Group #18085135 — subgroups

Subgroups — #18085135

Order 4864.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#11926924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926824	C₂	1	2	yes	maximal
3	C₂×#11926291	C₂	1	2	yes	maximal, complemented
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	—	2	2	no	—
7	C₂×#10597315	C₂²	1	2	yes	—
8	#11926924	—	2	4	no	—
9	#11926824	—	2	4	no	—
10	#11926824	—	2	4	no	—
11	C₂×#10597264	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×#10597289	—	2	2	no	—
14	#11926291	—	2	4	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂²×Dic₃₈	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂×Dic₇₆	—	2	8	no	—
33	C₂×Dic₇₆	—	4	4	no	—
34	C₂×Dic₇₆	—	4	4	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	#10597315	—	2	2	no	—
38	#10597315	D₄	1	4	yes	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	4	4	no	—
41	C₄×C₈×C₁₉	—	2	2	no	—
42	#10597289	—	2	8	no	—
43	#10597264	—	2	8	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
46	C₂⁴×C₁₉	—	2	1	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	—	2	1	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	Q₁₆	1	2	yes	complemented
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×Dic₁₉	—	4	2	no	—
60	C₂×Dic₃₈	—	2	4	no	—
61	C₂×Dic₃₈	—	4	4	no	—
62	C₂×Dic₃₈	—	4	4	no	—
63	C₂×Dic₃₈	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	D₈	1	4	yes	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	C₄⋊Dic₁₉	—	2	4	no	—
74	C₄⋊Dic₁₉	—	2	4	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	2	4	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	Dic₇₆	—	4	16	no	—
81	#10274	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	#121	1	1	yes	characteristic
88	D₄×C₁₉	—	2	4	no	—
89	D₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	8	2	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#120	1	2	yes	—
98	C₂×C₄×C₁₉	#121	1	2	yes	—
99	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
101	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
103	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₁₉	#137	1	2	yes	—
105	C₂×Dic₁₉	—	4	4	no	—
106	C₂×Dic₁₉	—	8	4	no	—
107	Dic₃₈	—	4	8	no	—
108	Dic₃₈	—	8	2	no	—
109	Dic₃₈	—	8	2	no	—
110	C₈×C₁₉	—	2	4	no	—
111	C₈×C₁₉	—	8	1	no	—
112	C₁₉⋊C₈	—	4	4	no	—
113	C₂×#494	—	19	1	no	—
114	C₂×#474	—	19	2	no	—
115	#1954	D₁₉	1	1	yes	characteristic
116	C₂×#332	—	19	2	no	—
117	#1277	—	19	1	no	—
118	C₂²×C₁₉	—	4	4	no	—
119	C₂²×C₁₉	—	4	2	no	—
120	C₂²×C₁₉	—	8	2	no	—
121	C₂²×C₁₉	—	8	1	no	—
122	C₂²×C₁₉	—	8	1	no	—
123	C₂²×C₁₉	#392	1	1	yes	characteristic
124	C₂²×C₁₉	#459	1	2	yes	—
125	C₂²×C₁₉	#467	1	1	yes	characteristic
126	C₂²×C₁₉	#470	1	1	yes	characteristic
127	C₂²×C₁₉	#473	1	2	yes	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	8	1	no	—
130	C₄×C₁₉	#447	1	2	yes	—
131	C₄×C₁₉	#451	1	2	yes	—
132	C₄×C₁₉	#452	1	2	yes	—
133	C₄×C₁₉	#493	1	1	yes	characteristic
134	C₄×C₁₉	#496	1	1	yes	characteristic
135	Dic₁₉	—	8	4	no	—
136	C₂²×Q₁₆	—	38	2	no	—
137	C₂×C₄⋊Q₈	—	19	2	no	—
138	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
139	#494	—	38	4	no	—
140	#474	—	38	4	no	—
141	#474	—	38	4	no	—
142	C₂×#107	—	38	2	no	—
143	C₂×C₄⋊C₈	—	19	2	no	—
144	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
145	C₂×#102	—	38	2	no	—
146	C₂×C₂²⋊C₈	—	2	2	no	—
147	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
148	#332	—	38	4	no	—
