Subgroups — C₂×#11927343 #14578381

Order 2432.

1484 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	C₂²×#64545	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927343	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10597364	C₂	1	2	yes	maximal, complemented
5	C₂×#10597388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10597360	C₂	1	2	yes	maximal, complemented
8	C₂×#10597395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10597365	C₂	1	2	yes	maximal, complemented
10	C₂×#10597362	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	#41×D₁₉	—	2	4	no	—
16	#41×D₁₉	C₂²	1	8	yes	complemented
17	C₂×#64545	—	2	1	no	—
18	C₂×#64545	—	2	1	no	—
19	C₂×#64545	—	2	4	no	—
20	C₂×#64545	C₂²	1	2	yes	—
21	C₂×#64545	C₂²	1	2	yes	complemented
22	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
23	C₂×#64545	C₂²	1	8	yes	complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#64543	—	2	1	no	—
26	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₉	—	2	1	no	—
28	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64541	—	2	1	no	—
30	C₂×#64541	C₂²	1	1	yes	characteristic
31	C₂²×D₇₆	—	2	1	no	—
32	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₁₉	—	2	1	no	—
34	C₂²×C₄×D₁₉	—	2	1	no	—
35	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#137	C₂²	1	8	yes	complemented
37	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
38	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
39	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	#10597395	C₂²	1	8	yes	complemented
41	C₂×#64528	C₂²	1	2	yes	complemented
42	#10597388	C₂²	1	8	yes	complemented
43	C₂×#64527	C₂²	1	2	yes	complemented
44	C₂×#64527	C₂²	1	2	yes	complemented
45	C₂×#64525	C₂²	1	2	yes	complemented
46	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
47	#10597365	C₂²	1	16	yes	complemented
48	#10597364	C₂²	1	16	yes	complemented
49	#10597362	C₂²	1	16	yes	complemented
50	#10597360	C₂²	1	16	yes	complemented
51	#10597354	C₂²	1	8	yes	complemented
52	M₁₆×D₁₉	C₂²	1	8	yes	complemented
53	C₂×D₁₅₂	C₂²	1	2	yes	complemented
54	C₂×#64516	C₂²	1	2	yes	complemented
55	C₂×#64515	C₂²	1	2	yes	complemented
56	C₂×C₈×D₁₉	C₂²	1	2	yes	complemented
57	C₂³×D₁₉	—	2	1	no	—
58	C₂³×D₁₉	—	2	1	no	—
59	C₂³×D₁₉	D₄	1	1	yes	characteristic
60	#41×C₁₉	—	2	2	no	—
61	#41×C₁₉	C₂³	1	4	yes	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
66	C₂×Q₈×C₁₉	C₂³	1	4	yes	complemented
