Subgroups — C₁₃₉×#37219 #48031815

Order 35584.

1778 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2806×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2797×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2790×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2733×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2732×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2730×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2724×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2708×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2682×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2680×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2651×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2531×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2529×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2464×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2326×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#399×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
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	#396×C₁₃₉	C₂²	1	2	yes	—
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#392×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#392×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×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	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#384×C₁₃₉	C₂²	1	2	yes	—
100	#382×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	#376×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×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	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×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	2	yes	—
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	#124×C₁₃₉	—	2	8	no	—
121	#124×C₁₃₉	—	4	2	no	—
122	#123×C₁₃₉	—	4	4	no	—
123	#123×C₁₃₉	—	4	4	no	—
124	#123×C₁₃₉	—	4	4	no	—
125	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
127	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
128	#121×C₁₃₉	—	4	2	no	—
129	#121×C₁₃₉	—	4	4	no	—
130	#121×C₁₃₉	—	4	2	no	—
131	C₄×Q₈×C₁₃₉	—	4	2	no	—
132	C₄×D₄×C₁₃₉	—	4	4	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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊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×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	2	yes	—
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	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	—	4	2	no	—
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×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	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×Q₈×C₁₃₉	—	4	1	no	—
213	C₂×Q₈×C₁₃₉	—	4	1	no	—
214	C₂×Q₈×C₁₃₉	—	4	1	no	—
215	C₂×Q₈×C₁₃₉	—	4	1	no	—
216	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	2	2	no	—
222	C₂×D₄×C₁₃₉	—	4	2	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	1	no	—
225	C₂×D₄×C₁₃₉	—	4	1	no	—
226	C₂×D₄×C₁₃₉	—	4	2	no	—
227	C₂×D₄×C₁₃₉	—	4	2	no	—
228	C₂×D₄×C₁₃₉	—	4	2	no	—
229	C₂×D₄×C₁₃₉	—	4	1	no	—
230	C₂×D₄×C₁₃₉	—	4	1	no	—
231	C₂×D₄×C₁₃₉	—	4	2	no	—
232	C₂×D₄×C₁₃₉	—	4	2	no	—
233	C₂×D₄×C₁₃₉	—	4	2	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	2	no	—
236	C₂²×C₄×C₁₃₉	—	2	2	no	—
237	C₂²×C₄×C₁₃₉	—	2	2	no	—
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	2	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	1	no	—
241	C₂²×C₄×C₁₃₉	—	4	1	no	—
242	C₂²×C₄×C₁₃₉	—	4	1	no	—
243	C₂²×C₄×C₁₃₉	—	4	1	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	C₂⁴	1	1	yes	characteristic
