
194	C₂×C₁₉	—	4	4	no	—
195	C₂×C₁₉	C₂×#135	1	2	yes	complemented
196	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
197	D₁₉	—	2	2	no	—
198	D₁₉	—	4	4	no	—
199	D₁₉	C₂×#135	1	4	yes	direct product factor
200	C₂×#41	—	19	16	no	—
201	C₂×#41	—	19	2	no	—
202	C₂×#41	—	19	2	no	—
203	C₂×#41	—	19	2	no	—
204	C₂×#41	—	38	2	no	—
205	C₂×#41	—	38	2	no	—
206	C₂×#41	—	38	8	no	—
207	C₂×#41	C₂×D₁₉	1	2	yes	complemented
208	C₂²×Q₈	—	19	2	no	—
209	C₂²×D₄	—	19	2	no	—
210	C₂²×D₄	—	38	2	no	—
211	C₂³×C₄	—	19	1	no	—
212	C₂³×C₄	—	38	2	no	—
213	#135	—	19	16	no	—
214	#135	—	19	8	no	—
215	#135	—	19	16	no	—
216	#135	—	19	8	no	—
217	#135	—	19	8	no	—
218	#135	C₂×D₁₉	1	8	yes	direct product factor
219	C₂×Q₁₆	—	19	2	no	—
220	C₂×Q₁₆	—	19	8	no	—
221	C₂×Q₁₆	—	19	1	no	—
222	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
223	C₂×SD₁₆	—	19	2	no	—
224	C₂×SD₁₆	—	19	2	no	—
225	C₂×SD₁₆	—	19	16	no	—
226	C₂×SD₁₆	—	19	2	no	—
227	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
228	C₂×D₈	—	19	2	no	—
229	C₂×D₈	—	19	8	no	—
230	C₂×D₈	—	19	1	no	—
231	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
232	C₂²×C₈	—	19	1	no	—
233	C₂²×C₈	—	19	1	no	—
234	C₂²×C₈	—	19	1	no	—
235	C₂²×C₈	—	19	1	no	—
236	C₂²×C₈	—	19	1	no	—
237	C₂²×C₈	—	19	8	no	—
238	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
239	C₁₉	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
240	C₂⁴	—	19	1	no	—
241	C₂⁴	—	38	2	no	—
242	#41	—	2	4	no	—
243	#41	—	19	8	no	—
244	#41	—	19	8	no	—
245	#41	—	19	8	no	—
246	#41	—	38	16	no	—
247	#41	—	38	16	no	—
248	#41	—	38	4	no	—
249	#41	—	38	4	no	—
250	#41	—	38	4	no	—
251	#41	C₂²×D₁₉	1	8	yes	complemented
252	C₂×Q₈	—	19	8	no	—
253	C₂×Q₈	—	19	2	no	—
254	C₂×Q₈	—	38	2	no	—
255	C₂×Q₈	—	38	4	no	—
256	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	19	8	no	—
259	C₂×D₄	—	19	2	no	—
260	C₂×D₄	—	38	2	no	—
261	C₂×D₄	—	38	4	no	—
262	C₂×D₄	—	38	2	no	—
263	C₂×D₄	—	38	16	no	—
264	C₂×D₄	—	38	2	no	—
265	C₂×D₄	—	38	2	no	—
266	C₂×D₄	C₂²×D₁₉	1	2	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	19	1	no	—
269	C₂²×C₄	—	19	4	no	—
270	C₂²×C₄	—	19	1	no	—
271	C₂²×C₄	—	19	1	no	—
272	C₂²×C₄	—	19	1	no	—
273	C₂²×C₄	—	19	1	no	—
274	C₂²×C₄	—	19	4	no	—
275	C₂²×C₄	—	38	2	no	—
276	C₂²×C₄	—	38	16	no	—
277	C₂²×C₄	—	38	2	no	—
278	C₂²×C₄	—	38	2	no	—
279	C₂²×C₄	—	38	2	no	—
280	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
281	Q₁₆	—	19	8	no	—
282	Q₁₆	—	19	4	no	—
283	Q₁₆	C₂²×D₁₉	1	4	yes	complemented
