Subgroups — C₁₃₉×#22134 #48016730

Order 35584.

916 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1955×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1954×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1940×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1923×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1869×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1850×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1798×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₃₉	—	2	4	no	—
17	#433×C₁₃₉	—	2	4	no	—
18	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	#398×C₁₃₉	C₄	1	1	yes	characteristic
33	#397×C₁₃₉	C₄	1	1	yes	characteristic
34	#396×C₁₃₉	C₄	1	2	yes	—
35	#394×C₁₃₉	C₄	1	1	yes	characteristic
36	#394×C₁₃₉	C₄	1	2	yes	—
37	#392×C₁₃₉	C₄	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	#336×C₁₃₉	C₂²	1	2	yes	—
41	#336×C₁₃₉	C₂²	1	2	yes	—
42	#336×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₉	—	2	4	no	—
48	C₂²×C₈×C₁₃₉	—	4	2	no	—
49	C₂²×C₈×C₁₃₉	—	4	2	no	—
50	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₁₃₉	—	2	2	no	—
57	C₄×D₄×C₁₃₉	—	2	2	no	—
58	C₄×D₄×C₁₃₉	—	4	2	no	—
59	C₄×D₄×C₁₃₉	—	4	2	no	—
60	#117×C₁₃₉	—	2	2	no	—
61	#117×C₁₃₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₁₃₉	—	2	2	no	—
78	C₄⋊C₈×C₁₃₉	—	2	2	no	—
79	C₄⋊C₈×C₁₃₉	—	2	2	no	—
80	C₄⋊C₈×C₁₃₉	—	2	2	no	—
81	C₄⋊C₈×C₁₃₉	—	4	2	no	—
82	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
83	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
84	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
85	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
86	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
87	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
88	#97×C₁₃₉	—	2	2	no	—
89	C₄×C₈×C₁₃₉	—	4	2	no	—
90	C₄×C₈×C₁₃₉	D₄	1	4	yes	complemented
91	#95×C₁₃₉	C₂×C₄	1	2	yes	—
92	#95×C₁₃₉	C₂×C₄	1	1	yes	characteristic
93	#95×C₁₃₉	C₂×C₄	1	2	yes	—
94	#95×C₁₃₉	C₂×C₄	1	1	yes	characteristic
95	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
96	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₁₃₉	—	2	4	no	—
98	C₂×D₄×C₁₃₉	—	2	4	no	—
99	C₂×D₄×C₁₃₉	—	2	2	no	—
100	C₂×D₄×C₁₃₉	—	2	4	no	—
101	C₂×D₄×C₁₃₉	—	4	2	no	—
102	C₂²×C₄×C₁₃₉	—	2	1	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	1	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	1	no	—
110	C₂²×C₄×C₁₃₉	—	2	1	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	—	2	2	no	—
113	C₂²×C₄×C₁₃₉	—	2	1	no	—
114	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₃₉	—	2	1	no	—
124	C₂×C₈×C₁₃₉	—	2	1	no	—
125	C₂×C₈×C₁₃₉	—	2	1	no	—
126	C₂×C₈×C₁₃₉	—	2	1	no	—
127	C₂×C₈×C₁₃₉	—	2	1	no	—
128	C₂×C₈×C₁₃₉	—	2	1	no	—
129	C₂×C₈×C₁₃₉	—	2	2	no	—
130	C₂×C₈×C₁₃₉	—	2	2	no	—
131	C₂×C₈×C₁₃₉	—	2	2	no	—
132	C₂×C₈×C₁₃₉	—	2	1	no	—
133	C₂×C₈×C₁₃₉	—	2	1	no	—
134	C₂×C₈×C₁₃₉	—	2	2	no	—
135	C₂×C₈×C₁₃₉	—	2	2	no	—
136	C₂×C₈×C₁₃₉	—	2	1	no	—
137	C₂×C₈×C₁₃₉	—	2	2	no	—
138	C₂×C₈×C₁₃₉	—	2	1	no	—
139	C₂×C₈×C₁₃₉	—	4	8	no	—
140	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₁₃₉	—	2	2	no	—
143	C₄⋊C₄×C₁₃₉	—	2	2	no	—
144	C₄⋊C₄×C₁₃₉	—	2	2	no	—
145	C₄⋊C₄×C₁₃₉	—	2	4	no	—
146	C₄⋊C₄×C₁₃₉	—	4	2	no	—
147	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
153	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
154	C₄²×C₁₃₉	—	2	1	no	—
155	C₄²×C₁₃₉	—	2	1	no	—
156	C₄²×C₁₃₉	—	2	2	no	—
157	C₄²×C₁₃₉	—	2	2	no	—
158	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃₉	#41	1	2	yes	—
