Subgroups — C₁₃₉×#20747 #48015343

Order 35584.

1428 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2920×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1826×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1806×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1789×C₁₃₉	C₂	1	2	yes	maximal
7	C₄×#104×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₄×#41×C₁₃₉	—	2	1	no	—
10	C₄×#41×C₁₃₉	—	2	1	no	—
11	C₄×#41×C₁₃₉	—	2	1	no	—
12	C₄×#41×C₁₃₉	—	2	1	no	—
13	C₄×#41×C₁₃₉	C₄	1	2	yes	complemented
14	C₄×#41×C₁₃₉	C₄	1	2	yes	complemented
15	C₄×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₄×#41×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₃₉	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×Q₈×C₁₃₉	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃₉	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄×D₄×C₁₃₉	C₄	1	1	yes	characteristic, complemented
23	C₂×#117×C₁₃₉	—	2	1	no	—
24	C₂×#117×C₁₃₉	—	2	1	no	—
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	—	2	1	no	—
27	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
28	#432×C₁₃₉	—	2	1	no	—
29	#432×C₁₃₉	—	2	1	no	—
30	#431×C₁₃₉	—	2	1	no	—
31	#431×C₁₃₉	—	2	1	no	—
32	#423×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#104×C₁₃₉	C₂²	1	8	yes	—
34	#407×C₁₃₉	C₂²	1	2	yes	—
35	C₄×M₁₆×C₁₃₉	C₂²	1	2	yes	complemented
36	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
38	C₄×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	#376×C₁₃₉	—	2	1	no	—
41	C₄³×C₁₃₉	C₂²	1	2	yes	complemented
42	#339×C₁₃₉	C₂²	1	8	yes	complemented
43	C₂×#41×C₁₃₉	—	2	8	no	—
44	C₂×#41×C₁₃₉	—	2	1	no	—
45	C₂×#41×C₁₃₉	—	2	1	no	—
46	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₉	—	2	1	no	—
50	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₉	—	2	1	no	—
52	C₂³×C₄×C₁₃₉	—	2	1	no	—
53	C₂³×C₄×C₁₃₉	—	2	1	no	—
54	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
58	C₄×Q₈×C₁₃₉	—	2	1	no	—
59	C₄×Q₈×C₁₃₉	—	2	1	no	—
60	C₄×Q₈×C₁₃₉	—	2	1	no	—
61	C₄×Q₈×C₁₃₉	—	2	1	no	—
62	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
63	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₃₉	—	2	2	no	—
67	C₄×D₄×C₁₃₉	—	2	2	no	—
68	C₄×D₄×C₁₃₉	—	2	2	no	—
69	C₄×D₄×C₁₃₉	—	2	2	no	—
70	C₄×D₄×C₁₃₉	—	2	2	no	—
71	C₄×D₄×C₁₃₉	—	2	2	no	—
72	C₄×D₄×C₁₃₉	—	2	2	no	—
73	C₄×D₄×C₁₃₉	—	2	2	no	—
74	C₄×D₄×C₁₃₉	—	2	1	no	—
75	C₄×D₄×C₁₃₉	—	2	1	no	—
76	C₄×D₄×C₁₃₉	—	2	1	no	—
77	C₄×D₄×C₁₃₉	—	2	1	no	—
78	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
81	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
82	#117×C₁₃₉	—	2	8	no	—
83	#117×C₁₃₉	—	2	1	no	—
84	#117×C₁₃₉	—	2	1	no	—
85	#117×C₁₃₉	—	2	2	no	—
86	#117×C₁₃₉	—	2	2	no	—
87	#117×C₁₃₉	—	2	2	no	—
88	#117×C₁₃₉	—	2	2	no	—
89	#117×C₁₃₉	C₂×C₄	1	2	yes	—
90	#117×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
100	C₂×C₄²×C₁₃₉	—	2	1	no	—
101	C₂×C₄²×C₁₃₉	—	2	1	no	—
102	C₂×C₄²×C₁₃₉	—	2	1	no	—
103	C₂×C₄²×C₁₃₉	—	2	2	no	—
104	C₂×C₄²×C₁₃₉	—	2	2	no	—
105	C₂×C₄²×C₁₃₉	—	2	2	no	—
106	C₂×C₄²×C₁₃₉	—	2	2	no	—
107	C₂×C₄²×C₁₃₉	—	2	2	no	—
