Subgroups — C₁₃₉×#37270 #48031866

Order 35584.

2746 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2847×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2703×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2696×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2673×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2669×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2615×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2562×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2541×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2537×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2535×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2314×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	#540×C₁₃₉	—	2	8	no	—
17	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	#525×C₁₃₉	—	2	8	no	—
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	#400×C₁₃₉	C₂²	1	4	yes	complemented
39	#397×C₁₃₉	C₂²	1	4	yes	complemented
40	#394×C₁₃₉	C₂²	1	4	yes	—
41	#394×C₁₃₉	C₂²	1	4	yes	—
42	#394×C₁₃₉	C₂²	1	4	yes	complemented
43	#393×C₁₃₉	C₂²	1	4	yes	complemented
44	#392×C₁₃₉	C₂²	1	4	yes	—
45	#392×C₁₃₉	C₂²	1	4	yes	—
46	#392×C₁₃₉	C₂²	1	4	yes	—
47	#392×C₁₃₉	C₂²	1	4	yes	—
48	#392×C₁₃₉	C₂²	1	4	yes	complemented
49	#392×C₁₃₉	C₂²	1	4	yes	complemented
50	#390×C₁₃₉	C₂²	1	4	yes	complemented
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	complemented
54	#387×C₁₃₉	C₂²	1	4	yes	complemented
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#386×C₁₃₉	C₂²	1	4	yes	—
59	#386×C₁₃₉	C₂²	1	4	yes	complemented
60	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#380×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	2	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	complemented
66	#380×C₁₃₉	C₂²	1	2	yes	complemented
67	#380×C₁₃₉	C₂²	1	4	yes	complemented
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
69	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₃₉	—	2	4	no	—
71	C₂×#41×C₁₃₉	—	4	2	no	—
72	C₂×#41×C₁₃₉	—	4	2	no	—
73	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₉	—	2	4	no	—
86	C₂³×C₄×C₁₃₉	—	4	2	no	—
87	C₂³×C₄×C₁₃₉	—	4	2	no	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	#127×C₁₃₉	—	2	4	no	—
95	#127×C₁₃₉	—	4	8	no	—
96	#125×C₁₃₉	—	2	4	no	—
97	#123×C₁₃₉	—	2	16	no	—
98	#123×C₁₃₉	—	2	8	no	—
99	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
100	#121×C₁₃₉	—	2	8	no	—
101	#121×C₁₃₉	—	2	8	no	—
102	#121×C₁₃₉	—	2	16	no	—
103	#121×C₁₃₉	—	4	8	no	—
104	#121×C₁₃₉	—	4	4	no	—
105	#121×C₁₃₉	—	4	4	no	—
106	#121×C₁₃₉	—	4	4	no	—
107	#121×C₁₃₉	—	4	4	no	—
108	#120×C₁₃₉	—	2	8	no	—
109	#120×C₁₃₉	—	4	8	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	#117×C₁₃₉	D₄	1	8	yes	complemented
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	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	C₂⁴×C₁₃₉	—	2	2	no	—
149	C₂⁴×C₁₃₉	—	2	4	no	—
150	C₂⁴×C₁₃₉	—	4	1	no	—
151	C₂⁴×C₁₃₉	—	4	1	no	—
152	C₂⁴×C₁₃₉	—	4	2	no	—
153	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
155	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
156	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
157	#41×C₁₃₉	—	4	16	no	—
158	C₂×Q₈×C₁₃₉	—	2	2	no	—
159	C₂×Q₈×C₁₃₉	—	4	1	no	—
160	C₂×Q₈×C₁₃₉	—	4	1	no	—
161	C₂×D₄×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	2	4	no	—
