Subgroups — D₄×#126×C₁₃₉ #48030702

Order 35584.

2508 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2852×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2512×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2496×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2481×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2480×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₁₃₉	C₂	1	3	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	3	yes	maximal
10	C₄×#126×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#126×C₁₃₉	—	2	16	no	—
14	C₂×#126×C₁₃₉	C₂²	1	6	yes	—
15	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#126×C₁₃₉	C₂²	1	6	yes	complemented
17	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
21	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
22	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
23	#400×C₁₃₉	C₂²	1	6	yes	complemented
24	#397×C₁₃₉	C₂²	1	6	yes	—
25	#397×C₁₃₉	C₂²	1	6	yes	complemented
26	#396×C₁₃₉	C₂²	1	6	yes	complemented
27	#390×C₁₃₉	C₂²	1	3	yes	—
28	#390×C₁₃₉	C₂²	1	3	yes	—
29	#389×C₁₃₉	C₂²	1	3	yes	complemented
30	#389×C₁₃₉	C₂²	1	3	yes	complemented
31	#388×C₁₃₉	C₂²	1	3	yes	—
32	#388×C₁₃₉	C₂²	1	6	yes	complemented
33	#388×C₁₃₉	C₂²	1	6	yes	complemented
34	#387×C₁₃₉	C₂²	1	3	yes	complemented
35	#387×C₁₃₉	C₂²	1	6	yes	complemented
36	#386×C₁₃₉	C₂²	1	6	yes	—
37	#386×C₁₃₉	C₂²	1	6	yes	—
38	#385×C₁₃₉	C₂²	1	6	yes	complemented
39	#385×C₁₃₉	C₂²	1	6	yes	complemented
40	#384×C₁₃₉	C₂²	1	3	yes	complemented
41	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	#380×C₁₃₉	C₂²	1	3	yes	—
43	#380×C₁₃₉	C₂²	1	6	yes	complemented
44	#379×C₁₃₉	C₂²	1	6	yes	—
45	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
47	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
49	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃₉	—	2	12	no	—
52	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
57	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
58	#126×C₁₃₉	—	2	24	no	—
59	#126×C₁₃₉	—	2	24	no	—
60	#126×C₁₃₉	—	2	8	no	—
61	#126×C₁₃₉	D₄	1	8	yes	direct product factor
62	C₄×D₄×C₁₃₉	—	2	12	no	—
63	C₄×D₄×C₁₃₉	—	2	12	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	2	24	no	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	24	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
83	C₂×C₄²×C₁₃₉	—	2	8	no	—
84	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
88	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
89	#95×C₁₃₉	C₂³	1	6	yes	—
90	#95×C₁₃₉	C₂³	1	6	yes	—
91	#95×C₁₃₉	C₂³	1	6	yes	—
92	#95×C₁₃₉	C₂³	1	3	yes	—
93	#95×C₁₃₉	C₂³	1	3	yes	—
94	#95×C₁₃₉	C₂³	1	6	yes	—
95	#95×C₁₃₉	C₂³	1	3	yes	—
96	#95×C₁₃₉	C₂³	1	3	yes	—
97	C₂⁴×C₁₃₉	—	2	4	no	—
98	C₂⁴×C₁₃₉	—	2	12	no	—
99	C₂⁴×C₁₃₉	—	4	6	no	—
100	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
101	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
102	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
103	C₂×D₄×C₁₃₉	—	2	12	no	—
104	C₂×D₄×C₁₃₉	—	2	6	no	—
105	C₂×D₄×C₁₃₉	—	4	16	no	—
106	C₂×D₄×C₁₃₉	#41	1	12	yes	—
107	C₂²×C₄×C₁₃₉	—	2	12	no	—
108	C₂²×C₄×C₁₃₉	—	2	12	no	—
109	C₂²×C₄×C₁₃₉	—	2	12	no	—
110	C₂²×C₄×C₁₃₉	—	2	12	no	—
111	C₂²×C₄×C₁₃₉	—	2	6	no	—
