Subgroups — C₁₃₉×#36301 #48030897

Order 35584.

1860 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2571×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2527×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2485×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2477×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2420×C₁₃₉	C₂	1	2	yes	maximal
11	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2344×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2293×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#401×C₁₃₉	C₂²	1	4	yes	—
30	#400×C₁₃₉	C₂²	1	4	yes	—
31	#397×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	—
33	#394×C₁₃₉	C₂²	1	4	yes	—
34	#393×C₁₃₉	C₂²	1	4	yes	—
35	#391×C₁₃₉	C₂²	1	2	yes	—
36	#391×C₁₃₉	C₂²	1	4	yes	—
37	#390×C₁₃₉	C₂²	1	1	yes	characteristic
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#389×C₁₃₉	C₂²	1	2	yes	—
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	1	yes	characteristic
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#388×C₁₃₉	C₂²	1	2	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	2	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#384×C₁₃₉	C₂²	1	1	yes	characteristic
60	#382×C₁₃₉	C₂²	1	2	yes	—
61	#382×C₁₃₉	C₂²	1	2	yes	—
62	#382×C₁₃₉	C₂²	1	2	yes	—
63	#381×C₁₃₉	C₂²	1	4	yes	—
64	#380×C₁₃₉	C₂²	1	1	yes	characteristic
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	#380×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	#376×C₁₃₉	C₂²	1	2	yes	—
82	C₄³×C₁₃₉	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
92	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
93	#121×C₁₃₉	—	2	4	no	—
94	C₄×D₄×C₁₃₉	—	2	8	no	—
95	C₄×D₄×C₁₃₉	—	2	8	no	—
96	C₄×D₄×C₁₃₉	—	2	4	no	—
97	#117×C₁₃₉	—	2	4	no	—
98	#117×C₁₃₉	—	2	4	no	—
99	#117×C₁₃₉	—	4	8	no	—
100	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃₉	—	2	4	no	—
130	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	#95×C₁₃₉	C₂³	1	2	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	4	yes	—
148	#95×C₁₃₉	C₂³	1	2	yes	—
149	#95×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	2	yes	—
153	#95×C₁₃₉	C₂³	1	4	yes	—
154	#95×C₁₃₉	C₂³	1	2	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂×Q₈×C₁₃₉	—	2	4	no	—
162	C₂×Q₈×C₁₃₉	—	4	2	no	—
163	C₂×Q₈×C₁₃₉	—	4	2	no	—
164	C₂×D₄×C₁₃₉	—	2	4	no	—
165	C₂×D₄×C₁₃₉	—	2	4	no	—
166	C₂×D₄×C₁₃₉	—	2	2	no	—
167	C₂×D₄×C₁₃₉	—	2	2	no	—
168	C₂×D₄×C₁₃₉	—	4	2	no	—
169	C₂×D₄×C₁₃₉	#41	1	4	yes	—
170	C₂²×C₄×C₁₃₉	—	2	2	no	—
171	C₂²×C₄×C₁₃₉	—	2	2	no	—
172	C₂²×C₄×C₁₃₉	—	2	8	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	8	no	—
176	C₂²×C₄×C₁₃₉	—	2	4	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	2	no	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	4	4	no	—
183	C₂²×C₄×C₁₃₉	—	4	1	no	—
184	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₁₃₉	—	2	8	no	—
201	C₄⋊C₄×C₁₃₉	—	2	4	no	—
202	C₄⋊C₄×C₁₃₉	—	2	2	no	—
203	C₄⋊C₄×C₁₃₉	—	2	2	no	—
204	C₄⋊C₄×C₁₃₉	—	2	2	no	—
205	C₄⋊C₄×C₁₃₉	—	2	4	no	—
206	C₄⋊C₄×C₁₃₉	—	2	4	no	—
207	C₄⋊C₄×C₁₃₉	—	2	2	no	—
208	C₄⋊C₄×C₁₃₉	—	2	2	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	2	4	no	—
211	C₄⋊C₄×C₁₃₉	—	2	8	no	—
212	C₄⋊C₄×C₁₃₉	—	2	2	no	—
213	C₄⋊C₄×C₁₃₉	—	4	4	no	—
214	C₄⋊C₄×C₁₃₉	—	4	4	no	—
215	C₄⋊C₄×C₁₃₉	—	4	2	no	—
216	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
217	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
220	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
221	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
222	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
