Subgroups — C₁₃₉×#35923 #48030519

Order 35584.

2606 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2663×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2564×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2562×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2553×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2537×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2535×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2464×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2430×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2388×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	#553×C₁₃₉	—	2	8	no	—
20	#547×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	2	yes	—
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#399×C₁₃₉	C₂²	1	1	yes	characteristic
46	#399×C₁₃₉	C₂²	1	1	yes	characteristic
47	#398×C₁₃₉	C₂²	1	4	yes	—
48	#397×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#395×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#393×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	4	yes	—
57	#392×C₁₃₉	C₂²	1	1	yes	characteristic
58	#392×C₁₃₉	C₂²	1	1	yes	characteristic
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#386×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#384×C₁₃₉	C₂²	1	2	yes	—
71	#382×C₁₃₉	C₂²	1	2	yes	—
72	#382×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	4	yes	—
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊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	4	yes	—
83	#376×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#41×C₁₃₉	—	2	8	no	—
86	C₂×#41×C₁₃₉	—	4	8	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
104	#126×C₁₃₉	—	2	8	no	—
105	#125×C₁₃₉	—	2	4	no	—
106	#123×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	2	16	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	2	4	no	—
111	#121×C₁₃₉	—	2	4	no	—
112	#121×C₁₃₉	—	2	8	no	—
113	#121×C₁₃₉	—	4	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	4	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	8	no	—
120	C₄×D₄×C₁₃₉	—	4	8	no	—
121	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
122	#117×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	1	yes	characteristic
164	#95×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	#41×C₁₃₉	—	4	32	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	4	4	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	4	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	8	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	2	no	—
192	C₂×D₄×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	4	1	no	—
197	C₂×D₄×C₁₃₉	—	4	2	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	—	4	4	no	—
200	C₂×D₄×C₁₃₉	—	4	4	no	—
201	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₃₉	—	2	8	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	8	no	—
213	C₂²×C₄×C₁₃₉	—	4	4	no	—
214	C₂²×C₄×C₁₃₉	—	4	4	no	—
215	C₂²×C₄×C₁₃₉	—	4	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	8	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	4	no	—
246	C₄⋊C₄×C₁₃₉	—	4	4	no	—
247	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
265	C₄²×C₁₃₉	—	2	4	no	—
266	C₄²×C₁₃₉	—	4	2	no	—
267	C₄²×C₁₃₉	—	4	4	no	—
268	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
269	C₄²×C₁₃₉	#41	1	8	yes	complemented
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	4	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	2	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
290	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
291	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
292	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
293	Q₈×C₁₃₉	—	4	8	no	—
294	D₄×C₁₃₉	—	2	16	no	—
295	D₄×C₁₃₉	—	2	8	no	—
296	D₄×C₁₃₉	—	2	8	no	—
297	D₄×C₁₃₉	—	4	4	no	—
298	D₄×C₁₃₉	—	4	8	no	—
299	D₄×C₁₃₉	—	4	8	no	—
300	D₄×C₁₃₉	—	4	16	no	—
301	D₄×C₁₃₉	—	8	4	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	4	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	4	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	4	8	no	—
