Subgroups — C₁₃₉×#36051 #48030647

Order 35584.

2352 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2661×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2640×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2557×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2543×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2491×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₁₃₉	—	2	8	no	—
19	#555×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	1	yes	characteristic
44	#400×C₁₃₉	C₂²	1	1	yes	characteristic
45	#399×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	4	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	1	yes	characteristic
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	1	yes	characteristic
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#393×C₁₃₉	C₂²	1	4	yes	—
57	#393×C₁₃₉	C₂²	1	2	yes	—
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	4	yes	—
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	4	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	4	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#387×C₁₃₉	C₂²	1	4	yes	—
71	#386×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	#376×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
100	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
101	#127×C₁₃₉	—	2	4	no	—
102	#124×C₁₃₉	—	2	4	no	—
103	#124×C₁₃₉	—	2	16	no	—
104	#124×C₁₃₉	—	2	8	no	—
105	#124×C₁₃₉	—	2	4	no	—
106	#123×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	2	8	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	2	8	no	—
111	#121×C₁₃₉	—	2	8	no	—
112	#121×C₁₃₉	—	4	8	no	—
113	C₄×Q₈×C₁₃₉	—	2	4	no	—
114	C₄×Q₈×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	8	no	—
116	C₄×D₄×C₁₃₉	—	2	4	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
120	#117×C₁₃₉	—	2	8	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂×Q₈×C₁₃₉	—	2	2	no	—
177	C₂×Q₈×C₁₃₉	—	2	2	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	4	1	no	—
182	C₂×Q₈×C₁₃₉	—	4	2	no	—
183	C₂×Q₈×C₁₃₉	—	4	2	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	2	8	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	8	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	4	2	no	—
194	C₂×D₄×C₁₃₉	—	4	2	no	—
195	C₂×D₄×C₁₃₉	—	4	4	no	—
196	C₂×D₄×C₁₃₉	—	4	4	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	—	4	4	no	—
199	C₂×D₄×C₁₃₉	—	4	4	no	—
200	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	4	no	—
205	C₂²×C₄×C₁₃₉	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	4	4	no	—
207	C₂²×C₄×C₁₃₉	—	4	4	no	—
208	C₂²×C₄×C₁₃₉	—	4	4	no	—
209	C₂²×C₄×C₁₃₉	—	4	4	no	—
210	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	2	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	2	no	—
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	2	8	no	—
233	C₄⋊C₄×C₁₃₉	—	2	8	no	—
234	C₄⋊C₄×C₁₃₉	—	4	4	no	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
237	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
253	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
254	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
255	C₄²×C₁₃₉	—	2	8	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	2	no	—
259	C₄²×C₁₃₉	—	2	4	no	—
260	C₄²×C₁₃₉	—	4	4	no	—
261	C₄²×C₁₃₉	—	4	2	no	—
262	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
263	C₂³×C₁₃₉	—	2	4	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	4	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
280	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃₉	—	4	4	no	—
282	Q₈×C₁₃₉	—	4	4	no	—
283	Q₈×C₁₃₉	—	8	4	no	—
284	D₄×C₁₃₉	—	2	8	no	—
285	D₄×C₁₃₉	—	4	8	no	—
286	D₄×C₁₃₉	—	4	4	no	—
287	D₄×C₁₃₉	—	4	4	no	—
288	D₄×C₁₃₉	—	8	8	no	—
289	D₄×C₁₃₉	—	8	4	no	—
290	D₄×C₁₃₉	—	8	8	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	4	8	no	—
321	C₂×C₄×C₁₃₉	—	4	8	no	—
322	C₂×C₄×C₁₃₉	—	8	4	no	—
323	C₂×C₄×C₁₃₉	—	8	8	no	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
329	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
330	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₁₃₉	—	2	4	no	—
332	C₂²×C₁₃₉	—	2	4	no	—
