Subgroups — C₁₃₉×#35757 #48030353

Order 35584.

5054 conjugacy classes of subgroups.

The subgroup lattice has 530 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×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#548×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2615×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2436×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2431×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	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃₉	C₂²	1	3	yes	—
19	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	#550×C₁₃₉	—	2	8	no	—
21	#548×C₁₃₉	—	2	16	no	—
22	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	6	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	3	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	3	yes	—
33	#394×C₁₃₉	C₂²	1	1	yes	characteristic
34	#394×C₁₃₉	C₂²	1	6	yes	—
35	#393×C₁₃₉	C₂²	1	6	yes	—
36	#393×C₁₃₉	C₂²	1	3	yes	—
37	#392×C₁₃₉	C₂²	1	3	yes	—
38	#392×C₁₃₉	C₂²	1	12	yes	—
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	12	yes	—
44	#386×C₁₃₉	C₂²	1	6	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	8	no	—
54	C₂×#41×C₁₃₉	—	2	4	no	—
55	C₂×#41×C₁₃₉	—	2	24	no	—
56	C₂×#41×C₁₃₉	—	2	12	no	—
57	C₂×#41×C₁₃₉	—	2	24	no	—
58	C₂×#41×C₁₃₉	—	2	24	no	—
59	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
60	C₂²×Q₈×C₁₃₉	—	2	24	no	—
61	C₂²×Q₈×C₁₃₉	—	2	8	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	6	yes	—
67	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
79	#127×C₁₃₉	—	2	12	no	—
80	#124×C₁₃₉	—	2	24	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
82	#121×C₁₃₉	—	2	12	no	—
83	#121×C₁₃₉	—	2	24	no	—
84	#121×C₁₃₉	—	2	12	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×Q₈×C₁₃₉	—	2	4	no	—
87	C₄×D₄×C₁₃₉	—	2	24	no	—
88	C₄×D₄×C₁₃₉	—	2	12	no	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	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	2	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	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	6	yes	—
103	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
104	#95×C₁₃₉	C₂³	1	3	yes	—
105	#95×C₁₃₉	C₂³	1	6	yes	—
106	#95×C₁₃₉	C₂³	1	1	yes	characteristic
107	#95×C₁₃₉	C₂³	1	6	yes	—
108	#95×C₁₃₉	C₂³	1	12	yes	—
109	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
110	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
111	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
112	#41×C₁₃₉	—	2	192	no	—
113	#41×C₁₃₉	—	2	96	no	—
114	#41×C₁₃₉	—	2	32	no	—
115	#41×C₁₃₉	—	4	16	no	—
116	C₂×Q₈×C₁₃₉	—	2	96	no	—
117	C₂×Q₈×C₁₃₉	—	2	64	no	—
118	C₂×Q₈×C₁₃₉	—	2	12	no	—
119	C₂×Q₈×C₁₃₉	—	2	6	no	—
120	C₂×Q₈×C₁₃₉	—	2	12	no	—
121	C₂×Q₈×C₁₃₉	—	2	12	no	—
122	C₂×Q₈×C₁₃₉	C₂×D₄	1	24	yes	—
123	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
125	C₂×D₄×C₁₃₉	—	2	12	no	—
126	C₂×D₄×C₁₃₉	—	2	4	no	—
127	C₂×D₄×C₁₃₉	—	2	12	no	—
128	C₂×D₄×C₁₃₉	—	2	12	no	—
129	C₂×D₄×C₁₃₉	—	2	6	no	—
130	C₂×D₄×C₁₃₉	—	2	12	no	—
131	C₂×D₄×C₁₃₉	—	2	12	no	—
132	C₂×D₄×C₁₃₉	—	2	2	no	—
133	C₂×D₄×C₁₃₉	—	2	12	no	—
134	C₂×D₄×C₁₃₉	—	2	12	no	—
135	C₂×D₄×C₁₃₉	—	2	6	no	—
136	C₂×D₄×C₁₃₉	—	2	6	no	—
137	C₂×D₄×C₁₃₉	—	4	3	no	—
138	C₂×D₄×C₁₃₉	—	4	6	no	—
139	C₂×D₄×C₁₃₉	—	4	6	no	—
140	C₂×D₄×C₁₃₉	—	4	12	no	—
141	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
142	C₂²×C₄×C₁₃₉	—	2	12	no	—
143	C₂²×C₄×C₁₃₉	—	2	24	no	—
144	C₂²×C₄×C₁₃₉	—	2	12	no	—
145	C₂²×C₄×C₁₃₉	—	2	12	no	—
146	C₂²×C₄×C₁₃₉	—	2	12	no	—
147	C₂²×C₄×C₁₃₉	—	2	6	no	—
148	C₂²×C₄×C₁₃₉	—	2	12	no	—
149	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
150	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
159	C₄⋊C₄×C₁₃₉	—	2	2	no	—
160	C₄⋊C₄×C₁₃₉	—	2	12	no	—
161	C₄⋊C₄×C₁₃₉	—	2	6	no	—
