Subgroups — C₁₃₉×#36135 #48030731

Order 35584.

2318 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2553×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2536×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2535×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2478×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2455×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2423×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2359×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2351×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#529×C₁₃₉	—	2	16	no	—
17	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
32	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
33	#399×C₁₃₉	C₂²	1	4	yes	—
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	4	yes	—
36	#397×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	4	yes	—
38	#394×C₁₃₉	C₂²	1	2	yes	—
39	#394×C₁₃₉	C₂²	1	4	yes	—
40	#392×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	1	yes	characteristic
42	#390×C₁₃₉	C₂²	1	1	yes	characteristic
43	#389×C₁₃₉	C₂²	1	4	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	4	yes	—
47	#389×C₁₃₉	C₂²	1	4	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#386×C₁₃₉	C₂²	1	4	yes	—
55	#385×C₁₃₉	C₂²	1	4	yes	—
56	#385×C₁₃₉	C₂²	1	4	yes	—
57	#385×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#384×C₁₃₉	C₂²	1	2	yes	—
60	#382×C₁₃₉	C₂²	1	1	yes	characteristic
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic
62	#382×C₁₃₉	C₂²	1	2	yes	—
63	#382×C₁₃₉	C₂²	1	1	yes	characteristic
64	#380×C₁₃₉	C₂²	1	2	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
74	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
75	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
85	#126×C₁₃₉	—	2	16	no	—
86	#125×C₁₃₉	—	2	8	no	—
87	#124×C₁₃₉	D₄	1	8	yes	complemented
88	#123×C₁₃₉	—	2	16	no	—
89	#123×C₁₃₉	—	2	16	no	—
90	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
91	#121×C₁₃₉	—	2	8	no	—
92	C₄×Q₈×C₁₃₉	—	2	8	no	—
93	C₄×Q₈×C₁₃₉	—	2	4	no	—
94	C₄×D₄×C₁₃₉	—	2	8	no	—
95	C₄×D₄×C₁₃₉	—	2	16	no	—
96	C₄×D₄×C₁₃₉	—	2	8	no	—
97	C₄×D₄×C₁₃₉	—	2	4	no	—
98	C₄×D₄×C₁₃₉	—	2	4	no	—
99	#117×C₁₃₉	—	2	16	no	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	—	2	8	no	—
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	#95×C₁₃₉	C₂³	1	2	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	#95×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	2	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	#95×C₁₃₉	C₂³	1	1	yes	characteristic
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	1	yes	characteristic
148	#95×C₁₃₉	C₂³	1	2	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	2	yes	—
151	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂×Q₈×C₁₃₉	—	2	2	no	—
154	C₂×Q₈×C₁₃₉	—	2	2	no	—
155	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
156	C₂×D₄×C₁₃₉	—	2	4	no	—
157	C₂×D₄×C₁₃₉	—	2	8	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	2	no	—
160	C₂×D₄×C₁₃₉	—	2	2	no	—
161	C₂×D₄×C₁₃₉	—	2	2	no	—
162	C₂×D₄×C₁₃₉	—	4	4	no	—
163	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃₉	—	2	8	no	—
165	C₂²×C₄×C₁₃₉	—	2	4	no	—
166	C₂²×C₄×C₁₃₉	—	2	4	no	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	2	4	no	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	8	no	—
172	C₂²×C₄×C₁₃₉	—	2	4	no	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	4	2	no	—
175	C₂²×C₄×C₁₃₉	—	4	2	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	—	4	4	no	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₁₃₉	—	2	8	no	—
192	C₄⋊C₄×C₁₃₉	—	2	8	no	—
193	C₄⋊C₄×C₁₃₉	—	2	4	no	—
194	C₄⋊C₄×C₁₃₉	—	2	8	no	—
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	8	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	2	2	no	—
