Subgroups — C₁₃₉×#36370 #48030966

Order 35584.

1958 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2860×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2507×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2479×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2468×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2458×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2445×C₁₃₉	C₂	1	2	yes	maximal
10	#2359×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2293×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
26	#399×C₁₃₉	C₂²	1	2	yes	—
27	#399×C₁₃₉	C₂²	1	2	yes	—
28	#398×C₁₃₉	C₂²	1	4	yes	—
29	#398×C₁₃₉	C₂²	1	4	yes	—
30	#394×C₁₃₉	C₂²	1	4	yes	—
31	#394×C₁₃₉	C₂²	1	4	yes	—
32	#393×C₁₃₉	C₂²	1	2	yes	—
33	#393×C₁₃₉	C₂²	1	2	yes	—
34	#390×C₁₃₉	C₂²	1	1	yes	characteristic
35	#390×C₁₃₉	C₂²	1	2	yes	—
36	#390×C₁₃₉	C₂²	1	1	yes	characteristic
37	#390×C₁₃₉	C₂²	1	4	yes	—
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	4	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×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	#388×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#386×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	1	yes	characteristic
60	#382×C₁₃₉	C₂²	1	1	yes	characteristic
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic
62	#381×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	4	yes	—
71	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
72	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
73	C₄³×C₁₃₉	C₂²	1	2	yes	—
74	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
82	#127×C₁₃₉	—	2	4	no	—
83	#126×C₁₃₉	—	4	8	no	—
84	#123×C₁₃₉	—	2	16	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×Q₈×C₁₃₉	—	2	4	no	—
87	C₄×D₄×C₁₃₉	—	2	8	no	—
88	C₄×D₄×C₁₃₉	—	2	4	no	—
89	C₄×D₄×C₁₃₉	—	2	4	no	—
90	C₄×D₄×C₁₃₉	—	4	8	no	—
91	#117×C₁₃₉	—	4	8	no	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊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	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
130	#95×C₁₃₉	C₂³	1	2	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	2	yes	—
136	#95×C₁₃₉	C₂³	1	2	yes	—
137	#95×C₁₃₉	C₂³	1	1	yes	characteristic
138	#95×C₁₃₉	C₂³	1	2	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	#95×C₁₃₉	C₂³	1	2	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	1	yes	characteristic
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
146	C₂×Q₈×C₁₃₉	—	2	4	no	—
147	C₂×Q₈×C₁₃₉	—	2	2	no	—
148	C₂×D₄×C₁₃₉	—	2	8	no	—
149	C₂×D₄×C₁₃₉	—	2	2	no	—
150	C₂×D₄×C₁₃₉	—	2	2	no	—
151	C₂×D₄×C₁₃₉	—	2	8	no	—
152	C₂×D₄×C₁₃₉	—	2	2	no	—
153	C₂×D₄×C₁₃₉	—	2	2	no	—
154	C₂×D₄×C₁₃₉	—	2	2	no	—
155	C₂×D₄×C₁₃₉	—	4	4	no	—
156	C₂×D₄×C₁₃₉	#41	1	4	yes	—
157	C₂²×C₄×C₁₃₉	—	2	8	no	—
158	C₂²×C₄×C₁₃₉	—	2	8	no	—
159	C₂²×C₄×C₁₃₉	—	2	4	no	—
160	C₂²×C₄×C₁₃₉	—	2	4	no	—
161	C₂²×C₄×C₁₃₉	—	4	4	no	—
162	C₂²×C₄×C₁₃₉	—	4	4	no	—
163	C₂²×C₄×C₁₃₉	—	4	4	no	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₄⋊C₄×C₁₃₉	—	2	4	no	—
178	C₄⋊C₄×C₁₃₉	—	2	2	no	—
179	C₄⋊C₄×C₁₃₉	—	2	2	no	—
180	C₄⋊C₄×C₁₃₉	—	2	4	no	—
181	C₄⋊C₄×C₁₃₉	—	2	4	no	—
182	C₄⋊C₄×C₁₃₉	—	2	4	no	—
183	C₄⋊C₄×C₁₃₉	—	2	2	no	—
184	C₄⋊C₄×C₁₃₉	—	2	8	no	—
185	C₄⋊C₄×C₁₃₉	—	2	8	no	—
186	C₄⋊C₄×C₁₃₉	—	2	4	no	—
