Subgroups — C₁₃₉×#35687 #48030283

Order 35584.

4964 conjugacy classes of subgroups.

The subgroup lattice has 526 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×D₄×Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2616×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2434×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2432×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2409×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2407×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2388×C₁₃₉	C₂	1	3	yes	maximal, complemented
10	#2341×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂×2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
13	C₂×2₋¹⁺⁴×C₁₃₉	—	2	16	no	—
14	C₂²×#41×C₁₃₉	C₂²	1	3	yes	—
15	C₂²×#41×C₁₃₉	C₂²	1	6	yes	—
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃₉	C₂²	1	3	yes	—
18	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	D₄×Q₈×C₁₃₉	—	2	16	no	—
21	#548×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	3	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	3	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
32	#395×C₁₃₉	C₂²	1	6	yes	—
33	#395×C₁₃₉	C₂²	1	3	yes	—
34	#394×C₁₃₉	C₂²	1	3	yes	—
35	#394×C₁₃₉	C₂²	1	12	yes	—
36	#394×C₁₃₉	C₂²	1	6	yes	—
37	#393×C₁₃₉	C₂²	1	3	yes	—
38	#392×C₁₃₉	C₂²	1	1	yes	characteristic
39	#392×C₁₃₉	C₂²	1	6	yes	—
40	#391×C₁₃₉	C₂²	1	6	yes	—
41	#391×C₁₃₉	C₂²	1	6	yes	—
42	#390×C₁₃₉	C₂²	1	6	yes	—
43	#386×C₁₃₉	C₂²	1	6	yes	—
44	#385×C₁₃₉	C₂²	1	12	yes	—
45	#385×C₁₃₉	C₂²	1	6	yes	—
46	#380×C₁₃₉	C₂²	1	6	yes	—
47	#380×C₁₃₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
49	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
50	2₋¹⁺⁴×C₁₃₉	—	2	128	no	—
51	C₂×#41×C₁₃₉	—	2	24	no	—
52	C₂×#41×C₁₃₉	—	2	8	no	—
53	C₂×#41×C₁₃₉	—	2	24	no	—
54	C₂×#41×C₁₃₉	—	2	12	no	—
55	C₂×#41×C₁₃₉	—	2	24	no	—
56	C₂×#41×C₁₃₉	—	2	24	no	—
57	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
58	C₂²×Q₈×C₁₃₉	—	2	24	no	—
59	C₂²×Q₈×C₁₃₉	—	2	8	no	—
60	C₂²×Q₈×C₁₃₉	—	2	8	no	—
61	C₂²×Q₈×C₁₃₉	—	2	4	no	—
62	C₂²×Q₈×C₁₃₉	—	2	8	no	—
63	C₂²×Q₈×C₁₃₉	—	2	12	no	—
64	C₂²×Q₈×C₁₃₉	D₄	1	16	yes	complemented
65	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
66	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
67	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₄⋊Q₈×C₁₃₉	—	2	24	no	—
79	#124×C₁₃₉	—	2	12	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
82	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
83	#121×C₁₃₉	—	2	12	no	—
84	C₄×Q₈×C₁₃₉	—	2	4	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×D₄×C₁₃₉	—	2	12	no	—
87	C₄×D₄×C₁₃₉	—	2	24	no	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	12	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
102	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
103	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
104	#95×C₁₃₉	C₂³	1	1	yes	characteristic
105	#95×C₁₃₉	C₂³	1	3	yes	—
106	#95×C₁₃₉	C₂³	1	6	yes	—
107	#95×C₁₃₉	C₂³	1	12	yes	—
108	#95×C₁₃₉	C₂³	1	6	yes	—
109	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
110	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
111	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
112	#41×C₁₃₉	—	2	192	no	—
113	#41×C₁₃₉	—	2	96	no	—
114	#41×C₁₃₉	—	2	32	no	—
