Group #18073453 — subgroups

Subgroups — C₄×#11926284 #18073453

Order 4864.

616 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597260	C₂	1	2	yes	maximal, complemented
2	C₂×#11926284	C₂	1	2	yes	maximal
3	#14561516	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597260	—	2	2	no	—
6	C₂×#10597260	C₂²	1	4	yes	—
7	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926284	C₄	1	8	yes	direct product factor
9	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
12	C₁₉×#391	C₄	1	1	yes	characteristic
13	C₁₉×#390	C₄	1	1	yes	characteristic
14	C₁₉×#388	—	2	2	no	—
15	C₁₉×#382	C₂²	1	1	yes	characteristic
16	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₁₉×#124	C₂×C₄	1	4	yes	—
23	C₄×Q₈×C₁₉	—	4	2	no	—
24	C₄×D₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄²×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	4	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₁₉×#95	—	2	2	no	—
40	#10597260	—	2	8	no	—
41	#10597260	—	2	4	no	—
42	#10597260	C₂×C₄	1	8	yes	complemented
43	C₄×C₁₉⋊C₈	—	2	8	no	—
44	C₂⁴×C₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
49	C₂×D₄×C₁₉	—	2	1	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	4	1	no	—
52	C₂×D₄×C₁₉	C₄²	1	2	yes	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	—	4	4	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄⋊C₄×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	2	8	no	—
67	C₂²⋊C₄×C₁₉	—	4	2	no	—
68	C₂²⋊C₄×C₁₉	—	4	4	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	4	no	—
71	C₄²×C₁₉	—	2	4	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
75	C₄²×C₁₉	#41	1	2	yes	—
76	C₂×C₁₉⋊C₈	—	2	8	no	—
77	C₂×C₁₉⋊C₈	—	2	8	no	—
78	C₂×C₁₉⋊C₈	—	2	8	no	—
79	C₄×#329	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	—	4	1	no	—
83	C₂³×C₁₉	—	4	2	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₁₉	—	4	2	no	—
87	Q₈×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	D₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	8	4	no	—
106	C₂×C₄×C₁₉	#100	1	2	yes	—
107	C₂×C₄×C₁₉	#104	1	4	yes	—
108	C₂×C₄×C₁₉	#104	1	4	yes	—
109	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
112	C₁₉⋊C₈	—	2	16	no	—
113	C₄×#124	D₁₉	1	1	yes	characteristic
114	C₄×#97	—	19	2	no	—
115	C₂×#329	—	19	2	no	—
116	#1295	—	19	2	no	—
117	C₂²×C₁₉	—	4	2	no	—
118	C₂²×C₁₉	—	4	4	no	—
119	C₂²×C₁₉	—	8	1	no	—
120	C₂²×C₁₉	—	8	2	no	—
121	C₂²×C₁₉	—	8	1	no	—
122	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
124	C₂²×C₁₉	#413	1	1	yes	characteristic
125	C₂²×C₁₉	C₂×#104	1	2	yes	—
126	C₂²×C₁₉	C₂×#104	1	2	yes	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	4	no	—
130	C₄×C₁₉	—	2	4	no	—
131	C₄×C₁₉	—	4	2	no	—
132	C₄×C₁₉	—	4	1	no	—
133	C₄×C₁₉	—	8	1	no	—
134	C₄×C₁₉	—	8	1	no	—
135	C₄×C₁₉	#329	1	4	yes	complemented
136	C₂×#124	C₂×D₁₉	1	1	yes	characteristic
137	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
138	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
139	C₂×#97	—	19	4	no	—
140	C₂×#97	—	38	2	no	—
141	C₂×C₄×C₈	—	38	2	no	—
142	#391	Dic₁₉	1	1	yes	characteristic