199	C₄⋊C₄×C₁₃₉	—	2	2	no	—
200	C₄⋊C₄×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	2	2	no	—
202	C₄⋊C₄×C₁₃₉	—	2	8	no	—
203	C₄⋊C₄×C₁₃₉	—	2	8	no	—
204	C₄⋊C₄×C₁₃₉	—	4	4	no	—
205	C₄⋊C₄×C₁₃₉	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
207	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
208	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
214	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
215	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
216	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
217	C₄²×C₁₃₉	—	2	4	no	—
218	C₄²×C₁₃₉	—	2	4	no	—
219	C₄²×C₁₃₉	—	2	4	no	—
220	C₄²×C₁₃₉	—	2	8	no	—
221	C₄²×C₁₃₉	—	2	4	no	—
222	C₄²×C₁₃₉	—	2	4	no	—
223	C₄²×C₁₃₉	—	2	2	no	—
224	C₄²×C₁₃₉	—	4	2	no	—
225	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
226	C₄²×C₁₃₉	#41	1	4	yes	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	2	no	—
229	C₂³×C₁₃₉	—	2	2	no	—
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	4	no	—
232	C₂³×C₁₃₉	—	2	2	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	4	no	—
236	C₂³×C₁₃₉	—	2	2	no	—
237	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
238	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
239	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₁₃₉	—	2	8	no	—
241	D₄×C₁₃₉	—	2	8	no	—
242	D₄×C₁₃₉	—	2	8	no	—
243	D₄×C₁₃₉	—	4	16	no	—
244	C₂×C₄×C₁₃₉	—	2	2	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	2	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	4	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	4	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	4	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	4	no	—
267	C₂×C₄×C₁₃₉	—	2	4	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	4	8	no	—
271	C₂×C₄×C₁₃₉	—	4	16	no	—
272	C₂×C₄×C₁₃₉	—	4	8	no	—
273	C₂×C₄×C₁₃₉	—	4	8	no	—
274	C₂×C₄×C₁₃₉	—	8	4	no	—
275	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
279	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
281	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
282	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
284	C₂²×C₁₃₉	—	2	4	no	—
285	C₂²×C₁₃₉	—	2	4	no	—
286	C₂²×C₁₃₉	—	2	4	no	—
287	C₂²×C₁₃₉	—	2	8	no	—
288	C₂²×C₁₃₉	—	2	4	no	—
289	C₂²×C₁₃₉	—	4	2	no	—
290	C₂²×C₁₃₉	—	4	2	no	—
291	C₂²×C₁₃₉	—	4	2	no	—
292	C₂²×C₁₃₉	—	4	2	no	—
293	C₂²×C₁₃₉	—	4	2	no	—
294	C₂²×C₁₃₉	—	4	2	no	—
295	C₂²×C₁₃₉	—	4	4	no	—
296	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
297	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
298	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
299	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
300	C₂²×C₁₃₉	#585	1	2	yes	—
301	C₄×C₁₃₉	—	2	2	no	—
302	C₄×C₁₃₉	—	2	4	no	—
303	C₄×C₁₃₉	—	2	4	no	—
304	C₄×C₁₃₉	—	2	4	no	—
305	C₄×C₁₃₉	—	2	2	no	—
306	C₄×C₁₃₉	—	2	4	no	—
307	C₄×C₁₃₉	—	4	2	no	—
308	C₄×C₁₃₉	—	4	2	no	—
309	C₄×C₁₃₉	—	4	2	no	—
310	C₄×C₁₃₉	—	4	4	no	—
311	C₄×C₁₃₉	—	4	4	no	—
312	C₄×C₁₃₉	—	4	2	no	—
313	C₄×C₁₃₉	#547	1	4	yes	—
314	C₂×C₁₃₉	—	4	4	no	—
315	C₂×C₁₃₉	—	4	4	no	—
316	C₂×C₁₃₉	#3444	1	1	yes	characteristic
317	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
318	C₂×C₁₃₉	D₄×#41	1	2	yes	—
319	C₂×C₁₃₉	#3510	1	1	yes	characteristic
320	C₂×C₁₃₉	#3515	1	2	yes	—
321	#36135	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₁₃₉	#36135	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#529	C₂×C₁₃₉	1	2	yes	complemented
324	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
325	#2851	C₂×C₁₃₉	1	2	yes	complemented
326	#2553	C₂×C₁₃₉	1	4	yes	complemented
327	#2536	C₂×C₁₃₉	1	1	yes	characteristic, complemented
328	#2535	C₂×C₁₃₉	1	1	yes	characteristic
329	#2478	C₂×C₁₃₉	1	4	yes	complemented
