Subgroups — C₁₃₉×#37022 #48031618

Order 35584.

1676 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2861×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2798×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2797×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2733×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2703×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2700×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2694×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2690×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2686×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2648×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2610×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2605×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2598×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2531×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2337×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2319×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	C₂²	1	1	yes	characteristic
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#399×C₁₃₉	C₂²	1	2	yes	—
33	#399×C₁₃₉	C₂²	1	1	yes	characteristic
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#397×C₁₃₉	C₂²	1	2	yes	—
36	#397×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#396×C₁₃₉	C₂²	1	2	yes	—
42	#395×C₁₃₉	C₂²	1	2	yes	—
43	#395×C₁₃₉	C₂²	1	1	yes	characteristic
44	#394×C₁₃₉	C₂²	1	2	yes	—
45	#394×C₁₃₉	C₂²	1	1	yes	characteristic
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	1	yes	characteristic
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	2	yes	—
51	#393×C₁₃₉	C₂²	1	1	yes	characteristic
52	#392×C₁₃₉	C₂²	1	2	yes	—
53	#392×C₁₃₉	C₂²	1	2	yes	—
54	#392×C₁₃₉	C₂²	1	1	yes	characteristic
55	#392×C₁₃₉	C₂²	1	1	yes	characteristic
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#390×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#386×C₁₃₉	C₂²	1	2	yes	—
90	#386×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#383×C₁₃₉	C₂²	1	1	yes	characteristic
96	#381×C₁₃₉	C₂²	1	2	yes	—
97	#380×C₁₃₉	C₂²	1	2	yes	—
98	#380×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	#125×C₁₃₉	—	4	4	no	—
119	#124×C₁₃₉	—	2	4	no	—
120	#124×C₁₃₉	—	4	4	no	—
121	#124×C₁₃₉	—	4	4	no	—
122	#123×C₁₃₉	—	4	4	no	—
123	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
124	#121×C₁₃₉	—	4	4	no	—
125	C₄×D₄×C₁₃₉	—	2	4	no	—
126	#117×C₁₃₉	—	2	4	no	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
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	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	#95×C₁₃₉	C₂³	1	1	yes	characteristic
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	1	yes	characteristic
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	1	yes	characteristic
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₁₃₉	—	2	2	no	—
207	C₂×Q₈×C₁₃₉	—	2	4	no	—
208	C₂×Q₈×C₁₃₉	—	4	2	no	—
209	C₂×Q₈×C₁₃₉	—	4	2	no	—
210	C₂×Q₈×C₁₃₉	—	4	2	no	—
211	C₂×D₄×C₁₃₉	—	2	2	no	—
212	C₂×D₄×C₁₃₉	—	2	2	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	4	2	no	—
215	C₂×D₄×C₁₃₉	—	4	2	no	—