163	C₂×D₄×C₁₃₉	—	2	4	no	—
164	C₂×D₄×C₁₃₉	—	2	8	no	—
165	C₂×D₄×C₁₃₉	—	2	8	no	—
166	C₂×D₄×C₁₃₉	—	2	8	no	—
167	C₂×D₄×C₁₃₉	—	2	4	no	—
168	C₂×D₄×C₁₃₉	—	2	4	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	2	no	—
171	C₂×D₄×C₁₃₉	—	2	8	no	—
172	C₂×D₄×C₁₃₉	—	2	4	no	—
173	C₂×D₄×C₁₃₉	—	2	4	no	—
174	C₂×D₄×C₁₃₉	—	4	2	no	—
175	C₂×D₄×C₁₃₉	—	4	2	no	—
176	C₂×D₄×C₁₃₉	—	4	1	no	—
177	C₂×D₄×C₁₃₉	—	4	1	no	—
178	C₂×D₄×C₁₃₉	—	4	2	no	—
179	C₂×D₄×C₁₃₉	—	4	2	no	—
180	C₂×D₄×C₁₃₉	—	4	4	no	—
181	C₂×D₄×C₁₃₉	—	4	4	no	—
182	C₂×D₄×C₁₃₉	—	4	4	no	—
183	C₂×D₄×C₁₃₉	—	4	4	no	—
184	C₂×D₄×C₁₃₉	—	4	4	no	—
185	C₂×D₄×C₁₃₉	—	4	4	no	—
186	C₂×D₄×C₁₃₉	—	4	4	no	—
187	C₂×D₄×C₁₃₉	—	4	4	no	—
188	C₂×D₄×C₁₃₉	—	4	4	no	—
189	C₂×D₄×C₁₃₉	—	4	4	no	—
190	C₂×D₄×C₁₃₉	—	4	4	no	—
191	C₂×D₄×C₁₃₉	—	4	4	no	—
192	C₂×D₄×C₁₃₉	—	4	4	no	—
193	C₂×D₄×C₁₃₉	—	4	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	8	no	—
205	C₂²×C₄×C₁₃₉	—	4	2	no	—
206	C₂²×C₄×C₁₃₉	—	4	2	no	—
207	C₂²×C₄×C₁₃₉	—	4	1	no	—
208	C₂²×C₄×C₁₃₉	—	4	1	no	—
209	C₂²×C₄×C₁₃₉	—	4	4	no	—
210	C₂²×C₄×C₁₃₉	—	4	4	no	—
211	C₂²×C₄×C₁₃₉	—	4	16	no	—
212	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	4	4	no	—
229	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
230	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
234	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
237	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
241	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
245	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
246	C₄²×C₁₃₉	—	4	4	no	—
247	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
249	C₂³×C₁₃₉	—	2	2	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	2	no	—
252	C₂³×C₁₃₉	—	2	1	no	—
253	C₂³×C₁₃₉	—	2	1	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	4	no	—
261	C₂³×C₁₃₉	—	2	4	no	—
262	C₂³×C₁₃₉	—	2	4	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	4	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	4	no	—
273	C₂³×C₁₃₉	—	4	8	no	—
274	C₂³×C₁₃₉	—	4	4	no	—
275	C₂³×C₁₃₉	—	4	4	no	—
276	C₂³×C₁₃₉	—	4	8	no	—
277	C₂³×C₁₃₉	—	4	4	no	—
278	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
279	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
280	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃₉	—	4	4	no	—
282	D₄×C₁₃₉	—	4	8	no	—
283	D₄×C₁₃₉	—	4	8	no	—
284	D₄×C₁₃₉	—	4	4	no	—
285	D₄×C₁₃₉	—	4	8	no	—
286	D₄×C₁₃₉	—	4	8	no	—
287	D₄×C₁₃₉	—	8	8	no	—
288	D₄×C₁₃₉	—	8	8	no	—
289	D₄×C₁₃₉	—	8	8	no	—
290	D₄×C₁₃₉	—	8	8	no	—
291	D₄×C₁₃₉	—	8	8	no	—
292	D₄×C₁₃₉	—	8	8	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	8	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	4	8	no	—
316	C₂×C₄×C₁₃₉	—	4	4	no	—
317	C₂×C₄×C₁₃₉	—	4	8	no	—
318	C₂×C₄×C₁₃₉	—	4	8	no	—
319	C₂×C₄×C₁₃₉	—	8	8	no	—
320	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
325	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
326	C₂²×C₁₃₉	—	2	2	no	—
327	C₂²×C₁₃₉	—	2	4	no	—
328	C₂²×C₁₃₉	—	2	4	no	—
329	C₂²×C₁₃₉	—	2	4	no	—
330	C₂²×C₁₃₉	—	2	4	no	—
331	C₂²×C₁₃₉	—	4	16	no	—
332	C₂²×C₁₃₉	—	4	2	no	—
333	C₂²×C₁₃₉	—	4	2	no	—
334	C₂²×C₁₃₉	—	4	1	no	—
335	C₂²×C₁₃₉	—	4	1	no	—
336	C₂²×C₁₃₉	—	4	2	no	—
337	C₂²×C₁₃₉	—	4	2	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	4	no	—
341	C₂²×C₁₃₉	—	4	4	no	—
342	C₂²×C₁₃₉	—	4	2	no	—
