Subgroups — C₁₃₉×#36206 #48030802

Order 35584.

2344 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2849×C₁₃₉	C₂	1	2	yes	maximal
2	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2569×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2510×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2505×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2488×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2438×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2419×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2368×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2343×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2280×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₂²×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
31	#401×C₁₃₉	C₂²	1	2	yes	complemented
32	#400×C₁₃₉	C₂²	1	2	yes	complemented
33	#400×C₁₃₉	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
39	#398×C₁₃₉	C₂²	1	2	yes	complemented
40	#398×C₁₃₉	C₂²	1	2	yes	complemented
41	#397×C₁₃₉	C₂²	1	2	yes	complemented
42	#397×C₁₃₉	C₂²	1	2	yes	complemented
43	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
44	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	#391×C₁₃₉	C₂²	1	2	yes	complemented
46	#389×C₁₃₉	C₂²	1	2	yes	complemented
47	#388×C₁₃₉	C₂²	1	2	yes	complemented
48	#388×C₁₃₉	C₂²	1	2	yes	complemented
49	#388×C₁₃₉	C₂²	1	2	yes	complemented
50	#387×C₁₃₉	C₂²	1	2	yes	complemented
51	#387×C₁₃₉	C₂²	1	2	yes	complemented
52	#387×C₁₃₉	C₂²	1	2	yes	complemented
53	#387×C₁₃₉	C₂²	1	2	yes	complemented
54	#387×C₁₃₉	C₂²	1	2	yes	complemented
55	#387×C₁₃₉	C₂²	1	2	yes	complemented
56	#387×C₁₃₉	C₂²	1	2	yes	complemented
57	#387×C₁₃₉	C₂²	1	2	yes	complemented
58	#387×C₁₃₉	C₂²	1	2	yes	complemented
59	#386×C₁₃₉	C₂²	1	1	yes	characteristic
60	#386×C₁₃₉	C₂²	1	2	yes	—
61	#386×C₁₃₉	C₂²	1	2	yes	—
62	#386×C₁₃₉	C₂²	1	2	yes	—
63	#386×C₁₃₉	C₂²	1	2	yes	—
64	#386×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	2	yes	—
66	#385×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	1	yes	characteristic
68	#385×C₁₃₉	C₂²	1	2	yes	—
69	#385×C₁₃₉	C₂²	1	2	yes	—
70	#385×C₁₃₉	C₂²	1	2	yes	—
71	#385×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	2	yes	—
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#385×C₁₃₉	C₂²	1	2	yes	complemented
75	#383×C₁₃₉	C₂²	1	2	yes	complemented
76	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#382×C₁₃₉	C₂²	1	2	yes	complemented
78	#381×C₁₃₉	C₂²	1	2	yes	—
79	#381×C₁₃₉	C₂²	1	2	yes	—
80	#381×C₁₃₉	C₂²	1	2	yes	—
81	#381×C₁₃₉	C₂²	1	2	yes	—
82	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	#380×C₁₃₉	C₂²	1	2	yes	—
84	#380×C₁₃₉	C₂²	1	2	yes	—
85	#380×C₁₃₉	C₂²	1	2	yes	—
86	#380×C₁₃₉	C₂²	1	2	yes	—
87	#380×C₁₃₉	C₂²	1	1	yes	characteristic
88	#380×C₁₃₉	C₂²	1	2	yes	—
89	#379×C₁₃₉	C₂²	1	1	yes	characteristic
90	#379×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
99	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
100	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
101	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
103	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	—	2	8	no	—
112	C₂³×C₄×C₁₃₉	—	2	8	no	—
113	C₂³×C₄×C₁₃₉	—	2	4	no	—
114	C₂³×C₄×C₁₃₉	—	4	4	no	—
115	C₂³×C₄×C₁₃₉	—	4	4	no	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	#123×C₁₃₉	—	2	8	no	—
128	#123×C₁₃₉	—	4	4	no	—
129	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
130	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
131	#120×C₁₃₉	—	2	4	no	—
132	C₄×D₄×C₁₃₉	—	2	4	no	—
133	C₄×D₄×C₁₃₉	—	4	4	no	—
134	#117×C₁₃₉	—	2	8	no	—
135	#117×C₁₃₉	—	4	4	no	—
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	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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×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	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	1	yes	characteristic