149	C₂×C₁₉	—	8	2	no	—
150	C₂×C₁₉	#1669	1	2	yes	—
151	C₂×C₁₉	#1689	1	2	yes	—
152	C₂×C₁₉	#2001	1	1	yes	characteristic
153	C₂×C₁₉	#2011	1	1	yes	characteristic
154	C₂×C₁₉	#2020	1	1	yes	characteristic
155	C₂²×Q₈	—	38	2	no	—
156	C₂²×D₄	D₇₆	1	1	yes	characteristic
157	C₂³×C₄	—	2	1	no	—
158	C₂×Q₁₆	—	38	8	no	—
159	C₂×Q₁₆	—	76	4	no	—
160	C₂×Q₁₆	—	76	4	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	38	2	no	—
163	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
164	C₄⋊Q₈	—	19	4	no	—
165	C₄⋊Q₈	—	38	2	no	—
166	C₄⋊Q₈	—	38	2	no	—
167	C₄⋊Q₈	—	38	2	no	—
168	C₄×D₄	—	2	2	no	—
169	C₄×D₄	—	2	2	no	—
170	C₂×C₄⋊C₄	—	38	2	no	—
171	C₂×C₄⋊C₄	—	38	2	no	—
172	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	—	2	1	no	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	#107	—	38	8	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	19	4	no	—
178	C₄⋊C₈	—	38	2	no	—
179	#102	—	38	8	no	—
180	C₂²⋊C₈	—	4	4	no	—
181	C₄×C₈	—	2	2	no	—
182	C₁₉	#10274	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	—	2	1	no	—
184	C₂×Q₈	—	38	4	no	—
185	C₂×Q₈	—	76	2	no	—
186	C₂×Q₈	—	76	4	no	—
187	C₂×Q₈	—	76	4	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	Dic₇₆	1	2	yes	complemented
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	—	76	2	no	—
198	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
199	C₂²×C₄	#64541	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	Q₁₆	—	76	16	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	2	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	38	4	no	—
207	C₂×C₈	—	76	2	no	—
208	C₂×C₈	—	76	2	no	—
209	C₂×C₈	#64525	1	4	yes	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	38	4	no	—
212	C₄⋊C₄	—	38	4	no	—
213	C₄⋊C₄	—	76	2	no	—
214	C₄⋊C₄	—	76	2	no	—
215	C₂²⋊C₄	—	4	2	no	—
216	C₄²	D₄×D₁₉	1	2	yes	—
217	C₄²	D₄×D₁₉	1	2	yes	—
218	C₂³	—	2	2	no	—
219	C₂³	—	4	1	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	1	no	—
222	C₂³	—	4	2	no	—
223	C₂³	#10597376	1	1	yes	characteristic
224	Q₈	—	76	8	no	—
225	Q₈	—	152	2	no	—
226	Q₈	—	152	2	no	—
227	D₄	—	2	4	no	—
228	D₄	—	4	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	—	8	1	no	—
235	C₂×C₄	—	76	4	no	—
236	C₂×C₄	—	152	4	no	—
237	C₂×C₄	#10597328	1	2	yes	—
238	C₂×C₄	#10597330	1	2	yes	—
239	C₂×C₄	#10597350	1	1	yes	characteristic
240	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
241	C₂×C₄	#10597355	1	2	yes	—
242	C₂×C₄	C₂×#64525	1	2	yes	—
243	C₂×C₄	#10597383	1	1	yes	characteristic
244	C₂×C₄	#10597386	1	1	yes	characteristic
245	C₂×C₄	#10597395	1	2	yes	—
246	C₈	—	2	4	no	—
247	C₈	—	8	1	no	—
248	C₈	—	76	4	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	4	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	8	1	no	—
253	C₂²	—	8	1	no	—
254	C₂²	#11926453	1	1	yes	characteristic
255	C₂²	#11926739	1	2	yes	—
256	C₂²	#11926785	1	1	yes	characteristic
257	C₂²	#11926802	1	1	yes	characteristic
258	C₂²	#11926819	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	8	1	no	—
261	C₄	—	152	4	no	—
262	C₄	#11926677	1	2	yes	—
263	C₄	#11926702	1	2	yes	—
264	C₄	#11926708	1	2	yes	—
265	C₄	#11926920	1	1	yes	characteristic
266	C₄	#11926934	1	1	yes	characteristic
267	C₂	—	8	2	no	—
268	C₂	#14563000	1	2	yes	—
269	C₂	#14563124	1	2	yes	—
270	C₂	#14564645	1	1	yes	characteristic
271	C₂	#14564705	1	1	yes	characteristic
272	C₂	#14564756	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926924

