Subgroups — C₁₃₉×#36060 #48030656

Order 35584.

3674 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	3	yes	maximal, complemented
2	C₂×#546×C₁₃₉	C₂	1	3	yes	maximal, complemented
3	#2658×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2656×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2542×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2540×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2539×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2501×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#399×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	3	yes	—
13	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	#547×C₁₃₉	—	2	24	no	—
15	#546×C₁₃₉	—	2	24	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
17	C₂×#124×C₁₃₉	C₂²	1	3	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	6	yes	—
19	C₂×#123×C₁₃₉	C₂²	1	12	yes	complemented
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	complemented
22	C₂×#121×C₁₃₉	C₂²	1	3	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
25	C₂×#120×C₁₃₉	C₂²	1	6	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
31	#399×C₁₃₉	C₂²	1	6	yes	—
32	#399×C₁₃₉	C₂²	1	1	yes	characteristic
33	#399×C₁₃₉	C₂²	1	6	yes	complemented
34	#399×C₁₃₉	C₂²	1	6	yes	complemented
35	#399×C₁₃₉	C₂²	1	6	yes	complemented
36	#399×C₁₃₉	C₂²	1	2	yes	complemented
37	#399×C₁₃₉	C₂²	1	3	yes	complemented
38	#392×C₁₃₉	C₂²	1	3	yes	—
39	#392×C₁₃₉	C₂²	1	6	yes	complemented
40	#392×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	#390×C₁₃₉	C₂²	1	6	yes	—
42	#390×C₁₃₉	C₂²	1	12	yes	complemented
43	#384×C₁₃₉	C₂²	1	6	yes	complemented
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
46	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
49	C₂×#41×C₁₃₉	—	2	12	no	—
50	C₂×#41×C₁₃₉	—	2	24	no	—
51	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
52	C₂²×D₄×C₁₃₉	—	2	12	no	—
53	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
54	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
64	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
65	#124×C₁₃₉	—	2	12	no	—
66	#123×C₁₃₉	—	2	24	no	—
67	#123×C₁₃₉	—	2	48	no	—
68	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
69	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
70	#121×C₁₃₉	—	2	24	no	—
71	#121×C₁₃₉	—	2	24	no	—
72	#121×C₁₃₉	—	2	12	no	—
73	#120×C₁₃₉	—	2	24	no	—
74	C₄×D₄×C₁₃₉	—	2	12	no	—
75	C₄×D₄×C₁₃₉	—	2	12	no	—
76	C₄×D₄×C₁₃₉	D₄	1	24	yes	complemented
77	C₂×C₄⋊C₄×C₁₃₉	—	2	24	no	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	12	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	24	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
97	#95×C₁₃₉	C₂³	1	1	yes	characteristic
98	#95×C₁₃₉	C₂³	1	6	yes	—
99	#95×C₁₃₉	C₂³	1	3	yes	—
100	C₂⁴×C₁₃₉	—	2	4	no	—
101	C₂⁴×C₁₃₉	—	2	12	no	—
102	C₂⁴×C₁₃₉	—	4	6	no	—
103	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
104	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
105	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
106	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
107	#41×C₁₃₉	—	4	48	no	—
108	C₂×Q₈×C₁₃₉	—	2	6	no	—
109	C₂×Q₈×C₁₃₉	—	2	12	no	—
110	C₂×D₄×C₁₃₉	—	2	12	no	—
111	C₂×D₄×C₁₃₉	—	2	12	no	—
112	C₂×D₄×C₁₃₉	—	2	24	no	—
113	C₂×D₄×C₁₃₉	—	2	6	no	—
114	C₂×D₄×C₁₃₉	—	2	6	no	—
115	C₂×D₄×C₁₃₉	—	2	6	no	—
116	C₂×D₄×C₁₃₉	—	2	6	no	—
117	C₂×D₄×C₁₃₉	—	2	12	no	—
