Subgroups — D₄×#125×C₁₃₉ #48030701

Order 35584.

2262 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×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	#2552×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2506×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2473×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2442×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
9	D₄×C₄⋊C₄×C₁₃₉	C₂	1	4	yes	maximal
10	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₁₃₉	—	2	16	no	—
13	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
14	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#125×C₁₃₉	C₂²	1	8	yes	—
16	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
21	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	8	yes	—
22	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
23	#400×C₁₃₉	C₂²	1	8	yes	—
24	#398×C₁₃₉	C₂²	1	8	yes	—
25	#398×C₁₃₉	C₂²	1	8	yes	—
26	#389×C₁₃₉	C₂²	1	4	yes	—
27	#389×C₁₃₉	C₂²	1	4	yes	—
28	#389×C₁₃₉	C₂²	1	2	yes	—
29	#389×C₁₃₉	C₂²	1	4	yes	—
30	#389×C₁₃₉	C₂²	1	4	yes	—
31	#389×C₁₃₉	C₂²	1	4	yes	—
32	#387×C₁₃₉	C₂²	1	4	yes	—
33	#387×C₁₃₉	C₂²	1	8	yes	—
34	#385×C₁₃₉	C₂²	1	8	yes	—
35	#385×C₁₃₉	C₂²	1	8	yes	—
36	#385×C₁₃₉	C₂²	1	8	yes	—
37	#384×C₁₃₉	C₂²	1	2	yes	—
38	#384×C₁₃₉	C₂²	1	4	yes	—
39	#382×C₁₃₉	C₂²	1	1	yes	characteristic
40	#382×C₁₃₉	C₂²	1	2	yes	—
41	#380×C₁₃₉	C₂²	1	4	yes	—
42	#380×C₁₃₉	C₂²	1	8	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
47	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
49	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
53	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
54	#125×C₁₃₉	—	2	16	no	—
55	#125×C₁₃₉	—	2	32	no	—
56	#125×C₁₃₉	—	2	8	no	—
57	#125×C₁₃₉	D₄	1	8	yes	direct product factor
58	C₄×D₄×C₁₃₉	—	2	8	no	—
59	C₄×D₄×C₁₃₉	—	2	16	no	—
60	C₄×D₄×C₁₃₉	Q₈	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	32	no	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₃₉	—	2	8	no	—
81	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
89	#95×C₁₃₉	C₂³	1	2	yes	—
90	#95×C₁₃₉	C₂³	1	4	yes	—
91	#95×C₁₃₉	C₂³	1	4	yes	—
92	#95×C₁₃₉	C₂³	1	8	yes	—
93	#95×C₁₃₉	C₂³	1	8	yes	—
94	#95×C₁₃₉	C₂³	1	8	yes	—
95	#95×C₁₃₉	C₂³	1	4	yes	—
96	#95×C₁₃₉	C₂³	1	4	yes	—
97	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
98	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
99	C₂×D₄×C₁₃₉	#41	1	8	yes	—
100	C₂²×C₄×C₁₃₉	—	2	4	no	—
101	C₂²×C₄×C₁₃₉	—	2	4	no	—
102	C₂²×C₄×C₁₃₉	—	2	8	no	—
103	C₂²×C₄×C₁₃₉	—	2	16	no	—
104	C₂²×C₄×C₁₃₉	—	2	8	no	—
105	C₂²×C₄×C₁₃₉	—	2	16	no	—
106	C₂²×C₄×C₁₃₉	—	4	4	no	—
107	C₂²×C₄×C₁₃₉	—	4	8	no	—
108	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
119	C₄⋊C₄×C₁₃₉	—	2	16	no	—
120	C₄⋊C₄×C₁₃₉	—	2	16	no	—
121	C₄⋊C₄×C₁₃₉	—	2	16	no	—
122	C₄⋊C₄×C₁₃₉	—	2	16	no	—
123	C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₄⋊C₄×C₁₃₉	—	2	8	no	—
126	C₄⋊C₄×C₁₃₉	—	2	4	no	—
127	C₄⋊C₄×C₁₃₉	—	4	4	no	—
128	C₄⋊C₄×C₁₃₉	—	4	4	no	—
129	C₄⋊C₄×C₁₃₉	—	4	8	no	—
130	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
131	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
132	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
133	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
135	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
136	C₄²×C₁₃₉	—	2	8	no	—
137	C₄²×C₁₃₉	—	2	4	no	—
138	C₄²×C₁₃₉	—	2	4	no	—
139	C₄²×C₁₃₉	—	2	8	no	—
140	C₄²×C₁₃₉	—	2	2	no	—
141	C₄²×C₁₃₉	—	4	2	no	—
142	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
143	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
144	C₂³×C₁₃₉	—	2	2	no	—
145	C₂³×C₁₃₉	—	2	2	no	—
146	C₂³×C₁₃₉	—	2	4	no	—
147	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
148	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
149	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
150	D₄×C₁₃₉	#125	1	16	yes	direct product factor
