Subgroups — C₁₃₉×#36078 #48030674

Order 35584.

5164 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	3	yes	maximal, complemented
3	#2615×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2614×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2436×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2430×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2409×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2404×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#393×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2339×C₁₃₉	C₂	1	3	yes	maximal, complemented
12	C₂×2₋¹⁺⁴×C₁₃₉	—	2	24	no	—
13	C₂²×#41×C₁₃₉	C₂²	1	3	yes	—
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#41×C₁₃₉	C₂²	1	6	yes	complemented
16	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
17	C₂³×Q₈×C₁₃₉	C₂²	1	3	yes	complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#546×C₁₃₉	—	2	24	no	—
20	C₂×#124×C₁₃₉	C₂²	1	3	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	6	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	3	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
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	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
29	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	#395×C₁₃₉	C₂²	1	6	yes	complemented
31	#394×C₁₃₉	C₂²	1	3	yes	complemented
32	#393×C₁₃₉	C₂²	1	1	yes	characteristic
33	#393×C₁₃₉	C₂²	1	6	yes	—
34	#393×C₁₃₉	C₂²	1	2	yes	complemented
35	#393×C₁₃₉	C₂²	1	6	yes	complemented
36	#393×C₁₃₉	C₂²	1	6	yes	complemented
37	#392×C₁₃₉	C₂²	1	3	yes	—
38	#392×C₁₃₉	C₂²	1	6	yes	complemented
39	#391×C₁₃₉	C₂²	1	6	yes	complemented
40	#386×C₁₃₉	C₂²	1	6	yes	—
41	#386×C₁₃₉	C₂²	1	12	yes	complemented
42	#386×C₁₃₉	C₂²	1	12	yes	complemented
43	#385×C₁₃₉	C₂²	1	6	yes	complemented
44	#381×C₁₃₉	C₂²	1	6	yes	complemented
45	#380×C₁₃₉	C₂²	1	3	yes	complemented
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
47	C₂×#95×C₁₃₉	C₂²	1	6	yes	complemented
48	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
49	2₋¹⁺⁴×C₁₃₉	—	2	128	no	—
50	C₂×#41×C₁₃₉	—	2	24	no	—
51	C₂×#41×C₁₃₉	—	2	48	no	—
52	C₂×#41×C₁₃₉	—	2	24	no	—
53	C₂×#41×C₁₃₉	—	2	12	no	—
54	C₂×#41×C₁₃₉	D₄	1	24	yes	complemented
55	C₂²×Q₈×C₁₃₉	—	2	24	no	—
56	C₂²×Q₈×C₁₃₉	—	2	24	no	—
57	C₂²×Q₈×C₁₃₉	—	2	12	no	—
58	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
60	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
61	C₂²×D₄×C₁₃₉	—	2	12	no	—
62	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
74	#124×C₁₃₉	—	2	12	no	—
75	#123×C₁₃₉	—	2	24	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
77	#121×C₁₃₉	—	2	24	no	—
78	#121×C₁₃₉	—	2	12	no	—
79	#120×C₁₃₉	—	2	24	no	—
80	C₄×D₄×C₁₃₉	—	2	12	no	—
81	C₄×D₄×C₁₃₉	—	2	12	no	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	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	6	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