118	C₂×D₄×C₁₃₉	—	4	3	no	—
119	C₂×D₄×C₁₃₉	—	4	6	no	—
120	C₂×D₄×C₁₃₉	—	4	12	no	—
121	C₂×D₄×C₁₃₉	—	4	16	no	—
122	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
123	C₂²×C₄×C₁₃₉	—	2	12	no	—
124	C₂²×C₄×C₁₃₉	—	2	24	no	—
125	C₂²×C₄×C₁₃₉	—	2	6	no	—
126	C₂²×C₄×C₁₃₉	—	2	6	no	—
127	C₂²×C₄×C₁₃₉	—	2	12	no	—
128	C₂²×C₄×C₁₃₉	—	4	12	no	—
129	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₁₃₉	—	2	6	no	—
138	C₄⋊C₄×C₁₃₉	—	2	12	no	—
139	C₄⋊C₄×C₁₃₉	—	2	24	no	—
140	C₄⋊C₄×C₁₃₉	—	2	6	no	—
141	C₄⋊C₄×C₁₃₉	—	2	12	no	—
142	C₄⋊C₄×C₁₃₉	—	2	12	no	—
143	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
144	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
145	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
146	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
147	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
148	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
149	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
152	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	24	yes	—
153	C₄²×C₁₃₉	—	4	6	no	—
154	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
155	C₂³×C₁₃₉	—	2	2	no	—
156	C₂³×C₁₃₉	—	2	6	no	—
157	C₂³×C₁₃₉	—	2	3	no	—
158	C₂³×C₁₃₉	—	2	3	no	—
159	C₂³×C₁₃₉	—	2	6	no	—
160	C₂³×C₁₃₉	—	2	6	no	—
161	C₂³×C₁₃₉	—	2	3	no	—
162	C₂³×C₁₃₉	—	2	3	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	3	no	—
165	C₂³×C₁₃₉	—	2	6	no	—
166	C₂³×C₁₃₉	—	2	6	no	—
167	C₂³×C₁₃₉	—	4	24	no	—
168	C₂³×C₁₃₉	—	4	8	no	—
169	C₂³×C₁₃₉	—	8	12	no	—
170	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
171	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
172	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
173	Q₈×C₁₃₉	—	4	12	no	—
174	D₄×C₁₃₉	—	4	12	no	—
175	D₄×C₁₃₉	—	4	12	no	—
176	D₄×C₁₃₉	—	4	8	no	—
177	D₄×C₁₃₉	—	4	24	no	—
178	D₄×C₁₃₉	—	4	4	no	—
179	D₄×C₁₃₉	—	8	12	no	—
180	D₄×C₁₃₉	#127	1	16	yes	—
181	C₂×C₄×C₁₃₉	—	2	3	no	—
182	C₂×C₄×C₁₃₉	—	2	3	no	—
183	C₂×C₄×C₁₃₉	—	2	12	no	—
184	C₂×C₄×C₁₃₉	—	2	6	no	—
185	C₂×C₄×C₁₃₉	—	2	3	no	—
186	C₂×C₄×C₁₃₉	—	2	6	no	—
187	C₂×C₄×C₁₃₉	—	2	6	no	—
188	C₂×C₄×C₁₃₉	—	2	3	no	—
189	C₂×C₄×C₁₃₉	—	2	12	no	—
190	C₂×C₄×C₁₃₉	—	4	24	no	—
191	C₂×C₄×C₁₃₉	—	4	24	no	—
192	C₂×C₄×C₁₃₉	—	4	4	no	—
193	C₂×C₄×C₁₃₉	—	4	12	no	—
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
195	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
196	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
197	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
198	C₂²×C₁₃₉	—	2	12	no	—
199	C₂²×C₁₃₉	—	2	12	no	—
200	C₂²×C₁₃₉	—	2	6	no	—
201	C₂²×C₁₃₉	—	4	1	no	—
202	C₂²×C₁₃₉	—	4	3	no	—
203	C₂²×C₁₃₉	—	4	3	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	4	6	no	—
206	C₂²×C₁₃₉	—	4	3	no	—
207	C₂²×C₁₃₉	—	4	6	no	—
208	C₂²×C₁₃₉	—	4	3	no	—
209	C₂²×C₁₃₉	—	4	6	no	—
210	C₂²×C₁₃₉	—	4	6	no	—
211	C₂²×C₁₃₉	—	8	16	no	—
212	C₂²×C₁₃₉	C₂×#127	1	8	yes	—
213	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
214	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	C₂²×C₁₃₉	#585	1	3	yes	—
216	C₄×C₁₃₉	—	2	6	no	—
217	C₄×C₁₃₉	—	2	12	no	—
218	C₄×C₁₃₉	—	2	6	no	—
219	C₄×C₁₃₉	—	4	3	no	—
220	C₄×C₁₃₉	—	4	1	no	—
221	C₄×C₁₃₉	—	4	6	no	—
222	C₄×C₁₃₉	C₂×#127	1	4	yes	—
223	C₂×C₁₃₉	—	2	8	no	—
224	C₂×C₁₃₉	—	4	2	no	—
225	C₂×C₁₃₉	—	8	3	no	—
226	C₂×C₁₃₉	—	8	2	no	—
227	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
228	C₂×C₁₃₉	#3485	1	3	yes	—