108	C₂×C₄²×C₁₃₉	—	2	2	no	—
109	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₁₃₉	—	2	2	no	—
123	C₄⋊C₈×C₁₃₉	—	2	2	no	—
124	#104×C₁₃₉	—	2	16	no	—
125	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
126	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
127	#97×C₁₃₉	—	2	2	no	—
128	C₄×C₈×C₁₃₉	—	2	2	no	—
129	#95×C₁₃₉	—	2	2	no	—
130	#95×C₁₃₉	—	2	2	no	—
131	C₂⁴×C₁₃₉	—	2	1	no	—
132	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
133	#41×C₁₃₉	—	2	8	no	—
134	#41×C₁₃₉	—	2	8	no	—
135	#41×C₁₃₉	—	2	4	no	—
136	#41×C₁₃₉	—	2	4	no	—
137	#41×C₁₃₉	—	2	4	no	—
138	#41×C₁₃₉	#41	1	8	yes	—
139	C₂×Q₈×C₁₃₉	—	2	4	no	—
140	C₂×Q₈×C₁₃₉	—	2	1	no	—
141	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₁₃₉	—	2	8	no	—
143	C₂×D₄×C₁₃₉	—	2	2	no	—
144	C₂×D₄×C₁₃₉	—	2	2	no	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	1	no	—
147	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₃₉	—	2	8	no	—
149	C₂²×C₄×C₁₃₉	—	2	1	no	—
150	C₂²×C₄×C₁₃₉	—	2	4	no	—
151	C₂²×C₄×C₁₃₉	—	2	2	no	—
152	C₂²×C₄×C₁₃₉	—	2	2	no	—
153	C₂²×C₄×C₁₃₉	—	2	4	no	—
154	C₂²×C₄×C₁₃₉	—	2	1	no	—
155	C₂²×C₄×C₁₃₉	—	2	1	no	—
156	C₂²×C₄×C₁₃₉	—	2	4	no	—
157	C₂²×C₄×C₁₃₉	—	2	2	no	—
158	C₂²×C₄×C₁₃₉	—	2	2	no	—
159	C₂²×C₄×C₁₃₉	—	2	2	no	—
160	C₂²×C₄×C₁₃₉	—	2	2	no	—
161	C₂²×C₄×C₁₃₉	—	4	2	no	—
162	C₂²×C₄×C₁₃₉	—	4	4	no	—
163	C₂²×C₄×C₁₃₉	—	4	4	no	—
164	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	M₁₆×C₁₃₉	—	2	8	no	—
183	C₂×C₈×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	—	2	8	no	—
185	C₄⋊C₄×C₁₃₉	—	2	2	no	—
186	C₄⋊C₄×C₁₃₉	—	2	2	no	—
187	C₄⋊C₄×C₁₃₉	—	2	2	no	—
188	C₄⋊C₄×C₁₃₉	—	2	2	no	—
189	C₄⋊C₄×C₁₃₉	—	2	1	no	—
190	C₄⋊C₄×C₁₃₉	—	2	1	no	—
191	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
192	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
193	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
200	C₄²×C₁₃₉	—	2	8	no	—
201	C₄²×C₁₃₉	—	2	2	no	—
202	C₄²×C₁₃₉	—	2	2	no	—
203	C₄²×C₁₃₉	—	2	2	no	—
204	C₄²×C₁₃₉	—	2	2	no	—
205	C₄²×C₁₃₉	—	2	2	no	—
206	C₄²×C₁₃₉	—	2	2	no	—
207	C₄²×C₁₃₉	—	2	8	no	—
208	C₄²×C₁₃₉	—	4	4	no	—
209	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
214	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
215	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
216	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
217	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₁₃₉	—	2	4	no	—
226	C₂³×C₁₃₉	—	2	2	no	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	2	no	—
229	C₂³×C₁₃₉	—	4	1	no	—
230	C₂³×C₁₃₉	—	4	2	no	—
231	C₂³×C₁₃₉	—	4	2	no	—
232	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₁₃₉	—	2	4	no	—
236	Q₈×C₁₃₉	—	2	2	no	—
237	Q₈×C₁₃₉	#117	1	4	yes	complemented
238	D₄×C₁₃₉	—	2	8	no	—
239	D₄×C₁₃₉	—	2	4	no	—
240	D₄×C₁₃₉	—	2	8	no	—
241	D₄×C₁₃₉	—	2	2	no	—
242	D₄×C₁₃₉	#117	1	4	yes	complemented
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	8	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	8	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	8	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	4	1	no	—