96	#95×C₁₃₉	C₂³	1	6	yes	—
97	#95×C₁₃₉	C₂³	1	3	yes	—
98	#95×C₁₃₉	C₂³	1	12	yes	—
99	#95×C₁₃₉	C₂³	1	3	yes	—
100	#95×C₁₃₉	C₂³	1	12	yes	—
101	C₂⁴×C₁₃₉	—	2	4	no	—
102	C₂⁴×C₁₃₉	—	2	12	no	—
103	C₂⁴×C₁₃₉	—	4	6	no	—
104	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
105	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
106	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
107	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
108	#41×C₁₃₉	—	2	192	no	—
109	#41×C₁₃₉	—	2	32	no	—
110	#41×C₁₃₉	—	2	96	no	—
111	C₂×Q₈×C₁₃₉	—	2	96	no	—
112	C₂×Q₈×C₁₃₉	—	2	64	no	—
113	C₂×Q₈×C₁₃₉	—	2	24	no	—
114	C₂×Q₈×C₁₃₉	—	2	6	no	—
115	C₂×Q₈×C₁₃₉	—	2	12	no	—
116	C₂×Q₈×C₁₃₉	—	2	12	no	—
117	C₂×Q₈×C₁₃₉	C₂×D₄	1	12	yes	—
118	C₂×D₄×C₁₃₉	—	2	12	no	—
119	C₂×D₄×C₁₃₉	—	2	24	no	—
120	C₂×D₄×C₁₃₉	—	2	6	no	—
121	C₂×D₄×C₁₃₉	—	2	12	no	—
122	C₂×D₄×C₁₃₉	—	2	6	no	—
123	C₂×D₄×C₁₃₉	—	2	12	no	—
124	C₂×D₄×C₁₃₉	—	2	6	no	—
125	C₂×D₄×C₁₃₉	—	2	6	no	—
126	C₂×D₄×C₁₃₉	—	4	3	no	—
127	C₂×D₄×C₁₃₉	—	4	12	no	—
128	C₂×D₄×C₁₃₉	—	4	16	no	—
129	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	—
130	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
131	C₂²×C₄×C₁₃₉	—	2	12	no	—
132	C₂²×C₄×C₁₃₉	—	2	24	no	—
133	C₂²×C₄×C₁₃₉	—	2	24	no	—
134	C₂²×C₄×C₁₃₉	—	2	12	no	—
135	C₂²×C₄×C₁₃₉	—	2	12	no	—
136	C₂²×C₄×C₁₃₉	—	2	6	no	—
137	C₂²×C₄×C₁₃₉	—	4	12	no	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
139	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₁₃₉	—	2	6	no	—
148	C₄⋊C₄×C₁₃₉	—	2	6	no	—
149	C₄⋊C₄×C₁₃₉	—	2	12	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
152	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
156	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
157	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
158	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
159	C₄²×C₁₃₉	—	2	6	no	—
160	C₂³×C₁₃₉	—	2	2	no	—
161	C₂³×C₁₃₉	—	2	6	no	—
162	C₂³×C₁₃₉	—	2	3	no	—
163	C₂³×C₁₃₉	—	2	6	no	—
164	C₂³×C₁₃₉	—	2	3	no	—
165	C₂³×C₁₃₉	—	2	3	no	—
166	C₂³×C₁₃₉	—	2	6	no	—
167	C₂³×C₁₃₉	—	2	3	no	—
168	C₂³×C₁₃₉	—	2	6	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	6	no	—
171	C₂³×C₁₃₉	—	4	24	no	—
172	C₂³×C₁₃₉	—	4	8	no	—
173	C₂³×C₁₃₉	—	8	12	no	—
174	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
175	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
176	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	complemented
177	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
178	Q₈×C₁₃₉	—	2	48	no	—
179	Q₈×C₁₃₉	—	2	8	no	—
180	Q₈×C₁₃₉	—	2	24	no	—
181	D₄×C₁₃₉	—	2	24	no	—
182	D₄×C₁₃₉	—	2	48	no	—
183	D₄×C₁₃₉	—	4	12	no	—
184	D₄×C₁₃₉	—	4	8	no	—
185	D₄×C₁₃₉	—	4	4	no	—
186	D₄×C₁₃₉	—	8	12	no	—
187	D₄×C₁₃₉	#120	1	16	yes	—
188	C₂×C₄×C₁₃₉	—	2	48	no	—