143	#390	Dic₁₉	1	1	yes	characteristic
144	#388	—	2	2	no	—
145	#382	C₂×D₁₉	1	1	yes	characteristic
146	C₄×C₂²⋊C₄	—	2	2	no	—
147	C₄³	C₂×D₁₉	1	1	yes	characteristic
148	#329	—	19	8	no	—
149	C₂×C₁₉	—	8	2	no	—
150	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
151	C₂×C₁₉	#1524	1	2	yes	—
152	C₂×C₁₉	#1525	1	1	yes	characteristic
153	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
154	C₂×C₁₉	C₄×#104	1	2	yes	—
155	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
156	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
157	C₂³×C₄	—	2	1	no	—
158	C₂²×C₈	—	38	4	no	—
159	#124	—	2	2	no	—
160	#124	C₄×D₁₉	1	4	yes	—
161	C₄×Q₈	—	4	2	no	—
162	C₄×D₄	—	4	2	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₄²	—	2	1	no	—
170	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
172	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
173	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	#97	—	19	8	no	—
176	#97	—	38	8	no	—
177	#97	—	38	4	no	—
178	C₄×C₈	—	38	8	no	—
179	#95	—	2	2	no	—
180	#95	—	2	2	no	—
181	C₁₉	C₄×#329	1	1	yes	characteristic, complemented, Sylow
182	C₂⁴	—	2	1	no	—
183	C₂×Q₈	—	2	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	4	2	no	—
195	C₂²×C₄	—	4	4	no	—
196	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
198	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
201	C₂×C₈	—	38	8	no	—
202	C₂×C₈	—	38	8	no	—
203	C₂×C₈	—	38	8	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	2	8	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	4	4	no	—
210	C₄²	—	2	2	no	—
211	C₄²	—	2	4	no	—
212	C₄²	—	2	4	no	—
213	C₄²	—	4	1	no	—
214	C₄²	—	4	2	no	—
215	C₄²	C₂×C₄×D₁₉	1	2	yes	—
216	C₄²	#64541	1	2	yes	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	1	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	1	no	—
222	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
223	Q₈	—	4	2	no	—
224	Q₈	—	4	2	no	—
225	D₄	—	4	2	no	—
226	D₄	—	4	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	8	4	no	—
243	C₂×C₄	#10597290	1	2	yes	—
244	C₂×C₄	#10597294	1	4	yes	—
245	C₂×C₄	#10597294	1	4	yes	—
246	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄	#10597372	1	1	yes	characteristic
248	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
249	C₈	—	38	16	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	4	no	—
252	C₂²	—	8	1	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	8	1	no	—
255	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
256	C₂²	C₂×#10597290	1	1	yes	characteristic
257	C₂²	#11926528	1	1	yes	characteristic
258	C₂²	C₂×#10597294	1	2	yes	—
259	C₂²	C₂×#10597294	1	2	yes	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	4	no	—
263	C₄	—	2	4	no	—
264	C₄	—	4	2	no	—
265	C₄	—	4	1	no	—
266	C₄	—	8	1	no	—
267	C₄	—	8	1	no	—
268	C₄	#11926284	1	4	yes	direct product factor
269	C₂	—	8	2	no	—
270	C₂	C₂×#11926284	1	1	yes	characteristic
271	C₂	#14562223	1	2	yes	—
272	C₂	#14562227	1	1	yes	characteristic
273	C₂	C₄×#10597290	1	1	yes	characteristic
274	C₂	C₄×#10597294	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597260

