Subgroups — C₁₃₉×#36929 #48031525

Order 35584.

1892 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2788×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2750×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2735×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2728×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2720×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2717×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2697×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2690×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2684×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2652×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2530×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2460×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2326×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2322×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	#400×C₁₃₉	C₂²	1	2	yes	complemented
34	#400×C₁₃₉	C₂²	1	2	yes	complemented
35	#400×C₁₃₉	C₂²	1	2	yes	complemented
36	#400×C₁₃₉	C₂²	1	2	yes	complemented
37	#400×C₁₃₉	C₂²	1	2	yes	complemented
38	#399×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	complemented
40	#398×C₁₃₉	C₂²	1	2	yes	complemented
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	2	yes	—
45	#397×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	2	yes	complemented
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#396×C₁₃₉	C₂²	1	2	yes	—
50	#396×C₁₃₉	C₂²	1	2	yes	complemented
51	#395×C₁₃₉	C₂²	1	2	yes	complemented
52	#395×C₁₃₉	C₂²	1	2	yes	complemented
53	#395×C₁₃₉	C₂²	1	2	yes	complemented
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#393×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#390×C₁₃₉	C₂²	1	1	yes	characteristic
60	#389×C₁₃₉	C₂²	1	2	yes	complemented
61	#389×C₁₃₉	C₂²	1	2	yes	complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×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	complemented
72	#387×C₁₃₉	C₂²	1	2	yes	complemented
73	#387×C₁₃₉	C₂²	1	2	yes	complemented
74	#387×C₁₃₉	C₂²	1	2	yes	complemented
75	#387×C₁₃₉	C₂²	1	2	yes	complemented
76	#387×C₁₃₉	C₂²	1	2	yes	complemented
77	#387×C₁₃₉	C₂²	1	2	yes	complemented
78	#387×C₁₃₉	C₂²	1	2	yes	complemented
79	#386×C₁₃₉	C₂²	1	1	yes	characteristic
80	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	1	yes	characteristic
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#385×C₁₃₉	C₂²	1	2	yes	—
85	#385×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	1	yes	characteristic
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	#385×C₁₃₉	C₂²	1	2	yes	complemented
94	#385×C₁₃₉	C₂²	1	2	yes	complemented
95	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
96	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
97	#380×C₁₃₉	C₂²	1	2	yes	—
98	#380×C₁₃₉	C₂²	1	2	yes	—
99	#380×C₁₃₉	C₂²	1	2	yes	—
100	#379×C₁₃₉	C₂²	1	1	yes	characteristic
101	#379×C₁₃₉	C₂²	1	2	yes	—
102	#379×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
106	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	—	4	4	no	—
113	C₂³×C₄×C₁₃₉	—	4	2	no	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	#125×C₁₃₉	—	4	4	no	—
122	#124×C₁₃₉	—	2	4	no	—
123	#123×C₁₃₉	—	2	4	no	—
124	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
125	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
127	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
128	#120×C₁₃₉	—	2	4	no	—
129	C₄×Q₈×C₁₃₉	—	4	2	no	—
130	C₄×D₄×C₁₃₉	—	4	2	no	—
131	C₄×D₄×C₁₃₉	—	4	4	no	—
132	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