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
77	#64545	—	2	4	no	—
78	#64545	—	2	8	no	—
79	#64545	—	2	8	no	—
80	#64545	—	2	4	no	—
81	#64545	—	2	2	no	—
82	#64545	C₂³	1	8	yes	—
83	#64545	C₂³	1	8	yes	complemented
84	#64545	C₂³	1	4	yes	complemented
85	Q₈×D₁₉	—	2	2	no	—
86	Q₈×D₁₉	C₂³	1	4	yes	complemented
87	#64543	—	2	8	no	—
88	#64543	—	2	2	no	—
89	#64543	C₂³	1	4	yes	complemented
90	D₄×D₁₉	—	2	8	no	—
91	D₄×D₁₉	—	2	2	no	—
92	D₄×D₁₉	C₂³	1	4	yes	complemented
93	#64541	—	2	2	no	—
94	#64541	—	2	8	no	—
95	#64541	C₂³	1	4	yes	—
96	C₂×D₇₆	—	2	2	no	—
97	C₂×D₇₆	—	2	8	no	—
98	C₂×D₇₆	—	2	2	no	—
99	C₂×D₇₆	—	2	1	no	—
100	C₂×D₇₆	—	2	2	no	—
101	C₂×D₇₆	—	2	1	no	—
102	C₂×D₇₆	C₂³	1	2	yes	—
103	C₂×D₇₆	C₂³	1	1	yes	characteristic
104	C₂×D₇₆	C₂³	1	4	yes	complemented
105	C₂×C₄×D₁₉	—	2	1	no	—
106	C₂×C₄×D₁₉	—	2	1	no	—
107	C₂×C₄×D₁₉	—	2	1	no	—
108	C₂×C₄×D₁₉	—	2	2	no	—
109	C₂×C₄×D₁₉	—	2	8	no	—
110	C₂×C₄×D₁₉	—	2	2	no	—
111	C₂×C₄×D₁₉	—	2	8	no	—
112	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄×D₁₉	D₄	1	4	yes	—
115	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₁₉	C₂³	1	4	yes	—
118	C₂×Dic₃₈	—	2	1	no	—
119	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
120	Q₁₆×C₁₉	C₂³	1	8	yes	complemented
121	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
122	M₁₆×C₁₉	C₂³	1	4	yes	complemented
123	C₂×C₈×C₁₉	C₂³	1	2	yes	—
124	#64528	C₂³	1	8	yes	complemented
125	#64527	C₂³	1	8	yes	complemented
126	#64527	C₂³	1	8	yes	complemented
127	#64525	C₂³	1	8	yes	complemented
128	#64520	C₂³	1	4	yes	complemented
129	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
130	D₁₅₂	C₂³	1	8	yes	complemented
131	#64516	C₂³	1	8	yes	complemented
132	#64515	C₂³	1	8	yes	complemented
133	C₈×D₁₉	C₂³	1	8	yes	complemented
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×D₁₉	—	2	2	no	—
137	C₂²×D₁₉	—	2	4	no	—
138	C₂²×D₁₉	—	2	1	no	—
139	C₂²×D₁₉	—	2	4	no	—
140	C₂²×D₁₉	—	4	2	no	—
141	C₂²×D₁₉	—	4	4	no	—
142	C₂²×D₁₉	—	4	4	no	—
143	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×D₁₉	C₂×D₄	1	4	yes	—
146	Q₈×C₁₉	—	2	1	no	—
147	Q₈×C₁₉	—	2	2	no	—
148	Q₈×C₁₉	—	2	4	no	—
149	Q₈×C₁₉	C₂⁴	1	2	yes	—
150	Q₈×C₁₉	C₂⁴	1	4	yes	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	2	1	no	—
153	D₄×C₁₉	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
162	C₂²⋊D₁₉	—	2	4	no	—
163	C₂²⋊D₁₉	—	2	4	no	—
164	C₂²⋊D₁₉	—	2	4	no	—
165	C₂×Dic₁₉	—	2	1	no	—
166	C₂×Dic₁₉	—	2	4	no	—