189	C₂×C₄×C₁₃₉	—	2	48	no	—
190	C₂×C₄×C₁₃₉	—	2	12	no	—
191	C₂×C₄×C₁₃₉	—	2	6	no	—
192	C₂×C₄×C₁₃₉	—	2	24	no	—
193	C₂×C₄×C₁₃₉	—	2	3	no	—
194	C₂×C₄×C₁₃₉	—	2	3	no	—
195	C₂×C₄×C₁₃₉	—	2	6	no	—
196	C₂×C₄×C₁₃₉	—	2	3	no	—
197	C₂×C₄×C₁₃₉	—	2	3	no	—
198	C₂×C₄×C₁₃₉	—	2	3	no	—
199	C₂×C₄×C₁₃₉	—	2	6	no	—
200	C₂×C₄×C₁₃₉	—	2	12	no	—
201	C₂×C₄×C₁₃₉	—	4	4	no	—
202	C₂×C₄×C₁₃₉	—	8	12	no	—
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
204	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
205	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
206	C₂²×C₁₃₉	—	2	12	no	—
207	C₂²×C₁₃₉	—	2	12	no	—
208	C₂²×C₁₃₉	—	2	6	no	—
209	C₂²×C₁₃₉	—	2	6	no	—
210	C₂²×C₁₃₉	—	2	6	no	—
211	C₂²×C₁₃₉	—	2	6	no	—
212	C₂²×C₁₃₉	—	4	1	no	—
213	C₂²×C₁₃₉	—	4	6	no	—
214	C₂²×C₁₃₉	—	4	6	no	—
215	C₂²×C₁₃₉	—	4	3	no	—
216	C₂²×C₁₃₉	—	4	2	no	—
217	C₂²×C₁₃₉	—	4	6	no	—
218	C₂²×C₁₃₉	—	4	6	no	—
219	C₂²×C₁₃₉	—	8	16	no	—
220	C₂²×C₁₃₉	C₂×#120	1	8	yes	—
221	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
222	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂²×C₁₃₉	#585	1	3	yes	—
224	C₄×C₁₃₉	—	2	12	no	—
225	C₄×C₁₃₉	—	2	6	no	—
226	C₄×C₁₃₉	—	4	1	no	—
227	C₄×C₁₃₉	—	4	3	no	—
228	C₄×C₁₃₉	—	4	3	no	—
229	C₄×C₁₃₉	—	4	6	no	—
230	C₄×C₁₃₉	C₂×#120	1	4	yes	—
231	C₂×C₁₃₉	—	2	8	no	—
232	C₂×C₁₃₉	—	4	6	no	—
233	C₂×C₁₃₉	—	4	2	no	—
234	C₂×C₁₃₉	—	8	2	no	—
235	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
236	C₂×C₁₃₉	#3489	1	3	yes	—
237	C₂×C₁₃₉	#3500	1	3	yes	—
238	#36078	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₉	#36078	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	C₂×#546	C₂×C₁₃₉	1	3	yes	complemented
242	#2615	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	#2614	C₂×C₁₃₉	1	2	yes	complemented
244	#2436	C₂×C₁₃₉	1	3	yes	complemented
245	#2430	C₂×C₁₃₉	1	6	yes	complemented
246	#2409	C₂×C₁₃₉	1	3	yes	complemented
247	#2404	C₂×C₁₃₉	1	6	yes	complemented
248	#2388	C₂×C₁₃₉	1	1	yes	characteristic, complemented
249	C₂×#393	C₂×C₁₃₉	1	2	yes	complemented
250	#2339	C₂×C₁₃₉	1	3	yes	complemented
251	C₂×2₋¹⁺⁴	—	2	24	no	—
252	C₂²×#41	C₂²×C₁₃₉	1	3	yes	—
253	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
254	C₂²×#41	C₂²×C₁₃₉	1	6	yes	complemented
255	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
256	C₂³×Q₈	C₂²×C₁₃₉	1	3	yes	complemented
257	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
258	#546	—	2	24	no	—
259	C₂×#124	C₂²×C₁₃₉	1	3	yes	—
260	C₂×#123	C₂²×C₁₃₉	1	6	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
262	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
263	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
264	C₂×#120	C₂²×C₁₃₉	1	6	yes	—
265	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
266	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
268	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