216	C₂×D₄×C₁₃₉	—	4	2	no	—
217	C₂×D₄×C₁₃₉	—	4	2	no	—
218	C₂×D₄×C₁₃₉	—	4	2	no	—
219	C₂×D₄×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	4	2	no	—
221	C₂×D₄×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂×D₄×C₁₃₉	—	4	2	no	—
226	C₂×D₄×C₁₃₉	—	4	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	4	1	no	—
230	C₂²×C₄×C₁₃₉	—	4	1	no	—
231	C₂²×C₄×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	2	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
293	C₄²×C₁₃₉	—	2	2	no	—
294	C₄²×C₁₃₉	—	2	4	no	—
295	C₄²×C₁₃₉	—	4	1	no	—
296	C₄²×C₁₃₉	—	4	1	no	—
297	C₄²×C₁₃₉	—	4	1	no	—
298	C₄²×C₁₃₉	—	4	1	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₄²×C₁₃₉	—	4	2	no	—
301	C₄²×C₁₃₉	—	4	2	no	—
302	C₄²×C₁₃₉	#41	1	4	yes	—
303	C₂³×C₁₃₉	—	2	1	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	—	2	1	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
323	Q₈×C₁₃₉	—	8	2	no	—
324	Q₈×C₁₃₉	—	8	4	no	—
325	D₄×C₁₃₉	—	4	4	no	—
326	D₄×C₁₃₉	—	8	2	no	—
327	D₄×C₁₃₉	—	8	4	no	—
328	D₄×C₁₃₉	—	8	4	no	—
329	D₄×C₁₃₉	—	8	4	no	—
330	D₄×C₁₃₉	—	8	4	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	4	4	no	—
372	C₂×C₄×C₁₃₉	—	8	4	no	—
373	C₂×C₄×C₁₃₉	—	8	4	no	—
374	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
376	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
377	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	1	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	—	4	1	no	—
382	C₂²×C₁₃₉	—	4	2	no	—
383	C₂²×C₁₃₉	—	4	2	no	—
384	C₂²×C₁₃₉	—	4	2	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	—	4	1	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	2	no	—
393	C₂²×C₁₃₉	—	4	2	no	—
394	C₂²×C₁₃₉	—	4	2	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₁₃₉	#585	1	2	yes	—
400	C₂²×C₁₃₉	#585	1	1	yes	characteristic
401	C₂²×C₁₃₉	#585	1	1	yes	characteristic
402	C₄×C₁₃₉	—	2	2	no	—
403	C₄×C₁₃₉	—	2	2	no	—
404	C₄×C₁₃₉	—	2	2	no	—
405	C₄×C₁₃₉	—	2	4	no	—
406	C₄×C₁₃₉	—	4	1	no	—
407	C₄×C₁₃₉	—	4	1	no	—
408	C₄×C₁₃₉	—	4	1	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	2	no	—
412	C₄×C₁₃₉	—	4	2	no	—
413	C₄×C₁₃₉	—	4	2	no	—
414	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	2	no	—
418	C₂×C₁₃₉	—	8	2	no	—
419	C₂×C₁₃₉	—	8	1	no	—
420	C₂×C₁₃₉	—	8	2	no	—
421	C₂×C₁₃₉	#3455	1	1	yes	characteristic
422	C₂×C₁₃₉	#3493	1	1	yes	characteristic
423	C₂×C₁₃₉	#3508	1	1	yes	characteristic
424	C₂×C₁₃₉	#3545	1	2	yes	—
425	C₂×C₁₃₉	#3562	1	2	yes	—
426	#37022	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₁₃₉	#37022	1	1	yes	characteristic, direct product factor, Sylow
428	#2861	C₂×C₁₃₉	1	2	yes	complemented
429	#2798	C₂×C₁₃₉	1	2	yes	complemented
430	#2797	C₂×C₁₃₉	1	2	yes	complemented
431	#2733	C₂×C₁₃₉	1	2	yes	complemented
432	#2703	C₂×C₁₃₉	1	2	yes	complemented
433	#2700	C₂×C₁₃₉	1	2	yes	complemented
434	#2694	C₂×C₁₃₉	1	2	yes	complemented
435	#2690	C₂×C₁₃₉	1	2	yes	complemented
436	#2686	C₂×C₁₃₉	1	2	yes	complemented
437	#2648	C₂×C₁₃₉	1	2	yes	complemented
438	#2610	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2605	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	#2598	C₂×C₁₃₉	1	1	yes	characteristic, complemented
441	#2557	C₂×C₁₃₉	1	2	yes	complemented