115	C₂×Q₈×C₁₃₉	—	2	96	no	—
116	C₂×Q₈×C₁₃₉	—	2	64	no	—
117	C₂×Q₈×C₁₃₉	—	2	12	no	—
118	C₂×Q₈×C₁₃₉	—	2	6	no	—
119	C₂×Q₈×C₁₃₉	—	2	12	no	—
120	C₂×Q₈×C₁₃₉	—	2	12	no	—
121	C₂×Q₈×C₁₃₉	—	2	6	no	—
122	C₂×Q₈×C₁₃₉	—	2	12	no	—
123	C₂×Q₈×C₁₃₉	—	4	16	no	—
124	C₂×Q₈×C₁₃₉	C₂×D₄	1	24	yes	—
125	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
127	C₂×D₄×C₁₃₉	—	2	4	no	—
128	C₂×D₄×C₁₃₉	—	2	12	no	—
129	C₂×D₄×C₁₃₉	—	2	4	no	—
130	C₂×D₄×C₁₃₉	—	2	12	no	—
131	C₂×D₄×C₁₃₉	—	2	4	no	—
132	C₂×D₄×C₁₃₉	—	2	6	no	—
133	C₂×D₄×C₁₃₉	—	2	6	no	—
134	C₂×D₄×C₁₃₉	—	2	12	no	—
135	C₂×D₄×C₁₃₉	—	2	2	no	—
136	C₂×D₄×C₁₃₉	—	2	12	no	—
137	C₂×D₄×C₁₃₉	—	2	4	no	—
138	C₂×D₄×C₁₃₉	—	4	3	no	—
139	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
140	C₂²×C₄×C₁₃₉	—	2	12	no	—
141	C₂²×C₄×C₁₃₉	—	2	24	no	—
142	C₂²×C₄×C₁₃₉	—	2	12	no	—
143	C₂²×C₄×C₁₃₉	—	2	12	no	—
144	C₂²×C₄×C₁₃₉	—	2	12	no	—
145	C₂²×C₄×C₁₃₉	—	2	6	no	—
146	C₂²×C₄×C₁₃₉	—	2	12	no	—
147	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
148	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
157	C₄⋊C₄×C₁₃₉	—	2	6	no	—
158	C₄⋊C₄×C₁₃₉	—	2	12	no	—
159	C₄⋊C₄×C₁₃₉	—	2	6	no	—
160	C₄⋊C₄×C₁₃₉	—	2	12	no	—
161	C₄⋊C₄×C₁₃₉	—	2	24	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
171	C₄²×C₁₃₉	—	2	6	no	—
172	C₄²×C₁₃₉	—	2	12	no	—
173	C₂³×C₁₃₉	—	2	2	no	—
174	C₂³×C₁₃₉	—	2	1	no	—
175	C₂³×C₁₃₉	—	2	6	no	—
176	C₂³×C₁₃₉	—	2	2	no	—
177	C₂³×C₁₃₉	—	2	2	no	—
178	C₂³×C₁₃₉	—	2	2	no	—
179	C₂³×C₁₃₉	—	2	6	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	2	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	3	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	3	no	—
186	C₂³×C₁₃₉	—	2	1	no	—
187	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
188	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
189	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	complemented
190	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
191	Q₈×C₁₃₉	—	2	24	no	—
192	Q₈×C₁₃₉	—	2	48	no	—
193	Q₈×C₁₃₉	—	4	12	no	—
194	Q₈×C₁₃₉	#120	1	16	yes	—
195	D₄×C₁₃₉	—	2	16	no	—
196	D₄×C₁₃₉	—	2	48	no	—
197	D₄×C₁₃₉	—	2	8	no	—
198	D₄×C₁₃₉	—	2	24	no	—
199	D₄×C₁₃₉	—	4	12	no	—
200	C₂×C₄×C₁₃₉	—	2	48	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	6	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	6	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	24	no	—
207	C₂×C₄×C₁₃₉	—	2	48	no	—
208	C₂×C₄×C₁₃₉	—	2	1	no	—
209	C₂×C₄×C₁₃₉	—	2	6	no	—
210	C₂×C₄×C₁₃₉	—	2	3	no	—
211	C₂×C₄×C₁₃₉	—	2	3	no	—
212	C₂×C₄×C₁₃₉	—	2	6	no	—
213	C₂×C₄×C₁₃₉	—	2	6	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	3	no	—
216	C₂×C₄×C₁₃₉	—	2	6	no	—
217	C₂×C₄×C₁₃₉	—	2	3	no	—
218	C₂×C₄×C₁₃₉	—	4	12	no	—
219	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
220	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
222	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
223	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	complemented
224	C₂²×C₁₃₉	—	2	6	no	—
225	C₂²×C₁₃₉	—	2	4	no	—
226	C₂²×C₁₃₉	—	2	4	no	—
227	C₂²×C₁₃₉	—	2	4	no	—
228	C₂²×C₁₃₉	—	2	2	no	—
229	C₂²×C₁₃₉	—	2	6	no	—
230	C₂²×C₁₃₉	—	2	4	no	—
231	C₂²×C₁₃₉	—	2	6	no	—
232	C₂²×C₁₃₉	—	4	1	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	4	6	no	—
235	C₂²×C₁₃₉	—	4	2	no	—
236	C₂²×C₁₃₉	—	4	2	no	—
237	C₂²×C₁₃₉	—	4	6	no	—