187	C₄⋊C₄×C₁₃₉	—	4	4	no	—
188	C₄⋊C₄×C₁₃₉	—	4	4	no	—
189	C₄⋊C₄×C₁₃₉	—	4	4	no	—
190	C₄⋊C₄×C₁₃₉	—	4	4	no	—
191	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
192	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
198	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
200	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
201	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
202	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
203	C₄²×C₁₃₉	—	2	4	no	—
204	C₄²×C₁₃₉	—	2	4	no	—
205	C₄²×C₁₃₉	—	2	4	no	—
206	C₄²×C₁₃₉	—	2	4	no	—
207	C₄²×C₁₃₉	—	2	4	no	—
208	C₄²×C₁₃₉	—	2	2	no	—
209	C₄²×C₁₃₉	—	2	4	no	—
210	C₄²×C₁₃₉	—	2	4	no	—
211	C₄²×C₁₃₉	—	2	4	no	—
212	C₄²×C₁₃₉	—	2	2	no	—
213	C₄²×C₁₃₉	—	4	4	no	—
214	C₄²×C₁₃₉	#41	1	4	yes	—
215	C₂³×C₁₃₉	—	2	2	no	—
216	C₂³×C₁₃₉	—	2	4	no	—
217	C₂³×C₁₃₉	—	2	4	no	—
218	C₂³×C₁₃₉	—	2	2	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	4	no	—
223	C₂³×C₁₃₉	—	2	2	no	—
224	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
225	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
226	Q₈×C₁₃₉	—	2	8	no	—
227	D₄×C₁₃₉	—	2	8	no	—
228	D₄×C₁₃₉	—	4	16	no	—
229	D₄×C₁₃₉	—	4	4	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	2	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	2	4	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	4	no	—
256	C₂×C₄×C₁₃₉	—	4	16	no	—
257	C₂×C₄×C₁₃₉	—	8	4	no	—
258	C₂×C₄×C₁₃₉	—	8	4	no	—
259	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
260	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
261	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
262	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
263	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
266	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
267	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
268	C₂²×C₁₃₉	—	2	4	no	—
269	C₂²×C₁₃₉	—	2	8	no	—
270	C₂²×C₁₃₉	—	4	2	no	—
271	C₂²×C₁₃₉	—	4	2	no	—
272	C₂²×C₁₃₉	—	4	4	no	—
273	C₂²×C₁₃₉	—	4	2	no	—
274	C₂²×C₁₃₉	—	4	2	no	—
275	C₂²×C₁₃₉	—	4	4	no	—
276	C₂²×C₁₃₉	—	4	2	no	—
277	C₂²×C₁₃₉	—	4	4	no	—
278	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
280	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
281	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
282	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
283	C₄×C₁₃₉	—	2	4	no	—
284	C₄×C₁₃₉	—	2	2	no	—
285	C₄×C₁₃₉	—	2	4	no	—
286	C₄×C₁₃₉	—	2	4	no	—
287	C₄×C₁₃₉	—	2	2	no	—
288	C₄×C₁₃₉	—	2	4	no	—
289	C₄×C₁₃₉	—	4	2	no	—
290	C₄×C₁₃₉	—	4	4	no	—
291	C₄×C₁₃₉	—	4	2	no	—
292	C₄×C₁₃₉	—	4	2	no	—
293	C₄×C₁₃₉	—	4	2	no	—
294	C₄×C₁₃₉	—	4	4	no	—
295	C₄×C₁₃₉	#552	1	4	yes	—
296	C₂×C₁₃₉	—	4	4	no	—
297	C₂×C₁₃₉	—	8	2	no	—
298	C₂×C₁₃₉	#3444	1	1	yes	characteristic
299	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
300	C₂×C₁₃₉	#3481	1	2	yes	—
301	C₂×C₁₃₉	#3508	1	1	yes	characteristic
302	C₂×C₁₃₉	#3522	1	2	yes	—
303	#36370	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₁₃₉	#36370	1	1	yes	characteristic, direct product factor, Sylow
305	#2864	C₂×C₁₃₉	1	1	yes	characteristic, complemented
306	#2860	C₂×C₁₃₉	1	2	yes	complemented
307	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
308	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