264	C₂×C₄×C₁₃₉	—	4	1	no	—
265	C₂×C₄×C₁₃₉	—	4	1	no	—
266	C₂×C₄×C₁₃₉	—	4	4	no	—
267	C₂×C₄×C₁₃₉	—	4	4	no	—
268	C₂×C₄×C₁₃₉	—	4	2	no	—
269	C₂×C₄×C₁₃₉	—	4	4	no	—
270	C₂×C₄×C₁₃₉	—	4	2	no	—
271	C₂×C₄×C₁₃₉	—	4	4	no	—
272	C₂×C₄×C₁₃₉	—	4	4	no	—
273	C₂×C₄×C₁₃₉	—	4	4	no	—
274	C₂×C₄×C₁₃₉	#104	1	4	yes	complemented
275	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
288	C₈×C₁₃₉	—	4	4	no	—
289	C₂²×C₁₃₉	—	2	1	no	—
290	C₂²×C₁₃₉	—	2	1	no	—
291	C₂²×C₁₃₉	—	2	1	no	—
292	C₂²×C₁₃₉	—	2	1	no	—
293	C₂²×C₁₃₉	—	2	1	no	—
294	C₂²×C₁₃₉	—	2	1	no	—
295	C₂²×C₁₃₉	—	2	1	no	—
296	C₂²×C₁₃₉	—	2	4	no	—
297	C₂²×C₁₃₉	—	4	4	no	—
298	C₂²×C₁₃₉	—	4	8	no	—
299	C₂²×C₁₃₉	—	4	2	no	—
300	C₂²×C₁₃₉	—	4	2	no	—
301	C₂²×C₁₃₉	C₂×#104	1	2	yes	—
302	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₁₃₉	#525	1	2	yes	—
304	C₄×C₁₃₉	—	2	1	no	—
305	C₄×C₁₃₉	—	2	1	no	—
306	C₄×C₁₃₉	—	2	1	no	—
307	C₄×C₁₃₉	—	2	1	no	—
308	C₄×C₁₃₉	—	2	1	no	—
309	C₄×C₁₃₉	—	2	1	no	—
310	C₄×C₁₃₉	—	2	4	no	—
311	C₄×C₁₃₉	—	2	1	no	—
312	C₄×C₁₃₉	—	4	8	no	—
313	C₄×C₁₃₉	—	4	2	no	—
314	C₄×C₁₃₉	—	4	2	no	—
315	C₄×C₁₃₉	C₂×#104	1	2	yes	—
316	C₄×C₁₃₉	C₂×#104	1	2	yes	—
317	C₄×C₁₃₉	#421	1	2	yes	—
318	C₄×C₁₃₉	C₂×#117	1	2	yes	—
319	C₄×C₁₃₉	#525	1	2	yes	—
320	C₂×C₁₃₉	—	2	2	no	—
321	C₂×C₁₃₉	—	2	2	no	—
322	C₂×C₁₃₉	—	4	1	no	—
323	C₂×C₁₃₉	—	4	4	no	—
324	C₂×C₁₃₉	#2280	1	1	yes	characteristic
325	C₂×C₁₃₉	C₂²×#104	1	1	yes	characteristic
326	C₂×C₁₃₉	C₂×#421	1	1	yes	characteristic
327	#20747	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₁₃₉	#20747	1	1	yes	characteristic, direct product factor, Sylow
329	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
330	#2920	C₂×C₁₃₉	1	1	yes	characteristic, complemented
331	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
332	#1826	C₂×C₁₃₉	1	2	yes	complemented
333	#1806	C₂×C₁₃₉	1	4	yes	complemented
334	#1789	C₂×C₁₃₉	1	2	yes	—
335	C₄×#104	C₂×C₁₃₉	1	4	yes	complemented
336	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
337	C₄×#41	—	2	1	no	—
338	C₄×#41	—	2	1	no	—
339	C₄×#41	—	2	1	no	—
340	C₄×#41	—	2	1	no	—
341	C₄×#41	C₄×C₁₃₉	1	2	yes	complemented
342	C₄×#41	C₄×C₁₃₉	1	2	yes	complemented
343	C₄×#41	C₂²×C₁₃₉	1	2	yes	—
344	C₄×#41	C₂²×C₁₃₉	1	2	yes	—
345	C₂×C₄×Q₈	C₄×C₁₃₉	1	1	yes	characteristic, complemented
346	C₂×C₄×Q₈	C₄×C₁₃₉	1	1	yes	characteristic, complemented
347	C₂×C₄×D₄	—	2	1	no	—
348	C₂×C₄×D₄	—	2	1	no	—
349	C₂×C₄×D₄	C₄×C₁₃₉	1	1	yes	characteristic, complemented
350	C₂×C₄×D₄	C₄×C₁₃₉	1	1	yes	characteristic, complemented
351	C₂×#117	—	2	1	no	—
352	C₂×#117	—	2	1	no	—
353	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
354	C₂²×C₄²	—	2	1	no	—
355	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
356	#432	—	2	1	no	—
357	#432	—	2	1	no	—
358	#431	—	2	1	no	—
359	#431	—	2	1	no	—
360	#423	C₂²×C₁₃₉	1	2	yes	complemented
361	C₂×#104	C₂²×C₁₃₉	1	8	yes	—
362	#407	C₂²×C₁₃₉	1	2	yes	—
363	C₄×M₁₆	C₂²×C₁₃₉	1	2	yes	complemented
364	C₄×C₄⋊C₄	—	2	1	no	—
365	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
366	C₄×C₂²⋊C₄	—	2	1	no	—