269	#395	C₂²×C₁₃₉	1	6	yes	complemented
270	#394	C₂²×C₁₃₉	1	3	yes	complemented
271	#393	C₂²×C₁₃₉	1	1	yes	characteristic
272	#393	C₂²×C₁₃₉	1	6	yes	—
273	#393	C₂²×C₁₃₉	1	2	yes	complemented
274	#393	C₂²×C₁₃₉	1	6	yes	complemented
275	#393	C₂²×C₁₃₉	1	6	yes	complemented
276	#392	C₂²×C₁₃₉	1	3	yes	—
277	#392	C₂²×C₁₃₉	1	6	yes	complemented
278	#391	C₂²×C₁₃₉	1	6	yes	complemented
279	#386	C₂²×C₁₃₉	1	6	yes	—
280	#386	C₂²×C₁₃₉	1	12	yes	complemented
281	#386	C₂²×C₁₃₉	1	12	yes	complemented
282	#385	C₂²×C₁₃₉	1	6	yes	complemented
283	#381	C₂²×C₁₃₉	1	6	yes	complemented
284	#380	C₂²×C₁₃₉	1	3	yes	complemented
285	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
286	C₂×#95	C₂²×C₁₃₉	1	6	yes	complemented
287	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
288	2₋¹⁺⁴	—	2	128	no	—
289	C₂×#41	—	2	24	no	—
290	C₂×#41	—	2	48	no	—
291	C₂×#41	—	2	24	no	—
292	C₂×#41	—	2	12	no	—
293	C₂×#41	D₄×C₁₃₉	1	24	yes	complemented
294	C₂²×Q₈	—	2	24	no	—
295	C₂²×Q₈	—	2	24	no	—
296	C₂²×Q₈	—	2	12	no	—
297	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
299	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
300	C₂²×D₄	—	2	12	no	—
301	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
302	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
304	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
305	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
306	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
307	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
310	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
311	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
312	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
313	#124	—	2	12	no	—
314	#123	—	2	24	no	—
315	C₂²⋊Q₈	—	2	12	no	—
316	#121	—	2	24	no	—
317	#121	—	2	12	no	—
318	#120	—	2	24	no	—
319	C₄×D₄	—	2	12	no	—
320	C₄×D₄	—	2	12	no	—
321	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
324	C₂×C₂²⋊C₄	—	2	24	no	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
334	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
335	#95	C₂³×C₁₃₉	1	3	yes	—
336	#95	C₂³×C₁₃₉	1	6	yes	—
337	#95	C₂³×C₁₃₉	1	12	yes	—
338	#95	C₂³×C₁₃₉	1	3	yes	—
339	#95	C₂³×C₁₃₉	1	12	yes	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	12	no	—
342	C₂⁴	—	4	6	no	—
343	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
344	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
345	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
346	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
347	#41	—	2	192	no	—
348	#41	—	2	32	no	—
349	#41	—	2	96	no	—
350	C₂×Q₈	—	2	96	no	—
351	C₂×Q₈	—	2	64	no	—
352	C₂×Q₈	—	2	24	no	—
353	C₂×Q₈	—	2	6	no	—
354	C₂×Q₈	—	2	12	no	—
355	C₂×Q₈	—	2	12	no	—
356	C₂×Q₈	C₂×D₄×C₁₃₉	1	12	yes	—
357	C₂×D₄	—	2	12	no	—
358	C₂×D₄	—	2	24	no	—
359	C₂×D₄	—	2	6	no	—
