Group #18080975 — subgroups

Subgroups — #18080975

Order 4864.

338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#14562407	C₂	1	1	yes	maximal, characteristic
3	#14562292	C₂	1	1	yes	maximal, characteristic
4	#14562038	C₂	1	1	yes	maximal, characteristic
5	#14561530	C₂	1	1	yes	maximal, characteristic
6	#14561468	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
13	#11926299	—	2	1	no	—
14	#11926294	—	2	2	no	—
15	#11926293	C₄	1	2	yes	complemented
16	#11926290	C₄	1	2	yes	complemented
17	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₄³×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#339	—	2	1	no	—
22	C₁₉×#339	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
26	C₁₉×#125	—	2	1	no	—
27	C₁₉×C₂²⋊Q₈	—	2	1	no	—
28	C₁₉×C₂²⋊Q₈	—	2	1	no	—
29	C₄×Q₈×C₁₉	—	2	1	no	—
30	C₄×Q₈×C₁₉	—	2	1	no	—
31	C₁₉×#117	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
47	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
48	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₄×C₁₉⋊C₈	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	2	1	no	—
53	C₂×Q₈×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	M₁₆×C₁₉	—	4	1	no	—
60	M₁₆×C₁₉	—	4	1	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₂²⋊C₄×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	—	2	4	no	—
70	C₄²×C₁₉	—	2	1	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	1	no	—
75	C₄²×C₁₉	SD₁₆	1	2	yes	—
76	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	4	1	no	—
88	#9579	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#123	1	1	yes	characteristic
90	Q₈×C₁₉	—	4	2	no	—
91	Q₈×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
98	C₂×C₄×C₁₉	—	4	1	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	#117	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
112	C₈×C₁₉	—	8	1	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	C₁₉⋊C₈	—	4	2	no	—
116	C₁₉⋊C₈	—	8	1	no	—
117	#1994	D₁₉	1	1	yes	characteristic
118	C₄×C₄⋊C₈	—	19	1	no	—
119	#1570	—	19	1	no	—
120	#1542	—	19	1	no	—
121	#1481	—	19	1	no	—
122	#1301	—	19	1	no	—
123	#1276	—	19	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	#388	1	1	yes	characteristic
127	C₂²×C₁₉	#483	1	1	yes	characteristic
128	C₂²×C₁₉	#485	1	1	yes	characteristic
129	C₄×C₁₉	—	2	4	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	4	2	no	—
134	C₄×C₁₉	—	8	1	no	—
135	C₄×C₁₉	—	8	1	no	—
136	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
137	C₄×C₁₉	#441	1	1	yes	characteristic
138	C₄×C₁₉	#443	1	2	yes	—
139	C₄×C₁₉	#461	1	1	yes	characteristic
140	C₄×C₁₉	#464	1	1	yes	characteristic
141	#533	C₂×D₁₉	1	1	yes	characteristic
142	#431	—	19	1	no	—
143	#431	—	19	1	no	—
144	#423	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₄⋊C₈	—	19	1	no	—
146	C₂×C₄⋊C₈	—	19	1	no	—
147	C₂×C₄×C₈	—	38	1	no	—
148	C₄³	C₂×D₁₉	1	1	yes	characteristic
149	#339	—	2	1	no	—
150	#339	—	2	1	no	—
151	#336	—	38	1	no	—
152	#334	—	38	2	no	—
153	#333	—	19	2	no	—
154	#332	—	19	2	no	—
155	Q₈⋊C₈	—	38	2	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	#1927	1	1	yes	characteristic