162	C₄⋊C₄×C₁₃₉	—	2	12	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
171	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
172	C₄²×C₁₃₉	—	2	12	no	—
173	C₄²×C₁₃₉	—	2	6	no	—
174	C₂³×C₁₃₉	—	2	6	no	—
175	C₂³×C₁₃₉	—	2	2	no	—
176	C₂³×C₁₃₉	—	2	2	no	—
177	C₂³×C₁₃₉	—	2	2	no	—
178	C₂³×C₁₃₉	—	2	3	no	—
179	C₂³×C₁₃₉	—	2	2	no	—
180	C₂³×C₁₃₉	—	2	3	no	—
181	C₂³×C₁₃₉	—	2	6	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	2	no	—
184	C₂³×C₁₃₉	—	2	6	no	—
185	C₂³×C₁₃₉	—	2	3	no	—
186	C₂³×C₁₃₉	—	2	3	no	—
187	C₂³×C₁₃₉	—	2	3	no	—
188	C₂³×C₁₃₉	—	2	6	no	—
189	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
190	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
191	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
192	Q₈×C₁₃₉	—	2	24	no	—
193	Q₈×C₁₃₉	—	2	48	no	—
194	Q₈×C₁₃₉	#120	1	16	yes	—
195	D₄×C₁₃₉	—	2	48	no	—
196	D₄×C₁₃₉	—	2	8	no	—
197	D₄×C₁₃₉	—	2	24	no	—
198	D₄×C₁₃₉	—	4	12	no	—
199	D₄×C₁₃₉	—	4	24	no	—
200	D₄×C₁₃₉	—	4	12	no	—
201	D₄×C₁₃₉	—	8	12	no	—
202	C₂×C₄×C₁₃₉	—	2	48	no	—
203	C₂×C₄×C₁₃₉	—	2	1	no	—
204	C₂×C₄×C₁₃₉	—	2	6	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	6	no	—
207	C₂×C₄×C₁₃₉	—	2	1	no	—
208	C₂×C₄×C₁₃₉	—	2	24	no	—
209	C₂×C₄×C₁₃₉	—	2	48	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	6	no	—
212	C₂×C₄×C₁₃₉	—	2	3	no	—
213	C₂×C₄×C₁₃₉	—	2	1	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	6	no	—
218	C₂×C₄×C₁₃₉	—	2	6	no	—
219	C₂×C₄×C₁₃₉	—	2	6	no	—
220	C₂×C₄×C₁₃₉	—	4	12	no	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
222	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
224	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
225	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	complemented
226	C₂²×C₁₃₉	—	2	6	no	—
227	C₂²×C₁₃₉	—	2	4	no	—
228	C₂²×C₁₃₉	—	2	4	no	—
229	C₂²×C₁₃₉	—	2	6	no	—
230	C₂²×C₁₃₉	—	2	4	no	—
231	C₂²×C₁₃₉	—	2	6	no	—
232	C₂²×C₁₃₉	—	4	2	no	—
233	C₂²×C₁₃₉	—	4	6	no	—
234	C₂²×C₁₃₉	—	4	2	no	—
235	C₂²×C₁₃₉	—	4	2	no	—
236	C₂²×C₁₃₉	—	4	6	no	—
237	C₂²×C₁₃₉	—	4	2	no	—
238	C₂²×C₁₃₉	—	4	3	no	—
239	C₂²×C₁₃₉	—	4	6	no	—
240	C₂²×C₁₃₉	—	4	3	no	—
241	C₂²×C₁₃₉	—	4	6	no	—
242	C₂²×C₁₃₉	—	4	3	no	—
243	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
244	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
246	C₂²×C₁₃₉	#585	1	1	yes	characteristic
247	C₂²×C₁₃₉	#585	1	2	yes	—
248	C₄×C₁₃₉	—	2	12	no	—
249	C₄×C₁₃₉	—	2	2	no	—
250	C₄×C₁₃₉	—	2	2	no	—
251	C₄×C₁₃₉	—	4	1	no	—
252	C₄×C₁₃₉	—	4	6	no	—
253	C₄×C₁₃₉	—	4	2	no	—
254	C₄×C₁₃₉	—	4	3	no	—
255	C₄×C₁₃₉	C₂×#120	1	12	yes	—
256	C₂×C₁₃₉	—	4	4	no	—
257	C₂×C₁₃₉	—	4	6	no	—
258	C₂×C₁₃₉	—	8	3	no	—
259	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
260	C₂×C₁₃₉	#3487	1	2	yes	—
261	C₂×C₁₃₉	#3489	1	1	yes	characteristic
262	C₂×C₁₃₉	#3497	1	2	yes	—
263	C₂×C₁₃₉	#3500	1	1	yes	characteristic
264	#35757	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₁₃₉	#35757	1	1	yes	characteristic, direct product factor, Sylow
266	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	C₂×#548	C₂×C₁₃₉	1	2	yes	complemented
269	#2615	C₂×C₁₃₉	1	3	yes	complemented
270	#2436	C₂×C₁₃₉	1	3	yes	complemented
271	#2431	C₂×C₁₃₉	1	6	yes	complemented
272	#2409	C₂×C₁₃₉	1	3	yes	complemented
273	#2407	C₂×C₁₃₉	1	6	yes	complemented
274	#2388	C₂×C₁₃₉	1	3	yes	complemented
275	#2341	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
277	C₂×2₋¹⁺⁴	—	2	8	no	—
278	C₂×2₋¹⁺⁴	—	2	16	no	—
279	C₂²×#41	C₂²×C₁₃₉	1	3	yes	—
280	C₂²×#41	C₂²×C₁₃₉	1	6	yes	—
281	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
283	C₂³×Q₈	C₂²×C₁₃₉	1	3	yes	—
284	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
285	#550	—	2	8	no	—
286	#548	—	2	16	no	—
287	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
288	C₂×#124	C₂²×C₁₃₉	1	6	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