367	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
368	#376	—	2	1	no	—
369	C₄³	C₂²×C₁₃₉	1	2	yes	complemented
370	#339	C₂²×C₁₃₉	1	8	yes	complemented
371	C₂×#41	—	2	8	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
375	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
376	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
383	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
385	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
391	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
392	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
393	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
407	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
408	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
409	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
410	#117	—	2	8	no	—
411	#117	—	2	1	no	—
412	#117	—	2	1	no	—
413	#117	—	2	2	no	—
414	#117	—	2	2	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	C₂×C₄×C₁₃₉	1	2	yes	—
418	#117	C₂³×C₁₃₉	1	2	yes	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	2	no	—
432	C₂×C₄²	—	2	2	no	—
433	C₂×C₄²	—	2	2	no	—
434	C₂×C₄²	—	2	2	no	—
435	C₂×C₄²	—	2	2	no	—
436	C₂×C₄²	—	2	2	no	—
437	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
442	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
443	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
444	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
446	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
448	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₄⋊C₈	—	2	2	no	—
451	C₄⋊C₈	—	2	2	no	—
452	#104	—	2	16	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	#97	—	2	2	no	—
456	C₄×C₈	—	2	2	no	—
457	#95	—	2	2	no	—
458	#95	—	2	2	no	—
459	C₂⁴	—	2	1	no	—
460	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
461	#41	—	2	8	no	—
462	#41	—	2	8	no	—
463	#41	—	2	4	no	—
464	#41	—	2	4	no	—
465	#41	—	2	4	no	—
466	#41	#41×C₁₃₉	1	8	yes	—
467	C₂×Q₈	—	2	4	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
493	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
495	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
496	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
497	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
510	M₁₆	—	2	8	no	—
511	C₂×C₈	—	2	4	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
520	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₄²	—	2	8	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	8	no	—
536	C₄²	—	4	4	no	—
537	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
538	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
539	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
540	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
541	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
542	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
543	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
544	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
545	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