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
199	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	1	yes	characteristic
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	C₂⁴×C₁₃₉	—	2	2	no	—
209	C₂⁴×C₁₃₉	—	2	4	no	—
210	C₂⁴×C₁₃₉	—	2	4	no	—
211	C₂⁴×C₁₃₉	—	2	2	no	—
212	C₂⁴×C₁₃₉	#41	1	4	yes	—
213	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₁₃₉	—	2	2	no	—
217	C₂×Q₈×C₁₃₉	—	4	2	no	—
218	C₂×D₄×C₁₃₉	—	2	2	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	4	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	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	4	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	2	no	—
245	C₂²×C₄×C₁₃₉	—	4	2	no	—
246	C₂²×C₄×C₁₃₉	—	4	2	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	—	4	32	no	—
253	C₂²×C₄×C₁₃₉	—	4	16	no	—
254	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
255	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	2	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	4	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	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	C₄⋊C₄×C₁₃₉	—	4	2	no	—
284	C₄⋊C₄×C₁₃₉	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
305	C₄²×C₁₃₉	—	2	4	no	—
306	C₄²×C₁₃₉	—	2	4	no	—
307	C₄²×C₁₃₉	—	2	2	no	—
308	C₄²×C₁₃₉	—	4	2	no	—
309	C₄²×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₂³×C₁₃₉	—	2	8	no	—
312	C₂³×C₁₃₉	—	2	8	no	—
313	C₂³×C₁₃₉	—	2	16	no	—
314	C₂³×C₁₃₉	—	2	16	no	—
315	C₂³×C₁₃₉	—	2	8	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	1	no	—
324	C₂³×C₁₃₉	—	2	1	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	1	no	—
327	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
328	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
329	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
330	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
331	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
332	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
333	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
334	Q₈×C₁₃₉	—	8	2	no	—
335	D₄×C₁₃₉	—	4	8	no	—
336	D₄×C₁₃₉	—	4	4	no	—
337	C₂×C₄×C₁₃₉	—	2	16	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	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	1	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	1	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	1	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	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	—	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	1	no	—
378	C₂×C₄×C₁₃₉	—	4	4	no	—
379	C₂×C₄×C₁₃₉	—	4	8	no	—
380	C₂×C₄×C₁₃₉	—	4	8	no	—
381	C₂×C₄×C₁₃₉	—	4	8	no	—
382	C₂×C₄×C₁₃₉	—	4	8	no	—
383	C₂×C₄×C₁₃₉	—	4	8	no	—
384	C₂×C₄×C₁₃₉	—	4	8	no	—
385	C₂×C₄×C₁₃₉	—	4	4	no	—
386	C₂×C₄×C₁₃₉	—	4	8	no	—
387	C₂×C₄×C₁₃₉	—	8	2	no	—
388	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
389	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
390	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
391	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
392	C₂²×C₁₃₉	—	2	32	no	—
393	C₂²×C₁₃₉	—	2	4	no	—
394	C₂²×C₁₃₉	—	2	2	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	4	no	—
398	C₂²×C₁₃₉	—	2	2	no	—
399	C₂²×C₁₃₉	—	2	4	no	—
400	C₂²×C₁₃₉	—	2	4	no	—
401	C₂²×C₁₃₉	—	2	4	no	—
402	C₂²×C₁₃₉	—	2	4	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	1	no	—
406	C₂²×C₁₃₉	—	4	1	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	#551	1	8	yes	—
409	C₂²×C₁₃₉	#552	1	4	yes	—
410	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
411	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
415	C₄×C₁₃₉	—	2	4	no	—
416	C₄×C₁₃₉	—	2	4	no	—
417	C₄×C₁₃₉	—	2	2	no	—
418	C₄×C₁₃₉	—	2	2	no	—
419	C₄×C₁₃₉	—	4	1	no	—
420	C₄×C₁₃₉	—	4	2	no	—