290	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
291	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
292	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
297	#395	C₂²×C₁₃₉	1	3	yes	—
298	#394	C₂²×C₁₃₉	1	1	yes	characteristic
299	#394	C₂²×C₁₃₉	1	6	yes	—
300	#393	C₂²×C₁₃₉	1	6	yes	—
301	#393	C₂²×C₁₃₉	1	3	yes	—
302	#392	C₂²×C₁₃₉	1	3	yes	—
303	#392	C₂²×C₁₃₉	1	12	yes	—
304	#392	C₂²×C₁₃₉	1	6	yes	—
305	#391	C₂²×C₁₃₉	1	6	yes	—
306	#391	C₂²×C₁₃₉	1	6	yes	—
307	#390	C₂²×C₁₃₉	1	6	yes	—
308	#386	C₂²×C₁₃₉	1	12	yes	—
309	#386	C₂²×C₁₃₉	1	6	yes	—
310	#385	C₂²×C₁₃₉	1	6	yes	—
311	#380	C₂²×C₁₃₉	1	6	yes	—
312	#380	C₂²×C₁₃₉	1	3	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
314	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
315	2₋¹⁺⁴	—	2	128	no	—
316	C₂×#41	—	2	24	no	—
317	C₂×#41	—	2	8	no	—
318	C₂×#41	—	2	8	no	—
319	C₂×#41	—	2	4	no	—
320	C₂×#41	—	2	24	no	—
321	C₂×#41	—	2	12	no	—
322	C₂×#41	—	2	24	no	—
323	C₂×#41	—	2	24	no	—
324	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
325	C₂²×Q₈	—	2	24	no	—
326	C₂²×Q₈	—	2	8	no	—
327	C₂²×Q₈	—	2	8	no	—
328	C₂²×Q₈	—	2	12	no	—
329	C₂²×Q₈	D₄×C₁₃₉	1	16	yes	complemented
330	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
331	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
332	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
334	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
336	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
337	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
338	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
339	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
340	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
341	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
342	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
343	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
344	#127	—	2	12	no	—
345	#124	—	2	24	no	—
346	C₂²⋊Q₈	—	2	24	no	—
347	#121	—	2	12	no	—
348	#121	—	2	24	no	—
349	#121	—	2	12	no	—
350	C₄×Q₈	—	2	8	no	—
351	C₄×Q₈	—	2	4	no	—
352	C₄×D₄	—	2	24	no	—
353	C₄×D₄	—	2	12	no	—
354	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
367	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
368	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
369	#95	C₂³×C₁₃₉	1	1	yes	characteristic
370	#95	C₂³×C₁₃₉	1	3	yes	—
371	#95	C₂³×C₁₃₉	1	6	yes	—
372	#95	C₂³×C₁₃₉	1	6	yes	—
373	#95	C₂³×C₁₃₉	1	12	yes	—
374	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
375	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
376	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
377	#41	—	2	192	no	—
378	#41	—	2	96	no	—
379	#41	—	2	32	no	—
380	#41	—	4	16	no	—
381	C₂×Q₈	—	2	96	no	—
382	C₂×Q₈	—	2	64	no	—
383	C₂×Q₈	—	2	12	no	—
384	C₂×Q₈	—	2	6	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	—	2	12	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	12	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	12	no	—
393	C₂×D₄	—	2	12	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	2	12	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	12	no	—
399	C₂×D₄	—	2	12	no	—
400	C₂×D₄	—	2	6	no	—
401	C₂×D₄	—	2	6	no	—
402	C₂×D₄	—	4	3	no	—
403	C₂×D₄	—	4	6	no	—
404	C₂×D₄	—	4	6	no	—
405	C₂×D₄	—	4	12	no	—
406	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
407	C₂²×C₄	—	2	12	no	—
408	C₂²×C₄	—	2	24	no	—
409	C₂²×C₄	—	2	12	no	—
410	C₂²×C₄	—	2	12	no	—
411	C₂²×C₄	—	2	12	no	—
412	C₂²×C₄	—	2	6	no	—
413	C₂²×C₄	—	2	12	no	—
414	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
416	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
421	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	12	no	—
426	C₄⋊C₄	—	2	6	no	—