309	#2507	C₂×C₁₃₉	1	2	yes	complemented
310	#2479	C₂×C₁₃₉	1	4	yes	complemented
311	#2468	C₂×C₁₃₉	1	4	yes	complemented
312	#2458	C₂×C₁₃₉	1	4	yes	complemented
313	#2445	C₂×C₁₃₉	1	2	yes	—
314	#2359	C₂×C₁₃₉	1	4	yes	complemented
315	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
316	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
317	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic
318	#2293	C₂×C₁₃₉	1	2	yes	complemented
319	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
320	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
321	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
322	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
323	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
328	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
329	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
330	#399	C₂²×C₁₃₉	1	2	yes	—
331	#399	C₂²×C₁₃₉	1	2	yes	—
332	#398	C₂²×C₁₃₉	1	4	yes	—
333	#398	C₂²×C₁₃₉	1	4	yes	—
334	#394	C₂²×C₁₃₉	1	4	yes	—
335	#394	C₂²×C₁₃₉	1	4	yes	—
336	#393	C₂²×C₁₃₉	1	2	yes	—
337	#393	C₂²×C₁₃₉	1	2	yes	—
338	#390	C₂²×C₁₃₉	1	1	yes	characteristic
339	#390	C₂²×C₁₃₉	1	4	yes	—
340	#390	C₂²×C₁₃₉	1	1	yes	characteristic
341	#390	C₂²×C₁₃₉	1	2	yes	—
342	#390	C₂²×C₁₃₉	1	2	yes	—
343	#390	C₂²×C₁₃₉	1	2	yes	—
344	#389	C₂²×C₁₃₉	1	2	yes	—
345	#389	C₂²×C₁₃₉	1	2	yes	—
346	#389	C₂²×C₁₃₉	1	2	yes	—
347	#389	C₂²×C₁₃₉	1	2	yes	—
348	#389	C₂²×C₁₃₉	1	2	yes	—
349	#389	C₂²×C₁₃₉	1	4	yes	—
350	#388	C₂²×C₁₃₉	1	4	yes	—
351	#388	C₂²×C₁₃₉	1	4	yes	—
352	#388	C₂²×C₁₃₉	1	4	yes	—
353	#388	C₂²×C₁₃₉	1	4	yes	—
354	#388	C₂²×C₁₃₉	1	4	yes	—
355	#388	C₂²×C₁₃₉	1	4	yes	—
356	#387	C₂²×C₁₃₉	1	4	yes	—
357	#387	C₂²×C₁₃₉	1	4	yes	—
358	#387	C₂²×C₁₃₉	1	4	yes	—
359	#386	C₂²×C₁₃₉	1	4	yes	—
360	#385	C₂²×C₁₃₉	1	4	yes	—
361	#385	C₂²×C₁₃₉	1	4	yes	—
362	#385	C₂²×C₁₃₉	1	4	yes	—
363	#384	C₂²×C₁₃₉	1	1	yes	characteristic
364	#382	C₂²×C₁₃₉	1	1	yes	characteristic
365	#382	C₂²×C₁₃₉	1	1	yes	characteristic
366	#381	C₂²×C₁₃₉	1	2	yes	—
367	#380	C₂²×C₁₃₉	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
376	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
377	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
378	C₄³	C₂²×C₁₃₉	1	2	yes	—
379	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
382	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
386	#127	—	2	4	no	—
387	#126	—	4	8	no	—
388	#123	—	2	16	no	—
389	C₄×Q₈	—	2	8	no	—
390	C₄×Q₈	—	2	4	no	—
391	C₄×D₄	—	2	8	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	4	8	no	—
395	#117	—	4	8	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
425	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
426	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
433	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
434	#95	C₂³×C₁₃₉	1	1	yes	characteristic
435	#95	C₂³×C₁₃₉	1	2	yes	—
436	#95	C₂³×C₁₃₉	1	4	yes	—
437	#95	C₂³×C₁₃₉	1	2	yes	—
438	#95	C₂³×C₁₃₉	1	4	yes	—
439	#95	C₂³×C₁₃₉	1	4	yes	—
440	#95	C₂³×C₁₃₉	1	1	yes	characteristic
441	#95	C₂³×C₁₃₉	1	2	yes	—
442	#95	C₂³×C₁₃₉	1	2	yes	—
443	#95	C₂³×C₁₃₉	1	4	yes	—
444	#95	C₂³×C₁₃₉	1	2	yes	—
445	#95	C₂³×C₁₃₉	1	2	yes	—
446	#95	C₂³×C₁₃₉	1	4	yes	—
447	#95	C₂³×C₁₃₉	1	4	yes	—