343	C₂²×C₁₃₉	—	4	2	no	—
344	C₂²×C₁₃₉	—	4	4	no	—
345	C₂²×C₁₃₉	—	4	4	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	4	no	—
348	C₂²×C₁₃₉	—	4	2	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	4	4	no	—
351	C₂²×C₁₃₉	—	4	4	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
357	C₂²×C₁₃₉	#585	1	2	yes	—
358	C₄×C₁₃₉	—	2	2	no	—
359	C₄×C₁₃₉	—	2	4	no	—
360	C₄×C₁₃₉	—	2	4	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	2	no	—
363	C₄×C₁₃₉	—	4	4	no	—
364	C₄×C₁₃₉	—	4	4	no	—
365	C₄×C₁₃₉	—	4	4	no	—
366	C₄×C₁₃₉	#535	1	4	yes	—
367	C₂×C₁₃₉	—	4	2	no	—
368	C₂×C₁₃₉	—	4	4	no	—
369	C₂×C₁₃₉	—	8	2	no	—
370	C₂×C₁₃₉	—	8	4	no	—
371	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
372	C₂×C₁₃₉	#3488	1	2	yes	—
373	C₂×C₁₃₉	#3537	1	1	yes	characteristic
374	C₂×C₁₃₉	#3539	1	1	yes	characteristic
375	C₂×C₁₃₉	#3542	1	2	yes	—
376	#37270	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₁₃₉	#37270	1	1	yes	characteristic, direct product factor, Sylow
378	C₂×#540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	C₂×#525	C₂×C₁₃₉	1	1	yes	characteristic, complemented
380	#2847	C₂×C₁₃₉	1	2	yes	complemented
381	#2703	C₂×C₁₃₉	1	4	yes	complemented
382	#2696	C₂×C₁₃₉	1	4	yes	complemented
383	#2673	C₂×C₁₃₉	1	4	yes	complemented
384	#2669	C₂×C₁₃₉	1	4	yes	complemented
385	#2615	C₂×C₁₃₉	1	2	yes	complemented
386	#2562	C₂×C₁₃₉	1	2	yes	complemented
387	#2541	C₂×C₁₃₉	1	2	yes	complemented
388	#2537	C₂×C₁₃₉	1	2	yes	complemented
389	#2535	C₂×C₁₃₉	1	2	yes	complemented
390	#2314	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
393	#540	—	2	8	no	—
394	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
395	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
396	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
397	#525	—	2	8	no	—
398	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
399	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
400	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
401	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
402	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
403	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
404	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
405	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
407	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
408	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
409	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
410	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
411	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
414	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
415	#400	C₂²×C₁₃₉	1	4	yes	complemented
416	#397	C₂²×C₁₃₉	1	4	yes	complemented
417	#394	C₂²×C₁₃₉	1	4	yes	—
418	#394	C₂²×C₁₃₉	1	4	yes	—
419	#394	C₂²×C₁₃₉	1	4	yes	complemented
420	#393	C₂²×C₁₃₉	1	4	yes	complemented
421	#392	C₂²×C₁₃₉	1	4	yes	—
422	#392	C₂²×C₁₃₉	1	4	yes	—
423	#392	C₂²×C₁₃₉	1	4	yes	—
424	#392	C₂²×C₁₃₉	1	4	yes	—
425	#392	C₂²×C₁₃₉	1	4	yes	complemented
426	#392	C₂²×C₁₃₉	1	4	yes	complemented
427	#390	C₂²×C₁₃₉	1	4	yes	complemented
428	#388	C₂²×C₁₃₉	1	4	yes	—
429	#388	C₂²×C₁₃₉	1	4	yes	—
430	#388	C₂²×C₁₃₉	1	4	yes	complemented
431	#387	C₂²×C₁₃₉	1	4	yes	complemented
432	#386	C₂²×C₁₃₉	1	4	yes	—
433	#386	C₂²×C₁₃₉	1	4	yes	—
434	#386	C₂²×C₁₃₉	1	4	yes	—