427	C₄⋊C₄	—	2	12	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₂²⋊C₄	—	2	6	no	—
431	C₂²⋊C₄	—	2	12	no	—
432	C₂²⋊C₄	—	2	24	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	4	6	no	—
435	C₂²⋊C₄	—	4	6	no	—
436	C₂²⋊C₄	—	4	6	no	—
437	C₄²	—	2	12	no	—
438	C₄²	—	2	6	no	—
439	C₂³	—	2	6	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	3	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	3	no	—
446	C₂³	—	2	6	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	6	no	—
450	C₂³	—	2	3	no	—
451	C₂³	—	2	3	no	—
452	C₂³	—	2	3	no	—
453	C₂³	—	2	6	no	—
454	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
455	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
456	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
457	Q₈	—	2	24	no	—
458	Q₈	—	2	48	no	—
459	Q₈	#120×C₁₃₉	1	16	yes	—
460	D₄	—	2	48	no	—
461	D₄	—	2	8	no	—
462	D₄	—	2	24	no	—
463	D₄	—	4	12	no	—
464	D₄	—	4	24	no	—
465	D₄	—	4	12	no	—
466	D₄	—	8	12	no	—
467	C₂×C₄	—	2	48	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	6	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	6	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	24	no	—
474	C₂×C₄	—	2	48	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	2	3	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	6	no	—
483	C₂×C₄	—	2	6	no	—
484	C₂×C₄	—	2	6	no	—
485	C₂×C₄	—	4	12	no	—
486	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
490	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	complemented
491	C₂²	—	2	6	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	6	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	6	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	6	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	6	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	3	no	—
504	C₂²	—	4	6	no	—
505	C₂²	—	4	3	no	—
506	C₂²	—	4	6	no	—
507	C₂²	—	4	3	no	—
508	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
509	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
510	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
511	C₂²	#585×C₁₃₉	1	1	yes	characteristic
512	C₂²	#585×C₁₃₉	1	2	yes	—
513	C₄	—	2	12	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	6	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	3	no	—
520	C₄	C₂×#120×C₁₃₉	1	12	yes	—
521	C₂	—	4	4	no	—
522	C₂	—	4	6	no	—
523	C₂	—	8	3	no	—
524	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
525	C₂	#3487×C₁₃₉	1	2	yes	—
526	C₂	#3489×C₁₃₉	1	1	yes	characteristic
527	C₂	#3497×C₁₃₉	1	2	yes	—
528	C₂	#3500×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×#550×C₁₃₉	C₂	semidirect
3. C₂×#548×C₁₃₉	C₂	semidirect
4. #2615×C₁₃₉	C₂	semidirect
5. #2436×C₁₃₉	C₂	semidirect
6. #2431×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
59. C₂×#41×C₁₃₉	D₄	semidirect
64. C₂²×Q₈×C₁₃₉	D₄	semidirect
225. C₂×C₄×C₁₃₉	2₋¹⁺⁴	semidirect
264. #35757	C₁₃₉	direct (N × H)
265. C₁₃₉	#35757	direct (N × H)
266. C₂²×2₋¹⁺⁴	C₂×C₁₃₉	semidirect
267. C₂×#550	C₂×C₁₃₉	semidirect
268. C₂×#548	C₂×C₁₃₉	semidirect
269. #2615	C₂×C₁₃₉	semidirect
270. #2436	C₂×C₁₃₉	semidirect
271. #2431	C₂×C₁₃₉	semidirect
272. #2409	C₂×C₁₃₉	semidirect
273. #2407	C₂×C₁₃₉	semidirect
274. #2388	C₂×C₁₃₉	semidirect
275. #2341	C₂×C₁₃₉	semidirect
276. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
324. C₂×#41	D₄×C₁₃₉	semidirect
329. C₂²×Q₈	D₄×C₁₃₉	semidirect
490. 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×#550×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2615×C₁₃₉	2
#2436×C₁₃₉	2
#2431×C₁₃₉	2
#2409×C₁₃₉	2
#2407×C₁₃₉	2
#2388×C₁₃₉	2
#2341×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#35757	139

Subgroups — C139×#35757 #48030353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35757 #48030353