112	C₂²×C₄×C₁₃₉	—	4	6	no	—
113	C₂²×C₄×C₁₃₉	—	4	6	no	—
114	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
116	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
118	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₁₃₉	—	2	12	no	—
123	C₄⋊C₄×C₁₃₉	—	2	12	no	—
124	C₄⋊C₄×C₁₃₉	—	2	12	no	—
125	C₄⋊C₄×C₁₃₉	—	2	6	no	—
126	C₄⋊C₄×C₁₃₉	—	2	6	no	—
127	C₄⋊C₄×C₁₃₉	—	4	3	no	—
128	C₄⋊C₄×C₁₃₉	—	4	6	no	—
129	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	complemented
130	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
131	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
132	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
133	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
135	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
136	C₂²⋊C₄×C₁₃₉	—	4	3	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
138	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
139	C₄²×C₁₃₉	—	2	12	no	—
140	C₄²×C₁₃₉	—	2	6	no	—
141	C₄²×C₁₃₉	—	2	6	no	—
142	C₄²×C₁₃₉	—	4	3	no	—
143	C₄²×C₁₃₉	C₂×D₄	1	4	yes	complemented
144	C₂³×C₁₃₉	—	2	2	no	—
145	C₂³×C₁₃₉	—	2	6	no	—
146	C₂³×C₁₃₉	—	2	3	no	—
147	C₂³×C₁₃₉	—	2	3	no	—
148	C₂³×C₁₃₉	—	2	2	no	—
149	C₂³×C₁₃₉	—	2	6	no	—
150	C₂³×C₁₃₉	—	2	6	no	—
151	C₂³×C₁₃₉	—	4	24	no	—
152	C₂³×C₁₃₉	—	4	8	no	—
153	C₂³×C₁₃₉	—	8	12	no	—
154	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₃₉	C₂×#41	1	12	yes	—
156	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
157	D₄×C₁₃₉	—	4	8	no	—
158	D₄×C₁₃₉	—	4	4	no	—
159	D₄×C₁₃₉	#126	1	16	yes	direct product factor
160	C₂×C₄×C₁₃₉	—	2	3	no	—
161	C₂×C₄×C₁₃₉	—	2	3	no	—
162	C₂×C₄×C₁₃₉	—	2	3	no	—
163	C₂×C₄×C₁₃₉	—	2	3	no	—
164	C₂×C₄×C₁₃₉	—	2	6	no	—
165	C₂×C₄×C₁₃₉	—	2	6	no	—
166	C₂×C₄×C₁₃₉	—	2	3	no	—
167	C₂×C₄×C₁₃₉	—	2	3	no	—
168	C₂×C₄×C₁₃₉	—	2	6	no	—
169	C₂×C₄×C₁₃₉	—	2	6	no	—
170	C₂×C₄×C₁₃₉	—	2	3	no	—
171	C₂×C₄×C₁₃₉	—	2	3	no	—
172	C₂×C₄×C₁₃₉	—	2	3	no	—
173	C₂×C₄×C₁₃₉	—	2	3	no	—
174	C₂×C₄×C₁₃₉	—	2	3	no	—
175	C₂×C₄×C₁₃₉	—	2	6	no	—
176	C₂×C₄×C₁₃₉	—	2	6	no	—
177	C₂×C₄×C₁₃₉	—	4	24	no	—
178	C₂×C₄×C₁₃₉	—	4	24	no	—
179	C₂×C₄×C₁₃₉	—	4	4	no	—
180	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
181	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
182	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
183	C₂²×C₁₃₉	—	2	12	no	—
184	C₂²×C₁₃₉	—	2	12	no	—
185	C₂²×C₁₃₉	—	2	6	no	—
186	C₂²×C₁₃₉	—	4	1	no	—
187	C₂²×C₁₃₉	—	4	3	no	—
188	C₂²×C₁₃₉	—	4	2	no	—
189	C₂²×C₁₃₉	—	4	6	no	—
190	C₂²×C₁₃₉	—	4	6	no	—
191	C₂²×C₁₃₉	—	8	16	no	—
192	C₂²×C₁₃₉	C₂×#126	1	8	yes	complemented
193	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
194	C₂²×C₁₃₉	C₂²×#41	1	3	yes	—
195	C₂²×C₁₃₉	#585	1	3	yes	—
196	C₄×C₁₃₉	—	2	6	no	—
197	C₄×C₁₃₉	—	2	6	no	—
198	C₄×C₁₃₉	—	4	1	no	—
199	C₄×C₁₃₉	—	4	6	no	—
200	C₄×C₁₃₉	—	4	6	no	—
201	C₄×C₁₃₉	—	4	3	no	—
202	C₄×C₁₃₉	—	4	3	no	—
203	C₄×C₁₃₉	C₂×#126	1	4	yes	complemented
204	C₂×C₁₃₉	—	2	8	no	—
205	C₂×C₁₃₉	—	4	2	no	—
206	C₂×C₁₃₉	—	8	2	no	—
207	C₂×C₁₃₉	C₂²×#126	1	1	yes	characteristic
208	C₂×C₁₃₉	D₄×#41	1	3	yes	—
209	C₂×C₁₃₉	#3521	1	3	yes	—
210	D₄×#126	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₉	D₄×#126	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²×#126	C₂×C₁₃₉	1	2	yes	complemented