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	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	1	no	—
272	C₄⋊C₄×C₁₃₉	—	4	1	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	1	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	1	no	—
279	C₄⋊C₄×C₁₃₉	—	4	1	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	1	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	C₄⋊C₄×C₁₃₉	—	4	2	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	—	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	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	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	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	2	no	—
314	C₄²×C₁₃₉	—	2	2	no	—
315	C₄²×C₁₃₉	—	2	4	no	—
316	C₄²×C₁₃₉	—	4	1	no	—
317	C₄²×C₁₃₉	—	4	1	no	—
318	C₄²×C₁₃₉	—	4	2	no	—
319	C₄²×C₁₃₉	—	4	2	no	—
320	C₂³×C₁₃₉	—	2	1	no	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	—	2	1	no	—
324	C₂³×C₁₃₉	—	2	1	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
341	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
342	Q₈×C₁₃₉	—	4	4	no	—
343	Q₈×C₁₃₉	—	8	2	no	—
344	D₄×C₁₃₉	—	4	8	no	—
345	D₄×C₁₃₉	—	8	2	no	—
346	D₄×C₁₃₉	—	8	2	no	—
347	D₄×C₁₃₉	—	8	4	no	—
348	D₄×C₁₃₉	—	8	4	no	—
349	D₄×C₁₃₉	—	8	4	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	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	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	4	4	no	—
394	C₂×C₄×C₁₃₉	—	4	4	no	—
395	C₂×C₄×C₁₃₉	—	4	4	no	—
396	C₂×C₄×C₁₃₉	—	8	4	no	—
397	C₂×C₄×C₁₃₉	—	8	4	no	—
398	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
399	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
400	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
403	C₂²×C₁₃₉	—	2	2	no	—
404	C₂²×C₁₃₉	—	2	2	no	—
405	C₂²×C₁₃₉	—	2	2	no	—
406	C₂²×C₁₃₉	—	4	1	no	—
407	C₂²×C₁₃₉	—	4	1	no	—
408	C₂²×C₁₃₉	—	4	1	no	—
409	C₂²×C₁₃₉	—	4	1	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	—	4	2	no	—
414	C₂²×C₁₃₉	—	4	2	no	—
415	C₂²×C₁₃₉	—	4	2	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	—	4	2	no	—
420	C₂²×C₁₃₉	—	4	2	no	—
421	C₂²×C₁₃₉	—	4	2	no	—
422	C₂²×C₁₃₉	—	4	2	no	—
423	C₂²×C₁₃₉	—	4	2	no	—
424	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	C₂²×C₁₃₉	#585	1	1	yes	characteristic
430	C₂²×C₁₃₉	#585	1	1	yes	characteristic
431	C₄×C₁₃₉	—	2	2	no	—
432	C₄×C₁₃₉	—	2	4	no	—
433	C₄×C₁₃₉	—	2	2	no	—
434	C₄×C₁₃₉	—	2	2	no	—
435	C₄×C₁₃₉	—	2	2	no	—
436	C₄×C₁₃₉	—	4	1	no	—
437	C₄×C₁₃₉	—	4	2	no	—
438	C₄×C₁₃₉	—	4	2	no	—
439	C₄×C₁₃₉	—	4	2	no	—
440	C₄×C₁₃₉	—	4	1	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	2	no	—
444	C₄×C₁₃₉	—	4	2	no	—
445	C₄×C₁₃₉	—	4	2	no	—
446	C₄×C₁₃₉	—	4	2	no	—
447	C₂×C₁₃₉	—	4	2	no	—
448	C₂×C₁₃₉	—	8	2	no	—
449	C₂×C₁₃₉	—	8	2	no	—
450	C₂×C₁₃₉	#3459	1	1	yes	characteristic
451	C₂×C₁₃₉	#3517	1	1	yes	characteristic
452	C₂×C₁₃₉	#3522	1	1	yes	characteristic
453	C₂×C₁₃₉	#3535	1	1	yes	characteristic
454	C₂×C₁₃₉	#3537	1	1	yes	characteristic
455	C₂×C₁₃₉	#3545	1	1	yes	characteristic
456	C₂×C₁₃₉	#3547	1	1	yes	characteristic
457	#37219	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₁₃₉	#37219	1	1	yes	characteristic, direct product factor, Sylow
459	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
461	#2806	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	#2797	C₂×C₁₃₉	1	2	yes	complemented
463	#2790	C₂×C₁₃₉	1	2	yes	complemented
464	#2733	C₂×C₁₃₉	1	1	yes	characteristic, complemented
465	#2732	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	#2730	C₂×C₁₃₉	1	2	yes	complemented
467	#2724	C₂×C₁₃₉	1	1	yes	characteristic, complemented
