Subgroups — C₁₃₉×#36191 #48030787

Order 35584.

1826 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2574×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2570×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2520×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2450×C₁₃₉	C₂	1	4	yes	maximal
8	#2440×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2439×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2368×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2352×C₁₃₉	C₂	1	2	yes	maximal
12	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
25	#400×C₁₃₉	C₂²	1	4	yes	—
26	#398×C₁₃₉	C₂²	1	4	yes	—
27	#398×C₁₃₉	C₂²	1	4	yes	—
28	#396×C₁₃₉	C₂²	1	4	yes	—
29	#395×C₁₃₉	C₂²	1	4	yes	—
30	#393×C₁₃₉	C₂²	1	4	yes	—
31	#391×C₁₃₉	C₂²	1	4	yes	—
32	#391×C₁₃₉	C₂²	1	4	yes	—
33	#391×C₁₃₉	C₂²	1	4	yes	—
34	#389×C₁₃₉	C₂²	1	2	yes	—
35	#389×C₁₃₉	C₂²	1	2	yes	—
36	#389×C₁₃₉	C₂²	1	2	yes	—
37	#388×C₁₃₉	C₂²	1	4	yes	—
38	#387×C₁₃₉	C₂²	1	4	yes	—
39	#387×C₁₃₉	C₂²	1	4	yes	—
40	#387×C₁₃₉	C₂²	1	4	yes	—
41	#387×C₁₃₉	C₂²	1	4	yes	—
42	#387×C₁₃₉	C₂²	1	4	yes	—
43	#387×C₁₃₉	C₂²	1	4	yes	—
44	#387×C₁₃₉	C₂²	1	4	yes	—
45	#386×C₁₃₉	C₂²	1	4	yes	—
46	#385×C₁₃₉	C₂²	1	4	yes	—
47	#385×C₁₃₉	C₂²	1	4	yes	—
48	#385×C₁₃₉	C₂²	1	4	yes	—
49	#384×C₁₃₉	C₂²	1	2	yes	—
50	#382×C₁₃₉	C₂²	1	4	yes	—
51	#382×C₁₃₉	C₂²	1	1	yes	characteristic
52	#382×C₁₃₉	C₂²	1	2	yes	—
53	#382×C₁₃₉	C₂²	1	1	yes	characteristic
54	#382×C₁₃₉	C₂²	1	1	yes	characteristic
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#380×C₁₃₉	C₂²	1	4	yes	—
57	#380×C₁₃₉	C₂²	1	2	yes	—
58	#380×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
69	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
70	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
79	#125×C₁₃₉	—	2	4	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
81	C₄×D₄×C₁₃₉	—	2	8	no	—
82	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
83	#117×C₁₃₉	—	4	4	no	—
84	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃₉	—	2	4	no	—
107	C₂×C₄²×C₁₃₉	—	2	4	no	—
108	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
119	#95×C₁₃₉	C₂³	1	2	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	2	yes	—
131	#95×C₁₃₉	C₂³	1	2	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	C₂×Q₈×C₁₃₉	—	2	8	no	—
138	C₂×Q₈×C₁₃₉	—	4	4	no	—
139	C₂×Q₈×C₁₃₉	—	4	4	no	—
140	C₂×D₄×C₁₃₉	—	2	4	no	—
141	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	2	no	—
144	C₂²×C₄×C₁₃₉	—	2	2	no	—
145	C₂²×C₄×C₁₃₉	—	2	2	no	—
146	C₂²×C₄×C₁₃₉	—	2	4	no	—
147	C₂²×C₄×C₁₃₉	—	2	8	no	—
148	C₂²×C₄×C₁₃₉	—	2	4	no	—
149	C₂²×C₄×C₁₃₉	—	2	4	no	—
150	C₂²×C₄×C₁₃₉	—	2	4	no	—
151	C₂²×C₄×C₁₃₉	—	4	2	no	—
152	C₂²×C₄×C₁₃₉	—	4	2	no	—
153	C₂²×C₄×C₁₃₉	—	4	4	no	—
154	C₂²×C₄×C₁₃₉	—	4	4	no	—
155	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
170	C₄⋊C₄×C₁₃₉	—	2	4	no	—
171	C₄⋊C₄×C₁₃₉	—	2	8	no	—
172	C₄⋊C₄×C₁₃₉	—	2	8	no	—
173	C₄⋊C₄×C₁₃₉	—	2	8	no	—
174	C₄⋊C₄×C₁₃₉	—	2	8	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	2	4	no	—
177	C₄⋊C₄×C₁₃₉	—	2	4	no	—
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	4	4	no	—
180	C₄⋊C₄×C₁₃₉	—	4	4	no	—
181	C₄⋊C₄×C₁₃₉	—	4	4	no	—
182	C₄⋊C₄×C₁₃₉	—	4	4	no	—
183	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
184	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
189	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