213	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
214	#2852	C₂×C₁₃₉	1	2	yes	complemented
215	#2512	C₂×C₁₃₉	1	3	yes	complemented
216	#2496	C₂×C₁₃₉	1	3	yes	complemented
217	#2481	C₂×C₁₃₉	1	6	yes	complemented
218	#2480	C₂×C₁₃₉	1	6	yes	complemented
219	D₄×C₄⋊C₄	C₂×C₁₃₉	1	3	yes	complemented
220	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	3	yes	—
221	C₄×#126	C₂×C₁₃₉	1	1	yes	characteristic, complemented
222	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
223	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
224	C₂×#126	—	2	16	no	—
225	C₂×#126	C₂²×C₁₃₉	1	6	yes	—
226	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
227	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
228	C₂×#126	C₂²×C₁₃₉	1	6	yes	complemented
229	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
230	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
232	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
233	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
234	#400	C₂²×C₁₃₉	1	6	yes	complemented
235	#397	C₂²×C₁₃₉	1	6	yes	—
236	#397	C₂²×C₁₃₉	1	6	yes	complemented
237	#396	C₂²×C₁₃₉	1	6	yes	complemented
238	#390	C₂²×C₁₃₉	1	3	yes	—
239	#390	C₂²×C₁₃₉	1	3	yes	—
240	#389	C₂²×C₁₃₉	1	3	yes	complemented
241	#389	C₂²×C₁₃₉	1	3	yes	complemented
242	#388	C₂²×C₁₃₉	1	3	yes	—
243	#388	C₂²×C₁₃₉	1	6	yes	complemented
244	#388	C₂²×C₁₃₉	1	6	yes	complemented
245	#387	C₂²×C₁₃₉	1	3	yes	complemented
246	#387	C₂²×C₁₃₉	1	6	yes	complemented
247	#386	C₂²×C₁₃₉	1	6	yes	—
248	#386	C₂²×C₁₃₉	1	6	yes	—
249	#385	C₂²×C₁₃₉	1	6	yes	complemented
250	#385	C₂²×C₁₃₉	1	6	yes	complemented
251	#384	C₂²×C₁₃₉	1	3	yes	complemented
252	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
253	#380	C₂²×C₁₃₉	1	3	yes	—
254	#380	C₂²×C₁₃₉	1	6	yes	complemented
255	#379	C₂²×C₁₃₉	1	6	yes	—
256	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
257	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
258	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
260	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
261	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
262	C₂²×D₄	—	2	12	no	—
263	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
265	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
268	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
269	#126	—	2	24	no	—
270	#126	—	2	24	no	—
271	#126	—	2	8	no	—
272	#126	D₄×C₁₃₉	1	8	yes	direct product factor
273	C₄×D₄	—	2	12	no	—
274	C₄×D₄	—	2	12	no	—
275	C₂×C₄⋊C₄	—	2	24	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
284	C₂×C₂²⋊C₄	—	2	24	no	—
285	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
296	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
297	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
298	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
299	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
300	#95	C₂³×C₁₃₉	1	3	yes	—
301	#95	C₂³×C₁₃₉	1	3	yes	—
302	#95	C₂³×C₁₃₉	1	6	yes	—
303	#95	C₂³×C₁₃₉	1	3	yes	—
304	#95	C₂³×C₁₃₉	1	3	yes	—
305	#95	C₂³×C₁₃₉	1	6	yes	—
306	#95	C₂³×C₁₃₉	1	6	yes	—
307	#95	C₂³×C₁₃₉	1	6	yes	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	12	no	—
310	C₂⁴	—	4	6	no	—