229	C₂×C₁₃₉	#3489	1	3	yes	—
230	#36060	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃₉	#36060	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#547	C₂×C₁₃₉	1	3	yes	complemented
233	C₂×#546	C₂×C₁₃₉	1	3	yes	complemented
234	#2658	C₂×C₁₃₉	1	1	yes	characteristic, complemented
235	#2656	C₂×C₁₃₉	1	2	yes	complemented
236	#2542	C₂×C₁₃₉	1	3	yes	complemented
237	#2540	C₂×C₁₃₉	1	3	yes	complemented
238	#2539	C₂×C₁₃₉	1	6	yes	complemented
239	#2501	C₂×C₁₃₉	1	6	yes	complemented
240	#2397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	C₂×#399	C₂×C₁₃₉	1	2	yes	complemented
242	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	C₂²×#41	C₂²×C₁₃₉	1	3	yes	—
244	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
245	#547	—	2	24	no	—
246	#546	—	2	24	no	—
247	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
248	C₂×#124	C₂²×C₁₃₉	1	3	yes	—
249	C₂×#123	C₂²×C₁₃₉	1	6	yes	—
250	C₂×#123	C₂²×C₁₃₉	1	12	yes	complemented
251	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	complemented
253	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
254	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
255	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
256	C₂×#120	C₂²×C₁₃₉	1	6	yes	—
257	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
258	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
259	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	complemented
260	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
261	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
262	#399	C₂²×C₁₃₉	1	1	yes	characteristic
263	#399	C₂²×C₁₃₉	1	6	yes	—
264	#399	C₂²×C₁₃₉	1	2	yes	complemented
265	#399	C₂²×C₁₃₉	1	6	yes	complemented
266	#399	C₂²×C₁₃₉	1	3	yes	complemented
267	#399	C₂²×C₁₃₉	1	6	yes	complemented
268	#399	C₂²×C₁₃₉	1	6	yes	complemented
269	#392	C₂²×C₁₃₉	1	3	yes	—
270	#392	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
271	#392	C₂²×C₁₃₉	1	6	yes	complemented
272	#390	C₂²×C₁₃₉	1	6	yes	—
273	#390	C₂²×C₁₃₉	1	12	yes	complemented
274	#384	C₂²×C₁₃₉	1	6	yes	complemented
275	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
276	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
277	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
278	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
279	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
280	C₂×#41	—	2	12	no	—
281	C₂×#41	—	2	24	no	—
282	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
283	C₂²×D₄	—	2	12	no	—
284	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
285	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
286	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
287	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
288	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
289	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
290	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
292	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
294	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
295	C₄⋊Q₈	—	2	12	no	—
296	#124	—	2	12	no	—
297	#123	—	2	24	no	—
298	#123	—	2	48	no	—
299	C₂²⋊Q₈	—	2	12	no	—
300	C₂²⋊Q₈	—	2	24	no	—
301	#121	—	2	24	no	—
302	#121	—	2	24	no	—
303	#121	—	2	12	no	—
304	#120	—	2	24	no	—
305	C₄×D₄	—	2	12	no	—
306	C₄×D₄	—	2	12	no	—
307	C₄×D₄	D₄×C₁₃₉	1	24	yes	complemented