159	C₂×C₁₉	#1932	1	1	yes	characteristic
160	C₂×C₁₉	#1937	1	1	yes	characteristic
161	C₂×M₁₆	—	2	1	no	—
162	C₂²×C₈	—	38	1	no	—
163	C₂²×C₈	—	38	1	no	—
164	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
165	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
166	#125	—	2	1	no	—
167	C₂²⋊Q₈	—	2	1	no	—
168	C₂²⋊Q₈	—	2	1	no	—
169	C₄×Q₈	—	2	1	no	—
170	C₄×Q₈	—	2	1	no	—
171	#117	—	2	1	no	—
172	C₂×C₄²	—	2	1	no	—
173	C₂×C₄²	—	2	1	no	—
174	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	19	2	no	—
180	C₄⋊C₈	—	19	2	no	—
181	C₄⋊C₈	—	19	2	no	—
182	C₄⋊C₈	—	38	1	no	—
183	C₄⋊C₈	—	38	1	no	—
184	C₄⋊C₈	—	38	1	no	—
185	C₂²⋊C₈	—	38	1	no	—
186	C₂²⋊C₈	—	38	1	no	—
187	C₄×C₈	—	38	1	no	—
188	C₄×C₈	—	38	1	no	—
189	C₄×C₈	—	76	2	no	—
190	C₁₉	#9579	1	1	yes	characteristic, complemented, Sylow
191	C₂×Q₈	—	2	1	no	—
192	C₂×Q₈	—	2	1	no	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	2	1	no	—
195	C₂²×C₄	#64543	1	1	yes	characteristic
196	C₂²×C₄	#64543	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	38	2	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	76	1	no	—
205	C₂×C₈	—	76	1	no	—
206	C₂×C₈	—	76	1	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	1	no	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	2	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	1	no	—
215	C₂²⋊C₄	—	4	1	no	—
216	C₄²	—	2	4	no	—
217	C₄²	—	2	1	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	4	2	no	—
221	C₄²	—	4	1	no	—
222	C₄²	#64527	1	2	yes	—
223	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
224	C₄²	#64541	1	1	yes	characteristic
225	C₄²	D₄×D₁₉	1	1	yes	characteristic
226	C₄²	#64543	1	1	yes	characteristic
227	C₂³	#10597381	1	1	yes	characteristic
228	Q₈	—	4	2	no	—
229	Q₈	—	8	1	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	#10597323	1	1	yes	characteristic
241	C₂×C₄	#10597325	1	1	yes	characteristic
242	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
243	C₂×C₄	#10597331	1	1	yes	characteristic
244	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×C₄	#10597384	1	1	yes	characteristic
246	C₂×C₄	C₂×#64527	1	1	yes	characteristic
247	C₂×C₄	#10597388	1	1	yes	characteristic
248	C₂×C₄	#10597396	1	1	yes	characteristic
249	C₂×C₄	#10597397	1	1	yes	characteristic
250	C₈	—	8	1	no	—
251	C₈	—	76	2	no	—
252	C₈	—	76	2	no	—
253	C₈	—	76	2	no	—
254	C₈	—	152	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	#11926432	1	1	yes	characteristic
258	C₂²	#11926872	1	1	yes	characteristic
259	C₂²	#11926882	1	1	yes	characteristic
260	C₄	—	2	4	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	4	2	no	—
265	C₄	—	8	1	no	—
266	C₄	—	8	1	no	—
267	C₄	C₄×#64527	1	1	yes	characteristic
268	C₄	#11926649	1	1	yes	characteristic
269	C₄	#11926658	1	2	yes	—
270	C₄	#11926746	1	1	yes	characteristic
271	C₄	#11926763	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	2	1	no	—
274	C₂	#14564266	1	1	yes	characteristic
275	C₂	#14564301	1	1	yes	characteristic
276	C₂	#14564336	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#14562407