330	#2455	C₂×C₁₃₉	1	4	yes	complemented
331	#2423	C₂×C₁₃₉	1	2	yes	complemented
332	#2422	C₂×C₁₃₉	1	2	yes	complemented
333	#2359	C₂×C₁₃₉	1	4	yes	complemented
334	#2351	C₂×C₁₃₉	1	1	yes	characteristic, complemented
335	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
336	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
337	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
338	#529	—	2	16	no	—
339	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
340	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
341	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
342	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
343	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
344	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
345	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
346	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
347	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
349	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
351	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
352	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
354	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
355	#399	C₂²×C₁₃₉	1	4	yes	—
356	#398	C₂²×C₁₃₉	1	4	yes	—
357	#398	C₂²×C₁₃₉	1	2	yes	—
358	#397	C₂²×C₁₃₉	1	4	yes	—
359	#397	C₂²×C₁₃₉	1	2	yes	—
360	#394	C₂²×C₁₃₉	1	4	yes	—
361	#394	C₂²×C₁₃₉	1	2	yes	—
362	#392	C₂²×C₁₃₉	1	2	yes	—
363	#391	C₂²×C₁₃₉	1	1	yes	characteristic
364	#390	C₂²×C₁₃₉	1	1	yes	characteristic
365	#389	C₂²×C₁₃₉	1	2	yes	—
366	#389	C₂²×C₁₃₉	1	2	yes	—
367	#389	C₂²×C₁₃₉	1	4	yes	—
368	#389	C₂²×C₁₃₉	1	4	yes	—
369	#389	C₂²×C₁₃₉	1	4	yes	—
370	#388	C₂²×C₁₃₉	1	4	yes	—
371	#388	C₂²×C₁₃₉	1	4	yes	—
372	#388	C₂²×C₁₃₉	1	4	yes	—
373	#387	C₂²×C₁₃₉	1	4	yes	—
374	#387	C₂²×C₁₃₉	1	4	yes	—
375	#387	C₂²×C₁₃₉	1	4	yes	—
376	#386	C₂²×C₁₃₉	1	4	yes	—
377	#385	C₂²×C₁₃₉	1	4	yes	—
378	#385	C₂²×C₁₃₉	1	4	yes	—
379	#385	C₂²×C₁₃₉	1	4	yes	—
380	#385	C₂²×C₁₃₉	1	4	yes	—
381	#384	C₂²×C₁₃₉	1	2	yes	—
382	#382	C₂²×C₁₃₉	1	1	yes	characteristic
383	#382	C₂²×C₁₃₉	1	1	yes	characteristic
384	#382	C₂²×C₁₃₉	1	1	yes	characteristic
385	#382	C₂²×C₁₃₉	1	2	yes	—
386	#380	C₂²×C₁₃₉	1	2	yes	—
387	#380	C₂²×C₁₃₉	1	2	yes	—
388	#380	C₂²×C₁₃₉	1	2	yes	—
389	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
391	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
392	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
397	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
401	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
407	#126	—	2	16	no	—
408	#125	—	2	8	no	—
409	#124	D₄×C₁₃₉	1	8	yes	complemented
410	#123	—	2	16	no	—
411	#123	—	2	16	no	—
412	C₂²⋊Q₈	—	2	8	no	—
413	#121	—	2	8	no	—
414	C₄×Q₈	—	2	8	no	—
415	C₄×Q₈	—	2	4	no	—
416	C₄×D₄	—	2	8	no	—
417	C₄×D₄	—	2	16	no	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	4	no	—
421	#117	—	2	16	no	—
422	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₄²	—	2	8	no	—
449	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
451	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
455	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
457	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
459	#95	C₂³×C₁₃₉	1	1	yes	characteristic
460	#95	C₂³×C₁₃₉	1	2	yes	—
461	#95	C₂³×C₁₃₉	1	4	yes	—
462	#95	C₂³×C₁₃₉	1	1	yes	characteristic
463	#95	C₂³×C₁₃₉	1	2	yes	—
464	#95	C₂³×C₁₃₉	1	2	yes	—
465	#95	C₂³×C₁₃₉	1	4	yes	—
466	#95	C₂³×C₁₃₉	1	4	yes	—
467	#95	C₂³×C₁₃₉	1	2	yes	—
468	#95	C₂³×C₁₃₉	1	4	yes	—
469	#95	C₂³×C₁₃₉	1	4	yes	—
470	#95	C₂³×C₁₃₉	1	2	yes	—
471	#95	C₂³×C₁₃₉	1	4	yes	—
472	#95	C₂³×C₁₃₉	1	2	yes	—
473	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
474	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	4	4	no	—