167	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
170	D₇₆	—	2	8	no	—
171	D₇₆	—	2	8	no	—
172	D₇₆	—	2	4	no	—
173	D₇₆	—	2	2	no	—
174	D₇₆	—	2	4	no	—
175	D₇₆	—	2	1	no	—
176	D₇₆	C₂⁴	1	4	yes	—
177	D₇₆	C₂⁴	1	2	yes	—
178	C₄×D₁₉	—	2	4	no	—
179	C₄×D₁₉	—	2	4	no	—
180	C₄×D₁₉	—	2	4	no	—
181	C₄×D₁₉	—	2	8	no	—
182	C₄×D₁₉	—	2	8	no	—
183	C₄×D₁₉	C₂×D₄	1	4	yes	—
184	C₄×D₁₉	C₂×D₄	1	4	yes	—
185	C₄×D₁₉	C₂×D₄	1	2	yes	—
186	C₄×D₁₉	C₂×D₄	1	2	yes	—
187	C₄×D₁₉	C₂⁴	1	2	yes	—
188	C₄×D₁₉	C₂⁴	1	2	yes	—
189	Dic₃₈	—	2	1	no	—
190	Dic₃₈	—	2	4	no	—
191	Dic₃₈	C₂⁴	1	2	yes	—
192	C₈×C₁₉	C₂⁴	1	4	yes	—
193	C₁₉⋊C₈	C₂⁴	1	4	yes	—
194	C₂×#575	—	19	1	no	maximal, Sylow
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
199	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×D₁₉	—	2	2	no	—
201	C₂×D₁₉	—	2	2	no	—
202	C₂×D₁₉	—	2	4	no	—
203	C₂×D₁₉	—	2	2	no	—
204	C₂×D₁₉	—	4	4	no	—
205	C₂×D₁₉	—	4	8	no	—
206	C₂×D₁₉	—	4	8	no	—
207	C₂×D₁₉	—	4	4	no	—
208	C₂×D₁₉	—	4	2	no	—
209	C₂×D₁₉	C₂²×D₄	1	2	yes	—
210	C₂×D₁₉	C₂²×D₄	1	2	yes	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	4	no	—
213	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₄×C₁₉	C₂²×D₄	1	2	yes	—
215	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
216	Dic₁₉	—	2	2	no	—
217	Dic₁₉	C₂²×D₄	1	2	yes	—
218	Dic₁₉	C₂²×D₄	1	2	yes	—
219	C₂²×#41	—	19	1	no	—
220	C₂²×#41	—	19	1	no	—
221	#575	—	19	16	no	—
222	C₂×#137	—	19	1	no	—
223	C₂×#137	—	19	2	no	—
224	C₂×#137	D₁₉	1	1	yes	characteristic, complemented
225	C₂×AGL(1,ℤ/8)	—	19	1	no	—
226	C₂×AGL(1,ℤ/8)	—	19	2	no	—
227	C₂×AGL(1,ℤ/8)	—	19	1	no	—
228	C₂×#135	—	19	2	no	—
229	C₂×#135	—	19	2	no	—
230	C₂²×M₁₆	—	19	1	no	—
231	C₂×C₁₉	—	2	2	no	—
232	C₂×C₁₉	—	4	2	no	—
233	C₂×C₁₉	#575	1	2	yes	complemented
234	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
235	D₁₉	—	2	2	no	—
236	D₁₉	—	2	2	no	—
237	D₁₉	—	4	4	no	—
238	D₁₉	—	4	2	no	—
239	C₂×#41	—	19	8	no	—
240	C₂×#41	—	19	2	no	—
241	C₂×#41	—	19	1	no	—
242	C₂×#41	—	19	2	no	—
243	C₂×#41	—	19	8	no	—
244	C₂×#41	—	19	1	no	—
245	C₂×#41	—	19	1	no	—
246	C₂×#41	—	38	1	no	—
247	C₂×#41	—	38	1	no	—
248	C₂×#41	—	38	1	no	—
249	C₂×#41	—	38	4	no	—
250	C₂×#41	—	38	1	no	—
251	C₂×#41	—	38	4	no	—
252	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
253	C₂²×Q₈	—	19	1	no	—
254	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
255	C₂²×D₄	—	19	1	no	—
256	C₂²×D₄	—	19	1	no	—
257	C₂²×D₄	—	38	1	no	—
258	C₂²×D₄	—	38	1	no	—