442	#2540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2531	C₂×C₁₃₉	1	2	yes	complemented
444	#2337	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2319	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
448	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
451	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
453	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
456	#400	C₂²×C₁₃₉	1	1	yes	characteristic
457	#400	C₂²×C₁₃₉	1	2	yes	—
458	#400	C₂²×C₁₃₉	1	2	yes	—
459	#399	C₂²×C₁₃₉	1	1	yes	characteristic
460	#399	C₂²×C₁₃₉	1	2	yes	—
461	#398	C₂²×C₁₃₉	1	2	yes	—
462	#397	C₂²×C₁₃₉	1	2	yes	—
463	#397	C₂²×C₁₃₉	1	2	yes	—
464	#397	C₂²×C₁₃₉	1	2	yes	—
465	#397	C₂²×C₁₃₉	1	2	yes	—
466	#397	C₂²×C₁₃₉	1	2	yes	—
467	#397	C₂²×C₁₃₉	1	2	yes	—
468	#396	C₂²×C₁₃₉	1	2	yes	—
469	#395	C₂²×C₁₃₉	1	2	yes	—
470	#395	C₂²×C₁₃₉	1	1	yes	characteristic
471	#394	C₂²×C₁₃₉	1	1	yes	characteristic
472	#394	C₂²×C₁₃₉	1	1	yes	characteristic
473	#394	C₂²×C₁₃₉	1	2	yes	—
474	#394	C₂²×C₁₃₉	1	2	yes	—
475	#394	C₂²×C₁₃₉	1	2	yes	—
476	#394	C₂²×C₁₃₉	1	2	yes	—
477	#393	C₂²×C₁₃₉	1	1	yes	characteristic
478	#393	C₂²×C₁₃₉	1	2	yes	—
479	#392	C₂²×C₁₃₉	1	1	yes	characteristic
480	#392	C₂²×C₁₃₉	1	1	yes	characteristic
481	#392	C₂²×C₁₃₉	1	2	yes	—
482	#392	C₂²×C₁₃₉	1	2	yes	—
483	#392	C₂²×C₁₃₉	1	2	yes	—
484	#391	C₂²×C₁₃₉	1	2	yes	—
485	#391	C₂²×C₁₃₉	1	2	yes	—
486	#391	C₂²×C₁₃₉	1	2	yes	—
487	#391	C₂²×C₁₃₉	1	2	yes	—
488	#390	C₂²×C₁₃₉	1	2	yes	—
489	#390	C₂²×C₁₃₉	1	2	yes	—
490	#390	C₂²×C₁₃₉	1	2	yes	—
491	#390	C₂²×C₁₃₉	1	2	yes	—
492	#390	C₂²×C₁₃₉	1	2	yes	—
493	#389	C₂²×C₁₃₉	1	2	yes	—
494	#388	C₂²×C₁₃₉	1	2	yes	—
495	#388	C₂²×C₁₃₉	1	2	yes	—
496	#388	C₂²×C₁₃₉	1	2	yes	—
497	#388	C₂²×C₁₃₉	1	2	yes	—
498	#388	C₂²×C₁₃₉	1	2	yes	—
499	#388	C₂²×C₁₃₉	1	2	yes	—
500	#388	C₂²×C₁₃₉	1	2	yes	—
501	#388	C₂²×C₁₃₉	1	2	yes	—
502	#388	C₂²×C₁₃₉	1	2	yes	—
503	#388	C₂²×C₁₃₉	1	2	yes	—
504	#388	C₂²×C₁₃₉	1	2	yes	—
505	#388	C₂²×C₁₃₉	1	2	yes	—
506	#388	C₂²×C₁₃₉	1	2	yes	—
507	#388	C₂²×C₁₃₉	1	2	yes	—
508	#387	C₂²×C₁₃₉	1	2	yes	—
509	#387	C₂²×C₁₃₉	1	2	yes	—
510	#387	C₂²×C₁₃₉	1	2	yes	—
511	#387	C₂²×C₁₃₉	1	2	yes	—
512	#387	C₂²×C₁₃₉	1	2	yes	—
513	#387	C₂²×C₁₃₉	1	2	yes	—
514	#386	C₂²×C₁₃₉	1	2	yes	—
515	#386	C₂²×C₁₃₉	1	2	yes	—
516	#386	C₂²×C₁₃₉	1	2	yes	—
517	#386	C₂²×C₁₃₉	1	2	yes	—
518	#386	C₂²×C₁₃₉	1	2	yes	—
519	#386	C₂²×C₁₃₉	1	2	yes	—
520	#385	C₂²×C₁₃₉	1	2	yes	—
521	#385	C₂²×C₁₃₉	1	2	yes	—
522	#383	C₂²×C₁₃₉	1	1	yes	characteristic
523	#381	C₂²×C₁₃₉	1	2	yes	—
524	#380	C₂²×C₁₃₉	1	2	yes	—
525	#380	C₂²×C₁₃₉	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
531	#376	C₂²×C₁₃₉	1	1	yes	characteristic
532	#376	C₂²×C₁₃₉	1	1	yes	characteristic
533	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
536	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
545	#125	—	4	4	no	—
546	#124	—	2	4	no	—
547	#124	—	4	4	no	—
548	#124	—	4	4	no	—
549	#123	—	4	4	no	—
550	C₂²⋊Q₈	—	4	4	no	—
551	#121	—	4	4	no	—
552	C₄×D₄	—	2	4	no	—
553	#117	—	2	4	no	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
605	#95	C₂³×C₁₃₉	1	1	yes	characteristic
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	1	yes	characteristic
