Subgroups — C₁₃₉×#36161 #48030757

Order 35584.

2816 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2485×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2480×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2466×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2447×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2435×C₁₃₉	C₂	1	2	yes	maximal
12	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2280×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
20	#556×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#126×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	#397×C₁₃₉	C₂²	1	4	yes	complemented
44	#397×C₁₃₉	C₂²	1	4	yes	complemented
45	#397×C₁₃₉	C₂²	1	4	yes	complemented
46	#396×C₁₃₉	C₂²	1	4	yes	complemented
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	complemented
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#389×C₁₃₉	C₂²	1	2	yes	complemented
57	#389×C₁₃₉	C₂²	1	2	yes	complemented
58	#389×C₁₃₉	C₂²	1	4	yes	complemented
59	#388×C₁₃₉	C₂²	1	4	yes	complemented
60	#388×C₁₃₉	C₂²	1	4	yes	complemented
61	#388×C₁₃₉	C₂²	1	4	yes	complemented
62	#387×C₁₃₉	C₂²	1	2	yes	complemented
63	#387×C₁₃₉	C₂²	1	4	yes	complemented
64	#385×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	4	yes	—
66	#385×C₁₃₉	C₂²	1	4	yes	complemented
67	#385×C₁₃₉	C₂²	1	4	yes	complemented
68	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
69	#381×C₁₃₉	C₂²	1	4	yes	complemented
70	#380×C₁₃₉	C₂²	1	1	yes	characteristic
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	complemented
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#380×C₁₃₉	C₂²	1	2	yes	complemented
76	#380×C₁₃₉	C₂²	1	2	yes	complemented
77	#379×C₁₃₉	C₂²	1	4	yes	—
78	#379×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	—	2	4	no	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	—	2	8	no	—
95	C₂³×C₄×C₁₃₉	—	2	8	no	—
96	C₂³×C₄×C₁₃₉	—	4	4	no	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
106	#126×C₁₃₉	—	2	16	no	—
107	#124×C₁₃₉	—	2	8	no	—
108	#124×C₁₃₉	—	2	8	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
112	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
113	C₄×Q₈×C₁₃₉	—	2	8	no	—
114	C₄×Q₈×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	4	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
121	#117×C₁₃₉	—	2	8	no	—
122	#117×C₁₃₉	—	4	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	—	2	4	no	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	C₂⁴×C₁₃₉	—	2	4	no	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	2	4	no	—
181	C₂⁴×C₁₃₉	—	2	4	no	—
182	C₂⁴×C₁₃₉	—	4	2	no	—
183	C₂⁴×C₁₃₉	—	4	2	no	—
184	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂×Q₈×C₁₃₉	—	2	2	no	—
188	C₂×Q₈×C₁₃₉	—	2	4	no	—
189	C₂×Q₈×C₁₃₉	—	2	4	no	—
190	C₂×Q₈×C₁₃₉	—	2	2	no	—
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	—	2	32	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	2	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
202	C₂×D₄×C₁₃₉	#41	1	4	yes	—
203	C₂²×C₄×C₁₃₉	—	2	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	4	2	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	—	4	1	no	—
224	C₂²×C₄×C₁₃₉	—	4	32	no	—
225	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
226	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
227	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	8	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	8	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	4	no	—
258	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
273	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
274	C₄²×C₁₃₉	—	2	2	no	—
275	C₄²×C₁₃₉	—	2	2	no	—
276	C₄²×C₁₃₉	—	2	2	no	—
277	C₄²×C₁₃₉	—	2	8	no	—
278	C₄²×C₁₃₉	—	2	4	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	4	4	no	—
281	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	16	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	2	no	—
298	C₂³×C₁₃₉	—	2	2	no	—
299	C₂³×C₁₃₉	—	4	8	no	—
300	C₂³×C₁₃₉	—	4	8	no	—
301	C₂³×C₁₃₉	—	4	8	no	—
302	C₂³×C₁₃₉	—	4	8	no	—
303	C₂³×C₁₃₉	—	4	8	no	—
304	C₂³×C₁₃₉	—	4	8	no	—
305	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
306	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
307	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
308	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
309	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
310	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