284	SD₁₆	—	19	8	no	—
285	SD₁₆	—	19	8	no	—
286	SD₁₆	—	19	8	no	—
287	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
288	D₈	—	19	8	no	—
289	D₈	—	19	4	no	—
290	D₈	C₂²×D₁₉	1	4	yes	complemented
291	C₂×C₈	—	19	1	no	—
292	C₂×C₈	—	19	1	no	—
293	C₂×C₈	—	19	4	no	—
294	C₂×C₈	—	19	4	no	—
295	C₂×C₈	—	19	4	no	—
296	C₂×C₈	—	19	4	no	—
297	C₂×C₈	—	19	4	no	—
298	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₉	1	4	yes	complemented
301	C₂³	—	2	2	no	—
302	C₂³	—	19	1	no	—
303	C₂³	—	19	4	no	—
304	C₂³	—	19	1	no	—
305	C₂³	—	38	4	no	—
306	C₂³	—	38	8	no	—
307	C₂³	—	38	2	no	—
308	C₂³	—	76	8	no	—
309	C₂³	D₄×D₁₉	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	19	4	no	—
312	Q₈	—	38	8	no	—
313	Q₈	—	38	2	no	—
314	Q₈	C₂³×D₁₉	1	4	yes	—
315	D₄	—	2	8	no	—
316	D₄	—	2	2	no	—
317	D₄	—	19	4	no	—
318	D₄	—	38	8	no	—
319	D₄	—	38	8	no	—
320	D₄	—	38	8	no	—
321	D₄	—	38	8	no	—
322	D₄	—	38	2	no	—
323	D₄	C₂³×D₁₉	1	4	yes	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	19	1	no	—
327	C₂×C₄	—	19	1	no	—
328	C₂×C₄	—	19	4	no	—
329	C₂×C₄	—	19	4	no	—
330	C₂×C₄	—	19	2	no	—
331	C₂×C₄	—	19	2	no	—
332	C₂×C₄	—	19	4	no	—
333	C₂×C₄	—	19	2	no	—
334	C₂×C₄	—	19	2	no	—
335	C₂×C₄	—	38	8	no	—
336	C₂×C₄	—	38	8	no	—
337	C₂×C₄	—	38	8	no	—
338	C₂×C₄	—	38	2	no	—
339	C₂×C₄	—	38	8	no	—
340	C₂×C₄	D₄×D₁₉	1	2	yes	—
341	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₁₉	1	2	yes	—
344	C₈	—	19	2	no	—
345	C₈	—	19	2	no	—
346	C₈	C₂³×D₁₉	1	2	yes	—
347	C₈	C₂³×D₁₉	1	2	yes	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	19	4	no	—
352	C₂²	—	19	2	no	—
353	C₂²	—	19	2	no	—
354	C₂²	—	38	8	no	—
355	C₂²	—	38	2	no	—
356	C₂²	—	38	4	no	—
357	C₂²	—	76	16	no	—
358	C₂²	—	76	4	no	—
359	C₂²	C₂×D₄×D₁₉	1	2	yes	—
360	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
361	C₄	—	2	4	no	—
362	C₄	—	19	2	no	—
363	C₄	—	19	2	no	—
364	C₄	—	38	4	no	—
365	C₄	C₂×D₄×D₁₉	1	2	yes	—
366	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
367	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
368	C₂	—	2	2	no	—
369	C₂	—	4	4	no	—
370	C₂	—	19	4	no	—
371	C₂	—	38	2	no	—
372	C₂	—	76	4	no	—
373	C₂	#135×D₁₉	1	2	yes	direct product factor
374	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#135	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×#135	D₁₉
hypocenter	C₁₉	C₂²×#135
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₉	C₂	semidirect
2. C₂×#10597365	C₂	semidirect
3. C₂×#10597350	C₂	semidirect
4. C₂×#10597362	C₂	semidirect