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	1	yes	characteristic
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	1	yes	characteristic
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	2	yes	—
625	#95	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	2	yes	—
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
632	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	4	2	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	4	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	4	1	no	—
723	C₄²	—	4	1	no	—
724	C₄²	—	4	1	no	—
725	C₄²	—	4	1	no	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	#41×C₁₃₉	1	4	yes	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
750	Q₈	—	8	4	no	—
751	Q₈	—	8	2	no	—
752	D₄	—	4	4	no	—
753	D₄	—	8	4	no	—
754	D₄	—	8	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
802	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
803	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
804	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
825	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
826	C₂²	#585×C₁₃₉	1	1	yes	characteristic
827	C₂²	#585×C₁₃₉	1	2	yes	—
828	C₂²	#585×C₁₃₉	1	1	yes	characteristic
829	C₄	—	2	4	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	1	no	—
848	C₂	#3455×C₁₃₉	1	1	yes	characteristic
849	C₂	#3493×C₁₃₉	1	1	yes	characteristic
850	C₂	#3508×C₁₃₉	1	1	yes	characteristic
851	C₂	#3545×C₁₃₉	1	2	yes	—
852	C₂	#3562×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. #2861×C₁₃₉	C₂	semidirect
2. #2798×C₁₃₉	C₂	semidirect
3. #2797×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2703×C₁₃₉	C₂	semidirect
6. #2700×C₁₃₉	C₂	semidirect
7. #2694×C₁₃₉	C₂	semidirect
8. #2690×C₁₃₉	C₂	semidirect
9. #2686×C₁₃₉	C₂	semidirect
10. #2648×C₁₃₉	C₂	semidirect
11. #2610×C₁₃₉	C₂	semidirect
12. #2605×C₁₃₉	C₂	semidirect
13. #2598×C₁₃₉	C₂	semidirect
14. #2557×C₁₃₉	C₂	semidirect
15. #2540×C₁₃₉	C₂	semidirect
16. #2531×C₁₃₉	C₂	semidirect
17. #2337×C₁₃₉	C₂	semidirect
18. #2319×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
426. #37022	C₁₃₉	direct (N × H)
427. C₁₃₉	#37022	direct (N × H)
428. #2861	C₂×C₁₃₉	semidirect
429. #2798	C₂×C₁₃₉	semidirect
430. #2797	C₂×C₁₃₉	semidirect
431. #2733	C₂×C₁₃₉	semidirect
432. #2703	C₂×C₁₃₉	semidirect
433. #2700	C₂×C₁₃₉	semidirect
434. #2694	C₂×C₁₃₉	semidirect
435. #2690	C₂×C₁₃₉	semidirect
436. #2686	C₂×C₁₃₉	semidirect
437. #2648	C₂×C₁₃₉	semidirect
438. #2610	C₂×C₁₃₉	semidirect
439. #2605	C₂×C₁₃₉	semidirect
440. #2598	C₂×C₁₃₉	semidirect
441. #2557	C₂×C₁₃₉	semidirect
442. #2540	C₂×C₁₃₉	semidirect
443. #2531	C₂×C₁₃₉	semidirect
444. #2337	C₂×C₁₃₉	semidirect
445. #2319	C₂×C₁₃₉	semidirect
446. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2861×C₁₃₉	2
#2798×C₁₃₉	2
#2797×C₁₃₉	2
#2733×C₁₃₉	2
#2703×C₁₃₉	2
#2700×C₁₃₉	2
#2694×C₁₃₉	2
#2690×C₁₃₉	2
#2686×C₁₃₉	2
#2648×C₁₃₉	2
#2610×C₁₃₉	2
#2605×C₁₃₉	2
#2598×C₁₃₉	2
#2557×C₁₃₉	2
#2540×C₁₃₉	2
#2531×C₁₃₉	2
#2337×C₁₃₉	2
#2319×C₁₃₉	2
#2298×C₁₃₉	2
#37022	139

Subgroups — C139×#37022 #48031618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37022 #48031618