421	C₄×C₁₃₉	—	4	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	1	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	C₄×C₁₃₉	—	4	2	no	—
431	C₂×C₁₃₉	—	2	8	no	—
432	C₂×C₁₃₉	—	2	4	no	—
433	C₂×C₁₃₉	—	8	1	no	—
434	C₂×C₁₃₉	#3444	1	1	yes	characteristic
435	C₂×C₁₃₉	C₂×#551	1	2	yes	—
436	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
437	C₂×C₁₃₉	#3490	1	1	yes	characteristic
438	C₂×C₁₃₉	#3492	1	2	yes	—
439	#36206	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₁₃₉	#36206	1	1	yes	characteristic, direct product factor, Sylow
441	#2849	C₂×C₁₃₉	1	2	yes	—
442	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2569	C₂×C₁₃₉	1	1	yes	characteristic, complemented
444	#2564	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2510	C₂×C₁₃₉	1	2	yes	complemented
446	#2505	C₂×C₁₃₉	1	2	yes	complemented
447	#2498	C₂×C₁₃₉	1	2	yes	complemented
448	#2493	C₂×C₁₃₉	1	2	yes	complemented
449	#2493	C₂×C₁₃₉	1	2	yes	complemented
450	#2488	C₂×C₁₃₉	1	2	yes	complemented
451	#2438	C₂×C₁₃₉	1	2	yes	complemented
452	#2419	C₂×C₁₃₉	1	2	yes	complemented
453	#2368	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2359	C₂×C₁₃₉	1	2	yes	complemented
455	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
456	#2343	C₂×C₁₃₉	1	2	yes	complemented
457	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic
458	#2280	C₂×C₁₃₉	1	2	yes	complemented
459	C₂²×#95	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
461	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
463	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
465	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
469	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
470	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
471	#401	C₂²×C₁₃₉	1	2	yes	complemented
472	#400	C₂²×C₁₃₉	1	1	yes	characteristic, 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	#400	C₂²×C₁₃₉	1	2	yes	complemented
478	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
479	#398	C₂²×C₁₃₉	1	2	yes	complemented
480	#398	C₂²×C₁₃₉	1	2	yes	complemented
481	#397	C₂²×C₁₃₉	1	2	yes	complemented
482	#397	C₂²×C₁₃₉	1	2	yes	complemented
483	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
484	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
485	#391	C₂²×C₁₃₉	1	2	yes	complemented
486	#389	C₂²×C₁₃₉	1	2	yes	complemented
487	#388	C₂²×C₁₃₉	1	2	yes	complemented
488	#388	C₂²×C₁₃₉	1	2	yes	complemented
489	#388	C₂²×C₁₃₉	1	2	yes	complemented
490	#387	C₂²×C₁₃₉	1	2	yes	complemented
491	#387	C₂²×C₁₃₉	1	2	yes	complemented
492	#387	C₂²×C₁₃₉	1	2	yes	complemented
493	#387	C₂²×C₁₃₉	1	2	yes	complemented
494	#387	C₂²×C₁₃₉	1	2	yes	complemented
495	#387	C₂²×C₁₃₉	1	2	yes	complemented
496	#387	C₂²×C₁₃₉	1	2	yes	complemented
497	#387	C₂²×C₁₃₉	1	2	yes	complemented
498	#387	C₂²×C₁₃₉	1	2	yes	complemented
499	#386	C₂²×C₁₃₉	1	2	yes	—
500	#386	C₂²×C₁₃₉	1	2	yes	—
501	#386	C₂²×C₁₃₉	1	2	yes	—
502	#386	C₂²×C₁₃₉	1	2	yes	—
503	#386	C₂²×C₁₃₉	1	2	yes	—
504	#386	C₂²×C₁₃₉	1	1	yes	characteristic
505	#385	C₂²×C₁₃₉	1	2	yes	—
506	#385	C₂²×C₁₃₉	1	2	yes	—
507	#385	C₂²×C₁₃₉	1	2	yes	—
508	#385	C₂²×C₁₃₉	1	2	yes	—
509	#385	C₂²×C₁₃₉	1	2	yes	—
510	#385	C₂²×C₁₃₉	1	2	yes	—
511	#385	C₂²×C₁₃₉	1	2	yes	—
512	#385	C₂²×C₁₃₉	1	2	yes	—
513	#385	C₂²×C₁₃₉	1	1	yes	characteristic
514	#385	C₂²×C₁₃₉	1	2	yes	complemented
515	#383	C₂²×C₁₃₉	1	2	yes	complemented
516	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
517	#382	C₂²×C₁₃₉	1	2	yes	complemented
518	#381	C₂²×C₁₃₉	1	2	yes	—
519	#381	C₂²×C₁₃₉	1	2	yes	—
520	#381	C₂²×C₁₃₉	1	2	yes	—
521	#381	C₂²×C₁₃₉	1	2	yes	—
522	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
523	#380	C₂²×C₁₃₉	1	2	yes	—
524	#380	C₂²×C₁₃₉	1	1	yes	characteristic
525	#380	C₂²×C₁₃₉	1	2	yes	—
526	#380	C₂²×C₁₃₉	1	2	yes	—
527	#380	C₂²×C₁₃₉	1	2	yes	—
528	#380	C₂²×C₁₃₉	1	2	yes	—
529	#379	C₂²×C₁₃₉	1	2	yes	—
530	#379	C₂²×C₁₃₉	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