238	C₂²×C₁₃₉	—	4	2	no	—
239	C₂²×C₁₃₉	—	4	1	no	—
240	C₂²×C₁₃₉	—	4	2	no	—
241	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
242	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
244	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₁₃₉	#585	1	1	yes	characteristic
246	C₄×C₁₃₉	—	2	12	no	—
247	C₄×C₁₃₉	—	2	2	no	—
248	C₄×C₁₃₉	—	2	4	no	—
249	C₄×C₁₃₉	—	4	3	no	—
250	C₄×C₁₃₉	—	4	3	no	—
251	C₄×C₁₃₉	—	4	6	no	—
252	C₄×C₁₃₉	—	4	1	no	—
253	C₄×C₁₃₉	C₂×#120	1	12	yes	—
254	C₂×C₁₃₉	—	4	4	no	—
255	C₂×C₁₃₉	—	4	6	no	—
256	C₂×C₁₃₉	—	4	2	no	—
257	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
258	C₂×C₁₃₉	#3486	1	2	yes	—
259	C₂×C₁₃₉	#3489	1	1	yes	characteristic
260	C₂×C₁₃₉	#3497	1	2	yes	—
261	C₂×C₁₃₉	#3499	1	1	yes	characteristic
262	#35687	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₁₃₉	#35687	1	1	yes	characteristic, direct product factor, Sylow
264	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic, complemented
265	C₂×D₄×Q₈	C₂×C₁₃₉	1	2	yes	complemented
266	C₂×#548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	#2616	C₂×C₁₃₉	1	3	yes	complemented
268	#2434	C₂×C₁₃₉	1	3	yes	complemented
269	#2432	C₂×C₁₃₉	1	6	yes	complemented
270	#2409	C₂×C₁₃₉	1	3	yes	complemented
271	#2407	C₂×C₁₃₉	1	6	yes	complemented
272	#2388	C₂×C₁₃₉	1	3	yes	complemented
273	#2341	C₂×C₁₃₉	1	1	yes	characteristic, complemented
274	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
275	C₂×2₋¹⁺⁴	—	2	8	no	—
276	C₂×2₋¹⁺⁴	—	2	16	no	—
277	C₂²×#41	C₂²×C₁₃₉	1	3	yes	—
278	C₂²×#41	C₂²×C₁₃₉	1	6	yes	—
279	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
280	C₂³×Q₈	C₂²×C₁₃₉	1	3	yes	—
281	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
283	D₄×Q₈	—	2	16	no	—
284	#548	—	2	8	no	—
285	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
286	C₂×#124	C₂²×C₁₃₉	1	3	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
290	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
291	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
293	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	—
294	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
295	#395	C₂²×C₁₃₉	1	6	yes	—
296	#395	C₂²×C₁₃₉	1	3	yes	—
297	#394	C₂²×C₁₃₉	1	3	yes	—
298	#394	C₂²×C₁₃₉	1	12	yes	—
299	#394	C₂²×C₁₃₉	1	6	yes	—
300	#393	C₂²×C₁₃₉	1	3	yes	—
301	#392	C₂²×C₁₃₉	1	1	yes	characteristic
302	#392	C₂²×C₁₃₉	1	6	yes	—
303	#391	C₂²×C₁₃₉	1	6	yes	—
304	#391	C₂²×C₁₃₉	1	6	yes	—
305	#390	C₂²×C₁₃₉	1	6	yes	—
306	#386	C₂²×C₁₃₉	1	6	yes	—
307	#385	C₂²×C₁₃₉	1	12	yes	—
308	#385	C₂²×C₁₃₉	1	6	yes	—
309	#380	C₂²×C₁₃₉	1	6	yes	—
310	#380	C₂²×C₁₃₉	1	3	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
313	2₋¹⁺⁴	—	2	128	no	—
314	C₂×#41	—	2	24	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	—	2	24	no	—
317	C₂×#41	—	2	12	no	—
318	C₂×#41	—	2	24	no	—
319	C₂×#41	—	2	24	no	—
320	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
321	C₂²×Q₈	—	2	24	no	—
322	C₂²×Q₈	—	2	8	no	—
323	C₂²×Q₈	—	2	8	no	—
324	C₂²×Q₈	—	2	4	no	—
325	C₂²×Q₈	—	2	8	no	—
326	C₂²×Q₈	—	2	12	no	—
327	C₂²×Q₈	D₄×C₁₃₉	1	16	yes	complemented
328	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
329	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
330	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