190	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
191	C₄²×C₁₃₉	—	2	4	no	—
192	C₄²×C₁₃₉	—	2	2	no	—
193	C₄²×C₁₃₉	—	2	4	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	2	4	no	—
196	C₄²×C₁₃₉	—	2	2	no	—
197	C₄²×C₁₃₉	—	4	2	no	—
198	C₄²×C₁₃₉	—	4	4	no	—
199	C₄²×C₁₃₉	—	4	4	no	—
200	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
201	C₄²×C₁₃₉	#41	1	4	yes	—
202	C₂³×C₁₃₉	—	2	1	no	—
203	C₂³×C₁₃₉	—	2	1	no	—
204	C₂³×C₁₃₉	—	2	2	no	—
205	C₂³×C₁₃₉	—	2	2	no	—
206	C₂³×C₁₃₉	—	2	1	no	—
207	C₂³×C₁₃₉	—	2	1	no	—
208	C₂³×C₁₃₉	—	2	2	no	—
209	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
210	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
211	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
212	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
213	Q₈×C₁₃₉	—	8	8	no	—
214	D₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	2	1	no	—
216	C₂×C₄×C₁₃₉	—	2	1	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	1	no	—
222	C₂×C₄×C₁₃₉	—	2	1	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	8	no	—
228	C₂×C₄×C₁₃₉	—	2	8	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	4	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	4	no	—
236	C₂×C₄×C₁₃₉	—	2	4	no	—
237	C₂×C₄×C₁₃₉	—	2	4	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	4	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	4	8	no	—
245	C₂×C₄×C₁₃₉	—	4	8	no	—
246	C₂×C₄×C₁₃₉	—	8	8	no	—
247	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
248	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
249	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
250	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
251	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
252	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
253	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
254	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
255	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
256	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
257	C₂²×C₁₃₉	—	2	2	no	—
258	C₂²×C₁₃₉	—	2	4	no	—
259	C₂²×C₁₃₉	—	2	2	no	—
260	C₂²×C₁₃₉	—	2	4	no	—
261	C₂²×C₁₃₉	—	2	2	no	—
262	C₂²×C₁₃₉	—	2	2	no	—
263	C₂²×C₁₃₉	—	2	2	no	—
264	C₂²×C₁₃₉	—	4	2	no	—
265	C₂²×C₁₃₉	—	4	2	no	—
266	C₂²×C₁₃₉	#533	1	4	yes	—
267	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
268	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
269	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₂²×C₁₃₉	#585	1	2	yes	—
272	C₄×C₁₃₉	—	2	2	no	—
273	C₄×C₁₃₉	—	2	2	no	—
274	C₄×C₁₃₉	—	2	2	no	—
275	C₄×C₁₃₉	—	2	4	no	—
276	C₄×C₁₃₉	—	2	4	no	—
277	C₄×C₁₃₉	—	2	2	no	—
278	C₄×C₁₃₉	—	2	4	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₄×C₁₃₉	—	4	2	no	—
281	C₄×C₁₃₉	—	4	4	no	—
282	C₄×C₁₃₉	—	4	4	no	—
283	C₄×C₁₃₉	—	4	4	no	—
284	C₄×C₁₃₉	#554	1	4	yes	—
285	C₂×C₁₃₉	—	2	4	no	—
286	C₂×C₁₃₉	—	4	2	no	—
287	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
288	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
289	C₂×C₁₃₉	#3475	1	2	yes	—
290	C₂×C₁₃₉	#3504	1	1	yes	characteristic
291	C₂×C₁₃₉	#3514	1	2	yes	—
292	#36191	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₁₃₉	#36191	1	1	yes	characteristic, direct product factor, Sylow
294	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
296	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