532	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
533	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
539	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
540	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
541	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
542	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
543	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
544	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
545	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
546	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
547	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂³×C₄	—	2	8	no	—
552	C₂³×C₄	—	2	8	no	—
553	C₂³×C₄	—	2	4	no	—
554	C₂³×C₄	—	4	4	no	—
555	C₂³×C₄	—	4	4	no	—
556	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	#123	—	2	8	no	—
568	#123	—	4	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	4	4	no	—
571	#120	—	2	4	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	—	4	4	no	—
574	#117	—	2	8	no	—
575	#117	—	4	4	no	—
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	1	yes	characteristic
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	2	yes	—
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×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×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	1	yes	characteristic
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	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₄²	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	1	yes	characteristic
616	#95	C₂³×C₁₃₉	1	1	yes	characteristic
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	1	yes	characteristic
622	#95	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	1	yes	characteristic
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	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
648	C₂⁴	—	2	2	no	—
649	C₂⁴	—	2	4	no	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	2	2	no	—
652	C₂⁴	#41×C₁₃₉	1	4	yes	—
653	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
654	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
655	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	32	no	—
693	C₂²×C₄	—	4	16	no	—
694	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
695	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₂³	—	2	8	no	—
752	C₂³	—	2	8	no	—
753	C₂³	—	2	16	no	—
754	C₂³	—	2	16	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
768	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
769	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
770	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
771	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
772	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
773	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
774	Q₈	—	8	2	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	16	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	1	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	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	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	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	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	1	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	8	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
829	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
830	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
831	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
832	C₂²	—	2	32	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	#551×C₁₃₉	1	8	yes	—
849	C₂²	#552×C₁₃₉	1	4	yes	—
850	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
851	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
852	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
853	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
