Subgroups — C₁₃₉×#36085 #48030681

Order 35584.

4998 conjugacy classes of subgroups.

The subgroup lattice has 458 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×#547×C₁₃₉	C₂	1	3	yes	maximal, complemented
3	#2616×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2614×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2434×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	#2406×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#395×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	1	yes	characteristic
14	C₂²×#41×C₁₃₉	C₂²	1	6	yes	—
15	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₁₃₉	C₂²	1	3	yes	—
17	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂³×Q₈×C₁₃₉	C₂²	1	3	yes	—
19	#547×C₁₃₉	—	2	24	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	6	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	6	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
25	C₂×#121×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×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
29	#395×C₁₃₉	C₂²	1	2	yes	—
30	#395×C₁₃₉	C₂²	1	6	yes	—
31	#395×C₁₃₉	C₂²	1	1	yes	characteristic
32	#395×C₁₃₉	C₂²	1	6	yes	—
33	#395×C₁₃₉	C₂²	1	6	yes	—
34	#394×C₁₃₉	C₂²	1	6	yes	—
35	#394×C₁₃₉	C₂²	1	3	yes	—
36	#393×C₁₃₉	C₂²	1	1	yes	characteristic
37	#393×C₁₃₉	C₂²	1	6	yes	—
38	#392×C₁₃₉	C₂²	1	3	yes	—
39	#391×C₁₃₉	C₂²	1	6	yes	—
40	#386×C₁₃₉	C₂²	1	12	yes	—
41	#386×C₁₃₉	C₂²	1	6	yes	—
42	#385×C₁₃₉	C₂²	1	6	yes	—
43	#385×C₁₃₉	C₂²	1	12	yes	—
44	#381×C₁₃₉	C₂²	1	6	yes	—
45	#380×C₁₃₉	C₂²	1	3	yes	—
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
47	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
48	2₋¹⁺⁴×C₁₃₉	—	2	128	no	—
49	C₂×#41×C₁₃₉	—	2	48	no	—
50	C₂×#41×C₁₃₉	—	2	24	no	—
51	C₂×#41×C₁₃₉	—	2	12	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	1	yes	characteristic
61	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
64	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
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	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
74	#123×C₁₃₉	—	2	24	no	—
75	#123×C₁₃₉	—	2	24	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
77	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
78	#121×C₁₃₉	—	2	24	no	—
79	C₄×D₄×C₁₃₉	—	2	12	no	—
80	C₄×D₄×C₁₃₉	—	2	12	no	—
81	C₂×C₄⋊C₄×C₁₃₉	—	2	24	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	6	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	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	3	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	6	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
96	#95×C₁₃₉	C₂³	1	3	yes	—
97	#95×C₁₃₉	C₂³	1	6	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	C₂⁴	1	1	yes	characteristic
102	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