360	C₂×D₄	—	2	12	no	—
361	C₂×D₄	—	2	6	no	—
362	C₂×D₄	—	2	12	no	—
363	C₂×D₄	—	2	6	no	—
364	C₂×D₄	—	2	6	no	—
365	C₂×D₄	—	4	3	no	—
366	C₂×D₄	—	4	12	no	—
367	C₂×D₄	—	4	16	no	—
368	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	—
369	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
370	C₂²×C₄	—	2	12	no	—
371	C₂²×C₄	—	2	24	no	—
372	C₂²×C₄	—	2	24	no	—
373	C₂²×C₄	—	2	12	no	—
374	C₂²×C₄	—	2	12	no	—
375	C₂²×C₄	—	2	6	no	—
376	C₂²×C₄	—	4	12	no	—
377	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
379	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
380	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
381	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
382	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
385	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
386	C₄⋊C₄	—	2	6	no	—
387	C₄⋊C₄	—	2	6	no	—
388	C₄⋊C₄	—	2	12	no	—
389	C₂²⋊C₄	—	2	12	no	—
390	C₂²⋊C₄	—	2	6	no	—
391	C₂²⋊C₄	—	2	6	no	—
392	C₂²⋊C₄	—	2	12	no	—
393	C₂²⋊C₄	—	2	12	no	—
394	C₂²⋊C₄	—	2	12	no	—
395	C₂²⋊C₄	—	2	12	no	—
396	C₂²⋊C₄	—	4	6	no	—
397	C₂²⋊C₄	—	4	6	no	—
398	C₄²	—	2	6	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	6	no	—
401	C₂³	—	2	3	no	—
402	C₂³	—	2	6	no	—
403	C₂³	—	2	3	no	—
404	C₂³	—	2	3	no	—
405	C₂³	—	2	6	no	—
406	C₂³	—	2	3	no	—
407	C₂³	—	2	6	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	4	24	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	8	12	no	—
413	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
414	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
415	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	complemented
416	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
417	Q₈	—	2	48	no	—
418	Q₈	—	2	8	no	—
419	Q₈	—	2	24	no	—
420	D₄	—	2	24	no	—
421	D₄	—	2	48	no	—
422	D₄	—	4	12	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	4	no	—
425	D₄	—	8	12	no	—
426	D₄	#120×C₁₃₉	1	16	yes	—
427	C₂×C₄	—	2	48	no	—
428	C₂×C₄	—	2	48	no	—
429	C₂×C₄	—	2	12	no	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	24	no	—
432	C₂×C₄	—	2	3	no	—
433	C₂×C₄	—	2	3	no	—
434	C₂×C₄	—	2	6	no	—
435	C₂×C₄	—	2	3	no	—
436	C₂×C₄	—	2	3	no	—
437	C₂×C₄	—	2	3	no	—
438	C₂×C₄	—	2	6	no	—
439	C₂×C₄	—	2	12	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	8	12	no	—
442	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
444	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
445	C₂²	—	2	12	no	—
446	C₂²	—	2	12	no	—
447	C₂²	—	2	6	no	—
448	C₂²	—	2	6	no	—
449	C₂²	—	2	6	no	—
450	C₂²	—	2	6	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	6	no	—
453	C₂²	—	4	3	no	—
454	C₂²	—	4	6	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	6	no	—
457	C₂²	—	4	6	no	—
458	C₂²	—	8	16	no	—
459	C₂²	C₂×#120×C₁₃₉	1	8	yes	—
460	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