308	C₂×C₄⋊C₄	—	2	24	no	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	12	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
316	C₂×C₂²⋊C₄	—	2	24	no	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
326	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
327	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
328	#95	C₂³×C₁₃₉	1	1	yes	characteristic
329	#95	C₂³×C₁₃₉	1	6	yes	—
330	#95	C₂³×C₁₃₉	1	3	yes	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	12	no	—
333	C₂⁴	—	4	6	no	—
334	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
335	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
336	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
337	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
338	#41	—	4	48	no	—
339	C₂×Q₈	—	2	6	no	—
340	C₂×Q₈	—	2	12	no	—
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	—	2	24	no	—
344	C₂×D₄	—	2	6	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	6	no	—
347	C₂×D₄	—	2	6	no	—
348	C₂×D₄	—	2	12	no	—
349	C₂×D₄	—	4	3	no	—
350	C₂×D₄	—	4	6	no	—
351	C₂×D₄	—	4	12	no	—
352	C₂×D₄	—	4	16	no	—
353	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
354	C₂²×C₄	—	2	12	no	—
355	C₂²×C₄	—	2	24	no	—
356	C₂²×C₄	—	2	6	no	—
357	C₂²×C₄	—	2	6	no	—
358	C₂²×C₄	—	2	12	no	—
359	C₂²×C₄	—	4	12	no	—
360	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
361	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
362	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
363	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
365	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
366	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
367	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	6	no	—
369	C₄⋊C₄	—	2	12	no	—
370	C₄⋊C₄	—	2	24	no	—
371	C₄⋊C₄	—	2	6	no	—
372	C₄⋊C₄	—	2	12	no	—
373	C₄⋊C₄	—	2	12	no	—
374	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
375	C₂²⋊C₄	—	2	6	no	—
376	C₂²⋊C₄	—	2	12	no	—
377	C₂²⋊C₄	—	2	12	no	—
378	C₂²⋊C₄	—	2	12	no	—
379	C₂²⋊C₄	—	2	6	no	—
380	C₂²⋊C₄	—	2	12	no	—
381	C₂²⋊C₄	—	2	12	no	—
382	C₂²⋊C₄	—	2	24	no	—
383	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	24	yes	—
384	C₄²	—	4	6	no	—
385	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	6	no	—
388	C₂³	—	2	3	no	—
389	C₂³	—	2	3	no	—
390	C₂³	—	2	6	no	—
391	C₂³	—	2	6	no	—
392	C₂³	—	2	3	no	—
393	C₂³	—	2	3	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	3	no	—
396	C₂³	—	2	6	no	—
397	C₂³	—	2	6	no	—
398	C₂³	—	4	24	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	8	12	no	—
401	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
402	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
403	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
404	Q₈	—	4	12	no	—
405	D₄	—	4	12	no	—
406	D₄	—	4	12	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	24	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	12	no	—
411	D₄	#127×C₁₃₉	1	16	yes	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	3	no	—
414	C₂×C₄	—	2	12	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	2	3	no	—
417	C₂×C₄	—	2	6	no	—
418	C₂×C₄	—	2	6	no	—
419	C₂×C₄	—	2	3	no	—
420	C₂×C₄	—	2	12	no	—
421	C₂×C₄	—	4	24	no	—
422	C₂×C₄	—	4	24	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	12	no	—
425	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
429	C₂²	—	2	12	no	—
430	C₂²	—	2	12	no	—