468	#2708	C₂×C₁₃₉	1	2	yes	complemented
469	#2682	C₂×C₁₃₉	1	2	yes	complemented
470	#2680	C₂×C₁₃₉	1	2	yes	complemented
471	#2651	C₂×C₁₃₉	1	2	yes	complemented
472	#2531	C₂×C₁₃₉	1	2	yes	complemented
473	#2529	C₂×C₁₃₉	1	2	yes	complemented
474	#2464	C₂×C₁₃₉	1	2	yes	complemented
475	#2461	C₂×C₁₃₉	1	2	yes	complemented
476	#2326	C₂×C₁₃₉	1	2	yes	complemented
477	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
478	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
481	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
482	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
483	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
486	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
488	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
489	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
491	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
492	#400	C₂²×C₁₃₉	1	2	yes	—
493	#399	C₂²×C₁₃₉	1	2	yes	—
494	#398	C₂²×C₁₃₉	1	2	yes	—
495	#398	C₂²×C₁₃₉	1	2	yes	—
496	#398	C₂²×C₁₃₉	1	2	yes	—
497	#398	C₂²×C₁₃₉	1	2	yes	—
498	#398	C₂²×C₁₃₉	1	2	yes	—
499	#397	C₂²×C₁₃₉	1	2	yes	—
500	#397	C₂²×C₁₃₉	1	2	yes	—
501	#397	C₂²×C₁₃₉	1	2	yes	—
502	#397	C₂²×C₁₃₉	1	2	yes	—
503	#397	C₂²×C₁₃₉	1	2	yes	—
504	#396	C₂²×C₁₃₉	1	2	yes	—
505	#396	C₂²×C₁₃₉	1	2	yes	—
506	#396	C₂²×C₁₃₉	1	2	yes	—
507	#395	C₂²×C₁₃₉	1	2	yes	—
508	#394	C₂²×C₁₃₉	1	2	yes	—
509	#394	C₂²×C₁₃₉	1	2	yes	—
510	#394	C₂²×C₁₃₉	1	2	yes	—
511	#394	C₂²×C₁₃₉	1	2	yes	—
512	#394	C₂²×C₁₃₉	1	2	yes	—
513	#392	C₂²×C₁₃₉	1	2	yes	—
514	#392	C₂²×C₁₃₉	1	2	yes	—
515	#392	C₂²×C₁₃₉	1	2	yes	—
516	#391	C₂²×C₁₃₉	1	2	yes	—
517	#391	C₂²×C₁₃₉	1	1	yes	characteristic
518	#391	C₂²×C₁₃₉	1	1	yes	characteristic
519	#390	C₂²×C₁₃₉	1	2	yes	—
520	#390	C₂²×C₁₃₉	1	1	yes	characteristic
521	#390	C₂²×C₁₃₉	1	1	yes	characteristic
522	#390	C₂²×C₁₃₉	1	1	yes	characteristic
523	#390	C₂²×C₁₃₉	1	2	yes	—
524	#390	C₂²×C₁₃₉	1	2	yes	—
525	#389	C₂²×C₁₃₉	1	1	yes	characteristic
526	#389	C₂²×C₁₃₉	1	1	yes	characteristic
527	#389	C₂²×C₁₃₉	1	2	yes	—
528	#389	C₂²×C₁₃₉	1	1	yes	characteristic
529	#388	C₂²×C₁₃₉	1	2	yes	—
530	#388	C₂²×C₁₃₉	1	2	yes	—
531	#388	C₂²×C₁₃₉	1	2	yes	—
532	#388	C₂²×C₁₃₉	1	2	yes	—
533	#388	C₂²×C₁₃₉	1	2	yes	—
534	#388	C₂²×C₁₃₉	1	2	yes	—
535	#388	C₂²×C₁₃₉	1	2	yes	—
536	#388	C₂²×C₁₃₉	1	2	yes	—
537	#388	C₂²×C₁₃₉	1	2	yes	—
538	#388	C₂²×C₁₃₉	1	2	yes	—
539	#388	C₂²×C₁₃₉	1	2	yes	—
540	#388	C₂²×C₁₃₉	1	2	yes	—
541	#387	C₂²×C₁₃₉	1	2	yes	—
542	#387	C₂²×C₁₃₉	1	2	yes	—
543	#387	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#386	C₂²×C₁₃₉	1	2	yes	—
546	#386	C₂²×C₁₃₉	1	2	yes	—
547	#386	C₂²×C₁₃₉	1	2	yes	—
548	#386	C₂²×C₁₃₉	1	2	yes	—
549	#386	C₂²×C₁₃₉	1	2	yes	—
550	#385	C₂²×C₁₃₉	1	2	yes	—
551	#385	C₂²×C₁₃₉	1	2	yes	—
552	#385	C₂²×C₁₃₉	1	2	yes	—
553	#385	C₂²×C₁₃₉	1	2	yes	—
554	#385	C₂²×C₁₃₉	1	2	yes	—
555	#385	C₂²×C₁₃₉	1	2	yes	—
556	#385	C₂²×C₁₃₉	1	2	yes	—
557	#384	C₂²×C₁₃₉	1	2	yes	—
558	#382	C₂²×C₁₃₉	1	1	yes	characteristic
559	#380	C₂²×C₁₃₉	1	1	yes	characteristic
560	#380	C₂²×C₁₃₉	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
563	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
564	#376	C₂²×C₁₃₉	1	2	yes	—
565	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
578	#124	—	2	8	no	—
579	#124	—	4	2	no	—
580	#123	—	4	4	no	—
581	#123	—	4	4	no	—
582	#123	—	4	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	—	4	2	no	—
585	C₂²⋊Q₈	—	4	4	no	—
586	#121	—	4	2	no	—
587	#121	—	4	4	no	—
588	#121	—	4	2	no	—
589	C₄×Q₈	—	4	2	no	—
590	C₄×D₄	—	4	4	no	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄²	—	4	2	no	—