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	2	no	—
156	C₂×C₄×C₁₃₉	—	2	2	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	16	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
166	C₂×C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄×C₁₃₉	—	2	4	no	—
170	C₂×C₄×C₁₃₉	—	2	8	no	—
171	C₂×C₄×C₁₃₉	—	4	16	no	—
172	C₂×C₄×C₁₃₉	—	4	32	no	—
173	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
174	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
175	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
178	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
179	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
181	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₁₃₉	—	2	4	no	—
183	C₂²×C₁₃₉	—	2	8	no	—
184	C₂²×C₁₃₉	—	2	4	no	—
185	C₂²×C₁₃₉	—	2	8	no	—
186	C₂²×C₁₃₉	C₂×#125	1	8	yes	complemented
187	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
188	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
189	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
190	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
191	C₂²×C₁₃₉	#585	1	2	yes	—
192	C₄×C₁₃₉	—	2	4	no	—
193	C₄×C₁₃₉	—	2	4	no	—
194	C₄×C₁₃₉	—	2	8	no	—
195	C₄×C₁₃₉	—	2	2	no	—
196	C₄×C₁₃₉	—	4	4	no	—
197	C₄×C₁₃₉	—	4	8	no	—
198	C₄×C₁₃₉	—	4	2	no	—
199	C₄×C₁₃₉	—	4	4	no	—
200	C₄×C₁₃₉	C₂×#125	1	4	yes	complemented
201	C₄×C₁₃₉	D₄×Q₈	1	4	yes	—
202	C₂×C₁₃₉	—	2	8	no	—
203	C₂×C₁₃₉	C₂²×#125	1	1	yes	characteristic
204	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
205	C₂×C₁₃₉	D₄×#41	1	2	yes	—
206	C₂×C₁₃₉	#3504	1	1	yes	characteristic
207	C₂×C₁₃₉	#3515	1	2	yes	—
208	D₄×#125	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₁₃₉	D₄×#125	1	1	yes	characteristic, direct product factor, Sylow
210	C₂²×#125	C₂×C₁₃₉	1	2	yes	complemented
211	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	#2851	C₂×C₁₃₉	1	2	yes	complemented
213	#2552	C₂×C₁₃₉	1	2	yes	complemented
214	#2506	C₂×C₁₃₉	1	4	yes	complemented
215	#2473	C₂×C₁₃₉	1	8	yes	complemented
216	#2442	C₂×C₁₃₉	1	4	yes	complemented
217	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	—
218	D₄×C₄⋊C₄	C₂×C₁₃₉	1	4	yes	—
219	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
220	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
221	C₂×#125	—	2	16	no	—
222	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
223	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
224	C₂×#125	C₂²×C₁₃₉	1	8	yes	—
225	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
227	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	8	yes	—
231	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
232	#400	C₂²×C₁₃₉	1	8	yes	—
233	#398	C₂²×C₁₃₉	1	8	yes	—
234	#398	C₂²×C₁₃₉	1	8	yes	—
235	#389	C₂²×C₁₃₉	1	2	yes	—
236	#389	C₂²×C₁₃₉	1	4	yes	—
237	#389	C₂²×C₁₃₉	1	4	yes	—
238	#389	C₂²×C₁₃₉	1	4	yes	—
239	#389	C₂²×C₁₃₉	1	4	yes	—
240	#389	C₂²×C₁₃₉	1	4	yes	—
241	#387	C₂²×C₁₃₉	1	4	yes	—
242	#387	C₂²×C₁₃₉	1	8	yes	—
243	#385	C₂²×C₁₃₉	1	8	yes	—
244	#385	C₂²×C₁₃₉	1	8	yes	—
245	#385	C₂²×C₁₃₉	1	8	yes	—
246	#384	C₂²×C₁₃₉	1	2	yes	—
247	#384	C₂²×C₁₃₉	1	4	yes	—
248	#382	C₂²×C₁₃₉	1	1	yes	characteristic
249	#382	C₂²×C₁₃₉	1	2	yes	—
250	#380	C₂²×C₁₃₉	1	4	yes	—
251	#380	C₂²×C₁₃₉	1	8	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
258	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
261	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
263	#125	—	2	16	no	—
264	#125	—	2	32	no	—
265	#125	—	2	8	no	—
266	#125	D₄×C₁₃₉	1	8	yes	direct product factor
267	C₄×D₄	—	2	16	no	—
268	C₄×D₄	—	2	8	no	—
269	C₄×D₄	Q₈×C₁₃₉	1	8	yes	—
270	C₂×C₄⋊C₄	—	2	16	no	—
271	C₂×C₄⋊C₄	—	2	32	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
289	C₂×C₄²	—	2	8	no	—
290	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
292	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
293	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
298	#95	C₂³×C₁₃₉	1	2	yes	—