103	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
104	#41×C₁₃₉	—	2	192	no	—
105	#41×C₁₃₉	—	2	32	no	—
106	#41×C₁₃₉	—	2	96	no	—
107	#41×C₁₃₉	—	4	16	no	—
108	C₂×Q₈×C₁₃₉	—	2	96	no	—
109	C₂×Q₈×C₁₃₉	—	2	64	no	—
110	C₂×Q₈×C₁₃₉	—	2	24	no	—
111	C₂×Q₈×C₁₃₉	—	2	6	no	—
112	C₂×Q₈×C₁₃₉	—	2	12	no	—
113	C₂×Q₈×C₁₃₉	—	2	12	no	—
114	C₂×Q₈×C₁₃₉	—	2	6	no	—
115	C₂×Q₈×C₁₃₉	C₂×D₄	1	12	yes	—
116	C₂×D₄×C₁₃₉	—	2	12	no	—
117	C₂×D₄×C₁₃₉	—	2	24	no	—
118	C₂×D₄×C₁₃₉	—	2	6	no	—
119	C₂×D₄×C₁₃₉	—	2	12	no	—
120	C₂×D₄×C₁₃₉	—	2	6	no	—
121	C₂×D₄×C₁₃₉	—	2	6	no	—
122	C₂×D₄×C₁₃₉	—	4	3	no	—
123	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	—
124	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
125	C₂²×C₄×C₁₃₉	—	2	12	no	—
126	C₂²×C₄×C₁₃₉	—	2	24	no	—
127	C₂²×C₄×C₁₃₉	—	2	24	no	—
128	C₂²×C₄×C₁₃₉	—	2	12	no	—
129	C₂²×C₄×C₁₃₉	—	2	12	no	—
130	C₂²×C₄×C₁₃₉	—	2	12	no	—
131	C₂²×C₄×C₁₃₉	—	2	6	no	—
132	C₂²×C₄×C₁₃₉	—	2	12	no	—
133	C₂²×C₄×C₁₃₉	—	4	6	no	—
134	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
135	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
138	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₁₃₉	—	2	6	no	—
145	C₄⋊C₄×C₁₃₉	—	2	12	no	—
146	C₄⋊C₄×C₁₃₉	—	2	12	no	—
147	C₄⋊C₄×C₁₃₉	—	2	12	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	12	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
157	C₄²×C₁₃₉	—	2	6	no	—
158	C₂³×C₁₃₉	—	2	6	no	—
159	C₂³×C₁₃₉	—	2	2	no	—
160	C₂³×C₁₃₉	—	2	6	no	—
161	C₂³×C₁₃₉	—	2	6	no	—
162	C₂³×C₁₃₉	—	2	3	no	—
163	C₂³×C₁₃₉	—	2	3	no	—
164	C₂³×C₁₃₉	—	2	3	no	—
165	C₂³×C₁₃₉	—	2	3	no	—
166	C₂³×C₁₃₉	—	2	1	no	—
167	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
168	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
169	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
170	Q₈×C₁₃₉	—	2	48	no	—
171	Q₈×C₁₃₉	—	2	8	no	—
172	Q₈×C₁₃₉	—	2	24	no	—
173	Q₈×C₁₃₉	—	4	4	no	—
174	D₄×C₁₃₉	—	2	24	no	—
175	D₄×C₁₃₉	—	2	48	no	—
176	D₄×C₁₃₉	—	4	12	no	—
177	D₄×C₁₃₉	—	4	8	no	—
178	D₄×C₁₃₉	#120	1	16	yes	—
179	C₂×C₄×C₁₃₉	—	2	48	no	—
180	C₂×C₄×C₁₃₉	—	2	48	no	—
181	C₂×C₄×C₁₃₉	—	2	3	no	—
182	C₂×C₄×C₁₃₉	—	2	12	no	—
183	C₂×C₄×C₁₃₉	—	2	6	no	—
184	C₂×C₄×C₁₃₉	—	2	3	no	—
185	C₂×C₄×C₁₃₉	—	2	24	no	—
186	C₂×C₄×C₁₃₉	—	2	3	no	—
187	C₂×C₄×C₁₃₉	—	2	6	no	—
188	C₂×C₄×C₁₃₉	—	2	3	no	—
189	C₂×C₄×C₁₃₉	—	2	6	no	—
190	C₂×C₄×C₁₃₉	—	2	6	no	—
191	C₂×C₄×C₁₃₉	—	2	6	no	—
192	C₂×C₄×C₁₃₉	—	2	6	no	—
193	C₂×C₄×C₁₃₉	—	4	24	no	—
194	C₂×C₄×C₁₃₉	—	4	8	no	—
195	C₂×C₄×C₁₃₉	—	4	4	no	—
196	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
197	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
198	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
199	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	6	yes	complemented
200	C₂²×C₁₃₉	—	2	12	no	—
201	C₂²×C₁₃₉	—	2	12	no	—
202	C₂²×C₁₃₉	—	2	6	no	—
203	C₂²×C₁₃₉	—	2	6	no	—