311	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
312	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
313	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
314	C₂×D₄	—	2	12	no	—
315	C₂×D₄	—	2	6	no	—
316	C₂×D₄	—	4	16	no	—
317	C₂×D₄	#41×C₁₃₉	1	12	yes	—
318	C₂²×C₄	—	2	12	no	—
319	C₂²×C₄	—	2	12	no	—
320	C₂²×C₄	—	2	12	no	—
321	C₂²×C₄	—	2	12	no	—
322	C₂²×C₄	—	2	6	no	—
323	C₂²×C₄	—	4	6	no	—
324	C₂²×C₄	—	4	6	no	—
325	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
327	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
328	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
329	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
331	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
332	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
333	C₄⋊C₄	—	2	12	no	—
334	C₄⋊C₄	—	2	12	no	—
335	C₄⋊C₄	—	2	12	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	4	3	no	—
339	C₄⋊C₄	—	4	6	no	—
340	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	complemented
341	C₂²⋊C₄	—	2	12	no	—
342	C₂²⋊C₄	—	2	12	no	—
343	C₂²⋊C₄	—	2	12	no	—
344	C₂²⋊C₄	—	2	12	no	—
345	C₂²⋊C₄	—	2	12	no	—
346	C₂²⋊C₄	—	4	6	no	—
347	C₂²⋊C₄	—	4	3	no	—
348	C₂²⋊C₄	—	4	6	no	—
349	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
350	C₄²	—	2	12	no	—
351	C₄²	—	2	6	no	—
352	C₄²	—	2	6	no	—
353	C₄²	—	4	3	no	—
354	C₄²	C₂×D₄×C₁₃₉	1	4	yes	complemented
355	C₂³	—	2	2	no	—
356	C₂³	—	2	6	no	—
357	C₂³	—	2	3	no	—
358	C₂³	—	2	3	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	6	no	—
361	C₂³	—	2	6	no	—
362	C₂³	—	4	24	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	8	12	no	—
365	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
366	C₂³	C₂×#41×C₁₃₉	1	12	yes	—
367	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
368	D₄	—	4	8	no	—
369	D₄	—	4	4	no	—
370	D₄	#126×C₁₃₉	1	16	yes	direct product factor
371	C₂×C₄	—	2	3	no	—
372	C₂×C₄	—	2	3	no	—
373	C₂×C₄	—	2	3	no	—
374	C₂×C₄	—	2	3	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	3	no	—
378	C₂×C₄	—	2	3	no	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	2	6	no	—
381	C₂×C₄	—	2	3	no	—
382	C₂×C₄	—	2	3	no	—
383	C₂×C₄	—	2	3	no	—
384	C₂×C₄	—	2	3	no	—
385	C₂×C₄	—	2	3	no	—
386	C₂×C₄	—	2	6	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	4	24	no	—
389	C₂×C₄	—	4	24	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
393	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
394	C₂²	—	2	12	no	—
395	C₂²	—	2	12	no	—
396	C₂²	—	2	6	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	3	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	6	no	—
401	C₂²	—	4	6	no	—
402	C₂²	—	8	16	no	—
403	C₂²	C₂×#126×C₁₃₉	1	8	yes	complemented
404	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
405	C₂²	C₂²×#41×C₁₃₉	1	3	yes	—
406	C₂²	#585×C₁₃₉	1	3	yes	—
407	C₄	—	2	6	no	—
408	C₄	—	2	6	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	6	no	—
411	C₄	—	4	6	no	—
412	C₄	—	4	3	no	—
413	C₄	—	4	3	no	—
414	C₄	C₂×#126×C₁₃₉	1	4	yes	complemented
415	C₂	—	2	8	no	—
416	C₂	—	4	2	no	—
417	C₂	—	8	2	no	—
418	C₂	C₂²×#126×C₁₃₉	1	1	yes	characteristic
419	C₂	D₄×#41×C₁₃₉	1	3	yes	—