228	C₄²×C₁₃₉	—	2	2	no	—
229	C₄²×C₁₃₉	—	2	2	no	—
230	C₄²×C₁₃₉	—	2	2	no	—
231	C₄²×C₁₃₉	—	2	4	no	—
232	C₄²×C₁₃₉	—	2	4	no	—
233	C₄²×C₁₃₉	—	2	4	no	—
234	C₄²×C₁₃₉	—	2	4	no	—
235	C₄²×C₁₃₉	—	2	4	no	—
236	C₄²×C₁₃₉	—	2	4	no	—
237	C₄²×C₁₃₉	—	4	2	no	—
238	C₄²×C₁₃₉	—	4	4	no	—
239	C₄²×C₁₃₉	#41	1	4	yes	—
240	C₂³×C₁₃₉	—	2	1	no	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	1	no	—
244	C₂³×C₁₃₉	—	2	2	no	—
245	C₂³×C₁₃₉	—	2	1	no	—
246	C₂³×C₁₃₉	—	2	2	no	—
247	C₂³×C₁₃₉	—	2	1	no	—
248	C₂³×C₁₃₉	—	2	1	no	—
249	C₂³×C₁₃₉	—	2	2	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	1	no	—
252	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
253	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
254	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
255	Q₈×C₁₃₉	—	8	4	no	—
256	D₄×C₁₃₉	—	2	8	no	—
257	D₄×C₁₃₉	—	4	8	no	—
258	C₂×C₄×C₁₃₉	—	2	1	no	—
259	C₂×C₄×C₁₃₉	—	2	1	no	—
260	C₂×C₄×C₁₃₉	—	2	1	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	1	no	—
264	C₂×C₄×C₁₃₉	—	2	1	no	—
265	C₂×C₄×C₁₃₉	—	2	1	no	—
266	C₂×C₄×C₁₃₉	—	2	8	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	4	no	—
281	C₂×C₄×C₁₃₉	—	2	4	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	4	4	no	—
295	C₂×C₄×C₁₃₉	—	4	16	no	—
296	C₂×C₄×C₁₃₉	—	4	8	no	—
297	C₂×C₄×C₁₃₉	—	4	4	no	—
298	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
299	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
300	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
301	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
302	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
303	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
304	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
305	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
306	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
307	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
308	C₂²×C₁₃₉	—	2	2	no	—
309	C₂²×C₁₃₉	—	2	4	no	—
310	C₂²×C₁₃₉	—	2	2	no	—
311	C₂²×C₁₃₉	—	2	4	no	—
312	C₂²×C₁₃₉	—	2	4	no	—
313	C₂²×C₁₃₉	—	2	2	no	—
314	C₂²×C₁₃₉	—	4	2	no	—
315	C₂²×C₁₃₉	—	4	1	no	—
316	C₂²×C₁₃₉	—	4	1	no	—
317	C₂²×C₁₃₉	—	4	1	no	—
318	C₂²×C₁₃₉	—	4	2	no	—
319	C₂²×C₁₃₉	—	4	2	no	—
320	C₂²×C₁₃₉	—	4	1	no	—
321	C₂²×C₁₃₉	—	4	2	no	—
322	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂²×C₁₃₉	#585	1	1	yes	characteristic
329	C₄×C₁₃₉	—	2	2	no	—
330	C₄×C₁₃₉	—	2	4	no	—
331	C₄×C₁₃₉	—	2	2	no	—
332	C₄×C₁₃₉	—	2	2	no	—
333	C₄×C₁₃₉	—	4	2	no	—
334	C₄×C₁₃₉	—	4	1	no	—
335	C₄×C₁₃₉	—	4	2	no	—
336	C₄×C₁₃₉	—	4	2	no	—
337	C₄×C₁₃₉	—	4	4	no	—
338	C₄×C₁₃₉	—	4	4	no	—
339	C₄×C₁₃₉	—	4	2	no	—
340	C₄×C₁₃₉	—	4	2	no	—
341	C₄×C₁₃₉	—	4	2	no	—
342	C₄×C₁₃₉	#529	1	4	yes	—
343	C₄×C₁₃₉	#552	1	4	yes	—
344	C₂×C₁₃₉	—	4	2	no	—
345	C₂×C₁₃₉	—	4	4	no	—
346	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
347	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
348	C₂×C₁₃₉	#3475	1	1	yes	characteristic
349	C₂×C₁₃₉	#3481	1	1	yes	characteristic
350	C₂×C₁₃₉	#3494	1	1	yes	characteristic
351	C₂×C₁₃₉	#3511	1	1	yes	characteristic
352	C₂×C₁₃₉	#3518	1	1	yes	characteristic
353	#36301	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₁₃₉	#36301	1	1	yes	characteristic, direct product factor, Sylow
355	#2864	C₂×C₁₃₉	1	2	yes	complemented
356	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
357	#2571	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
359	#2527	C₂×C₁₃₉	1	4	yes	complemented
360	#2494	C₂×C₁₃₉	1	2	yes	complemented
361	#2494	C₂×C₁₃₉	1	2	yes	complemented
362	#2485	C₂×C₁₃₉	1	2	yes	complemented