638	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
643	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	2	yes	—
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
667	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	1	no	—
672	C₂×Q₈	—	4	1	no	—
673	C₂×Q₈	—	4	1	no	—
674	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	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	C₂⁴×C₁₃₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	4	1	no	—
775	C₄²	—	4	1	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
799	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
800	Q₈	—	4	4	no	—
801	Q₈	—	8	2	no	—
802	D₄	—	4	8	no	—
803	D₄	—	8	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	4	no	—
806	D₄	—	8	4	no	—
807	D₄	—	8	4	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	8	4	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
857	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
858	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
859	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
860	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
883	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
884	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
885	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
886	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
887	C₂²	#585×C₁₃₉	1	1	yes	characteristic
888	C₂²	#585×C₁₃₉	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₂	—	4	2	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	2	no	—
908	C₂	#3459×C₁₃₉	1	1	yes	characteristic
909	C₂	#3517×C₁₃₉	1	1	yes	characteristic
910	C₂	#3522×C₁₃₉	1	1	yes	characteristic
911	C₂	#3535×C₁₃₉	1	1	yes	characteristic
912	C₂	#3537×C₁₃₉	1	1	yes	characteristic
913	C₂	#3545×C₁₃₉	1	1	yes	characteristic
914	C₂	#3547×C₁₃₉	1	1	yes	characteristic

	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. #2854×C₁₃₉	C₂	semidirect
2. #2850×C₁₃₉	C₂	semidirect
3. #2806×C₁₃₉	C₂	semidirect
4. #2797×C₁₃₉	C₂	semidirect
5. #2790×C₁₃₉	C₂	semidirect
6. #2733×C₁₃₉	C₂	semidirect
7. #2732×C₁₃₉	C₂	semidirect
8. #2730×C₁₃₉	C₂	semidirect
9. #2724×C₁₃₉	C₂	semidirect
10. #2708×C₁₃₉	C₂	semidirect
11. #2682×C₁₃₉	C₂	semidirect
12. #2680×C₁₃₉	C₂	semidirect
13. #2651×C₁₃₉	C₂	semidirect
14. #2531×C₁₃₉	C₂	semidirect
15. #2529×C₁₃₉	C₂	semidirect
16. #2464×C₁₃₉	C₂	semidirect
17. #2461×C₁₃₉	C₂	semidirect
18. #2326×C₁₃₉	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
457. #37219	C₁₃₉	direct (N × H)
458. C₁₃₉	#37219	direct (N × H)
459. #2854	C₂×C₁₃₉	semidirect
460. #2850	C₂×C₁₃₉	semidirect
461. #2806	C₂×C₁₃₉	semidirect
462. #2797	C₂×C₁₃₉	semidirect
463. #2790	C₂×C₁₃₉	semidirect
464. #2733	C₂×C₁₃₉	semidirect
465. #2732	C₂×C₁₃₉	semidirect
466. #2730	C₂×C₁₃₉	semidirect
467. #2724	C₂×C₁₃₉	semidirect
468. #2708	C₂×C₁₃₉	semidirect
469. #2682	C₂×C₁₃₉	semidirect
470. #2680	C₂×C₁₃₉	semidirect
471. #2651	C₂×C₁₃₉	semidirect
472. #2531	C₂×C₁₃₉	semidirect
473. #2529	C₂×C₁₃₉	semidirect
474. #2464	C₂×C₁₃₉	semidirect
475. #2461	C₂×C₁₃₉	semidirect
476. #2326	C₂×C₁₃₉	semidirect
477. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2854×C₁₃₉	2
#2850×C₁₃₉	2
#2806×C₁₃₉	2
#2797×C₁₃₉	2
#2790×C₁₃₉	2
#2733×C₁₃₉	2
#2732×C₁₃₉	2
#2730×C₁₃₉	2
#2724×C₁₃₉	2
#2708×C₁₃₉	2
#2682×C₁₃₉	2
#2680×C₁₃₉	2
#2651×C₁₃₉	2
#2531×C₁₃₉	2
#2529×C₁₃₉	2
#2464×C₁₃₉	2
#2461×C₁₃₉	2
#2326×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#37219	139

Subgroups — C139×#37219 #48031815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37219 #48031815