435	#386	C₂²×C₁₃₉	1	4	yes	—
436	#386	C₂²×C₁₃₉	1	4	yes	complemented
437	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
438	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
439	#380	C₂²×C₁₃₉	1	2	yes	—
440	#380	C₂²×C₁₃₉	1	2	yes	—
441	#380	C₂²×C₁₃₉	1	2	yes	—
442	#380	C₂²×C₁₃₉	1	2	yes	complemented
443	#380	C₂²×C₁₃₉	1	2	yes	complemented
444	#380	C₂²×C₁₃₉	1	4	yes	complemented
445	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
446	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂×#41	—	2	4	no	—
448	C₂×#41	—	4	2	no	—
449	C₂×#41	—	4	2	no	—
450	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
456	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
460	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂³×C₄	—	2	4	no	—
463	C₂³×C₄	—	4	2	no	—
464	C₂³×C₄	—	4	2	no	—
465	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	#127	—	2	4	no	—
472	#127	—	4	8	no	—
473	#125	—	2	4	no	—
474	#123	—	2	16	no	—
475	#123	—	2	8	no	—
476	C₂²⋊Q₈	—	2	8	no	—
477	#121	—	2	8	no	—
478	#121	—	2	8	no	—
479	#121	—	2	16	no	—
480	#121	—	4	8	no	—
481	#121	—	4	4	no	—
482	#121	—	4	4	no	—
483	#121	—	4	4	no	—
484	#121	—	4	4	no	—
485	#120	—	2	8	no	—
486	#120	—	4	8	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	8	no	—
490	#117	D₄×C₁₃₉	1	8	yes	complemented
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
518	#95	C₂³×C₁₃₉	1	4	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	4	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	4	1	no	—
528	C₂⁴	—	4	1	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
531	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
532	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
534	#41	—	4	16	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	4	1	no	—
537	C₂×Q₈	—	4	1	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	1	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	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	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	1	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	16	no	—
589	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
623	C₄²	—	4	4	no	—
624	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
625	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	8	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	8	no	—
654	C₂³	—	4	4	no	—
655	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
656	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
657	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
658	Q₈	—	4	4	no	—
659	D₄	—	4	8	no	—
660	D₄	—	4	8	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	8	no	—
664	D₄	—	8	8	no	—
665	D₄	—	8	8	no	—
666	D₄	—	8	8	no	—
667	D₄	—	8	8	no	—
668	D₄	—	8	8	no	—
669	D₄	—	8	8	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	8	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	8	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	—	8	8	no	—
697	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
699	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
701	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
702	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	4	16	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
731	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
