Subgroups — C₁₃₉×#36165 #48030761

Order 35584.

1854 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2571×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2508×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2505×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2442×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2349×C₁₃₉	C₂	1	4	yes	maximal
8	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
9	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#382×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
19	#400×C₁₃₉	C₂²	1	8	yes	—
20	#400×C₁₃₉	C₂²	1	8	yes	—
21	#398×C₁₃₉	C₂²	1	8	yes	—
22	#389×C₁₃₉	C₂²	1	2	yes	—
23	#389×C₁₃₉	C₂²	1	4	yes	—
24	#389×C₁₃₉	C₂²	1	4	yes	—
25	#389×C₁₃₉	C₂²	1	4	yes	—
26	#389×C₁₃₉	C₂²	1	4	yes	—
27	#389×C₁₃₉	C₂²	1	4	yes	—
28	#387×C₁₃₉	C₂²	1	4	yes	—
29	#387×C₁₃₉	C₂²	1	8	yes	—
30	#385×C₁₃₉	C₂²	1	8	yes	—
31	#385×C₁₃₉	C₂²	1	8	yes	—
32	#385×C₁₃₉	C₂²	1	8	yes	—
33	#384×C₁₃₉	C₂²	1	2	yes	—
34	#382×C₁₃₉	C₂²	1	1	yes	characteristic
35	#382×C₁₃₉	C₂²	1	4	yes	—
36	#382×C₁₃₉	C₂²	1	2	yes	—
37	#382×C₁₃₉	C₂²	1	8	yes	—
38	#382×C₁₃₉	C₂²	1	4	yes	—
39	#380×C₁₃₉	C₂²	1	4	yes	—
40	#380×C₁₃₉	C₂²	1	8	yes	—
41	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
47	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
48	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
53	#125×C₁₃₉	—	2	4	no	—
54	#125×C₁₃₉	—	4	4	no	—
55	C₄×D₄×C₁₃₉	—	2	8	no	—
56	C₄×D₄×C₁₃₉	—	2	16	no	—
57	C₄×D₄×C₁₃₉	Q₈	1	8	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃₉	—	2	8	no	—
75	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
83	#95×C₁₃₉	C₂³	1	4	yes	—
84	#95×C₁₃₉	C₂³	1	8	yes	—
85	#95×C₁₃₉	C₂³	1	8	yes	—
86	#95×C₁₃₉	C₂³	1	2	yes	—
87	#95×C₁₃₉	C₂³	1	8	yes	—
88	#95×C₁₃₉	C₂³	1	4	yes	—
89	#95×C₁₃₉	C₂³	1	4	yes	—
90	#95×C₁₃₉	C₂³	1	8	yes	—
91	#95×C₁₃₉	C₂³	1	4	yes	—
92	#95×C₁₃₉	C₂³	1	8	yes	—
93	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
94	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
95	C₂×D₄×C₁₃₉	#41	1	8	yes	—
96	C₂²×C₄×C₁₃₉	—	2	4	no	—
97	C₂²×C₄×C₁₃₉	—	2	4	no	—
98	C₂²×C₄×C₁₃₉	—	2	8	no	—
99	C₂²×C₄×C₁₃₉	—	2	16	no	—
100	C₂²×C₄×C₁₃₉	—	2	8	no	—
101	C₂²×C₄×C₁₃₉	—	4	4	no	—
102	C₂²×C₄×C₁₃₉	—	4	8	no	—
103	C₂²×C₄×C₁₃₉	—	4	8	no	—
104	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
105	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₄⋊C₄×C₁₃₉	—	2	8	no	—
117	C₄⋊C₄×C₁₃₉	—	2	8	no	—
118	C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₄⋊C₄×C₁₃₉	—	2	8	no	—
121	C₄⋊C₄×C₁₃₉	—	4	8	no	—
122	C₄⋊C₄×C₁₃₉	—	4	4	no	—
123	C₄⋊C₄×C₁₃₉	—	4	4	no	—
124	C₄⋊C₄×C₁₃₉	—	4	8	no	—
125	C₄⋊C₄×C₁₃₉	—	4	8	no	—
126	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
127	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
129	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
130	C₄²×C₁₃₉	—	2	8	no	—
131	C₄²×C₁₃₉	—	2	4	no	—
132	C₄²×C₁₃₉	—	2	4	no	—
133	C₄²×C₁₃₉	—	2	8	no	—
134	C₄²×C₁₃₉	—	2	2	no	—
135	C₄²×C₁₃₉	—	4	2	no	—
136	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
137	C₄²×C₁₃₉	#41	1	4	yes	—
138	C₂³×C₁₃₉	—	2	2	no	—
139	C₂³×C₁₃₉	—	2	2	no	—
140	C₂³×C₁₃₉	—	2	4	no	—
141	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
142	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
143	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
144	D₄×C₁₃₉	#125	1	16	yes	complemented
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	16	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	4	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	4	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	8	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	2	no	—