311	Q₈×C₁₃₉	—	4	8	no	—
312	Q₈×C₁₃₉	—	4	4	no	—
313	D₄×C₁₃₉	—	2	16	no	—
314	D₄×C₁₃₉	—	2	8	no	—
315	D₄×C₁₃₉	—	2	8	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	8	no	—
325	C₂×C₄×C₁₃₉	—	2	8	no	—
326	C₂×C₄×C₁₃₉	—	2	16	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	2	4	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	4	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	1	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	4	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	4	8	no	—
352	C₂×C₄×C₁₃₉	—	4	4	no	—
353	C₂×C₄×C₁₃₉	—	4	8	no	—
354	C₂×C₄×C₁₃₉	—	4	8	no	—
355	C₂×C₄×C₁₃₉	—	4	8	no	—
356	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
363	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
364	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
365	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
366	C₂²×C₁₃₉	—	2	2	no	—
367	C₂²×C₁₃₉	—	2	2	no	—
368	C₂²×C₁₃₉	—	2	2	no	—
369	C₂²×C₁₃₉	—	2	2	no	—
370	C₂²×C₁₃₉	—	2	2	no	—
371	C₂²×C₁₃₉	—	2	2	no	—
372	C₂²×C₁₃₉	—	2	4	no	—
373	C₂²×C₁₃₉	—	2	4	no	—
374	C₂²×C₁₃₉	—	2	4	no	—
375	C₂²×C₁₃₉	—	2	4	no	—
376	C₂²×C₁₃₉	—	2	4	no	—
377	C₂²×C₁₃₉	—	2	4	no	—
378	C₂²×C₁₃₉	—	4	32	no	—
379	C₂²×C₁₃₉	—	4	2	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	—	4	2	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	2	no	—
387	C₂²×C₁₃₉	#556	1	4	yes	complemented
388	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
389	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
394	C₂²×C₁₃₉	#585	1	1	yes	characteristic
395	C₄×C₁₃₉	—	2	2	no	—
396	C₄×C₁₃₉	—	2	2	no	—
397	C₄×C₁₃₉	—	2	4	no	—
398	C₄×C₁₃₉	—	2	2	no	—
399	C₄×C₁₃₉	—	4	4	no	—
400	C₄×C₁₃₉	—	4	2	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	2	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₄×C₁₃₉	—	4	1	no	—
405	C₄×C₁₃₉	—	4	4	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	#525	1	4	yes	—
408	C₄×C₁₃₉	#546	1	4	yes	—
409	C₂×C₁₃₉	—	2	4	no	—
410	C₂×C₁₃₉	—	4	4	no	—
411	C₂×C₁₃₉	—	4	4	no	—
412	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
413	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
414	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
415	C₂×C₁₃₉	#3475	1	1	yes	characteristic
416	C₂×C₁₃₉	#3489	1	1	yes	characteristic
417	C₂×C₁₃₉	#3506	1	1	yes	characteristic
418	C₂×C₁₃₉	#3520	1	1	yes	characteristic
419	#36161	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₁₃₉	#36161	1	1	yes	characteristic, direct product factor, Sylow
421	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
423	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
424	#2848	C₂×C₁₃₉	1	2	yes	complemented
425	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
427	#2485	C₂×C₁₃₉	1	2	yes	complemented
428	#2480	C₂×C₁₃₉	1	4	yes	complemented
429	#2466	C₂×C₁₃₉	1	4	yes	complemented
430	#2447	C₂×C₁₃₉	1	2	yes	complemented
431	#2435	C₂×C₁₃₉	1	2	yes	—
432	#2415	C₂×C₁₃₉	1	2	yes	complemented
433	#2367	C₂×C₁₃₉	1	2	yes	complemented
434	#2360	C₂×C₁₃₉	1	2	yes	complemented
435	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
437	#2280	C₂×C₁₃₉	1	2	yes	complemented
438	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
440	#556	—	2	8	no	—
441	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
442	C₂×#126	C₂²×C₁₃₉	1	4	yes	complemented
443	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
444	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
445	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
448	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
449	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
450	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
451	C₂×C₄×D₄	—	2	8	no	—
452	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
456	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
459	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
460	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
463	#397	C₂²×C₁₃₉	1	4	yes	complemented
464	#397	C₂²×C₁₃₉	1	4	yes	complemented
465	#397	C₂²×C₁₃₉	1	4	yes	complemented
466	#396	C₂²×C₁₃₉	1	4	yes	complemented
467	#394	C₂²×C₁₃₉	1	4	yes	—
468	#394	C₂²×C₁₃₉	1	4	yes	—
469	#391	C₂²×C₁₃₉	1	2	yes	complemented
470	#391	C₂²×C₁₃₉	1	2	yes	complemented
471	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
472	#390	C₂²×C₁₃₉	1	2	yes	—
473	#390	C₂²×C₁₃₉	1	2	yes	—
474	#389	C₂²×C₁₃₉	1	2	yes	complemented
475	#389	C₂²×C₁₃₉	1	2	yes	complemented
476	#389	C₂²×C₁₃₉	1	4	yes	complemented