732	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
733	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
734	C₂²	#585×C₁₃₉	1	2	yes	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	4	4	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	#535×C₁₃₉	1	4	yes	—
744	C₂	—	4	4	no	—
745	C₂	—	4	2	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	4	no	—
748	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
749	C₂	#3488×C₁₃₉	1	2	yes	—
750	C₂	#3537×C₁₃₉	1	1	yes	characteristic
751	C₂	#3539×C₁₃₉	1	1	yes	characteristic
752	C₂	#3542×C₁₃₉	1	2	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. C₂×#540×C₁₃₉	C₂	semidirect
2. C₂×#525×C₁₃₉	C₂	semidirect
3. #2847×C₁₃₉	C₂	semidirect
4. #2703×C₁₃₉	C₂	semidirect
5. #2696×C₁₃₉	C₂	semidirect
6. #2673×C₁₃₉	C₂	semidirect
7. #2669×C₁₃₉	C₂	semidirect
8. #2615×C₁₃₉	C₂	semidirect
9. #2562×C₁₃₉	C₂	semidirect
10. #2541×C₁₃₉	C₂	semidirect
11. #2537×C₁₃₉	C₂	semidirect
12. #2535×C₁₃₉	C₂	semidirect
13. #2314×C₁₃₉	C₂	semidirect
18. C₂×#127×C₁₃₉	C₂²	semidirect
19. C₂×#125×C₁₃₉	C₂²	semidirect
22. C₂×#123×C₁₃₉	C₂²	semidirect
30. C₂×#121×C₁₃₉	C₂²	semidirect
31. C₂×#121×C₁₃₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
38. #400×C₁₃₉	C₂²	semidirect
39. #397×C₁₃₉	C₂²	semidirect
42. #394×C₁₃₉	C₂²	semidirect
43. #393×C₁₃₉	C₂²	semidirect
48. #392×C₁₃₉	C₂²	semidirect
49. #392×C₁₃₉	C₂²	semidirect
50. #390×C₁₃₉	C₂²	semidirect
53. #388×C₁₃₉	C₂²	semidirect
54. #387×C₁₃₉	C₂²	semidirect
59. #386×C₁₃₉	C₂²	semidirect
60. #384×C₁₃₉	C₂²	semidirect
61. #382×C₁₃₉	C₂²	semidirect
65. #380×C₁₃₉	C₂²	semidirect
66. #380×C₁₃₉	C₂²	semidirect
67. #380×C₁₃₉	C₂²	semidirect
68. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
113. #117×C₁₃₉	D₄	semidirect
376. #37270	C₁₃₉	direct (N × H)
377. C₁₃₉	#37270	direct (N × H)
378. C₂×#540	C₂×C₁₃₉	semidirect
379. C₂×#525	C₂×C₁₃₉	semidirect
380. #2847	C₂×C₁₃₉	semidirect
381. #2703	C₂×C₁₃₉	semidirect
382. #2696	C₂×C₁₃₉	semidirect
383. #2673	C₂×C₁₃₉	semidirect
384. #2669	C₂×C₁₃₉	semidirect
385. #2615	C₂×C₁₃₉	semidirect
386. #2562	C₂×C₁₃₉	semidirect
387. #2541	C₂×C₁₃₉	semidirect
388. #2537	C₂×C₁₃₉	semidirect
389. #2535	C₂×C₁₃₉	semidirect
390. #2314	C₂×C₁₃₉	semidirect
395. C₂×#127	C₂²×C₁₃₉	semidirect
396. C₂×#125	C₂²×C₁₃₉	semidirect
399. C₂×#123	C₂²×C₁₃₉	semidirect
407. C₂×#121	C₂²×C₁₃₉	semidirect
408. C₂×#121	C₂²×C₁₃₉	semidirect
413. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
415. #400	C₂²×C₁₃₉	semidirect
416. #397	C₂²×C₁₃₉	semidirect
419. #394	C₂²×C₁₃₉	semidirect
420. #393	C₂²×C₁₃₉	semidirect
425. #392	C₂²×C₁₃₉	semidirect
426. #392	C₂²×C₁₃₉	semidirect
427. #390	C₂²×C₁₃₉	semidirect
430. #388	C₂²×C₁₃₉	semidirect
431. #387	C₂²×C₁₃₉	semidirect
436. #386	C₂²×C₁₃₉	semidirect
437. #384	C₂²×C₁₃₉	semidirect
438. #382	C₂²×C₁₃₉	semidirect
442. #380	C₂²×C₁₃₉	semidirect
443. #380	C₂²×C₁₃₉	semidirect
444. #380	C₂²×C₁₃₉	semidirect
445. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
490. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₁₃₉	2
C₂×#525×C₁₃₉	2
#2847×C₁₃₉	2
#2703×C₁₃₉	2
#2696×C₁₃₉	2
#2673×C₁₃₉	2
#2669×C₁₃₉	2
#2615×C₁₃₉	2
#2562×C₁₃₉	2
#2541×C₁₃₉	2
#2537×C₁₃₉	2
#2535×C₁₃₉	2
#2314×C₁₃₉	2
#37270	139

Subgroups — C139×#37270 #48031866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37270 #48031866