C₂

yes

maximal, complemented

C₂×#11926284

C₂

yes

maximal

#14561516

C₂

yes

maximal, complemented

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

C₂×#10597260

—

C₂×#10597260

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

—

#11926284

C₄

yes

direct product factor

C₂×C₁₉×#124

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#390

C₄

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₂²

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×#124

—

C₁₉×#124

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

#10597260

—

#10597260

—

#10597260

C₂×C₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₄×#329

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

#100

yes

—

107

C₂×C₄×C₁₉

#104

yes

—

108

C₂×C₄×C₁₉

#104

yes

—

109

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

110

C₂×C₄×C₁₉

#117

yes

characteristic

111

C₂×C₄×C₁₉

C₄×D₄

yes

—

112

C₁₉⋊C₈

—

113

C₄×#124

D₁₉

yes

characteristic

114

C₄×#97

—

115

C₂×#329

—

116

#1295

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

123

C₂²×C₁₉

C₂×#100

yes

characteristic

124

C₂²×C₁₉

#413

yes

characteristic

125

C₂²×C₁₉

C₂×#104

yes

—

126

C₂²×C₁₉

C₂×#104

yes

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

#329

yes

complemented

136

C₂×#124

C₂×D₁₉

yes

characteristic

137

C₂×C₄×Q₈

Dic₁₉

yes

characteristic

138

C₂×C₄×D₄

Dic₁₉

yes

characteristic

139

C₂×#97

—

140

C₂×#97

—

141

C₂×C₄×C₈

—

142

#391

Dic₁₉

yes

characteristic

143

#390

Dic₁₉

yes

characteristic

144

#388

—

145

#382

C₂×D₁₉

yes

characteristic

146

C₄×C₂²⋊C₄

—

147

C₄³

C₂×D₁₉

yes

characteristic

148

#329

—

149

C₂×C₁₉

—

150

C₂×C₁₉

C₂×#329

yes

characteristic

151

C₂×C₁₉

#1524

yes

—

152

C₂×C₁₉

#1525

yes

characteristic

153

C₂×C₁₉

C₄×#100

yes

characteristic

154

C₂×C₁₉

C₄×#104

yes

—

155

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

156

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

157

C₂³×C₄

—

158

C₂²×C₈

—

159

#124

—

160

#124

C₄×D₁₉

yes

—

161

C₄×Q₈

—

162

C₄×D₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

165

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

171

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

172

C₂×C₄²

C₂²⋊D₁₉

yes

—

173

C₂×C₄²

C₂²⋊D₁₉

yes

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

#97

—

176

#97

—

177

#97

—

178

C₄×C₈

—

179

#95

—

180

#95

—

181

C₁₉

C₄×#329

yes

characteristic, complemented, Sylow

182

C₂⁴

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

C₄×Dic₁₉

yes

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

C₄×Dic₁₉

yes

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

197

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

198

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

199

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

C₂×C₄×D₁₉

yes

—

216

C₄²

#64541

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

#10597290

yes

—

244

C₂×C₄

#10597294

yes

—

245

C₂×C₄

#10597294

yes

—

246

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

247

C₂×C₄

#10597372

yes

characteristic

248

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

249

C₈

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₄×C₂²⋊Dic₁₉

yes

characteristic

256

C₂²

C₂×#10597290

yes

characteristic

257

C₂²

#11926528

yes

characteristic

258

C₂²

C₂×#10597294

yes

—

259

C₂²

C₂×#10597294

yes

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

#11926284

yes

direct product factor

269

C₂

—

270

C₂

C₂×#11926284

yes

characteristic

271

C₂

#14562223

yes

—

272

C₂

#14562227

yes

characteristic

273

C₂

C₄×#10597290

yes

characteristic

274

C₂

C₄×#10597294

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#124	D₁₉
hypocenter	C₁₉	C₄×#329
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#124

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#124

N	H ≅ G/N	type
1. C₄×#10597260	C₂	semidirect
3. #14561516	C₂	semidirect
8. #11926284	C₄	direct (N × H)
42. #10597260	C₂×C₄	semidirect
135. C₄×C₁₉	#329	semidirect
181. C₁₉	C₄×#329	semidirect
268. C₄	#11926284	direct (N × H)

H ≅ G/N

type

1. C₄×#10597260

C₂

semidirect

3. #14561516

C₂

semidirect

8. #11926284

C₄

direct (N × H)

42. #10597260

C₂×C₄

semidirect

135. C₄×C₁₉

#329

semidirect

181. C₁₉

C₄×#329

semidirect

268. C₄

#11926284

direct (N × H)

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

subgroup	index
C₄×#10597260	2
C₂×#11926284	2
#14561516	2
C₄×C₁₉×#124	2
C₄×#329	19

subgroup

index

C₄×C₁₉×#124

Subgroups — C₄×#11926284 #18073453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#11926284 #18073453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926284 #18073453