477	#389	C₂²×C₁₃₉	1	2	yes	complemented
478	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
479	#388	C₂²×C₁₃₉	1	4	yes	complemented
480	#388	C₂²×C₁₃₉	1	4	yes	complemented
481	#388	C₂²×C₁₃₉	1	4	yes	complemented
482	#387	C₂²×C₁₃₉	1	4	yes	complemented
483	#387	C₂²×C₁₃₉	1	2	yes	complemented
484	#385	C₂²×C₁₃₉	1	4	yes	—
485	#385	C₂²×C₁₃₉	1	2	yes	—
486	#385	C₂²×C₁₃₉	1	4	yes	complemented
487	#385	C₂²×C₁₃₉	1	4	yes	complemented
488	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
489	#381	C₂²×C₁₃₉	1	4	yes	complemented
490	#380	C₂²×C₁₃₉	1	2	yes	—
491	#380	C₂²×C₁₃₉	1	2	yes	—
492	#380	C₂²×C₁₃₉	1	1	yes	characteristic
493	#380	C₂²×C₁₃₉	1	2	yes	complemented
494	#380	C₂²×C₁₃₉	1	2	yes	complemented
495	#380	C₂²×C₁₃₉	1	2	yes	complemented
496	#380	C₂²×C₁₃₉	1	2	yes	complemented
497	#379	C₂²×C₁₃₉	1	4	yes	—
498	#379	C₂²×C₁₃₉	1	4	yes	—
499	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
500	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
501	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
502	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
505	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
506	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	4	no	—
511	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂³×C₄	—	2	8	no	—
515	C₂³×C₄	—	2	8	no	—
516	C₂³×C₄	—	4	4	no	—
517	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₄⋊Q₈	—	2	4	no	—
526	#126	—	2	16	no	—
527	#124	—	2	8	no	—
528	#124	—	2	8	no	—
529	C₂²⋊Q₈	—	2	8	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	4	4	no	—
533	C₄×Q₈	—	2	8	no	—
534	C₄×Q₈	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	8	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
541	#117	—	2	8	no	—
542	#117	—	4	4	no	—
543	C₂×C₄⋊C₄	—	2	4	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	1	yes	characteristic
561	C₂×C₂²⋊C₄	—	2	8	no	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄²	—	2	4	no	—
578	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
586	#95	C₂³×C₁₃₉	1	4	yes	—
587	#95	C₂³×C₁₃₉	1	4	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	4	yes	—
592	#95	C₂³×C₁₃₉	1	4	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	4	yes	—
596	#95	C₂³×C₁₃₉	1	4	yes	—
597	C₂⁴	—	2	4	no	—
598	C₂⁴	—	2	4	no	—
599	C₂⁴	—	2	4	no	—
600	C₂⁴	—	2	4	no	—
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	4	2	no	—
604	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
606	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×D₄	—	2	32	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
622	C₂×D₄	#41×C₁₃₉	1	4	yes	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	—	4	32	no	—
645	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
646	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
647	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
648	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	8	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	4	no	—
678	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	4	4	no	—
691	C₂²⋊C₄	—	4	4	no	—
692	C₂²⋊C₄	—	4	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	8	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	4	4	no	—
701	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	16	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	4	8	no	—
720	C₂³	—	4	8	no	—
721	C₂³	—	4	8	no	—
722	C₂³	—	4	8	no	—
723	C₂³	—	4	8	no	—
724	C₂³	—	4	8	no	—
725	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
726	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
727	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
728	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
729	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
730	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
731	Q₈	—	4	8	no	—
732	Q₈	—	4	4	no	—
733	D₄	—	2	16	no	—
734	D₄	—	2	8	no	—
735	D₄	—	2	8	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	8	no	—
746	C₂×C₄	—	2	16	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	8	no	—
776	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
777	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
780	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
781	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
782	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
783	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
784	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