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	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	C₂⁴×C₁₃₉	—	2	2	no	—
209	C₂⁴×C₁₃₉	—	2	4	no	—
210	C₂⁴×C₁₃₉	—	4	2	no	—
211	C₂⁴×C₁₃₉	—	4	1	no	—
212	C₂⁴×C₁₃₉	—	4	1	no	—
213	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃₉	—	2	2	no	—
217	C₂×Q₈×C₁₃₉	—	2	4	no	—
218	C₂×Q₈×C₁₃₉	—	4	1	no	—
219	C₂×Q₈×C₁₃₉	—	4	1	no	—
220	C₂×Q₈×C₁₃₉	—	4	2	no	—
221	C₂×Q₈×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	4	no	—
224	C₂×D₄×C₁₃₉	—	4	1	no	—
225	C₂×D₄×C₁₃₉	—	4	2	no	—
226	C₂×D₄×C₁₃₉	—	4	1	no	—
227	C₂×D₄×C₁₃₉	#41	1	4	yes	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	1	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	1	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	—	4	1	no	—
242	C₂²×C₄×C₁₃₉	—	4	1	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	2	no	—
245	C₂²×C₄×C₁₃₉	—	4	16	no	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	4	2	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	1	no	—
273	C₄⋊C₄×C₁₃₉	—	4	1	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	2	no	—
279	C₄⋊C₄×C₁₃₉	—	4	2	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	2	no	—
282	C₄⋊C₄×C₁₃₉	—	4	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄²×C₁₃₉	—	2	2	no	—
308	C₄²×C₁₃₉	—	2	2	no	—
309	C₄²×C₁₃₉	—	4	1	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₄²×C₁₃₉	—	4	2	no	—
312	C₄²×C₁₃₉	—	4	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	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	1	no	—
327	C₂³×C₁₃₉	—	4	8	no	—
328	C₂³×C₁₃₉	—	4	4	no	—
329	C₂³×C₁₃₉	—	4	4	no	—
330	C₂³×C₁₃₉	—	4	8	no	—
331	C₂³×C₁₃₉	—	4	4	no	—
332	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
333	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
334	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
335	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
336	Q₈×C₁₃₉	—	4	4	no	—
337	Q₈×C₁₃₉	—	8	4	no	—
338	D₄×C₁₃₉	—	4	4	no	—
339	D₄×C₁₃₉	—	4	8	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	1	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	1	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	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	1	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	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	4	8	no	—
382	C₂×C₄×C₁₃₉	—	4	4	no	—
383	C₂×C₄×C₁₃₉	—	4	4	no	—
384	C₂×C₄×C₁₃₉	—	4	8	no	—
385	C₂×C₄×C₁₃₉	—	4	4	no	—
386	C₂×C₄×C₁₃₉	—	8	2	no	—
387	C₂×C₄×C₁₃₉	—	8	2	no	—
388	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
389	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
391	C₂²×C₁₃₉	—	2	2	no	—
392	C₂²×C₁₃₉	—	2	2	no	—
393	C₂²×C₁₃₉	—	2	4	no	—
394	C₂²×C₁₃₉	—	2	4	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	4	no	—
398	C₂²×C₁₃₉	—	4	16	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	1	no	—
402	C₂²×C₁₃₉	—	4	2	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	1	no	—
405	C₂²×C₁₃₉	—	4	1	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
412	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
413	C₂²×C₁₃₉	#585	1	1	yes	characteristic
414	C₄×C₁₃₉	—	2	2	no	—
415	C₄×C₁₃₉	—	2	2	no	—
416	C₄×C₁₃₉	—	2	4	no	—
417	C₄×C₁₃₉	—	4	2	no	—
418	C₄×C₁₃₉	—	4	2	no	—
419	C₄×C₁₃₉	—	4	2	no	—
420	C₄×C₁₃₉	—	4	2	no	—
421	C₄×C₁₃₉	—	4	2	no	—
422	C₄×C₁₃₉	—	4	1	no	—
423	C₄×C₁₃₉	—	4	1	no	—
424	C₄×C₁₃₉	—	4	2	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₂×C₁₃₉	—	4	2	no	—
431	C₂×C₁₃₉	—	4	2	no	—
432	C₂×C₁₃₉	—	4	4	no	—
433	C₂×C₁₃₉	#3459	1	1	yes	characteristic
434	C₂×C₁₃₉	#3520	1	2	yes	—
435	C₂×C₁₃₉	#3532	1	1	yes	characteristic