329	C₂×C₄×C₁₃₉	—	4	16	no	—
330	C₂×C₄×C₁₃₉	—	4	8	no	—
331	C₂×C₄×C₁₃₉	—	4	4	no	—
332	C₂×C₄×C₁₃₉	—	4	4	no	—
333	C₂×C₄×C₁₃₉	—	8	4	no	—
334	C₂×C₄×C₁₃₉	—	8	8	no	—
335	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
342	C₂²×C₁₃₉	—	2	4	no	—
343	C₂²×C₁₃₉	—	2	4	no	—
344	C₂²×C₁₃₉	—	2	4	no	—
345	C₂²×C₁₃₉	—	2	2	no	—
346	C₂²×C₁₃₉	—	2	4	no	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	4	no	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	4	2	no	—
351	C₂²×C₁₃₉	—	4	1	no	—
352	C₂²×C₁₃₉	—	4	1	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	4	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	4	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	1	no	—
360	C₂²×C₁₃₉	—	4	1	no	—
361	C₂²×C₁₃₉	—	4	1	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
366	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₁₃₉	#585	1	1	yes	characteristic
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	2	2	no	—
371	C₄×C₁₃₉	—	2	2	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	2	4	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	1	no	—
377	C₄×C₁₃₉	—	4	4	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	4	no	—
381	C₄×C₁₃₉	#532	1	4	yes	—
382	C₂×C₁₃₉	—	4	4	no	—
383	C₂×C₁₃₉	—	4	4	no	—
384	C₂×C₁₃₉	—	4	2	no	—
385	C₂×C₁₃₉	—	8	1	no	—
386	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
387	C₂×C₁₃₉	#3484	1	1	yes	characteristic
388	C₂×C₁₃₉	#3489	1	1	yes	characteristic
389	C₂×C₁₃₉	#3492	1	2	yes	—
390	C₂×C₁₃₉	#3494	1	2	yes	—
391	#35923	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₁₃₉	#35923	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2663	C₂×C₁₃₉	1	2	yes	complemented
396	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	#2564	C₂×C₁₃₉	1	2	yes	complemented
398	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2562	C₂×C₁₃₉	1	1	yes	characteristic, complemented
400	#2553	C₂×C₁₃₉	1	4	yes	complemented
401	#2537	C₂×C₁₃₉	1	2	yes	complemented
402	#2535	C₂×C₁₃₉	1	2	yes	complemented
403	#2464	C₂×C₁₃₉	1	4	yes	complemented
404	#2430	C₂×C₁₃₉	1	2	yes	complemented
405	#2397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2388	C₂×C₁₃₉	1	2	yes	complemented
407	#2352	C₂×C₁₃₉	1	2	yes	complemented
408	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
409	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
411	#553	—	2	8	no	—
412	#547	—	2	8	no	—
413	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
415	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
417	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
420	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
421	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
435	#400	C₂²×C₁₃₉	1	2	yes	—
436	#399	C₂²×C₁₃₉	1	1	yes	characteristic
437	#399	C₂²×C₁₃₉	1	1	yes	characteristic
438	#399	C₂²×C₁₃₉	1	2	yes	—
439	#398	C₂²×C₁₃₉	1	4	yes	—
440	#397	C₂²×C₁₃₉	1	4	yes	—
441	#395	C₂²×C₁₃₉	1	2	yes	—
442	#395	C₂²×C₁₃₉	1	2	yes	—
443	#394	C₂²×C₁₃₉	1	2	yes	—
444	#394	C₂²×C₁₃₉	1	4	yes	—
445	#394	C₂²×C₁₃₉	1	4	yes	—
446	#393	C₂²×C₁₃₉	1	2	yes	—
447	#393	C₂²×C₁₃₉	1	2	yes	—
448	#392	C₂²×C₁₃₉	1	1	yes	characteristic
449	#392	C₂²×C₁₃₉	1	4	yes	—
450	#392	C₂²×C₁₃₉	1	1	yes	characteristic
451	#392	C₂²×C₁₃₉	1	2	yes	—
452	#390	C₂²×C₁₃₉	1	2	yes	—
453	#389	C₂²×C₁₃₉	1	4	yes	—
454	#388	C₂²×C₁₃₉	1	4	yes	—
455	#388	C₂²×C₁₃₉	1	4	yes	—
456	#387	C₂²×C₁₃₉	1	4	yes	—
457	#386	C₂²×C₁₃₉	1	4	yes	—
458	#386	C₂²×C₁₃₉	1	4	yes	—
459	#386	C₂²×C₁₃₉	1	4	yes	—
460	#385	C₂²×C₁₃₉	1	4	yes	—
461	#385	C₂²×C₁₃₉	1	4	yes	—
462	#384	C₂²×C₁₃₉	1	2	yes	—
463	#382	C₂²×C₁₃₉	1	2	yes	—
464	#382	C₂²×C₁₃₉	1	2	yes	—
465	#380	C₂²×C₁₃₉	1	2	yes	—
466	#380	C₂²×C₁₃₉	1	2	yes	—
467	#380	C₂²×C₁₃₉	1	2	yes	—
468	#380	C₂²×C₁₃₉	1	2	yes	—
469	#380	C₂²×C₁₃₉	1	4	yes	—
470	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
475	#376	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#41	—	2	8	no	—
478	C₂×#41	—	4	8	no	—
479	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
480	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₄⋊Q₈	—	2	4	no	—