C₂

yes

maximal, characteristic

#14562292

C₂

yes

maximal, characteristic

#14562038

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561468

C₂

yes

maximal, characteristic

C₁₉×#1994

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

—

#11926299

—

#11926294

—

#11926293

C₄

yes

complemented

#11926290

C₄

yes

complemented

Q₈⋊(C₁₉⋊C₈)

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#339

—

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×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

#117

yes

characteristic

103

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

104

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

105

C₂×C₄×C₁₉

#121

yes

characteristic

106

C₂×C₄×C₁₉

#124

yes

characteristic

107

C₂×C₄×C₁₉

#126

yes

characteristic

108

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

109

C₂×C₄×C₁₉

#135

yes

characteristic

110

C₂×C₄×C₁₉

#137

yes

characteristic

111

C₂×C₄×C₁₉

#137

yes

characteristic

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

#1994

D₁₉

yes

characteristic

118

C₄×C₄⋊C₈

—

119

#1570

—

120

#1542

—

121

#1481

—

122

#1301

—

123

#1276

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#388

yes

characteristic

127

C₂²×C₁₉

#483

yes

characteristic

128

C₂²×C₁₉

#485

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

C₄×SD₁₆

yes

characteristic

137

C₄×C₁₉

#441

yes

characteristic

138

C₄×C₁₉

#443

yes

—

139

C₄×C₁₉

#461

yes

characteristic

140

C₄×C₁₉

#464

yes

characteristic

141

#533

C₂×D₁₉

yes

characteristic

142

#431

—

143

#431

—

144

#423

C₂×D₁₉

yes

characteristic

145

C₂×C₄⋊C₈

—

146

C₂×C₄⋊C₈

—

147

C₂×C₄×C₈

—

148

C₄³

C₂×D₁₉

yes

characteristic

149

#339

—

150

#339

—

151

#336

—

152

#334

—

153

#333

—

154

#332

—

155

Q₈⋊C₈

—

156

C₂×C₁₉

—

157

C₂×C₁₉

—

158

C₂×C₁₉

#1927

yes

characteristic

159

C₂×C₁₉

#1932

yes

characteristic

160

C₂×C₁₉

#1937

yes

characteristic

161

C₂×M₁₆

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

165

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

166

#125

—

167

C₂²⋊Q₈

—

168

C₂²⋊Q₈

—

169

C₄×Q₈

—

170

C₄×Q₈

—

171

#117

—

172

C₂×C₄²

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

175

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

176

C₂×C₄²

C₂²×D₁₉

yes

characteristic

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₂²⋊C₈

—

186

C₂²⋊C₈

—

187

C₄×C₈

—

188

C₄×C₈

—

189

C₄×C₈

—

190

C₁₉

#9579

yes

characteristic, complemented, Sylow

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

#64543

yes

characteristic

196

C₂²×C₄

#64543

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

#64527

yes

—

223

C₄²

C₂×C₄×D₁₉

yes

characteristic

224

C₄²

#64541

yes

characteristic

225

C₄²

D₄×D₁₉

yes

characteristic

226

C₄²

#64543

yes

characteristic

227

C₂³

#10597381

yes

characteristic

228

Q₈

—

229

Q₈

—

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

#10597323

yes

characteristic

241

C₂×C₄

#10597325

yes

characteristic

242

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

243

C₂×C₄

#10597331

yes

characteristic

244

C₂×C₄

C₄×C₂²⋊D₁₉

yes

characteristic

245

C₂×C₄

#10597384

yes

characteristic

246

C₂×C₄

C₂×#64527

yes

characteristic

247

C₂×C₄

#10597388

yes

characteristic

248

C₂×C₄

#10597396

yes

characteristic

249

C₂×C₄

#10597397

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

254

C₈

—

152

—

255

C₂²

—

256

C₂²

—

257

C₂²

#11926432

yes

characteristic

258

C₂²

#11926872

yes

characteristic

259

C₂²

#11926882

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

C₄×#64527

yes

characteristic

268

C₄

#11926649

yes

characteristic

269

C₄

#11926658

yes

—

270

C₄

#11926746

yes

characteristic

271

C₄

#11926763

yes

characteristic

272

C₂

—

273

C₂

—

274

C₂

#14564266

yes

characteristic

275

C₂

#14564301

yes

characteristic

276

C₂

#14564336

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1994	C₂
socle	C₂²×C₁₉	#388
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1994	D₁₉
hypocenter	C₁₉	#9579
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1994

subgroup

G/H

center

C₂×C₄

#10597384

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1994

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1994

N	H ≅ G/N	type
15. #11926293	C₄	semidirect
16. #11926290	C₄	semidirect
190. C₁₉	#9579	semidirect

H ≅ G/N

type

15. #11926293

C₄

semidirect

16. #11926290

C₄

semidirect

190. C₁₉

#9579

semidirect

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

subgroup	index
C₄×C₄⋊(C₁₉⋊C₈)	2
#14562407	2
#14562292	2
#14562038	2
#14561530	2
#14561468	2
C₁₉×#1994	2
#9579	19

subgroup

index

C₄×C₄⋊(C₁₉⋊C₈)

C₁₉×#1994

Subgroups — #18080975

Conjugacy classes of subgroups

Complements

Maximal subgroups