436	C₂×C₁₃₉	#3538	1	1	yes	characteristic
437	C₂×C₁₃₉	#3541	1	2	yes	—
438	#36929	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₁₃₉	#36929	1	1	yes	characteristic, direct product factor, Sylow
440	#2848	C₂×C₁₃₉	1	2	yes	complemented
441	#2788	C₂×C₁₃₉	1	2	yes	complemented
442	#2750	C₂×C₁₃₉	1	2	yes	complemented
443	#2735	C₂×C₁₃₉	1	2	yes	complemented
444	#2728	C₂×C₁₃₉	1	2	yes	complemented
445	#2720	C₂×C₁₃₉	1	2	yes	complemented
446	#2717	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	#2697	C₂×C₁₃₉	1	1	yes	characteristic
448	#2690	C₂×C₁₃₉	1	2	yes	complemented
449	#2684	C₂×C₁₃₉	1	1	yes	characteristic
450	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2652	C₂×C₁₃₉	1	2	yes	complemented
452	#2530	C₂×C₁₃₉	1	2	yes	complemented
453	#2465	C₂×C₁₃₉	1	2	yes	complemented
454	#2460	C₂×C₁₃₉	1	2	yes	complemented
455	#2449	C₂×C₁₃₉	1	2	yes	complemented
456	#2326	C₂×C₁₃₉	1	1	yes	characteristic, complemented
457	#2322	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic
459	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
461	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
466	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
467	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
469	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
471	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
472	#400	C₂²×C₁₃₉	1	2	yes	complemented
473	#400	C₂²×C₁₃₉	1	2	yes	complemented
474	#400	C₂²×C₁₃₉	1	2	yes	complemented
475	#400	C₂²×C₁₃₉	1	2	yes	complemented
476	#400	C₂²×C₁₃₉	1	2	yes	complemented
477	#399	C₂²×C₁₃₉	1	2	yes	—
478	#398	C₂²×C₁₃₉	1	2	yes	complemented
479	#398	C₂²×C₁₃₉	1	2	yes	complemented
480	#397	C₂²×C₁₃₉	1	2	yes	—
481	#397	C₂²×C₁₃₉	1	2	yes	—
482	#397	C₂²×C₁₃₉	1	2	yes	—
483	#397	C₂²×C₁₃₉	1	2	yes	—
484	#397	C₂²×C₁₃₉	1	2	yes	—
485	#397	C₂²×C₁₃₉	1	2	yes	complemented
486	#396	C₂²×C₁₃₉	1	2	yes	—
487	#396	C₂²×C₁₃₉	1	2	yes	—
488	#396	C₂²×C₁₃₉	1	2	yes	—
489	#396	C₂²×C₁₃₉	1	2	yes	complemented
490	#395	C₂²×C₁₃₉	1	2	yes	complemented
491	#395	C₂²×C₁₃₉	1	2	yes	complemented
492	#395	C₂²×C₁₃₉	1	2	yes	complemented
493	#394	C₂²×C₁₃₉	1	2	yes	—
494	#394	C₂²×C₁₃₉	1	2	yes	—
495	#393	C₂²×C₁₃₉	1	2	yes	—
496	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
497	#391	C₂²×C₁₃₉	1	2	yes	complemented
498	#390	C₂²×C₁₃₉	1	1	yes	characteristic
499	#389	C₂²×C₁₃₉	1	2	yes	complemented
500	#389	C₂²×C₁₃₉	1	2	yes	complemented
501	#389	C₂²×C₁₃₉	1	2	yes	complemented
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	#388	C₂²×C₁₃₉	1	2	yes	—
509	#388	C₂²×C₁₃₉	1	2	yes	—
510	#388	C₂²×C₁₃₉	1	2	yes	complemented
511	#387	C₂²×C₁₃₉	1	2	yes	complemented
512	#387	C₂²×C₁₃₉	1	2	yes	complemented
513	#387	C₂²×C₁₃₉	1	2	yes	complemented
514	#387	C₂²×C₁₃₉	1	2	yes	complemented
515	#387	C₂²×C₁₃₉	1	2	yes	complemented
516	#387	C₂²×C₁₃₉	1	2	yes	complemented
517	#387	C₂²×C₁₃₉	1	2	yes	complemented
518	#386	C₂²×C₁₃₉	1	1	yes	characteristic
519	#386	C₂²×C₁₃₉	1	1	yes	characteristic
520	#386	C₂²×C₁₃₉	1	2	yes	—
521	#386	C₂²×C₁₃₉	1	2	yes	—
522	#386	C₂²×C₁₃₉	1	2	yes	—
523	#385	C₂²×C₁₃₉	1	2	yes	—
524	#385	C₂²×C₁₃₉	1	2	yes	—
525	#385	C₂²×C₁₃₉	1	2	yes	—
526	#385	C₂²×C₁₃₉	1	2	yes	—
527	#385	C₂²×C₁₃₉	1	2	yes	—
528	#385	C₂²×C₁₃₉	1	2	yes	—
529	#385	C₂²×C₁₃₉	1	1	yes	characteristic
530	#385	C₂²×C₁₃₉	1	2	yes	—
531	#385	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
532	#385	C₂²×C₁₃₉	1	2	yes	complemented
533	#385	C₂²×C₁₃₉	1	2	yes	complemented
534	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
535	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
536	#380	C₂²×C₁₃₉	1	2	yes	—