297	#2574	C₂×C₁₃₉	1	4	yes	complemented
298	#2570	C₂×C₁₃₉	1	2	yes	complemented
299	#2520	C₂×C₁₃₉	1	4	yes	complemented
300	#2450	C₂×C₁₃₉	1	4	yes	—
301	#2440	C₂×C₁₃₉	1	2	yes	complemented
302	#2439	C₂×C₁₃₉	1	2	yes	complemented
303	#2368	C₂×C₁₃₉	1	4	yes	complemented
304	#2352	C₂×C₁₃₉	1	2	yes	—
305	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
306	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
307	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
308	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
310	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
311	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
312	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
314	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
315	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
316	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
318	#400	C₂²×C₁₃₉	1	4	yes	—
319	#398	C₂²×C₁₃₉	1	4	yes	—
320	#398	C₂²×C₁₃₉	1	4	yes	—
321	#396	C₂²×C₁₃₉	1	4	yes	—
322	#395	C₂²×C₁₃₉	1	4	yes	—
323	#393	C₂²×C₁₃₉	1	4	yes	—
324	#391	C₂²×C₁₃₉	1	4	yes	—
325	#391	C₂²×C₁₃₉	1	4	yes	—
326	#391	C₂²×C₁₃₉	1	4	yes	—
327	#389	C₂²×C₁₃₉	1	2	yes	—
328	#389	C₂²×C₁₃₉	1	2	yes	—
329	#389	C₂²×C₁₃₉	1	2	yes	—
330	#388	C₂²×C₁₃₉	1	4	yes	—
331	#387	C₂²×C₁₃₉	1	4	yes	—
332	#387	C₂²×C₁₃₉	1	4	yes	—
333	#387	C₂²×C₁₃₉	1	4	yes	—
334	#387	C₂²×C₁₃₉	1	4	yes	—
335	#387	C₂²×C₁₃₉	1	4	yes	—
336	#387	C₂²×C₁₃₉	1	4	yes	—
337	#387	C₂²×C₁₃₉	1	4	yes	—
338	#386	C₂²×C₁₃₉	1	4	yes	—
339	#385	C₂²×C₁₃₉	1	4	yes	—
340	#385	C₂²×C₁₃₉	1	4	yes	—
341	#385	C₂²×C₁₃₉	1	4	yes	—
342	#384	C₂²×C₁₃₉	1	2	yes	—
343	#382	C₂²×C₁₃₉	1	1	yes	characteristic
344	#382	C₂²×C₁₃₉	1	2	yes	—
345	#382	C₂²×C₁₃₉	1	2	yes	—
346	#382	C₂²×C₁₃₉	1	4	yes	—
347	#382	C₂²×C₁₃₉	1	1	yes	characteristic
348	#382	C₂²×C₁₃₉	1	1	yes	characteristic
349	#380	C₂²×C₁₃₉	1	4	yes	—
350	#380	C₂²×C₁₃₉	1	2	yes	—
351	#380	C₂²×C₁₃₉	1	2	yes	—
352	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
353	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
354	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
356	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
361	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
362	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
363	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
364	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
365	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
371	C₄⋊Q₈	—	4	4	no	—
372	#125	—	2	4	no	—
373	C₂²⋊Q₈	—	2	16	no	—
374	C₄×D₄	—	2	8	no	—
375	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
376	#117	—	4	4	no	—
377	C₂×C₄⋊C₄	—	4	4	no	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
399	C₂×C₄²	—	2	4	no	—
400	C₂×C₄²	—	2	4	no	—
401	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
412	#95	C₂³×C₁₃₉	1	4	yes	—
413	#95	C₂³×C₁₃₉	1	4	yes	—
414	#95	C₂³×C₁₃₉	1	4	yes	—
415	#95	C₂³×C₁₃₉	1	4	yes	—
416	#95	C₂³×C₁₃₉	1	2	yes	—
417	#95	C₂³×C₁₃₉	1	2	yes	—
418	#95	C₂³×C₁₃₉	1	2	yes	—
419	#95	C₂³×C₁₃₉	1	4	yes	—
420	#95	C₂³×C₁₃₉	1	4	yes	—
421	#95	C₂³×C₁₃₉	1	4	yes	—
422	#95	C₂³×C₁₃₉	1	4	yes	—
423	#95	C₂³×C₁₃₉	1	4	yes	—
424	#95	C₂³×C₁₃₉	1	4	yes	—
425	#95	C₂³×C₁₃₉	1	4	yes	—
426	#95	C₂³×C₁₃₉	1	4	yes	—
427	#95	C₂³×C₁₃₉	1	4	yes	—
428	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