5. C₂×#10597396	C₂	semidirect
6. C₂×#10597358	C₂	semidirect
7. #135×D₁₉	C₂	direct (N × H)
8. C₂×Q₁₆×D₁₉	C₂	semidirect
9. C₂×SD₁₆×D₁₉	C₂	semidirect
10. C₂×D₈×D₁₉	C₂	semidirect
11. C₂²×C₈×D₁₉	C₂	semidirect
12. C₂×C₁₉×#135	C₂	semidirect
13. C₂×#41×C₁₉	C₂²	semidirect
15. #41×D₁₉	C₂²	semidirect
16. C₂×#64545	C₂²	semidirect
19. C₂×#64543	C₂²	semidirect
23. C₂×#64541	C₂²	semidirect
26. C₁₉×#135	C₂²	semidirect
27. C₂×Q₁₆×C₁₉	C₂²	semidirect
28. C₂×SD₁₆×C₁₉	C₂²	semidirect
29. C₂×D₈×C₁₉	C₂²	semidirect
30. C₂²×C₈×C₁₉	C₂²	semidirect
31. #10597396	C₂²	semidirect
32. C₂×#64528	C₂²	semidirect
33. C₂×#64527	C₂²	semidirect
34. C₂×#64526	C₂²	semidirect
35. C₂×#64525	C₂²	semidirect
36. C₂²×C₁₉⋊C₈	C₂²	semidirect
37. #10597365	C₂²	semidirect
38. Q₁₆×D₁₉	C₂²	semidirect
39. #10597362	C₂²	semidirect
40. SD₁₆×D₁₉	C₂²	semidirect
41. #10597358	C₂²	semidirect
42. D₈×D₁₉	C₂²	semidirect
43. C₂×Dic₇₆	C₂²	semidirect
44. #10597350	C₂²	semidirect
45. C₂×D₁₅₂	C₂²	semidirect
46. C₂×#64516	C₂²	semidirect
49. C₂×C₈×D₁₉	C₂²	semidirect
50. C₂×C₈×D₁₉	C₂²	semidirect
51. C₂×C₈×D₁₉	C₂²	semidirect
55. #41×C₁₉	C₂³	semidirect
67. #64545	C₂³	semidirect
72. #64543	C₂³	semidirect
78. #64541	C₂³	semidirect
93. Q₁₆×C₁₉	C₂³	semidirect
94. SD₁₆×C₁₉	C₂³	semidirect
95. D₈×C₁₉	C₂³	semidirect
98. C₂×C₈×C₁₉	C₂³	semidirect
99. #64528	C₂³	semidirect
100. #64527	C₂³	semidirect
101. #64526	C₂³	semidirect
102. #64525	C₂³	semidirect
105. C₂×C₁₉⋊C₈	C₂³	semidirect
106. Dic₇₆	C₂³	semidirect
107. D₁₅₂	C₂³	semidirect
108. #64516	C₂³	semidirect
111. C₈×D₁₉	C₂³	semidirect
112. C₈×D₁₉	C₂³	semidirect
171. C₂×D₁₉	#135	direct (N × H)
188. C₂×#135	D₁₉	direct (N × H)
195. C₂×C₁₉	C₂×#135	semidirect
199. D₁₉	C₂×#135	direct (N × H)
207. C₂×#41	C₂×D₁₉	semidirect
218. #135	C₂×D₁₉	direct (N × H)
222. C₂×Q₁₆	C₂×D₁₉	semidirect
227. C₂×SD₁₆	C₂×D₁₉	semidirect
231. C₂×D₈	C₂×D₁₉	semidirect
238. C₂²×C₈	C₂×D₁₉	semidirect
239. C₁₉	C₂²×#135	semidirect
251. #41	C₂²×D₁₉	semidirect
283. Q₁₆	C₂²×D₁₉	semidirect
287. SD₁₆	C₂²×D₁₉	semidirect
290. D₈	C₂²×D₁₉	semidirect
300. C₂×C₈	C₂²×D₁₉	semidirect
373. C₂	#135×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₉	2
C₂×#10597365	2
C₂×#10597350	2
C₂×#10597362	2
C₂×#10597396	2
C₂×#10597358	2
#135×D₁₉	2
C₂×Q₁₆×D₁₉	2
C₂×SD₁₆×D₁₉	2
C₂×D₈×D₁₉	2
C₂²×C₈×D₁₉	2
C₂×C₁₉×#135	2
C₂²×#135	19

Subgroups — C2×#135×D19 #14578359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#135×D₁₉ #14578359