537	#380	C₂²×C₁₃₉	1	2	yes	—
538	#380	C₂²×C₁₃₉	1	2	yes	—
539	#379	C₂²×C₁₃₉	1	2	yes	—
540	#379	C₂²×C₁₃₉	1	2	yes	—
541	#379	C₂²×C₁₃₉	1	1	yes	characteristic
542	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
543	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
545	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
546	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
549	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂³×C₄	—	4	4	no	—
552	C₂³×C₄	—	4	2	no	—
553	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	#125	—	4	4	no	—
561	#124	—	2	4	no	—
562	#123	—	2	4	no	—
563	C₂²⋊Q₈	—	4	4	no	—
564	C₂²⋊Q₈	—	4	4	no	—
565	C₂²⋊Q₈	—	4	4	no	—
566	C₂²⋊Q₈	—	4	4	no	—
567	#120	—	2	4	no	—
568	C₄×Q₈	—	4	2	no	—
569	C₄×D₄	—	4	2	no	—
570	C₄×D₄	—	4	4	no	—
571	C₂×C₄⋊C₄	—	4	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊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×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	2	yes	—
633	#95	C₂³×C₁₃₉	1	2	yes	—
634	#95	C₂³×C₁₃₉	1	2	yes	—
635	#95	C₂³×C₁₃₉	1	2	yes	—
636	#95	C₂³×C₁₃₉	1	2	yes	—
637	#95	C₂³×C₁₃₉	1	2	yes	—
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	#95	C₂³×C₁₃₉	1	2	yes	—
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	C₂⁴	—	2	2	no	—
648	C₂⁴	—	2	4	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	1	no	—
652	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
653	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
654	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	1	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	4	1	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	1	no	—
666	C₂×D₄	#41×C₁₃₉	1	4	yes	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	16	no	—
685	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	1	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	1	no	—
736	C₂²⋊C₄	—	4	1	no	—
737	C₂²⋊C₄	—	4	1	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	4	1	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	8	no	—
768	C₂³	—	4	8	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	4	no	—
771	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
772	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
773	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
774	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	8	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	8	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	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	2	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	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
828	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
829	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	4	16	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
849	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
850	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
851	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
852	C₂²	#585×C₁₃₉	1	1	yes	characteristic
853	C₄	—	2	2	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	4	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₂	—	4	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	2	no	—
872	C₂	#3459×C₁₃₉	1	1	yes	characteristic
873	C₂	#3520×C₁₃₉	1	2	yes	—
874	C₂	#3532×C₁₃₉	1	1	yes	characteristic
875	C₂	#3538×C₁₃₉	1	1	yes	characteristic
876	C₂	#3541×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#120×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #2848×C₁₃₉	C₂	semidirect
2. #2788×C₁₃₉	C₂	semidirect
3. #2750×C₁₃₉	C₂	semidirect