331	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
335	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
336	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
337	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
338	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
339	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
340	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
341	C₄⋊Q₈	—	2	24	no	—
342	#124	—	2	12	no	—
343	C₂²⋊Q₈	—	2	24	no	—
344	C₂²⋊Q₈	—	2	12	no	—
345	C₂²⋊Q₈	—	2	24	no	—
346	#121	—	2	12	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	—	2	8	no	—
349	C₄×D₄	—	2	12	no	—
350	C₄×D₄	—	2	24	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	12	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
365	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
366	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
367	#95	C₂³×C₁₃₉	1	1	yes	characteristic
368	#95	C₂³×C₁₃₉	1	3	yes	—
369	#95	C₂³×C₁₃₉	1	6	yes	—
370	#95	C₂³×C₁₃₉	1	6	yes	—
371	#95	C₂³×C₁₃₉	1	12	yes	—
372	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
373	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
374	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
375	#41	—	2	192	no	—
376	#41	—	2	96	no	—
377	#41	—	2	32	no	—
378	C₂×Q₈	—	2	96	no	—
379	C₂×Q₈	—	2	64	no	—
380	C₂×Q₈	—	2	12	no	—
381	C₂×Q₈	—	2	6	no	—
382	C₂×Q₈	—	2	12	no	—
383	C₂×Q₈	—	2	12	no	—
384	C₂×Q₈	—	2	6	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	—	4	16	no	—
387	C₂×Q₈	C₂×D₄×C₁₃₉	1	24	yes	—
388	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
389	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	12	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	12	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	6	no	—
397	C₂×D₄	—	2	12	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	12	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	4	3	no	—
402	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
403	C₂²×C₄	—	2	12	no	—
404	C₂²×C₄	—	2	24	no	—
405	C₂²×C₄	—	2	12	no	—
406	C₂²×C₄	—	2	12	no	—
407	C₂²×C₄	—	2	12	no	—
408	C₂²×C₄	—	2	6	no	—
409	C₂²×C₄	—	2	12	no	—
410	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
411	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
412	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
414	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
415	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
416	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
420	C₄⋊C₄	—	2	6	no	—
421	C₄⋊C₄	—	2	12	no	—
422	C₄⋊C₄	—	2	6	no	—
423	C₄⋊C₄	—	2	12	no	—
424	C₄⋊C₄	—	2	24	no	—
425	C₂²⋊C₄	—	2	12	no	—
426	C₂²⋊C₄	—	2	6	no	—
427	C₂²⋊C₄	—	2	12	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	12	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	12	no	—
432	C₂²⋊C₄	—	4	6	no	—
433	C₂²⋊C₄	—	4	6	no	—
434	C₄²	—	2	6	no	—
435	C₄²	—	2	12	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	6	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	3	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	3	no	—
449	C₂³	—	2	1	no	—
450	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
451	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
452	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	complemented