420	C₂	#3521×C₁₃₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×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. C₂²×#126×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2852×C₁₃₉	C₂	semidirect
4. #2512×C₁₃₉	C₂	semidirect
5. #2496×C₁₃₉	C₂	semidirect
6. #2481×C₁₃₉	C₂	semidirect
7. #2480×C₁₃₉	C₂	semidirect
8. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
10. C₄×#126×C₁₃₉	C₂	semidirect
11. C₄²×D₄×C₁₃₉	C₂	semidirect
16. C₂×#126×C₁₃₉	C₂²	semidirect
17. C₂×#126×C₁₃₉	C₂²	semidirect
20. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
22. C₂²×C₄²×C₁₃₉	C₂²	semidirect
23. #400×C₁₃₉	C₂²	semidirect
25. #397×C₁₃₉	C₂²	semidirect
26. #396×C₁₃₉	C₂²	semidirect
29. #389×C₁₃₉	C₂²	semidirect
30. #389×C₁₃₉	C₂²	semidirect
32. #388×C₁₃₉	C₂²	semidirect
33. #388×C₁₃₉	C₂²	semidirect
34. #387×C₁₃₉	C₂²	semidirect
35. #387×C₁₃₉	C₂²	semidirect
38. #385×C₁₃₉	C₂²	semidirect
39. #385×C₁₃₉	C₂²	semidirect
40. #384×C₁₃₉	C₂²	semidirect
41. #383×C₁₃₉	C₂²	semidirect
43. #380×C₁₃₉	C₂²	semidirect
45. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
46. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
48. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
49. C₄³×C₁₃₉	C₂²	semidirect
61. #126×C₁₃₉	D₄	direct (N × H)
129. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
143. C₄²×C₁₃₉	C₂×D₄	semidirect
159. D₄×C₁₃₉	#126	direct (N × H)
192. C₂²×C₁₃₉	C₂×#126	semidirect
203. C₄×C₁₃₉	C₂×#126	semidirect
210. D₄×#126	C₁₃₉	direct (N × H)
211. C₁₃₉	D₄×#126	direct (N × H)
212. C₂²×#126	C₂×C₁₃₉	semidirect
213. #2860	C₂×C₁₃₉	semidirect
214. #2852	C₂×C₁₃₉	semidirect
215. #2512	C₂×C₁₃₉	semidirect
216. #2496	C₂×C₁₃₉	semidirect
217. #2481	C₂×C₁₃₉	semidirect
218. #2480	C₂×C₁₃₉	semidirect
219. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
221. C₄×#126	C₂×C₁₃₉	semidirect
222. C₄²×D₄	C₂×C₁₃₉	semidirect
227. C₂×#126	C₂²×C₁₃₉	semidirect
228. C₂×#126	C₂²×C₁₃₉	semidirect
231. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
233. C₂²×C₄²	C₂²×C₁₃₉	semidirect
234. #400	C₂²×C₁₃₉	semidirect
236. #397	C₂²×C₁₃₉	semidirect
237. #396	C₂²×C₁₃₉	semidirect
240. #389	C₂²×C₁₃₉	semidirect
241. #389	C₂²×C₁₃₉	semidirect
243. #388	C₂²×C₁₃₉	semidirect
244. #388	C₂²×C₁₃₉	semidirect
245. #387	C₂²×C₁₃₉	semidirect
246. #387	C₂²×C₁₃₉	semidirect
249. #385	C₂²×C₁₃₉	semidirect
250. #385	C₂²×C₁₃₉	semidirect
251. #384	C₂²×C₁₃₉	semidirect
252. #383	C₂²×C₁₃₉	semidirect
254. #380	C₂²×C₁₃₉	semidirect
256. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
257. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
259. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
260. C₄³	C₂²×C₁₃₉	semidirect
272. #126	D₄×C₁₃₉	direct (N × H)
340. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
354. C₄²	C₂×D₄×C₁₃₉	semidirect
370. D₄	#126×C₁₃₉	direct (N × H)
403. C₂²	C₂×#126×C₁₃₉	semidirect
414. C₄	C₂×#126×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#126×C₁₃₉	2
#2860×C₁₃₉	2
#2852×C₁₃₉	2
#2512×C₁₃₉	2
#2496×C₁₃₉	2
#2481×C₁₃₉	2
#2480×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#126×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
D₄×#126	139

Subgroups — D4×#126×C139 #48030702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#126×C₁₃₉ #48030702