204	C₂²×C₁₃₉	—	2	6	no	—
205	C₂²×C₁₃₉	—	4	6	no	—
206	C₂²×C₁₃₉	—	4	6	no	—
207	C₂²×C₁₃₉	—	4	1	no	—
208	C₂²×C₁₃₉	—	4	3	no	—
209	C₂²×C₁₃₉	—	4	3	no	—
210	C₂²×C₁₃₉	C₂×#120	1	8	yes	—
211	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
212	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	3	yes	—
213	C₂²×C₁₃₉	#585	1	1	yes	characteristic
214	C₄×C₁₃₉	—	2	12	no	—
215	C₄×C₁₃₉	—	2	6	no	—
216	C₄×C₁₃₉	—	2	6	no	—
217	C₄×C₁₃₉	—	4	1	no	—
218	C₄×C₁₃₉	—	4	2	no	—
219	C₄×C₁₃₉	—	4	6	no	—
220	C₄×C₁₃₉	—	4	3	no	—
221	C₄×C₁₃₉	C₂×#120	1	4	yes	—
222	C₂×C₁₃₉	—	2	8	no	—
223	C₂×C₁₃₉	—	4	6	no	—
224	C₂×C₁₃₉	—	8	1	no	—
225	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
226	C₂×C₁₃₉	#3489	1	3	yes	—
227	C₂×C₁₃₉	#3499	1	3	yes	—
228	#36085	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃₉	#36085	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic, complemented
231	C₂×#547	C₂×C₁₃₉	1	3	yes	complemented
232	#2616	C₂×C₁₃₉	1	1	yes	characteristic, complemented
233	#2614	C₂×C₁₃₉	1	2	yes	complemented
234	#2434	C₂×C₁₃₉	1	3	yes	complemented
235	#2430	C₂×C₁₃₉	1	6	yes	complemented
236	#2409	C₂×C₁₃₉	1	3	yes	complemented
237	#2406	C₂×C₁₃₉	1	6	yes	complemented
238	#2388	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	C₂×#395	C₂×C₁₃₉	1	2	yes	complemented
240	#2339	C₂×C₁₃₉	1	3	yes	complemented
241	C₂×2₋¹⁺⁴	—	2	24	no	—
242	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
243	C₂²×#41	C₂²×C₁₃₉	1	6	yes	—
244	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
245	C₂²×#41	C₂²×C₁₃₉	1	3	yes	—
246	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
247	C₂³×Q₈	C₂²×C₁₃₉	1	3	yes	—
248	#547	—	2	24	no	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
250	C₂×#123	C₂²×C₁₃₉	1	6	yes	—
251	C₂×#123	C₂²×C₁₃₉	1	6	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
254	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
256	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
258	#395	C₂²×C₁₃₉	1	2	yes	—
259	#395	C₂²×C₁₃₉	1	6	yes	—
260	#395	C₂²×C₁₃₉	1	1	yes	characteristic
261	#395	C₂²×C₁₃₉	1	6	yes	—
262	#395	C₂²×C₁₃₉	1	6	yes	—
263	#394	C₂²×C₁₃₉	1	6	yes	—
264	#394	C₂²×C₁₃₉	1	3	yes	—
265	#393	C₂²×C₁₃₉	1	1	yes	characteristic
266	#393	C₂²×C₁₃₉	1	6	yes	—
267	#392	C₂²×C₁₃₉	1	3	yes	—
268	#391	C₂²×C₁₃₉	1	6	yes	—
269	#386	C₂²×C₁₃₉	1	12	yes	—
270	#386	C₂²×C₁₃₉	1	6	yes	—
271	#385	C₂²×C₁₃₉	1	6	yes	—
272	#385	C₂²×C₁₃₉	1	12	yes	—
273	#381	C₂²×C₁₃₉	1	6	yes	—
274	#380	C₂²×C₁₃₉	1	3	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
276	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
277	2₋¹⁺⁴	—	2	128	no	—
278	C₂×#41	—	2	48	no	—
279	C₂×#41	—	2	24	no	—
280	C₂×#41	—	2	12	no	—
281	C₂×#41	—	2	24	no	—
282	C₂×#41	—	2	12	no	—
283	C₂×#41	D₄×C₁₃₉	1	24	yes	complemented
284	C₂²×Q₈	—	2	24	no	—
285	C₂²×Q₈	—	2	24	no	—
286	C₂²×Q₈	—	2	12	no	—