259	C₂³×C₄	—	19	1	no	—
260	C₂³×C₄	—	38	1	no	—
261	C₂³×C₄	—	38	1	no	—
262	#137	—	19	8	no	—
263	#137	—	19	16	no	—
264	#137	C₂×D₁₉	1	8	yes	complemented
265	AGL(1,ℤ/8)	—	19	8	no	—
266	AGL(1,ℤ/8)	—	19	16	no	—
267	AGL(1,ℤ/8)	—	19	8	no	—
268	#135	—	19	16	no	—
269	#135	—	19	16	no	—
270	C₂×Q₁₆	—	19	2	no	—
271	C₂×Q₁₆	C₂×D₁₉	1	2	yes	complemented
272	C₂×SD₁₆	—	19	2	no	—
273	C₂×SD₁₆	—	19	2	no	—
274	C₂×SD₁₆	—	19	2	no	—
275	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
276	C₂×D₈	—	19	2	no	—
277	C₂×D₈	—	19	2	no	—
278	C₂×M₁₆	—	19	1	no	—
279	C₂×M₁₆	—	19	8	no	—
280	C₂×M₁₆	—	19	2	no	—
281	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₈	—	19	2	no	—
283	C₁₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
284	C₂⁴	—	19	1	no	—
285	C₂⁴	—	38	1	no	—
286	C₂⁴	—	38	1	no	—
287	#41	—	2	2	no	—
288	#41	—	19	8	no	—
289	#41	—	19	4	no	—
290	#41	—	19	8	no	—
291	#41	—	19	4	no	—
292	#41	—	19	4	no	—
293	#41	—	38	8	no	—
294	#41	—	38	8	no	—
295	#41	—	38	2	no	—
296	#41	—	38	8	no	—
297	#41	—	38	4	no	—
298	#41	—	38	4	no	—
299	#41	—	38	8	no	—
300	#41	—	38	2	no	—
301	#41	—	38	2	no	—
302	#41	C₂²×D₁₉	1	4	yes	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	19	4	no	—
306	C₂×Q₈	—	19	1	no	—
307	C₂×Q₈	—	38	1	no	—
308	C₂×Q₈	—	38	2	no	—
309	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
311	C₂×Q₈	C₂²×D₁₉	1	4	yes	complemented
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	19	4	no	—
314	C₂×D₄	—	19	2	no	—
315	C₂×D₄	—	19	1	no	—
316	C₂×D₄	—	19	4	no	—
317	C₂×D₄	—	38	8	no	—
318	C₂×D₄	—	38	1	no	—
319	C₂×D₄	—	38	2	no	—
320	C₂×D₄	—	38	2	no	—
321	C₂×D₄	—	38	2	no	—
322	C₂×D₄	—	38	1	no	—
323	C₂×D₄	—	38	8	no	—
324	C₂×D₄	—	38	1	no	—
325	C₂×D₄	—	38	1	no	—
326	C₂×D₄	—	38	2	no	—
327	C₂×D₄	—	38	1	no	—
328	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	19	1	no	—
332	C₂²×C₄	—	19	1	no	—
333	C₂²×C₄	—	19	4	no	—
334	C₂²×C₄	—	19	1	no	—
335	C₂²×C₄	—	19	1	no	—
336	C₂²×C₄	—	19	1	no	—
337	C₂²×C₄	—	19	4	no	—
338	C₂²×C₄	—	38	8	no	—
339	C₂²×C₄	—	38	1	no	—
340	C₂²×C₄	—	38	2	no	—
341	C₂²×C₄	—	38	2	no	—
342	C₂²×C₄	—	38	8	no	—
343	C₂²×C₄	—	38	1	no	—
344	C₂²×C₄	—	38	1	no	—
345	C₂²×C₄	—	38	1	no	—
346	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
347	Q₁₆	—	19	8	no	—
348	Q₁₆	C₂²×D₁₉	1	8	yes	complemented
349	SD₁₆	—	19	8	no	—
350	SD₁₆	—	19	8	no	—
351	SD₁₆	—	19	8	no	—
352	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
353	D₈	—	19	8	no	—