333	C₂²×C₁₃₉	—	2	4	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	4	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	2	no	—
341	C₂²×C₁₃₉	—	4	2	no	—
342	C₂²×C₁₃₉	—	4	2	no	—
343	C₂²×C₁₃₉	—	4	4	no	—
344	C₂²×C₁₃₉	—	4	2	no	—
345	C₂²×C₁₃₉	—	4	2	no	—
346	C₂²×C₁₃₉	—	4	4	no	—
347	C₂²×C₁₃₉	—	4	2	no	—
348	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
349	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
350	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₁₃₉	#585	1	2	yes	—
352	C₂²×C₁₃₉	#585	1	1	yes	characteristic
353	C₄×C₁₃₉	—	2	2	no	—
354	C₄×C₁₃₉	—	2	4	no	—
355	C₄×C₁₃₉	—	2	2	no	—
356	C₄×C₁₃₉	—	2	2	no	—
357	C₄×C₁₃₉	—	2	8	no	—
358	C₄×C₁₃₉	—	4	2	no	—
359	C₄×C₁₃₉	—	4	2	no	—
360	C₄×C₁₃₉	—	4	1	no	—
361	C₄×C₁₃₉	—	4	1	no	—
362	C₄×C₁₃₉	—	4	4	no	—
363	C₄×C₁₃₉	—	4	1	no	—
364	C₄×C₁₃₉	—	4	2	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	#532	1	4	yes	—
367	C₂×C₁₃₉	—	4	4	no	—
368	C₂×C₁₃₉	—	8	2	no	—
369	C₂×C₁₃₉	—	8	2	no	—
370	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
371	C₂×C₁₃₉	#3485	1	1	yes	characteristic
372	C₂×C₁₃₉	#3488	1	1	yes	characteristic
373	C₂×C₁₃₉	#3514	1	2	yes	—
374	C₂×C₁₃₉	#3524	1	2	yes	—
375	#36051	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₁₃₉	#36051	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	#2661	C₂×C₁₃₉	1	2	yes	complemented
380	#2640	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	#2557	C₂×C₁₃₉	1	4	yes	complemented
382	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	#2543	C₂×C₁₃₉	1	2	yes	complemented
384	#2540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#2498	C₂×C₁₃₉	1	2	yes	complemented
386	#2491	C₂×C₁₃₉	1	4	yes	complemented
387	#2428	C₂×C₁₃₉	1	2	yes	complemented
388	#2427	C₂×C₁₃₉	1	2	yes	complemented
389	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
390	#2395	C₂×C₁₃₉	1	2	yes	complemented
391	#2363	C₂×C₁₃₉	1	2	yes	complemented
392	#2362	C₂×C₁₃₉	1	2	yes	complemented
393	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#559	—	2	8	no	—
395	#555	—	2	8	no	—
396	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
398	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
399	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
401	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
402	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
403	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
404	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
405	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
408	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
409	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
410	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
418	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
419	#400	C₂²×C₁₃₉	1	1	yes	characteristic
420	#400	C₂²×C₁₃₉	1	1	yes	characteristic
421	#399	C₂²×C₁₃₉	1	2	yes	—
422	#398	C₂²×C₁₃₉	1	2	yes	—
423	#398	C₂²×C₁₃₉	1	2	yes	—
424	#397	C₂²×C₁₃₉	1	2	yes	—
425	#397	C₂²×C₁₃₉	1	2	yes	—
426	#397	C₂²×C₁₃₉	1	4	yes	—
427	#397	C₂²×C₁₃₉	1	2	yes	—
428	#394	C₂²×C₁₃₉	1	4	yes	—
429	#394	C₂²×C₁₃₉	1	1	yes	characteristic
430	#394	C₂²×C₁₃₉	1	1	yes	characteristic
431	#394	C₂²×C₁₃₉	1	4	yes	—
432	#393	C₂²×C₁₃₉	1	4	yes	—
433	#393	C₂²×C₁₃₉	1	2	yes	—
434	#392	C₂²×C₁₃₉	1	4	yes	—
435	#392	C₂²×C₁₃₉	1	2	yes	—
436	#391	C₂²×C₁₃₉	1	2	yes	—
437	#391	C₂²×C₁₃₉	1	2	yes	—
438	#390	C₂²×C₁₃₉	1	2	yes	—
439	#390	C₂²×C₁₃₉	1	4	yes	—
440	#390	C₂²×C₁₃₉	1	4	yes	—
441	#389	C₂²×C₁₃₉	1	2	yes	—
442	#389	C₂²×C₁₃₉	1	2	yes	—
443	#388	C₂²×C₁₃₉	1	4	yes	—
444	#388	C₂²×C₁₃₉	1	4	yes	—
445	#388	C₂²×C₁₃₉	1	4	yes	—
446	#387	C₂²×C₁₃₉	1	4	yes	—
447	#386	C₂²×C₁₃₉	1	4	yes	—
448	#386	C₂²×C₁₃₉	1	4	yes	—
449	#386	C₂²×C₁₃₉	1	4	yes	—
450	#380	C₂²×C₁₃₉	1	4	yes	—
451	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
459	#376	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
461	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
464	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
470	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
474	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₄⋊Q₈	—	2	4	no	—