299	#95	C₂³×C₁₃₉	1	4	yes	—
300	#95	C₂³×C₁₃₉	1	4	yes	—
301	#95	C₂³×C₁₃₉	1	4	yes	—
302	#95	C₂³×C₁₃₉	1	4	yes	—
303	#95	C₂³×C₁₃₉	1	8	yes	—
304	#95	C₂³×C₁₃₉	1	8	yes	—
305	#95	C₂³×C₁₃₉	1	8	yes	—
306	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
307	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
308	C₂×D₄	#41×C₁₃₉	1	8	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	4	8	no	—
317	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
318	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
322	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	16	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	16	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	8	no	—
339	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
340	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
341	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	8	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	2	no	—
351	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
352	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	4	no	—
356	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
357	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
358	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
359	D₄	#125×C₁₃₉	1	16	yes	direct product factor
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	16	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	32	no	—
382	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
384	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
385	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
387	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
388	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
389	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
390	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	8	no	—
395	C₂²	C₂×#125×C₁₃₉	1	8	yes	complemented
396	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
397	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
398	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
399	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
400	C₂²	#585×C₁₃₉	1	2	yes	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	8	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	8	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	4	no	—
409	C₄	C₂×#125×C₁₃₉	1	4	yes	complemented
410	C₄	D₄×Q₈×C₁₃₉	1	4	yes	—
411	C₂	—	2	8	no	—
412	C₂	C₂²×#125×C₁₃₉	1	1	yes	characteristic
413	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
414	C₂	D₄×#41×C₁₃₉	1	2	yes	—
415	C₂	#3504×C₁₃₉	1	1	yes	characteristic
416	C₂	#3515×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. C₂²×#125×C₁₃₉	C₂	semidirect
2. #2859×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2552×C₁₃₉	C₂	semidirect
5. #2506×C₁₃₉	C₂	semidirect
6. #2473×C₁₃₉	C₂	semidirect
7. #2442×C₁₃₉	C₂	semidirect
10. C₄×#125×C₁₃₉	C₂	semidirect
57. #125×C₁₃₉	D₄	direct (N × H)
150. D₄×C₁₃₉	#125	direct (N × H)
186. C₂²×C₁₃₉	C₂×#125	semidirect
200. C₄×C₁₃₉	C₂×#125	semidirect
208. D₄×#125	C₁₃₉	direct (N × H)
209. C₁₃₉	D₄×#125	direct (N × H)
210. C₂²×#125	C₂×C₁₃₉	semidirect
211. #2859	C₂×C₁₃₉	semidirect
212. #2851	C₂×C₁₃₉	semidirect
213. #2552	C₂×C₁₃₉	semidirect
214. #2506	C₂×C₁₃₉	semidirect
215. #2473	C₂×C₁₃₉	semidirect
216. #2442	C₂×C₁₃₉	semidirect
219. C₄×#125	C₂×C₁₃₉	semidirect
266. #125	D₄×C₁₃₉	direct (N × H)
359. D₄	#125×C₁₃₉	direct (N × H)
395. C₂²	C₂×#125×C₁₃₉	semidirect
409. C₄	C₂×#125×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₃₉	2
#2859×C₁₃₉	2
#2851×C₁₃₉	2
#2552×C₁₃₉	2
#2506×C₁₃₉	2
#2473×C₁₃₉	2
#2442×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
C₄×#125×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
D₄×#125	139

Subgroups — D4×#125×C139 #48030701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#125×C₁₃₉ #48030701