354	D₈	—	19	8	no	—
355	M₁₆	—	19	4	no	—
356	M₁₆	—	19	8	no	—
357	M₁₆	C₂²×D₁₉	1	4	yes	complemented
358	C₂×C₈	—	19	2	no	—
359	C₂×C₈	—	19	8	no	—
360	C₂×C₈	C₂²×D₁₉	1	2	yes	—
361	C₂³	—	2	1	no	—
362	C₂³	—	19	1	no	—
363	C₂³	—	19	1	no	—
364	C₂³	—	19	4	no	—
365	C₂³	—	38	4	no	—
366	C₂³	—	38	4	no	—
367	C₂³	—	38	2	no	—
368	C₂³	—	38	1	no	—
369	C₂³	—	76	2	no	—
370	C₂³	—	76	4	no	—
371	C₂³	—	76	4	no	—
372	C₂³	D₄×D₁₉	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	19	2	no	—
377	Q₈	—	38	4	no	—
378	Q₈	—	38	1	no	—
379	Q₈	C₂³×D₁₉	1	2	yes	—
380	Q₈	C₂³×D₁₉	1	4	yes	—
381	D₄	—	2	4	no	—
382	D₄	—	2	1	no	—
383	D₄	—	19	4	no	—
384	D₄	—	19	2	no	—
385	D₄	—	38	4	no	—
386	D₄	—	38	8	no	—
387	D₄	—	38	8	no	—
388	D₄	—	38	4	no	—
389	D₄	—	38	4	no	—
390	D₄	—	38	4	no	—
391	D₄	—	38	4	no	—
392	D₄	—	38	1	no	—
393	D₄	—	38	2	no	—
394	D₄	C₂³×D₁₉	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	19	4	no	—
400	C₂×C₄	—	19	1	no	—
401	C₂×C₄	—	19	1	no	—
402	C₂×C₄	—	19	4	no	—
403	C₂×C₄	—	19	2	no	—
404	C₂×C₄	—	19	2	no	—
405	C₂×C₄	—	19	4	no	—
406	C₂×C₄	—	19	2	no	—
407	C₂×C₄	—	19	2	no	—
408	C₂×C₄	—	38	4	no	—
409	C₂×C₄	—	38	8	no	—
410	C₂×C₄	—	38	8	no	—
411	C₂×C₄	—	38	4	no	—
412	C₂×C₄	—	38	4	no	—
413	C₂×C₄	—	38	1	no	—
414	C₂×C₄	—	38	4	no	—
415	C₂×C₄	D₄×D₁₉	1	2	yes	—
416	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₁₉	1	2	yes	—
418	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
419	C₈	—	19	4	no	—
420	C₈	C₂³×D₁₉	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	19	2	no	—
425	C₂²	—	19	2	no	—
426	C₂²	—	38	2	no	—
427	C₂²	—	38	2	no	—
428	C₂²	—	38	4	no	—
429	C₂²	—	38	2	no	—
430	C₂²	—	76	4	no	—
431	C₂²	—	76	8	no	—
432	C₂²	—	76	8	no	—
433	C₂²	—	76	4	no	—
434	C₂²	—	76	2	no	—
435	C₂²	C₂×D₄×D₁₉	1	2	yes	—
436	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	19	2	no	—
440	C₄	—	19	2	no	—
441	C₄	—	38	2	no	—
442	C₄	C₂×D₄×D₁₉	1	2	yes	—
443	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
444	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	—	38	2	no	—
448	C₂	—	38	2	no	—
449	C₂	—	76	4	no	—
450	C₂	—	76	2	no	—
451	C₂	#11927343	1	2	yes	direct product factor
452	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#137	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×#137	D₁₉
hypocenter	C₁₉	C₂×#575
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
1. C₂²×#64545	C₂	semidirect
2. C₂×#41×D₁₉	C₂	semidirect
3. #11927343	C₂	direct (N × H)