160	C₂³×C₁₃₉	—	2	2	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	1	no	—
167	C₂³×C₁₃₉	—	2	1	no	—
168	C₂³×C₁₃₉	—	2	1	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	2	no	—
171	C₂³×C₁₃₉	#131	1	4	yes	—
172	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
173	D₄×C₁₃₉	—	2	8	no	—
174	D₄×C₁₃₉	—	4	8	no	—
175	C₂×C₄×C₁₃₉	—	2	2	no	—
176	C₂×C₄×C₁₃₉	—	2	2	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	1	no	—
180	C₂×C₄×C₁₃₉	—	2	1	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	1	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	2	1	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	1	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	4	2	no	—
193	C₂×C₄×C₁₃₉	—	4	1	no	—
194	C₂×C₄×C₁₃₉	—	4	2	no	—
195	C₂×C₄×C₁₃₉	—	4	1	no	—
196	C₂×C₄×C₁₃₉	—	4	2	no	—
197	C₂×C₄×C₁₃₉	—	4	1	no	—
198	C₂×C₄×C₁₃₉	—	4	2	no	—
199	C₂×C₄×C₁₃₉	—	4	1	no	—
200	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₁₃₉	#131	1	4	yes	—
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₃₉	—	2	2	no	—
210	C₈×C₁₃₉	—	2	2	no	—
211	C₈×C₁₃₉	—	4	1	no	—
212	C₈×C₁₃₉	—	4	2	no	—
213	C₈×C₁₃₉	—	4	1	no	—
214	C₈×C₁₃₉	—	4	2	no	—
215	C₂²×C₁₃₉	—	2	4	no	—
216	C₂²×C₁₃₉	—	2	4	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	4	2	no	—
219	C₂²×C₁₃₉	—	4	2	no	—
220	C₂²×C₁₃₉	—	4	2	no	—
221	C₂²×C₁₃₉	—	4	2	no	—
222	C₂²×C₁₃₉	—	4	1	no	—
223	C₂²×C₁₃₉	—	4	1	no	—
224	C₂²×C₁₃₉	—	4	1	no	—
225	C₂²×C₁₃₉	—	4	2	no	—
226	C₂²×C₁₃₉	—	4	2	no	—
227	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₃₉	#518	1	1	yes	characteristic
229	C₂²×C₁₃₉	#520	1	1	yes	characteristic
230	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
231	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
232	C₄×C₁₃₉	—	2	2	no	—
233	C₄×C₁₃₉	—	2	2	no	—
234	C₄×C₁₃₉	—	2	4	no	—
235	C₄×C₁₃₉	—	4	2	no	—
236	C₄×C₁₃₉	—	4	1	no	—
237	C₄×C₁₃₉	—	4	1	no	—
238	C₄×C₁₃₉	—	4	1	no	—
239	C₄×C₁₃₉	—	4	2	no	—
240	C₄×C₁₃₉	#535	1	1	yes	characteristic
241	C₄×C₁₃₉	#537	1	1	yes	characteristic
242	C₄×C₁₃₉	#540	1	1	yes	characteristic
243	C₄×C₁₃₉	#542	1	1	yes	characteristic
244	C₂×C₁₃₉	—	4	4	no	—
245	C₂×C₁₃₉	—	8	1	no	—
246	C₂×C₁₃₉	#2324	1	1	yes	characteristic
247	C₂×C₁₃₉	#2929	1	1	yes	characteristic
248	C₂×C₁₃₉	#2931	1	1	yes	characteristic
249	C₂×C₁₃₉	#2977	1	2	yes	—
250	C₂×C₁₃₉	#2994	1	2	yes	—
251	#22134	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₁₃₉	#22134	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×C₈×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	C₂×#433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
255	#2392	C₂×C₁₃₉	1	1	yes	characteristic
256	#1955	C₂×C₁₃₉	1	1	yes	characteristic, complemented
257	#1954	C₂×C₁₃₉	1	2	yes	complemented
258	#1940	C₂×C₁₃₉	1	1	yes	characteristic, complemented
259	#1923	C₂×C₁₃₉	1	2	yes	complemented
260	#1869	C₂×C₁₃₉	1	2	yes	complemented
261	#1850	C₂×C₁₃₉	1	2	yes	complemented
262	#1798	C₂×C₁₃₉	1	1	yes	characteristic, complemented
263	C₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
264	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
267	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
268	C₈×D₄	—	2	4	no	—
269	#433	—	2	4	no	—
270	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
279	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
281	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
283	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
284	#398	C₄×C₁₃₉	1	1	yes	characteristic
285	#397	C₄×C₁₃₉	1	1	yes	characteristic