496	#126	—	2	8	no	—
497	#125	—	2	4	no	—
498	#123	—	2	8	no	—
499	#123	—	2	16	no	—
500	C₂²⋊Q₈	—	2	8	no	—
501	#121	—	2	8	no	—
502	#121	—	2	4	no	—
503	#121	—	2	4	no	—
504	#121	—	2	8	no	—
505	#121	—	4	8	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	8	no	—
512	C₄×D₄	—	4	8	no	—
513	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
514	#117	—	2	4	no	—
515	C₂×C₄⋊C₄	—	2	8	no	—
516	C₂×C₄⋊C₄	—	2	4	no	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	1	yes	characteristic
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	1	yes	characteristic
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	4	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
567	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	#41	—	4	32	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	8	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	4	4	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	4	no	—
660	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₄²	#41×C₁₃₉	1	8	yes	complemented
662	C₂³	—	2	2	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
682	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
683	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
684	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
685	Q₈	—	4	8	no	—
686	D₄	—	2	8	no	—
687	D₄	—	2	16	no	—
688	D₄	—	2	8	no	—
689	D₄	—	4	4	no	—
690	D₄	—	4	8	no	—
691	D₄	—	4	16	no	—
692	D₄	—	4	8	no	—
693	D₄	—	8	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	16	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	8	no	—
727	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
732	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
733	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
758	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
759	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²	#585×C₁₃₉	1	1	yes	characteristic
761	C₄	—	2	4	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	4	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	4	no	—
773	C₄	#532×C₁₃₉	1	4	yes	—
774	C₂	—	4	4	no	—
775	C₂	—	4	4	no	—
776	C₂	—	4	2	no	—
777	C₂	—	8	1	no	—
778	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
779	C₂	#3484×C₁₃₉	1	1	yes	characteristic
780	C₂	#3489×C₁₃₉	1	1	yes	characteristic
781	C₂	#3492×C₁₃₉	1	2	yes	—
782	C₂	#3494×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×#553×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. #2663×C₁₃₉	C₂	semidirect
4. #2660×C₁₃₉	C₂	semidirect
5. #2564×C₁₃₉	C₂	semidirect
6. #2563×C₁₃₉	C₂	semidirect
7. #2562×C₁₃₉	C₂	semidirect
8. #2553×C₁₃₉	C₂	semidirect
9. #2537×C₁₃₉	C₂	semidirect
10. #2535×C₁₃₉	C₂	semidirect
11. #2464×C₁₃₉	C₂	semidirect
12. #2430×C₁₃₉	C₂	semidirect
13. #2397×C₁₃₉	C₂	semidirect
14. #2388×C₁₃₉	C₂	semidirect
15. #2352×C₁₃₉	C₂	semidirect
16. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
121. C₄×D₄×C₁₃₉	D₄	semidirect
269. C₄²×C₁₃₉	#41	semidirect
391. #35923	C₁₃₉	direct (N × H)
392. C₁₃₉	#35923	direct (N × H)
393. C₂×#553	C₂×C₁₃₉	semidirect
394. C₂×#547	C₂×C₁₃₉	semidirect
395. #2663	C₂×C₁₃₉	semidirect
396. #2660	C₂×C₁₃₉	semidirect
397. #2564	C₂×C₁₃₉	semidirect
398. #2563	C₂×C₁₃₉	semidirect
399. #2562	C₂×C₁₃₉	semidirect
400. #2553	C₂×C₁₃₉	semidirect
401. #2537	C₂×C₁₃₉	semidirect
402. #2535	C₂×C₁₃₉	semidirect
403. #2464	C₂×C₁₃₉	semidirect
404. #2430	C₂×C₁₃₉	semidirect
405. #2397	C₂×C₁₃₉	semidirect
406. #2388	C₂×C₁₃₉	semidirect
407. #2352	C₂×C₁₃₉	semidirect
408. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
409. #2275	C₂×C₁₃₉	semidirect
513. C₄×D₄	D₄×C₁₃₉	semidirect
661. C₄²	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
C₂×#547×C₁₃₉	2
#2663×C₁₃₉	2
#2660×C₁₃₉	2
#2564×C₁₃₉	2
#2563×C₁₃₉	2
#2562×C₁₃₉	2
#2553×C₁₃₉	2
#2537×C₁₃₉	2
#2535×C₁₃₉	2
#2464×C₁₃₉	2
#2430×C₁₃₉	2
#2397×C₁₃₉	2
#2388×C₁₃₉	2
#2352×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35923	139

Subgroups — C139×#35923 #48030519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35923 #48030519