4. C₂×#10597364	C₂	semidirect
5. C₂×#10597388	C₂	semidirect
6. C₂×#10597354	C₂	semidirect
7. C₂×#10597360	C₂	semidirect
8. C₂×#10597395	C₂	semidirect
9. C₂×#10597365	C₂	semidirect
10. C₂×#10597362	C₂	semidirect
11. C₂×M₁₆×D₁₉	C₂	semidirect
12. C₂×C₁₉×#137	C₂	semidirect
14. C₂²×Q₈×C₁₉	C₂²	semidirect
16. #41×D₁₉	C₂²	semidirect
21. C₂×#64545	C₂²	semidirect
22. C₂×#64545	C₂²	semidirect
23. C₂×#64545	C₂²	semidirect
24. C₂×Q₈×D₁₉	C₂²	semidirect
26. C₂×#64543	C₂²	semidirect
28. C₂×D₄×D₁₉	C₂²	semidirect
32. C₂²×D₇₆	C₂²	semidirect
36. C₁₉×#137	C₂²	semidirect
37. C₂×Q₁₆×C₁₉	C₂²	semidirect
38. C₂×SD₁₆×C₁₉	C₂²	semidirect
39. C₂×M₁₆×C₁₉	C₂²	semidirect
40. #10597395	C₂²	semidirect
41. C₂×#64528	C₂²	semidirect
42. #10597388	C₂²	semidirect
43. C₂×#64527	C₂²	semidirect
44. C₂×#64527	C₂²	semidirect
45. C₂×#64525	C₂²	semidirect
46. C₂×#64520	C₂²	semidirect
47. #10597365	C₂²	semidirect
48. #10597364	C₂²	semidirect
49. #10597362	C₂²	semidirect
50. #10597360	C₂²	semidirect
51. #10597354	C₂²	semidirect
52. M₁₆×D₁₉	C₂²	semidirect
53. C₂×D₁₅₂	C₂²	semidirect
54. C₂×#64516	C₂²	semidirect
55. C₂×#64515	C₂²	semidirect
56. C₂×C₈×D₁₉	C₂²	semidirect
66. C₂×Q₈×C₁₉	C₂³	semidirect
83. #64545	C₂³	semidirect
84. #64545	C₂³	semidirect
86. Q₈×D₁₉	C₂³	semidirect
89. #64543	C₂³	semidirect
92. D₄×D₁₉	C₂³	semidirect
104. C₂×D₇₆	C₂³	semidirect
120. Q₁₆×C₁₉	C₂³	semidirect
121. SD₁₆×C₁₉	C₂³	semidirect
122. M₁₆×C₁₉	C₂³	semidirect
124. #64528	C₂³	semidirect
125. #64527	C₂³	semidirect
126. #64527	C₂³	semidirect
127. #64525	C₂³	semidirect
128. #64520	C₂³	semidirect
130. D₁₅₂	C₂³	semidirect
131. #64516	C₂³	semidirect
132. #64515	C₂³	semidirect
133. C₈×D₁₉	C₂³	semidirect
224. C₂×#137	D₁₉	semidirect
233. C₂×C₁₉	#575	semidirect
254. C₂²×Q₈	C₂×D₁₉	semidirect
264. #137	C₂×D₁₉	semidirect
271. C₂×Q₁₆	C₂×D₁₉	semidirect
275. C₂×SD₁₆	C₂×D₁₉	semidirect
281. C₂×M₁₆	C₂×D₁₉	semidirect
283. C₁₉	C₂×#575	semidirect
311. C₂×Q₈	C₂²×D₁₉	semidirect
348. Q₁₆	C₂²×D₁₉	semidirect
352. SD₁₆	C₂²×D₁₉	semidirect
357. M₁₆	C₂²×D₁₉	semidirect
451. C₂	#11927343	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#64545	2
C₂×#41×D₁₉	2
#11927343	2
C₂×#10597364	2
C₂×#10597388	2
C₂×#10597354	2
C₂×#10597360	2
C₂×#10597395	2
C₂×#10597365	2
C₂×#10597362	2
C₂×M₁₆×D₁₉	2
C₂×C₁₉×#137	2
C₂×#575	19

Subgroups — C2×#11927343 #14578381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927343 #14578381