286	#396	C₄×C₁₃₉	1	2	yes	—
287	#394	C₄×C₁₃₉	1	2	yes	—
288	#394	C₄×C₁₃₉	1	1	yes	characteristic
289	#392	C₄×C₁₃₉	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
292	#336	C₂²×C₁₃₉	1	2	yes	—
293	#336	C₂²×C₁₃₉	1	2	yes	—
294	#336	C₂²×C₁₃₉	1	2	yes	—
295	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
296	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
299	C₂²×C₈	—	2	4	no	—
300	C₂²×C₈	—	4	2	no	—
301	C₂²×C₈	—	4	2	no	—
302	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	4	2	no	—
311	C₄×D₄	—	4	2	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	4	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	4	2	no	—
338	C₂²⋊C₈	—	4	2	no	—
339	C₂²⋊C₈	—	4	2	no	—
340	#97	—	2	2	no	—
341	C₄×C₈	—	4	2	no	—
342	C₄×C₈	D₄×C₁₃₉	1	4	yes	complemented
343	#95	C₂×C₄×C₁₃₉	1	2	yes	—
344	#95	C₂×C₄×C₁₃₉	1	2	yes	—
345	#95	C₂×C₄×C₁₃₉	1	1	yes	characteristic
346	#95	C₂×C₄×C₁₃₉	1	1	yes	characteristic
347	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
348	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	4	8	no	—
392	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
393	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
411	C₄²	#41×C₁₃₉	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	#131×C₁₃₉	1	4	yes	—
424	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
425	D₄	—	2	8	no	—
426	D₄	—	4	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
453	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
454	C₂×C₄	#131×C₁₃₉	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
458	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
460	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
480	C₂²	#518×C₁₃₉	1	1	yes	characteristic
481	C₂²	#520×C₁₃₉	1	1	yes	characteristic
482	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
483	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	2	no	—
492	C₄	#535×C₁₃₉	1	1	yes	characteristic
493	C₄	#537×C₁₃₉	1	1	yes	characteristic
494	C₄	#540×C₁₃₉	1	1	yes	characteristic
495	C₄	#542×C₁₃₉	1	1	yes	characteristic
496	C₂	—	4	4	no	—
497	C₂	—	8	1	no	—
498	C₂	#2324×C₁₃₉	1	1	yes	characteristic
499	C₂	#2929×C₁₃₉	1	1	yes	characteristic
500	C₂	#2931×C₁₃₉	1	1	yes	characteristic
501	C₂	#2977×C₁₃₉	1	2	yes	—
502	C₂	#2994×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂³×C₄
prime radical	#392×C₁₃₉	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₃₉	C₂	semidirect
2. C₂×#433×C₁₃₉	C₂	semidirect
4. #1955×C₁₃₉	C₂	semidirect
5. #1954×C₁₃₉	C₂	semidirect
6. #1940×C₁₃₉	C₂	semidirect
7. #1923×C₁₃₉	C₂	semidirect
8. #1869×C₁₃₉	C₂	semidirect
9. #1850×C₁₃₉	C₂	semidirect
10. #1798×C₁₃₉	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
90. C₄×C₈×C₁₃₉	D₄	semidirect
251. #22134	C₁₃₉	direct (N × H)
252. C₁₃₉	#22134	direct (N × H)
253. C₂×C₈×D₄	C₂×C₁₃₉	semidirect
254. C₂×#433	C₂×C₁₃₉	semidirect
256. #1955	C₂×C₁₃₉	semidirect
257. #1954	C₂×C₁₃₉	semidirect
258. #1940	C₂×C₁₃₉	semidirect
259. #1923	C₂×C₁₃₉	semidirect
260. #1869	C₂×C₁₃₉	semidirect
261. #1850	C₂×C₁₃₉	semidirect
262. #1798	C₂×C₁₃₉	semidirect
263. C₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
342. C₄×C₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃₉	2
C₂×#433×C₁₃₉	2
#2392×C₁₃₉	2
#1955×C₁₃₉	2
#1954×C₁₃₉	2
#1940×C₁₃₉	2
#1923×C₁₃₉	2
#1869×C₁₃₉	2
#1850×C₁₃₉	2
#1798×C₁₃₉	2
C₈×C₄⋊C₄×C₁₃₉	2
#22134	139

Subgroups — C139×#22134 #48016730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#22134 #48016730