431	C₂²	—	2	6	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	3	no	—
434	C₂²	—	4	3	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	4	3	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	3	no	—
440	C₂²	—	4	6	no	—
441	C₂²	—	4	6	no	—
442	C₂²	—	8	16	no	—
443	C₂²	C₂×#127×C₁₃₉	1	8	yes	—
444	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
445	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
446	C₂²	#585×C₁₃₉	1	3	yes	—
447	C₄	—	2	6	no	—
448	C₄	—	2	12	no	—
449	C₄	—	2	6	no	—
450	C₄	—	4	3	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	6	no	—
453	C₄	C₂×#127×C₁₃₉	1	4	yes	—
454	C₂	—	2	8	no	—
455	C₂	—	4	2	no	—
456	C₂	—	8	2	no	—
457	C₂	—	8	3	no	—
458	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic
459	C₂	#3485×C₁₃₉	1	3	yes	—
460	C₂	#3489×C₁₃₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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. C₂×#547×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. #2658×C₁₃₉	C₂	semidirect
4. #2656×C₁₃₉	C₂	semidirect
5. #2542×C₁₃₉	C₂	semidirect
6. #2540×C₁₃₉	C₂	semidirect
7. #2539×C₁₃₉	C₂	semidirect
8. #2501×C₁₃₉	C₂	semidirect
9. #2397×C₁₃₉	C₂	semidirect
10. C₂×#399×C₁₃₉	C₂	semidirect
11. #2275×C₁₃₉	C₂	semidirect
16. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
19. C₂×#123×C₁₃₉	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#121×C₁₃₉	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
29. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
33. #399×C₁₃₉	C₂²	semidirect
34. #399×C₁₃₉	C₂²	semidirect
35. #399×C₁₃₉	C₂²	semidirect
36. #399×C₁₃₉	C₂²	semidirect
37. #399×C₁₃₉	C₂²	semidirect
39. #392×C₁₃₉	C₂²	semidirect
40. #392×C₁₃₉	C₂²	semidirect
42. #390×C₁₃₉	C₂²	semidirect
43. #384×C₁₃₉	C₂²	semidirect
44. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
46. #376×C₁₃₉	C₂²	semidirect
47. C₂×#95×C₁₃₉	C₂²	semidirect
76. C₄×D₄×C₁₃₉	D₄	semidirect
230. #36060	C₁₃₉	direct (N × H)
231. C₁₃₉	#36060	direct (N × H)
232. C₂×#547	C₂×C₁₃₉	semidirect
233. C₂×#546	C₂×C₁₃₉	semidirect
234. #2658	C₂×C₁₃₉	semidirect
235. #2656	C₂×C₁₃₉	semidirect
236. #2542	C₂×C₁₃₉	semidirect
237. #2540	C₂×C₁₃₉	semidirect
238. #2539	C₂×C₁₃₉	semidirect
239. #2501	C₂×C₁₃₉	semidirect
240. #2397	C₂×C₁₃₉	semidirect
241. C₂×#399	C₂×C₁₃₉	semidirect
242. #2275	C₂×C₁₃₉	semidirect
247. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
250. C₂×#123	C₂²×C₁₃₉	semidirect
252. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
255. C₂×#121	C₂²×C₁₃₉	semidirect
259. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
260. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
264. #399	C₂²×C₁₃₉	semidirect
265. #399	C₂²×C₁₃₉	semidirect
266. #399	C₂²×C₁₃₉	semidirect
267. #399	C₂²×C₁₃₉	semidirect
268. #399	C₂²×C₁₃₉	semidirect
270. #392	C₂²×C₁₃₉	semidirect
271. #392	C₂²×C₁₃₉	semidirect
273. #390	C₂²×C₁₃₉	semidirect
274. #384	C₂²×C₁₃₉	semidirect
275. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
276. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
277. #376	C₂²×C₁₃₉	semidirect
278. C₂×#95	C₂²×C₁₃₉	semidirect
307. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2658×C₁₃₉	2
#2656×C₁₃₉	2
#2542×C₁₃₉	2
#2540×C₁₃₉	2
#2539×C₁₃₉	2
#2501×C₁₃₉	2
#2397×C₁₃₉	2
C₂×#399×C₁₃₉	2
#2275×C₁₃₉	2
#36060	139

Subgroups — C139×#36060 #48030656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36060 #48030656