453	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
454	Q₈	—	2	24	no	—
455	Q₈	—	2	48	no	—
456	Q₈	—	4	12	no	—
457	Q₈	#120×C₁₃₉	1	16	yes	—
458	D₄	—	2	48	no	—
459	D₄	—	2	8	no	—
460	D₄	—	2	16	no	—
461	D₄	—	2	24	no	—
462	D₄	—	4	12	no	—
463	C₂×C₄	—	2	48	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	6	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	6	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	24	no	—
470	C₂×C₄	—	2	48	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	6	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	2	3	no	—
475	C₂×C₄	—	2	6	no	—
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	3	no	—
479	C₂×C₄	—	2	6	no	—
480	C₂×C₄	—	2	3	no	—
481	C₂×C₄	—	4	12	no	—
482	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
486	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	complemented
487	C₂²	—	2	6	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	6	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	6	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	6	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	6	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
505	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
506	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
507	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
508	C₂²	#585×C₁₃₉	1	1	yes	characteristic
509	C₄	—	2	12	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	4	no	—
512	C₄	—	4	3	no	—
513	C₄	—	4	3	no	—
514	C₄	—	4	6	no	—
515	C₄	—	4	1	no	—
516	C₄	C₂×#120×C₁₃₉	1	12	yes	—
517	C₂	—	4	4	no	—
518	C₂	—	4	6	no	—
519	C₂	—	4	2	no	—
520	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
521	C₂	#3486×C₁₃₉	1	2	yes	—
522	C₂	#3489×C₁₃₉	1	1	yes	characteristic
523	C₂	#3497×C₁₃₉	1	2	yes	—
524	C₂	#3499×C₁₃₉	1	1	yes	characteristic

	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×D₄×Q₈×C₁₃₉	C₂	semidirect
3. C₂×#548×C₁₃₉	C₂	semidirect
4. #2616×C₁₃₉	C₂	semidirect
5. #2434×C₁₃₉	C₂	semidirect
6. #2432×C₁₃₉	C₂	semidirect
7. #2409×C₁₃₉	C₂	semidirect
8. #2407×C₁₃₉	C₂	semidirect
9. #2388×C₁₃₉	C₂	semidirect
10. #2341×C₁₃₉	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
57. C₂×#41×C₁₃₉	D₄	semidirect
64. C₂²×Q₈×C₁₃₉	D₄	semidirect
189. C₂³×C₁₃₉	2₋¹⁺⁴	semidirect
223. C₂×C₄×C₁₃₉	2₋¹⁺⁴	semidirect
262. #35687	C₁₃₉	direct (N × H)
263. C₁₃₉	#35687	direct (N × H)
264. C₂²×2₋¹⁺⁴	C₂×C₁₃₉	semidirect
265. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
266. C₂×#548	C₂×C₁₃₉	semidirect
267. #2616	C₂×C₁₃₉	semidirect
268. #2434	C₂×C₁₃₉	semidirect
269. #2432	C₂×C₁₃₉	semidirect
270. #2409	C₂×C₁₃₉	semidirect
271. #2407	C₂×C₁₃₉	semidirect
272. #2388	C₂×C₁₃₉	semidirect
273. #2341	C₂×C₁₃₉	semidirect
274. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
320. C₂×#41	D₄×C₁₃₉	semidirect
327. C₂²×Q₈	D₄×C₁₃₉	semidirect
452. C₂³	2₋¹⁺⁴×C₁₃₉	semidirect
486. C₂×C₄	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×D₄×Q₈×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2616×C₁₃₉	2
#2434×C₁₃₉	2
#2432×C₁₃₉	2
#2409×C₁₃₉	2
#2407×C₁₃₉	2
#2388×C₁₃₉	2
#2341×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#35687	139

Subgroups — C139×#35687 #48030283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35687 #48030283