430	C₂×Q₈	—	2	8	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
449	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	8	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	4	4	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
482	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
483	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	4	2	no	—
491	C₄²	—	4	4	no	—
492	C₄²	—	4	4	no	—
493	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
494	C₄²	#41×C₁₃₉	1	4	yes	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
503	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
504	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
505	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
506	Q₈	—	8	8	no	—
507	D₄	—	2	8	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	8	8	no	—
540	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
541	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
542	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
543	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
544	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
545	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
546	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
547	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
548	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
549	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	#533×C₁₃₉	1	4	yes	—
560	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
561	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
562	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
563	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
564	C₂²	#585×C₁₃₉	1	2	yes	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	4	no	—
577	C₄	#554×C₁₃₉	1	4	yes	—
578	C₂	—	2	4	no	—
579	C₂	—	4	2	no	—
580	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
581	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
582	C₂	#3475×C₁₃₉	1	2	yes	—
583	C₂	#3504×C₁₃₉	1	1	yes	characteristic
584	C₂	#3514×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2862×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2574×C₁₃₉	C₂	semidirect
5. #2570×C₁₃₉	C₂	semidirect
6. #2520×C₁₃₉	C₂	semidirect
8. #2440×C₁₃₉	C₂	semidirect
9. #2439×C₁₃₉	C₂	semidirect
10. #2368×C₁₃₉	C₂	semidirect
12. C₄×#125×C₁₃₉	C₂	semidirect
13. #2285×C₁₃₉	C₂	semidirect
14. C₂×#382×C₁₃₉	C₂	semidirect
82. C₄×D₄×C₁₃₉	Q₈	semidirect
292. #36191	C₁₃₉	direct (N × H)
293. C₁₃₉	#36191	direct (N × H)
294. #2862	C₂×C₁₃₉	semidirect
295. #2851	C₂×C₁₃₉	semidirect
296. #2851	C₂×C₁₃₉	semidirect
297. #2574	C₂×C₁₃₉	semidirect
298. #2570	C₂×C₁₃₉	semidirect
299. #2520	C₂×C₁₃₉	semidirect
301. #2440	C₂×C₁₃₉	semidirect
302. #2439	C₂×C₁₃₉	semidirect
303. #2368	C₂×C₁₃₉	semidirect
305. C₄×#125	C₂×C₁₃₉	semidirect
306. #2285	C₂×C₁₃₉	semidirect
307. C₂×#382	C₂×C₁₃₉	semidirect
375. C₄×D₄	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2862×C₁₃₉	2
#2851×C₁₃₉	2
#2574×C₁₃₉	2
#2570×C₁₃₉	2
#2520×C₁₃₉	2
#2450×C₁₃₉	2
#2440×C₁₃₉	2
#2439×C₁₃₉	2
#2368×C₁₃₉	2
#2352×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2285×C₁₃₉	2
C₂×#382×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36191	139

Subgroups — C139×#36191 #48030787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36191 #48030787