854	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₂	—	2	8	no	—
872	C₂	—	2	4	no	—
873	C₂	—	8	1	no	—
874	C₂	#3444×C₁₃₉	1	1	yes	characteristic
875	C₂	C₂×#551×C₁₃₉	1	2	yes	—
876	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
877	C₂	#3490×C₁₃₉	1	1	yes	characteristic
878	C₂	#3492×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
2. #2848×C₁₃₉	C₂	semidirect
3. #2569×C₁₃₉	C₂	semidirect
4. #2564×C₁₃₉	C₂	semidirect
5. #2510×C₁₃₉	C₂	semidirect
6. #2505×C₁₃₉	C₂	semidirect
7. #2498×C₁₃₉	C₂	semidirect
8. #2493×C₁₃₉	C₂	semidirect
9. #2493×C₁₃₉	C₂	semidirect
10. #2488×C₁₃₉	C₂	semidirect
11. #2438×C₁₃₉	C₂	semidirect
12. #2419×C₁₃₉	C₂	semidirect
13. #2368×C₁₃₉	C₂	semidirect
14. #2359×C₁₃₉	C₂	semidirect
15. #2353×C₁₃₉	C₂	semidirect
16. #2343×C₁₃₉	C₂	semidirect
18. #2280×C₁₃₉	C₂	semidirect
19. C₂²×#95×C₁₃₉	C₂	semidirect
31. #401×C₁₃₉	C₂²	semidirect
32. #400×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
38. #399×C₁₃₉	C₂²	semidirect
39. #398×C₁₃₉	C₂²	semidirect
40. #398×C₁₃₉	C₂²	semidirect
41. #397×C₁₃₉	C₂²	semidirect
42. #397×C₁₃₉	C₂²	semidirect
43. #395×C₁₃₉	C₂²	semidirect
44. #393×C₁₃₉	C₂²	semidirect
45. #391×C₁₃₉	C₂²	semidirect
46. #389×C₁₃₉	C₂²	semidirect
47. #388×C₁₃₉	C₂²	semidirect
48. #388×C₁₃₉	C₂²	semidirect
49. #388×C₁₃₉	C₂²	semidirect
50. #387×C₁₃₉	C₂²	semidirect
51. #387×C₁₃₉	C₂²	semidirect
52. #387×C₁₃₉	C₂²	semidirect
53. #387×C₁₃₉	C₂²	semidirect
54. #387×C₁₃₉	C₂²	semidirect
55. #387×C₁₃₉	C₂²	semidirect
56. #387×C₁₃₉	C₂²	semidirect
57. #387×C₁₃₉	C₂²	semidirect
58. #387×C₁₃₉	C₂²	semidirect
74. #385×C₁₃₉	C₂²	semidirect
75. #383×C₁₃₉	C₂²	semidirect
76. #383×C₁₃₉	C₂²	semidirect
77. #382×C₁₃₉	C₂²	semidirect
82. #381×C₁₃₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
99. #376×C₁₃₉	C₂²	semidirect
439. #36206	C₁₃₉	direct (N × H)
440. C₁₃₉	#36206	direct (N × H)
442. #2848	C₂×C₁₃₉	semidirect
443. #2569	C₂×C₁₃₉	semidirect
444. #2564	C₂×C₁₃₉	semidirect
445. #2510	C₂×C₁₃₉	semidirect
446. #2505	C₂×C₁₃₉	semidirect
447. #2498	C₂×C₁₃₉	semidirect
448. #2493	C₂×C₁₃₉	semidirect
449. #2493	C₂×C₁₃₉	semidirect
450. #2488	C₂×C₁₃₉	semidirect
451. #2438	C₂×C₁₃₉	semidirect
452. #2419	C₂×C₁₃₉	semidirect
453. #2368	C₂×C₁₃₉	semidirect
454. #2359	C₂×C₁₃₉	semidirect
455. #2353	C₂×C₁₃₉	semidirect
456. #2343	C₂×C₁₃₉	semidirect
458. #2280	C₂×C₁₃₉	semidirect
459. C₂²×#95	C₂×C₁₃₉	semidirect
471. #401	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
477. #400	C₂²×C₁₃₉	semidirect
478. #399	C₂²×C₁₃₉	semidirect
479. #398	C₂²×C₁₃₉	semidirect
480. #398	C₂²×C₁₃₉	semidirect
481. #397	C₂²×C₁₃₉	semidirect
482. #397	C₂²×C₁₃₉	semidirect
483. #395	C₂²×C₁₃₉	semidirect
484. #393	C₂²×C₁₃₉	semidirect
485. #391	C₂²×C₁₃₉	semidirect
486. #389	C₂²×C₁₃₉	semidirect
487. #388	C₂²×C₁₃₉	semidirect
488. #388	C₂²×C₁₃₉	semidirect
489. #388	C₂²×C₁₃₉	semidirect
490. #387	C₂²×C₁₃₉	semidirect
491. #387	C₂²×C₁₃₉	semidirect
492. #387	C₂²×C₁₃₉	semidirect
493. #387	C₂²×C₁₃₉	semidirect
494. #387	C₂²×C₁₃₉	semidirect
495. #387	C₂²×C₁₃₉	semidirect
496. #387	C₂²×C₁₃₉	semidirect
497. #387	C₂²×C₁₃₉	semidirect
498. #387	C₂²×C₁₃₉	semidirect
514. #385	C₂²×C₁₃₉	semidirect
515. #383	C₂²×C₁₃₉	semidirect
516. #383	C₂²×C₁₃₉	semidirect
517. #382	C₂²×C₁₃₉	semidirect
522. #381	C₂²×C₁₃₉	semidirect
531. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
538. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
539. #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
#2849×C₁₃₉	2
#2848×C₁₃₉	2
#2569×C₁₃₉	2
#2564×C₁₃₉	2
#2510×C₁₃₉	2
#2505×C₁₃₉	2
#2498×C₁₃₉	2
#2493×C₁₃₉	2
#2488×C₁₃₉	2
#2438×C₁₃₉	2
#2419×C₁₃₉	2
#2368×C₁₃₉	2
#2359×C₁₃₉	2
#2353×C₁₃₉	2
#2343×C₁₃₉	2
C₄×#120×C₁₃₉	2
#2280×C₁₃₉	2
C₂²×#95×C₁₃₉	2
#36206	139

Subgroups — C139×#36206 #48030802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36206 #48030802