159	C₂×C₄×C₁₃₉	—	2	8	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	2	no	—
162	C₂×C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄×C₁₃₉	—	2	4	no	—
164	C₂×C₄×C₁₃₉	—	2	8	no	—
165	C₂×C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄×C₁₃₉	—	4	16	no	—
167	C₂×C₄×C₁₃₉	—	8	16	no	—
168	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
170	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
172	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
173	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
174	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	2	8	no	—
178	C₂²×C₁₃₉	—	2	4	no	—
179	C₂²×C₁₃₉	—	2	8	no	—
180	C₂²×C₁₃₉	C₂×#125	1	8	yes	—
181	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
183	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
185	C₂²×C₁₃₉	#585	1	2	yes	—
186	C₄×C₁₃₉	—	2	4	no	—
187	C₄×C₁₃₉	—	2	4	no	—
188	C₄×C₁₃₉	—	2	2	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	—	4	4	no	—
191	C₄×C₁₃₉	—	4	2	no	—
192	C₄×C₁₃₉	—	4	8	no	—
193	C₄×C₁₃₉	—	4	4	no	—
194	C₄×C₁₃₉	C₂×#125	1	4	yes	—
195	C₄×C₁₃₉	#554	1	4	yes	—
196	C₂×C₁₃₉	—	2	8	no	—
197	C₂×C₁₃₉	C₂²×#125	1	1	yes	characteristic
198	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
199	C₂×C₁₃₉	#3475	1	2	yes	—
200	C₂×C₁₃₉	#3504	1	1	yes	characteristic
201	C₂×C₁₃₉	#3514	1	2	yes	—
202	#36165	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₉	#36165	1	1	yes	characteristic, direct product factor, Sylow
204	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	#2851	C₂×C₁₃₉	1	2	yes	complemented
206	#2571	C₂×C₁₃₉	1	2	yes	complemented
207	#2508	C₂×C₁₃₉	1	4	yes	complemented
208	#2505	C₂×C₁₃₉	1	8	yes	complemented
209	#2442	C₂×C₁₃₉	1	4	yes	complemented
210	#2349	C₂×C₁₃₉	1	4	yes	—
211	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	—
212	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
213	C₂×#382	C₂×C₁₃₉	1	2	yes	complemented
214	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
215	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
216	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
217	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
218	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
221	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
222	#400	C₂²×C₁₃₉	1	8	yes	—
223	#400	C₂²×C₁₃₉	1	8	yes	—
224	#398	C₂²×C₁₃₉	1	8	yes	—
225	#389	C₂²×C₁₃₉	1	2	yes	—
226	#389	C₂²×C₁₃₉	1	4	yes	—
227	#389	C₂²×C₁₃₉	1	4	yes	—
228	#389	C₂²×C₁₃₉	1	4	yes	—
229	#389	C₂²×C₁₃₉	1	4	yes	—
230	#389	C₂²×C₁₃₉	1	4	yes	—
231	#387	C₂²×C₁₃₉	1	4	yes	—
232	#387	C₂²×C₁₃₉	1	8	yes	—
233	#385	C₂²×C₁₃₉	1	8	yes	—
234	#385	C₂²×C₁₃₉	1	8	yes	—
235	#385	C₂²×C₁₃₉	1	8	yes	—
236	#384	C₂²×C₁₃₉	1	2	yes	—
237	#382	C₂²×C₁₃₉	1	1	yes	characteristic
238	#382	C₂²×C₁₃₉	1	4	yes	—
239	#382	C₂²×C₁₃₉	1	4	yes	—
240	#382	C₂²×C₁₃₉	1	2	yes	—
241	#382	C₂²×C₁₃₉	1	8	yes	—
242	#380	C₂²×C₁₃₉	1	4	yes	—
243	#380	C₂²×C₁₃₉	1	8	yes	—
244	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
245	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
248	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
250	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
251	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
256	#125	—	2	4	no	—
257	#125	—	4	4	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	16	no	—
260	C₄×D₄	Q₈×C₁₃₉	1	8	yes	—
261	C₂×C₄⋊C₄	—	4	8	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
277	C₂×C₄²	—	2	8	no	—
278	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