4. #2735×C₁₃₉	C₂	semidirect
5. #2728×C₁₃₉	C₂	semidirect
6. #2720×C₁₃₉	C₂	semidirect
7. #2717×C₁₃₉	C₂	semidirect
9. #2690×C₁₃₉	C₂	semidirect
11. #2683×C₁₃₉	C₂	semidirect
12. #2652×C₁₃₉	C₂	semidirect
13. #2530×C₁₃₉	C₂	semidirect
14. #2465×C₁₃₉	C₂	semidirect
15. #2460×C₁₃₉	C₂	semidirect
16. #2449×C₁₃₉	C₂	semidirect
17. #2326×C₁₃₉	C₂	semidirect
18. #2322×C₁₃₉	C₂	semidirect
21. C₂×#125×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
33. #400×C₁₃₉	C₂²	semidirect
34. #400×C₁₃₉	C₂²	semidirect
35. #400×C₁₃₉	C₂²	semidirect
36. #400×C₁₃₉	C₂²	semidirect
37. #400×C₁₃₉	C₂²	semidirect
39. #398×C₁₃₉	C₂²	semidirect
40. #398×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
50. #396×C₁₃₉	C₂²	semidirect
51. #395×C₁₃₉	C₂²	semidirect
52. #395×C₁₃₉	C₂²	semidirect
53. #395×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
60. #389×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
71. #388×C₁₃₉	C₂²	semidirect
72. #387×C₁₃₉	C₂²	semidirect
73. #387×C₁₃₉	C₂²	semidirect
74. #387×C₁₃₉	C₂²	semidirect
75. #387×C₁₃₉	C₂²	semidirect
76. #387×C₁₃₉	C₂²	semidirect
77. #387×C₁₃₉	C₂²	semidirect
78. #387×C₁₃₉	C₂²	semidirect
92. #385×C₁₃₉	C₂²	semidirect
93. #385×C₁₃₉	C₂²	semidirect
94. #385×C₁₃₉	C₂²	semidirect
95. #384×C₁₃₉	C₂²	semidirect
96. #381×C₁₃₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
106. #376×C₁₃₉	C₂²	semidirect
438. #36929	C₁₃₉	direct (N × H)
439. C₁₃₉	#36929	direct (N × H)
440. #2848	C₂×C₁₃₉	semidirect
441. #2788	C₂×C₁₃₉	semidirect
442. #2750	C₂×C₁₃₉	semidirect
443. #2735	C₂×C₁₃₉	semidirect
444. #2728	C₂×C₁₃₉	semidirect
445. #2720	C₂×C₁₃₉	semidirect
446. #2717	C₂×C₁₃₉	semidirect
448. #2690	C₂×C₁₃₉	semidirect
450. #2683	C₂×C₁₃₉	semidirect
451. #2652	C₂×C₁₃₉	semidirect
452. #2530	C₂×C₁₃₉	semidirect
453. #2465	C₂×C₁₃₉	semidirect
454. #2460	C₂×C₁₃₉	semidirect
455. #2449	C₂×C₁₃₉	semidirect
456. #2326	C₂×C₁₃₉	semidirect
457. #2322	C₂×C₁₃₉	semidirect
460. C₂×#125	C₂²×C₁₃₉	semidirect
466. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
468. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
471. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
472. #400	C₂²×C₁₃₉	semidirect
473. #400	C₂²×C₁₃₉	semidirect
474. #400	C₂²×C₁₃₉	semidirect
475. #400	C₂²×C₁₃₉	semidirect
476. #400	C₂²×C₁₃₉	semidirect
478. #398	C₂²×C₁₃₉	semidirect
479. #398	C₂²×C₁₃₉	semidirect
485. #397	C₂²×C₁₃₉	semidirect
489. #396	C₂²×C₁₃₉	semidirect
490. #395	C₂²×C₁₃₉	semidirect
491. #395	C₂²×C₁₃₉	semidirect
492. #395	C₂²×C₁₃₉	semidirect
496. #391	C₂²×C₁₃₉	semidirect
497. #391	C₂²×C₁₃₉	semidirect
499. #389	C₂²×C₁₃₉	semidirect
500. #389	C₂²×C₁₃₉	semidirect
501. #389	C₂²×C₁₃₉	semidirect
510. #388	C₂²×C₁₃₉	semidirect
511. #387	C₂²×C₁₃₉	semidirect
512. #387	C₂²×C₁₃₉	semidirect
513. #387	C₂²×C₁₃₉	semidirect
514. #387	C₂²×C₁₃₉	semidirect
515. #387	C₂²×C₁₃₉	semidirect
516. #387	C₂²×C₁₃₉	semidirect
517. #387	C₂²×C₁₃₉	semidirect
531. #385	C₂²×C₁₃₉	semidirect
532. #385	C₂²×C₁₃₉	semidirect
533. #385	C₂²×C₁₃₉	semidirect
534. #384	C₂²×C₁₃₉	semidirect
535. #381	C₂²×C₁₃₉	semidirect
544. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
545. #376	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2848×C₁₃₉	2
#2788×C₁₃₉	2
#2750×C₁₃₉	2
#2735×C₁₃₉	2
#2728×C₁₃₉	2
#2720×C₁₃₉	2
#2717×C₁₃₉	2
#2697×C₁₃₉	2
#2690×C₁₃₉	2
#2684×C₁₃₉	2
#2683×C₁₃₉	2
#2652×C₁₃₉	2
#2530×C₁₃₉	2
#2465×C₁₃₉	2
#2460×C₁₃₉	2
#2449×C₁₃₉	2
#2326×C₁₃₉	2
#2322×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36929	139

Subgroups — C139×#36929 #48031525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36929 #48031525