476	C₄⋊Q₈	—	4	4	no	—
477	#127	—	2	4	no	—
478	#124	—	2	4	no	—
479	#124	—	2	16	no	—
480	#124	—	2	8	no	—
481	#124	—	2	4	no	—
482	#123	—	2	8	no	—
483	#123	—	2	8	no	—
484	C₂²⋊Q₈	—	2	8	no	—
485	#121	—	2	8	no	—
486	#121	—	2	8	no	—
487	#121	—	2	8	no	—
488	#121	—	4	8	no	—
489	C₄×Q₈	—	2	4	no	—
490	C₄×Q₈	—	2	4	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
496	#117	—	2	8	no	—
497	#117	—	2	8	no	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
536	#95	C₂³×C₁₃₉	1	1	yes	characteristic
537	#95	C₂³×C₁₃₉	1	4	yes	—
538	#95	C₂³×C₁₃₉	1	2	yes	—
539	#95	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	1	yes	characteristic
541	#95	C₂³×C₁₃₉	1	2	yes	—
542	#95	C₂³×C₁₃₉	1	2	yes	—
543	#95	C₂³×C₁₃₉	1	2	yes	—
544	#95	C₂³×C₁₃₉	1	2	yes	—
545	#95	C₂³×C₁₃₉	1	4	yes	—
546	#95	C₂³×C₁₃₉	1	4	yes	—
547	#95	C₂³×C₁₃₉	1	4	yes	—
548	#95	C₂³×C₁₃₉	1	4	yes	—
549	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
550	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
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	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
612	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
631	C₄²	—	2	8	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	4	4	no	—
637	C₄²	—	4	2	no	—
638	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	2	2	no	—
655	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
656	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
657	Q₈	—	4	4	no	—
658	Q₈	—	4	4	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	8	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	8	8	no	—
665	D₄	—	8	4	no	—
666	D₄	—	8	8	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	4	8	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	8	4	no	—
699	C₂×C₄	—	8	8	no	—
700	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
704	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
705	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
706	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
726	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
727	C₂²	#585×C₁₃₉	1	2	yes	—
728	C₂²	#585×C₁₃₉	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	8	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	4	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	#532×C₁₃₉	1	4	yes	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
747	C₂	#3485×C₁₃₉	1	1	yes	characteristic
748	C₂	#3488×C₁₃₉	1	1	yes	characteristic
749	C₂	#3514×C₁₃₉	1	2	yes	—
750	C₂	#3524×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×#559×C₁₃₉	C₂	semidirect
2. C₂×#555×C₁₃₉	C₂	semidirect
3. #2661×C₁₃₉	C₂	semidirect
4. #2640×C₁₃₉	C₂	semidirect
5. #2557×C₁₃₉	C₂	semidirect
6. #2546×C₁₃₉	C₂	semidirect
7. #2543×C₁₃₉	C₂	semidirect
8. #2540×C₁₃₉	C₂	semidirect
9. #2498×C₁₃₉	C₂	semidirect
10. #2491×C₁₃₉	C₂	semidirect
11. #2428×C₁₃₉	C₂	semidirect
12. #2427×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2363×C₁₃₉	C₂	semidirect
16. #2362×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
119. C₄×D₄×C₁₃₉	D₄	semidirect
375. #36051	C₁₃₉	direct (N × H)
376. C₁₃₉	#36051	direct (N × H)
377. C₂×#559	C₂×C₁₃₉	semidirect
378. C₂×#555	C₂×C₁₃₉	semidirect
379. #2661	C₂×C₁₃₉	semidirect
380. #2640	C₂×C₁₃₉	semidirect
381. #2557	C₂×C₁₃₉	semidirect
382. #2546	C₂×C₁₃₉	semidirect
383. #2543	C₂×C₁₃₉	semidirect
384. #2540	C₂×C₁₃₉	semidirect
385. #2498	C₂×C₁₃₉	semidirect
386. #2491	C₂×C₁₃₉	semidirect
387. #2428	C₂×C₁₃₉	semidirect
388. #2427	C₂×C₁₃₉	semidirect
389. #2398	C₂×C₁₃₉	semidirect
390. #2395	C₂×C₁₃₉	semidirect
391. #2363	C₂×C₁₃₉	semidirect
392. #2362	C₂×C₁₃₉	semidirect
393. #2275	C₂×C₁₃₉	semidirect
495. C₄×D₄	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×#559×C₁₃₉	2
C₂×#555×C₁₃₉	2
#2661×C₁₃₉	2
#2640×C₁₃₉	2
#2557×C₁₃₉	2
#2546×C₁₃₉	2
#2543×C₁₃₉	2
#2540×C₁₃₉	2
#2498×C₁₃₉	2
#2491×C₁₃₉	2
#2428×C₁₃₉	2
#2427×C₁₃₉	2
#2398×C₁₃₉	2
#2395×C₁₃₉	2
#2363×C₁₃₉	2
#2362×C₁₃₉	2
#2275×C₁₃₉	2
#36051	139

Subgroups — C139×#36051 #48030647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36051 #48030647