546	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
547	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
548	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
549	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
550	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
561	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
562	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
563	Q₈	—	2	4	no	—
564	Q₈	—	2	2	no	—
565	Q₈	#117×C₁₃₉	1	4	yes	complemented
566	D₄	—	2	8	no	—
567	D₄	—	2	4	no	—
568	D₄	—	2	8	no	—
569	D₄	—	2	2	no	—
570	D₄	#117×C₁₃₉	1	4	yes	complemented
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	4	no	—
601	C₂×C₄	—	4	4	no	—
602	C₂×C₄	#104×C₁₃₉	1	4	yes	complemented
603	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
616	C₈	—	4	4	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	C₂×#104×C₁₃₉	1	2	yes	—
630	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
631	C₂²	#525×C₁₃₉	1	2	yes	—
632	C₄	—	2	1	no	—
633	C₄	—	2	4	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	4	8	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	C₂×#104×C₁₃₉	1	2	yes	—
644	C₄	C₂×#104×C₁₃₉	1	2	yes	—
645	C₄	#421×C₁₃₉	1	2	yes	—
646	C₄	C₂×#117×C₁₃₉	1	2	yes	—
647	C₄	#525×C₁₃₉	1	2	yes	—
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	4	4	no	—
652	C₂	#2280×C₁₃₉	1	1	yes	characteristic
653	C₂	C₂²×#104×C₁₃₉	1	1	yes	characteristic
654	C₂	C₂×#421×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2920×C₁₃₉	C₂	semidirect
3. C₄×#117×C₁₃₉	C₂	semidirect
4. #1826×C₁₃₉	C₂	semidirect
5. #1806×C₁₃₉	C₂	semidirect
7. C₄×#104×C₁₃₉	C₂	semidirect
13. C₄×#41×C₁₃₉	C₄	semidirect
14. C₄×#41×C₁₃₉	C₄	semidirect
17. C₂×C₄×Q₈×C₁₃₉	C₄	semidirect
18. C₂×C₄×Q₈×C₁₃₉	C₄	semidirect
21. C₂×C₄×D₄×C₁₃₉	C₄	semidirect
22. C₂×C₄×D₄×C₁₃₉	C₄	semidirect
32. #423×C₁₃₉	C₂²	semidirect
35. C₄×M₁₆×C₁₃₉	C₂²	semidirect
37. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
41. C₄³×C₁₃₉	C₂²	semidirect
42. #339×C₁₃₉	C₂²	semidirect
237. Q₈×C₁₃₉	#117	semidirect
242. D₄×C₁₃₉	#117	semidirect
274. C₂×C₄×C₁₃₉	#104	semidirect
327. #20747	C₁₃₉	direct (N × H)
328. C₁₃₉	#20747	direct (N × H)
330. #2920	C₂×C₁₃₉	semidirect
331. C₄×#117	C₂×C₁₃₉	semidirect
332. #1826	C₂×C₁₃₉	semidirect
333. #1806	C₂×C₁₃₉	semidirect
335. C₄×#104	C₂×C₁₃₉	semidirect
341. C₄×#41	C₄×C₁₃₉	semidirect
342. C₄×#41	C₄×C₁₃₉	semidirect
345. C₂×C₄×Q₈	C₄×C₁₃₉	semidirect
346. C₂×C₄×Q₈	C₄×C₁₃₉	semidirect
349. C₂×C₄×D₄	C₄×C₁₃₉	semidirect
350. C₂×C₄×D₄	C₄×C₁₃₉	semidirect
360. #423	C₂²×C₁₃₉	semidirect
363. C₄×M₁₆	C₂²×C₁₃₉	semidirect
365. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
369. C₄³	C₂²×C₁₃₉	semidirect
370. #339	C₂²×C₁₃₉	semidirect
565. Q₈	#117×C₁₃₉	semidirect
570. D₄	#117×C₁₃₉	semidirect
602. C₂×C₄	#104×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₃₉	2
#2920×C₁₃₉	2
C₄×#117×C₁₃₉	2
#1826×C₁₃₉	2
#1806×C₁₃₉	2
#1789×C₁₃₉	2
C₄×#104×C₁₃₉	2
#20747	139

Subgroups — C139×#20747 #48015343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20747 #48015343