461	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
462	C₂²	#585×C₁₃₉	1	3	yes	—
463	C₄	—	2	12	no	—
464	C₄	—	2	6	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	3	no	—
467	C₄	—	4	3	no	—
468	C₄	—	4	6	no	—
469	C₄	C₂×#120×C₁₃₉	1	4	yes	—
470	C₂	—	2	8	no	—
471	C₂	—	4	2	no	—
472	C₂	—	4	6	no	—
473	C₂	—	8	2	no	—
474	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
475	C₂	#3489×C₁₃₉	1	3	yes	—
476	C₂	#3500×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. C₂²×2₋¹⁺⁴×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. #2615×C₁₃₉	C₂	semidirect
4. #2614×C₁₃₉	C₂	semidirect
5. #2436×C₁₃₉	C₂	semidirect
6. #2430×C₁₃₉	C₂	semidirect
7. #2409×C₁₃₉	C₂	semidirect
8. #2404×C₁₃₉	C₂	semidirect
9. #2388×C₁₃₉	C₂	semidirect
10. C₂×#393×C₁₃₉	C₂	semidirect
11. #2339×C₁₃₉	C₂	semidirect
14. C₂²×#41×C₁₃₉	C₂²	semidirect
15. C₂²×#41×C₁₃₉	C₂²	semidirect
16. C₂³×Q₈×C₁₃₉	C₂²	semidirect
17. C₂³×Q₈×C₁₃₉	C₂²	semidirect
29. #395×C₁₃₉	C₂²	semidirect
30. #395×C₁₃₉	C₂²	semidirect
31. #394×C₁₃₉	C₂²	semidirect
34. #393×C₁₃₉	C₂²	semidirect
35. #393×C₁₃₉	C₂²	semidirect
36. #393×C₁₃₉	C₂²	semidirect
38. #392×C₁₃₉	C₂²	semidirect
39. #391×C₁₃₉	C₂²	semidirect
41. #386×C₁₃₉	C₂²	semidirect
42. #386×C₁₃₉	C₂²	semidirect
43. #385×C₁₃₉	C₂²	semidirect
44. #381×C₁₃₉	C₂²	semidirect
45. #380×C₁₃₉	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
47. C₂×#95×C₁₃₉	C₂²	semidirect
54. C₂×#41×C₁₃₉	D₄	semidirect
176. C₂³×C₁₃₉	2₋¹⁺⁴	semidirect
238. #36078	C₁₃₉	direct (N × H)
239. C₁₃₉	#36078	direct (N × H)
240. C₂²×2₋¹⁺⁴	C₂×C₁₃₉	semidirect
241. C₂×#546	C₂×C₁₃₉	semidirect
242. #2615	C₂×C₁₃₉	semidirect
243. #2614	C₂×C₁₃₉	semidirect
244. #2436	C₂×C₁₃₉	semidirect
245. #2430	C₂×C₁₃₉	semidirect
246. #2409	C₂×C₁₃₉	semidirect
247. #2404	C₂×C₁₃₉	semidirect
248. #2388	C₂×C₁₃₉	semidirect
249. C₂×#393	C₂×C₁₃₉	semidirect
250. #2339	C₂×C₁₃₉	semidirect
253. C₂²×#41	C₂²×C₁₃₉	semidirect
254. C₂²×#41	C₂²×C₁₃₉	semidirect
255. C₂³×Q₈	C₂²×C₁₃₉	semidirect
256. C₂³×Q₈	C₂²×C₁₃₉	semidirect
268. #395	C₂²×C₁₃₉	semidirect
269. #395	C₂²×C₁₃₉	semidirect
270. #394	C₂²×C₁₃₉	semidirect
273. #393	C₂²×C₁₃₉	semidirect
274. #393	C₂²×C₁₃₉	semidirect
275. #393	C₂²×C₁₃₉	semidirect
277. #392	C₂²×C₁₃₉	semidirect
278. #391	C₂²×C₁₃₉	semidirect
280. #386	C₂²×C₁₃₉	semidirect
281. #386	C₂²×C₁₃₉	semidirect
282. #385	C₂²×C₁₃₉	semidirect
283. #381	C₂²×C₁₃₉	semidirect
284. #380	C₂²×C₁₃₉	semidirect
285. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
286. C₂×#95	C₂²×C₁₃₉	semidirect
293. C₂×#41	D₄×C₁₃₉	semidirect
415. C₂³	2₋¹⁺⁴×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2615×C₁₃₉	2
#2614×C₁₃₉	2
#2436×C₁₃₉	2
#2430×C₁₃₉	2
#2409×C₁₃₉	2
#2404×C₁₃₉	2
#2388×C₁₃₉	2
C₂×#393×C₁₃₉	2
#2339×C₁₃₉	2
#36078	139

Subgroups — C139×#36078 #48030674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36078 #48030674