287	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
290	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
291	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
292	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
293	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
294	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
295	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
299	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
300	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
301	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
302	C₄⋊Q₈	—	2	12	no	—
303	#123	—	2	24	no	—
304	#123	—	2	24	no	—
305	C₂²⋊Q₈	—	2	12	no	—
306	C₂²⋊Q₈	—	2	12	no	—
307	#121	—	2	24	no	—
308	C₄×D₄	—	2	12	no	—
309	C₄×D₄	—	2	12	no	—
310	C₂×C₄⋊C₄	—	2	24	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	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×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
324	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
325	#95	C₂³×C₁₃₉	1	3	yes	—
326	#95	C₂³×C₁₃₉	1	6	yes	—
327	#95	C₂³×C₁₃₉	1	12	yes	—
328	#95	C₂³×C₁₃₉	1	3	yes	—
329	#95	C₂³×C₁₃₉	1	12	yes	—
330	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
331	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
332	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
333	#41	—	2	192	no	—
334	#41	—	2	32	no	—
335	#41	—	2	96	no	—
336	#41	—	4	16	no	—
337	C₂×Q₈	—	2	96	no	—
338	C₂×Q₈	—	2	64	no	—
339	C₂×Q₈	—	2	24	no	—
340	C₂×Q₈	—	2	6	no	—
341	C₂×Q₈	—	2	12	no	—
342	C₂×Q₈	—	2	12	no	—
343	C₂×Q₈	—	2	6	no	—
344	C₂×Q₈	C₂×D₄×C₁₃₉	1	12	yes	—
345	C₂×D₄	—	2	12	no	—
346	C₂×D₄	—	2	24	no	—
347	C₂×D₄	—	2	6	no	—
348	C₂×D₄	—	2	12	no	—
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	6	no	—
351	C₂×D₄	—	4	3	no	—
352	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	—
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	24	no	—
357	C₂²×C₄	—	2	12	no	—
358	C₂²×C₄	—	2	12	no	—
359	C₂²×C₄	—	2	12	no	—
360	C₂²×C₄	—	2	6	no	—
361	C₂²×C₄	—	2	12	no	—
362	C₂²×C₄	—	4	6	no	—
363	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	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	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
369	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
371	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
372	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
373	C₄⋊C₄	—	2	6	no	—
374	C₄⋊C₄	—	2	12	no	—
375	C₄⋊C₄	—	2	12	no	—
376	C₄⋊C₄	—	2	12	no	—
377	C₄⋊C₄	—	2	6	no	—
378	C₄⋊C₄	—	2	12	no	—
379	C₂²⋊C₄	—	2	12	no	—
380	C₂²⋊C₄	—	2	6	no	—
381	C₂²⋊C₄	—	2	12	no	—
382	C₂²⋊C₄	—	2	6	no	—
383	C₂²⋊C₄	—	2	12	no	—
384	C₂²⋊C₄	—	2	12	no	—
385	C₂²⋊C₄	—	4	6	no	—
386	C₄²	—	2	6	no	—
387	C₂³	—	2	6	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	6	no	—
390	C₂³	—	2	6	no	—