C₂

yes

maximal, characteristic, complemented

C₂×#11926824

C₂

yes

maximal

C₂×#11926291

C₂

yes

maximal, complemented

#14561470

C₂

yes

maximal, characteristic, complemented

C₁₉×#1954

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

—

C₂×#10597315

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597289

—

#11926291

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

—

—

—

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597289

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₁₆

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

#10274

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

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

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

100

C₂×C₄×C₁₉

C₂×D₈

yes

—

101

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

102

C₂×C₄×C₁₉

#135

yes

characteristic

103

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

104

C₂×C₄×C₁₉

#137

yes

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

Dic₃₈

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

C₂×#494

—

114

C₂×#474

—

115

#1954

D₁₉

yes

characteristic

116

C₂×#332

—

117

#1277

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#392

yes

characteristic

124

C₂²×C₁₉

#459

yes

—

125

C₂²×C₁₉

#467

yes

characteristic

126

C₂²×C₁₉

#470

yes

characteristic

127

C₂²×C₁₉

#473

yes

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#447

yes

—

131

C₄×C₁₉

#451

yes

—

132

C₄×C₁₉

#452

yes

—

133

C₄×C₁₉

#493

yes

characteristic

134

C₄×C₁₉

#496

yes

characteristic

135

Dic₁₉

—

136

C₂²×Q₁₆

—

137

C₂×C₄⋊Q₈

—

138

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

139

#494

—

140

#474

—

141

#474

—

142

C₂×#107

—

143

C₂×C₄⋊C₈

—

144

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

145

C₂×#102

—

146

C₂×C₂²⋊C₈

—

147

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

148

#332

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#1669

yes

—

151

C₂×C₁₉

#1689

yes

—

152

C₂×C₁₉

#2001

yes

characteristic

153

C₂×C₁₉

#2011

yes

characteristic

154

C₂×C₁₉

#2020

yes

characteristic

155

C₂²×Q₈

—

156

C₂²×D₄

D₇₆

yes

characteristic

157

C₂³×C₄

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

C₂²⋊D₁₉

yes

—

164

C₄⋊Q₈

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄×D₄

—

169

C₄×D₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

D₇₆

yes

characteristic

173

C₂×C₂²⋊C₄

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

#107

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

#102

—

180

C₂²⋊C₈

—

181

C₄×C₈

—

182

C₁₉

#10274

yes

characteristic, complemented, Sylow

183

C₂⁴

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

Dic₇₆

yes

complemented

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

C₂×D₇₆

yes

characteristic

199

C₂²×C₄

#64541

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

201

Q₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

#64525

yes

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

D₄×D₁₉

yes

—

217

C₄²

D₄×D₁₉

yes

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

#10597376

yes

characteristic

224

Q₈

—

225

Q₈

—

152

—

226

Q₈

—

152

—

227

D₄

—

228

D₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

152

—

237

C₂×C₄

#10597328

yes

—

238

C₂×C₄

#10597330

yes

—

239

C₂×C₄

#10597350

yes

characteristic

240

C₂×C₄

C₂×Dic₇₆

yes

characteristic

241

C₂×C₄

#10597355

yes

—

242

C₂×C₄

C₂×#64525

yes

—

243

C₂×C₄

#10597383

yes

characteristic

244

C₂×C₄

#10597386

yes

characteristic

245

C₂×C₄

#10597395

yes

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926453

yes

characteristic

255

C₂²

#11926739

yes

—

256

C₂²

#11926785

yes

characteristic

257

C₂²

#11926802

yes

characteristic

258

C₂²

#11926819

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

152

—

262

C₄

#11926677

yes

—

263

C₄

#11926702

yes

—

264

C₄

#11926708

yes

—

265

C₄

#11926920

yes

characteristic

266

C₄

#11926934

yes

characteristic

267

C₂

—

268

C₂

#14563000

yes

—

269

C₂

#14563124

yes

—

270

C₂

#14564645

yes

characteristic

271

C₂

#14564705

yes

characteristic

272

C₂

#14564756

yes

characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1954	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	D₄
hypercenter	#1954	D₁₉
hypocenter	C₁₉	#10274
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#10597376

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1954

C₂

socle

C₂³×C₁₉

#121

prime radical

C₂²×D₄×C₁₉

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. C₂×#11926924	C₂	semidirect
3. C₂×#11926291	C₂	semidirect
4. #14561470	C₂	semidirect
50. C₂×D₄×C₁₉	Q₁₆	semidirect
182. C₁₉	#10274	semidirect
191. C₂×D₄	Dic₇₆	semidirect

H ≅ G/N

type

1. C₂×#11926924

C₂

semidirect

3. C₂×#11926291

C₂

semidirect

4. #14561470

C₂

semidirect

50. C₂×D₄×C₁₉

Q₁₆

semidirect

182. C₁₉

#10274

semidirect

191. C₂×D₄

Dic₇₆

semidirect

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

subgroup	index
C₂×#11926924	2
C₂×#11926824	2
C₂×#11926291	2
#14561470	2
C₁₉×#1954	2
#10274	19

subgroup

index

C₁₉×#1954

Subgroups — #18085135

Conjugacy classes of subgroups

Complements

Maximal subgroups