280	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
282	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
286	#95	C₂³×C₁₃₉	1	4	yes	—
287	#95	C₂³×C₁₃₉	1	8	yes	—
288	#95	C₂³×C₁₃₉	1	8	yes	—
289	#95	C₂³×C₁₃₉	1	8	yes	—
290	#95	C₂³×C₁₃₉	1	4	yes	—
291	#95	C₂³×C₁₃₉	1	2	yes	—
292	#95	C₂³×C₁₃₉	1	4	yes	—
293	#95	C₂³×C₁₃₉	1	4	yes	—
294	#95	C₂³×C₁₃₉	1	8	yes	—
295	#95	C₂³×C₁₃₉	1	8	yes	—
296	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
297	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
298	C₂×D₄	#41×C₁₃₉	1	8	yes	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	8	no	—
306	C₂²×C₄	—	4	8	no	—
307	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
308	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
312	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	8	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	8	no	—
328	C₄⋊C₄	—	4	8	no	—
329	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
333	C₄²	—	2	8	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
340	C₄²	#41×C₁₃₉	1	4	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
345	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
346	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
347	D₄	#125×C₁₃₉	1	16	yes	complemented
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	16	no	—
370	C₂×C₄	—	8	16	no	—
371	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
372	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
373	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
374	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
375	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
376	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
377	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
378	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	8	no	—
383	C₂²	C₂×#125×C₁₃₉	1	8	yes	—
384	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
385	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
386	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
387	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
388	C₂²	#585×C₁₃₉	1	2	yes	—
389	C₄	—	2	4	no	—
390	C₄	—	2	4	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	8	no	—
396	C₄	—	4	2	no	—
397	C₄	C₂×#125×C₁₃₉	1	4	yes	—
398	C₄	#554×C₁₃₉	1	4	yes	—
399	C₂	—	2	8	no	—
400	C₂	C₂²×#125×C₁₃₉	1	1	yes	characteristic
401	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
402	C₂	#3475×C₁₃₉	1	2	yes	—
403	C₂	#3504×C₁₃₉	1	1	yes	characteristic
404	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. #2859×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2571×C₁₃₉	C₂	semidirect
4. #2508×C₁₃₉	C₂	semidirect
5. #2505×C₁₃₉	C₂	semidirect
6. #2442×C₁₃₉	C₂	semidirect
9. C₄×#125×C₁₃₉	C₂	semidirect
10. C₂×#382×C₁₃₉	C₂	semidirect
144. D₄×C₁₃₉	#125	semidirect
202. #36165	C₁₃₉	direct (N × H)
203. C₁₃₉	#36165	direct (N × H)
204. #2859	C₂×C₁₃₉	semidirect
205. #2851	C₂×C₁₃₉	semidirect
206. #2571	C₂×C₁₃₉	semidirect
207. #2508	C₂×C₁₃₉	semidirect
208. #2505	C₂×C₁₃₉	semidirect
209. #2442	C₂×C₁₃₉	semidirect
212. C₄×#125	C₂×C₁₃₉	semidirect
213. C₂×#382	C₂×C₁₃₉	semidirect
347. D₄	#125×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₉	2
#2851×C₁₃₉	2
#2571×C₁₃₉	2
#2508×C₁₃₉	2
#2505×C₁₃₉	2
#2442×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
C₄×#125×C₁₃₉	2
C₂×#382×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36165	139

Subgroups — C139×#36165 #48030761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36165 #48030761