448	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	#41×C₁₃₉	1	4	yes	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	4	4	no	—
492	C₄⋊C₄	—	4	4	no	—
493	C₄⋊C₄	—	4	4	no	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
496	C₂²⋊C₄	—	2	8	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	4	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	2	4	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	4	4	no	—
518	C₄²	#41×C₁₃₉	1	4	yes	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	2	no	—
528	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
529	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
530	Q₈	—	2	8	no	—
531	D₄	—	2	8	no	—
532	D₄	—	4	16	no	—
533	D₄	—	4	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	4	16	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
564	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
565	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
566	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
567	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
568	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
569	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
570	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
571	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
583	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
584	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
585	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
586	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
587	C₄	—	2	4	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	4	no	—
590	C₄	—	2	4	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	4	no	—
599	C₄	#552×C₁₃₉	1	4	yes	—
600	C₂	—	4	4	no	—
601	C₂	—	8	2	no	—
602	C₂	#3444×C₁₃₉	1	1	yes	characteristic
603	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
604	C₂	#3481×C₁₃₉	1	2	yes	—
605	C₂	#3508×C₁₃₉	1	1	yes	characteristic
606	C₂	#3522×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
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. #2864×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2580×C₁₃₉	C₂	semidirect
4. #2580×C₁₃₉	C₂	semidirect
5. #2507×C₁₃₉	C₂	semidirect
6. #2479×C₁₃₉	C₂	semidirect
7. #2468×C₁₃₉	C₂	semidirect
8. #2458×C₁₃₉	C₂	semidirect
10. #2359×C₁₃₉	C₂	semidirect
11. #2357×C₁₃₉	C₂	semidirect
12. #2349×C₁₃₉	C₂	semidirect
14. #2293×C₁₃₉	C₂	semidirect
15. C₄²×Q₈×C₁₃₉	C₂	semidirect
303. #36370	C₁₃₉	direct (N × H)
304. C₁₃₉	#36370	direct (N × H)
305. #2864	C₂×C₁₃₉	semidirect
306. #2860	C₂×C₁₃₉	semidirect
307. #2580	C₂×C₁₃₉	semidirect
308. #2580	C₂×C₁₃₉	semidirect
309. #2507	C₂×C₁₃₉	semidirect
310. #2479	C₂×C₁₃₉	semidirect
311. #2468	C₂×C₁₃₉	semidirect
312. #2458	C₂×C₁₃₉	semidirect
314. #2359	C₂×C₁₃₉	semidirect
315. #2357	C₂×C₁₃₉	semidirect
316. #2349	C₂×C₁₃₉	semidirect
318. #2293	C₂×C₁₃₉	semidirect
319. C₄²×Q₈	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₉	2
#2860×C₁₃₉	2
#2580×C₁₃₉	2
#2507×C₁₃₉	2
#2479×C₁₃₉	2
#2468×C₁₃₉	2
#2458×C₁₃₉	2
#2445×C₁₃₉	2
#2359×C₁₃₉	2
#2357×C₁₃₉	2
#2349×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2293×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36370	139

Subgroups — C139×#36370 #48030966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36370 #48030966