363	#2477	C₂×C₁₃₉	1	4	yes	complemented
364	#2420	C₂×C₁₃₉	1	2	yes	—
365	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
366	#2352	C₂×C₁₃₉	1	2	yes	complemented
367	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2344	C₂×C₁₃₉	1	2	yes	complemented
369	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic
370	#2293	C₂×C₁₃₉	1	2	yes	complemented
371	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
372	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
374	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
376	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
378	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
379	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
381	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
382	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
383	#401	C₂²×C₁₃₉	1	4	yes	—
384	#400	C₂²×C₁₃₉	1	4	yes	—
385	#397	C₂²×C₁₃₉	1	4	yes	—
386	#397	C₂²×C₁₃₉	1	4	yes	—
387	#394	C₂²×C₁₃₉	1	4	yes	—
388	#393	C₂²×C₁₃₉	1	4	yes	—
389	#391	C₂²×C₁₃₉	1	2	yes	—
390	#391	C₂²×C₁₃₉	1	4	yes	—
391	#390	C₂²×C₁₃₉	1	2	yes	—
392	#390	C₂²×C₁₃₉	1	1	yes	characteristic
393	#389	C₂²×C₁₃₉	1	2	yes	—
394	#389	C₂²×C₁₃₉	1	2	yes	—
395	#389	C₂²×C₁₃₉	1	2	yes	—
396	#389	C₂²×C₁₃₉	1	2	yes	—
397	#389	C₂²×C₁₃₉	1	2	yes	—
398	#389	C₂²×C₁₃₉	1	1	yes	characteristic
399	#389	C₂²×C₁₃₉	1	2	yes	—
400	#389	C₂²×C₁₃₉	1	2	yes	—
401	#388	C₂²×C₁₃₉	1	4	yes	—
402	#388	C₂²×C₁₃₉	1	4	yes	—
403	#388	C₂²×C₁₃₉	1	4	yes	—
404	#388	C₂²×C₁₃₉	1	2	yes	—
405	#387	C₂²×C₁₃₉	1	4	yes	—
406	#387	C₂²×C₁₃₉	1	4	yes	—
407	#387	C₂²×C₁₃₉	1	4	yes	—
408	#387	C₂²×C₁₃₉	1	4	yes	—
409	#387	C₂²×C₁₃₉	1	4	yes	—
410	#386	C₂²×C₁₃₉	1	4	yes	—
411	#386	C₂²×C₁₃₉	1	2	yes	—
412	#385	C₂²×C₁₃₉	1	4	yes	—
413	#384	C₂²×C₁₃₉	1	1	yes	characteristic
414	#382	C₂²×C₁₃₉	1	2	yes	—
415	#382	C₂²×C₁₃₉	1	2	yes	—
416	#382	C₂²×C₁₃₉	1	2	yes	—
417	#381	C₂²×C₁₃₉	1	4	yes	—
418	#380	C₂²×C₁₃₉	1	2	yes	—
419	#380	C₂²×C₁₃₉	1	2	yes	—
420	#380	C₂²×C₁₃₉	1	2	yes	—
421	#380	C₂²×C₁₃₉	1	2	yes	—
422	#380	C₂²×C₁₃₉	1	2	yes	—
423	#380	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
435	#376	C₂²×C₁₃₉	1	2	yes	—
436	C₄³	C₂²×C₁₃₉	1	2	yes	—
437	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
438	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
439	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
443	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₄⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	—	4	4	no	—
447	#121	—	2	4	no	—
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	—	2	8	no	—
450	C₄×D₄	—	2	4	no	—
451	#117	—	2	4	no	—
452	#117	—	2	4	no	—
453	#117	—	4	8	no	—
454	C₂×C₄⋊C₄	—	2	8	no	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄²	—	2	4	no	—
484	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
494	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
496	#95	C₂³×C₁₃₉	1	2	yes	—
497	#95	C₂³×C₁₃₉	1	2	yes	—
498	#95	C₂³×C₁₃₉	1	2	yes	—
499	#95	C₂³×C₁₃₉	1	2	yes	—
500	#95	C₂³×C₁₃₉	1	4	yes	—
501	#95	C₂³×C₁₃₉	1	2	yes	—
502	#95	C₂³×C₁₃₉	1	4	yes	—
503	#95	C₂³×C₁₃₉	1	2	yes	—
504	#95	C₂³×C₁₃₉	1	4	yes	—
505	#95	C₂³×C₁₃₉	1	2	yes	—
506	#95	C₂³×C₁₃₉	1	4	yes	—
507	#95	C₂³×C₁₃₉	1	4	yes	—
508	#95	C₂³×C₁₃₉	1	4	yes	—
509	#95	C₂³×C₁₃₉	1	4	yes	—
510	#95	C₂³×C₁₃₉	1	4	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	4	2	no	—
517	C₂×Q₈	—	4	2	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	#41×C₁₃₉	1	4	yes	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	8	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	1	no	—