391	C₂³	—	2	3	no	—
392	C₂³	—	2	3	no	—
393	C₂³	—	2	3	no	—
394	C₂³	—	2	3	no	—
395	C₂³	—	2	1	no	—
396	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
397	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
398	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
399	Q₈	—	2	48	no	—
400	Q₈	—	2	8	no	—
401	Q₈	—	2	24	no	—
402	Q₈	—	4	4	no	—
403	D₄	—	2	24	no	—
404	D₄	—	2	48	no	—
405	D₄	—	4	12	no	—
406	D₄	—	4	8	no	—
407	D₄	#120×C₁₃₉	1	16	yes	—
408	C₂×C₄	—	2	48	no	—
409	C₂×C₄	—	2	48	no	—
410	C₂×C₄	—	2	3	no	—
411	C₂×C₄	—	2	12	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	3	no	—
414	C₂×C₄	—	2	24	no	—
415	C₂×C₄	—	2	3	no	—
416	C₂×C₄	—	2	6	no	—
417	C₂×C₄	—	2	3	no	—
418	C₂×C₄	—	2	6	no	—
419	C₂×C₄	—	2	6	no	—
420	C₂×C₄	—	2	6	no	—
421	C₂×C₄	—	2	6	no	—
422	C₂×C₄	—	4	24	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
428	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	6	yes	complemented
429	C₂²	—	2	12	no	—
430	C₂²	—	2	12	no	—
431	C₂²	—	2	6	no	—
432	C₂²	—	2	6	no	—
433	C₂²	—	2	6	no	—
434	C₂²	—	4	6	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	3	no	—
438	C₂²	—	4	3	no	—
439	C₂²	C₂×#120×C₁₃₉	1	8	yes	—
440	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
441	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	3	yes	—
442	C₂²	#585×C₁₃₉	1	1	yes	characteristic
443	C₄	—	2	12	no	—
444	C₄	—	2	6	no	—
445	C₄	—	2	6	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	6	no	—
449	C₄	—	4	3	no	—
450	C₄	C₂×#120×C₁₃₉	1	4	yes	—
451	C₂	—	2	8	no	—
452	C₂	—	4	6	no	—
453	C₂	—	8	1	no	—
454	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
455	C₂	#3489×C₁₃₉	1	3	yes	—
456	C₂	#3499×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×#547×C₁₃₉	C₂	semidirect
3. #2616×C₁₃₉	C₂	semidirect
4. #2614×C₁₃₉	C₂	semidirect
5. #2434×C₁₃₉	C₂	semidirect
6. #2430×C₁₃₉	C₂	semidirect
7. #2409×C₁₃₉	C₂	semidirect
8. #2406×C₁₃₉	C₂	semidirect
9. #2388×C₁₃₉	C₂	semidirect
10. C₂×#395×C₁₃₉	C₂	semidirect
11. #2339×C₁₃₉	C₂	semidirect
54. C₂×#41×C₁₃₉	D₄	semidirect
199. C₂×C₄×C₁₃₉	2₋¹⁺⁴	semidirect
228. #36085	C₁₃₉	direct (N × H)
229. C₁₃₉	#36085	direct (N × H)
230. C₂²×2₋¹⁺⁴	C₂×C₁₃₉	semidirect
231. C₂×#547	C₂×C₁₃₉	semidirect
232. #2616	C₂×C₁₃₉	semidirect
233. #2614	C₂×C₁₃₉	semidirect
234. #2434	C₂×C₁₃₉	semidirect
235. #2430	C₂×C₁₃₉	semidirect
236. #2409	C₂×C₁₃₉	semidirect
237. #2406	C₂×C₁₃₉	semidirect
238. #2388	C₂×C₁₃₉	semidirect
239. C₂×#395	C₂×C₁₃₉	semidirect
240. #2339	C₂×C₁₃₉	semidirect
283. C₂×#41	D₄×C₁₃₉	semidirect
428. 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×#547×C₁₃₉	2
#2616×C₁₃₉	2
#2614×C₁₃₉	2
#2434×C₁₃₉	2
#2430×C₁₃₉	2
#2409×C₁₃₉	2
#2406×C₁₃₉	2
#2388×C₁₃₉	2
C₂×#395×C₁₃₉	2
#2339×C₁₃₉	2
#36085	139

Subgroups — C139×#36085 #48030681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36085 #48030681