485	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	8	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	4	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	8	no	—
526	C₄⋊C₄	—	4	4	no	—
527	C₄⋊C₄	—	4	4	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	4	4	no	—
537	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
538	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
539	C₄²	—	2	4	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	8	no	—
543	C₄²	—	2	4	no	—
544	C₄²	—	2	4	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	4	2	no	—
547	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
548	C₄²	#41×C₁₃₉	1	4	yes	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	2	no	—
559	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
560	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
561	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
562	Q₈	—	2	8	no	—
563	D₄	—	2	8	no	—
564	D₄	—	2	8	no	—
565	D₄	—	4	16	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	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	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	16	no	—
594	C₂×C₄	—	4	8	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	8	4	no	—
597	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
599	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
600	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
601	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
602	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
603	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
604	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
605	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	4	no	—
618	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
620	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
621	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²	#585×C₁₃₉	1	2	yes	—
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	4	no	—
633	C₄	—	4	4	no	—
634	C₄	—	4	2	no	—
635	C₄	#547×C₁₃₉	1	4	yes	—
636	C₂	—	4	4	no	—
637	C₂	—	4	4	no	—
638	C₂	#3444×C₁₃₉	1	1	yes	characteristic
639	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
640	C₂	D₄×#41×C₁₃₉	1	2	yes	—
641	C₂	#3510×C₁₃₉	1	1	yes	characteristic
642	C₂	#3515×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2535×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₁₃₉	C₂	semidirect
2. #2859×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2553×C₁₃₉	C₂	semidirect
5. #2536×C₁₃₉	C₂	semidirect
7. #2478×C₁₃₉	C₂	semidirect
8. #2455×C₁₃₉	C₂	semidirect
9. #2423×C₁₃₉	C₂	semidirect
10. #2422×C₁₃₉	C₂	semidirect
11. #2359×C₁₃₉	C₂	semidirect
12. #2351×C₁₃₉	C₂	semidirect
13. #2349×C₁₃₉	C₂	semidirect
14. C₄×#124×C₁₃₉	C₂	semidirect
15. C₄²×D₄×C₁₃₉	C₂	semidirect
87. #124×C₁₃₉	D₄	semidirect
321. #36135	C₁₃₉	direct (N × H)
322. C₁₃₉	#36135	direct (N × H)
323. C₂×#529	C₂×C₁₃₉	semidirect
324. #2859	C₂×C₁₃₉	semidirect
325. #2851	C₂×C₁₃₉	semidirect
326. #2553	C₂×C₁₃₉	semidirect
327. #2536	C₂×C₁₃₉	semidirect
329. #2478	C₂×C₁₃₉	semidirect
330. #2455	C₂×C₁₃₉	semidirect
331. #2423	C₂×C₁₃₉	semidirect
332. #2422	C₂×C₁₃₉	semidirect
333. #2359	C₂×C₁₃₉	semidirect
334. #2351	C₂×C₁₃₉	semidirect
335. #2349	C₂×C₁₃₉	semidirect
336. C₄×#124	C₂×C₁₃₉	semidirect
337. C₄²×D₄	C₂×C₁₃₉	semidirect
409. #124	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×#529×C₁₃₉	2
#2859×C₁₃₉	2
#2851×C₁₃₉	2
#2553×C₁₃₉	2
#2536×C₁₃₉	2
#2535×C₁₃₉	2
#2478×C₁₃₉	2
#2455×C₁₃₉	2
#2423×C₁₃₉	2
#2422×C₁₃₉	2
#2359×C₁₃₉	2
#2351×C₁₃₉	2
#2349×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36135	139

Subgroups — C139×#36135 #48030731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36135 #48030731