538	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	4	4	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	8	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	4	4	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₄²	—	2	2	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	4	2	no	—
592	C₄²	—	4	4	no	—
593	C₄²	#41×C₁₃₉	1	4	yes	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	1	no	—
606	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
607	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
608	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
609	Q₈	—	8	4	no	—
610	D₄	—	2	8	no	—
611	D₄	—	4	8	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
653	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
654	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
655	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
656	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
657	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
658	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
660	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
661	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	2	no	—
676	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
677	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
678	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
679	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
680	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
681	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
682	C₂²	#585×C₁₃₉	1	1	yes	characteristic
683	C₄	—	2	2	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	#529×C₁₃₉	1	4	yes	—
697	C₄	#552×C₁₃₉	1	4	yes	—
698	C₂	—	4	2	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
701	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
702	C₂	#3475×C₁₃₉	1	1	yes	characteristic
703	C₂	#3481×C₁₃₉	1	1	yes	characteristic
704	C₂	#3494×C₁₃₉	1	1	yes	characteristic
705	C₂	#3511×C₁₃₉	1	1	yes	characteristic
706	C₂	#3518×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
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. #2864×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
3. #2571×C₁₃₉	C₂	semidirect
4. #2563×C₁₃₉	C₂	semidirect
5. #2527×C₁₃₉	C₂	semidirect
6. #2494×C₁₃₉	C₂	semidirect
7. #2494×C₁₃₉	C₂	semidirect
8. #2485×C₁₃₉	C₂	semidirect
9. #2477×C₁₃₉	C₂	semidirect
11. #2369×C₁₃₉	C₂	semidirect
12. #2352×C₁₃₉	C₂	semidirect
13. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
14. #2344×C₁₃₉	C₂	semidirect
16. #2293×C₁₃₉	C₂	semidirect
17. C₄×#117×C₁₃₉	C₂	semidirect
353. #36301	C₁₃₉	direct (N × H)
354. C₁₃₉	#36301	direct (N × H)
355. #2864	C₂×C₁₃₉	semidirect
356. #2857	C₂×C₁₃₉	semidirect
357. #2571	C₂×C₁₃₉	semidirect
358. #2563	C₂×C₁₃₉	semidirect
359. #2527	C₂×C₁₃₉	semidirect
360. #2494	C₂×C₁₃₉	semidirect
361. #2494	C₂×C₁₃₉	semidirect
362. #2485	C₂×C₁₃₉	semidirect
363. #2477	C₂×C₁₃₉	semidirect
365. #2369	C₂×C₁₃₉	semidirect
366. #2352	C₂×C₁₃₉	semidirect
367. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
368. #2344	C₂×C₁₃₉	semidirect
370. #2293	C₂×C₁₃₉	semidirect
371. C₄×#117	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₉	2
#2857×C₁₃₉	2
#2571×C₁₃₉	2
#2563×C₁₃₉	2
#2527×C₁₃₉	2
#2494×C₁₃₉	2
#2485×C₁₃₉	2
#2477×C₁₃₉	2
#2420×C₁₃₉	2
#2369×C₁₃₉	2
#2352×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2293×C₁₃₉	2
C₄×#117×C₁₃₉	2
#36301	139

Subgroups — C139×#36301 #48030897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36301 #48030897