785	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	4	32	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	#556×C₁₃₉	1	4	yes	complemented
808	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
809	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
810	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
811	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
812	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
813	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
814	C₂²	#585×C₁₃₉	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	4	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	2	no	—
827	C₄	#525×C₁₃₉	1	4	yes	—
828	C₄	#546×C₁₃₉	1	4	yes	—
829	C₂	—	2	4	no	—
830	C₂	—	4	4	no	—
831	C₂	—	4	4	no	—
832	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
833	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
834	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
835	C₂	#3475×C₁₃₉	1	1	yes	characteristic
836	C₂	#3489×C₁₃₉	1	1	yes	characteristic
837	C₂	#3506×C₁₃₉	1	1	yes	characteristic
838	C₂	#3520×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×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. C₂×#556×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2547×C₁₃₉	C₂	semidirect
6. #2538×C₁₃₉	C₂	semidirect
7. #2485×C₁₃₉	C₂	semidirect
8. #2480×C₁₃₉	C₂	semidirect
9. #2466×C₁₃₉	C₂	semidirect
10. #2447×C₁₃₉	C₂	semidirect
12. #2415×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2360×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. #2280×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#126×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
38. C₂×#117×C₁₃₉	C₂²	semidirect
39. C₂×#117×C₁₃₉	C₂²	semidirect
43. #397×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
45. #397×C₁₃₉	C₂²	semidirect
46. #396×C₁₃₉	C₂²	semidirect
49. #391×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
57. #389×C₁₃₉	C₂²	semidirect
58. #389×C₁₃₉	C₂²	semidirect
59. #388×C₁₃₉	C₂²	semidirect
60. #388×C₁₃₉	C₂²	semidirect
61. #388×C₁₃₉	C₂²	semidirect
62. #387×C₁₃₉	C₂²	semidirect
63. #387×C₁₃₉	C₂²	semidirect
66. #385×C₁₃₉	C₂²	semidirect
67. #385×C₁₃₉	C₂²	semidirect
68. #384×C₁₃₉	C₂²	semidirect
69. #381×C₁₃₉	C₂²	semidirect
73. #380×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
76. #380×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
387. C₂²×C₁₃₉	#556	semidirect
419. #36161	C₁₃₉	direct (N × H)
420. C₁₃₉	#36161	direct (N × H)
421. C₂×#556	C₂×C₁₃₉	semidirect
423. #2857	C₂×C₁₃₉	semidirect
424. #2848	C₂×C₁₃₉	semidirect
425. #2547	C₂×C₁₃₉	semidirect
426. #2538	C₂×C₁₃₉	semidirect
427. #2485	C₂×C₁₃₉	semidirect
428. #2480	C₂×C₁₃₉	semidirect
429. #2466	C₂×C₁₃₉	semidirect
430. #2447	C₂×C₁₃₉	semidirect
432. #2415	C₂×C₁₃₉	semidirect
433. #2367	C₂×C₁₃₉	semidirect
434. #2360	C₂×C₁₃₉	semidirect
435. #2354	C₂×C₁₃₉	semidirect
436. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
437. #2280	C₂×C₁₃₉	semidirect
441. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
442. C₂×#126	C₂²×C₁₃₉	semidirect
447. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
448. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
449. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
450. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
458. C₂×#117	C₂²×C₁₃₉	semidirect
459. C₂×#117	C₂²×C₁₃₉	semidirect
463. #397	C₂²×C₁₃₉	semidirect
464. #397	C₂²×C₁₃₉	semidirect
465. #397	C₂²×C₁₃₉	semidirect
466. #396	C₂²×C₁₃₉	semidirect
469. #391	C₂²×C₁₃₉	semidirect
470. #391	C₂²×C₁₃₉	semidirect
471. #391	C₂²×C₁₃₉	semidirect
474. #389	C₂²×C₁₃₉	semidirect
475. #389	C₂²×C₁₃₉	semidirect
476. #389	C₂²×C₁₃₉	semidirect
477. #389	C₂²×C₁₃₉	semidirect
478. #389	C₂²×C₁₃₉	semidirect
479. #388	C₂²×C₁₃₉	semidirect
480. #388	C₂²×C₁₃₉	semidirect
481. #388	C₂²×C₁₃₉	semidirect
482. #387	C₂²×C₁₃₉	semidirect
483. #387	C₂²×C₁₃₉	semidirect
486. #385	C₂²×C₁₃₉	semidirect
487. #385	C₂²×C₁₃₉	semidirect
488. #384	C₂²×C₁₃₉	semidirect
489. #381	C₂²×C₁₃₉	semidirect
493. #380	C₂²×C₁₃₉	semidirect
494. #380	C₂²×C₁₃₉	semidirect
495. #380	C₂²×C₁₃₉	semidirect
496. #380	C₂²×C₁₃₉	semidirect
499. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
500. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
501. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
504. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
807. C₂²	#556×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2857×C₁₃₉	2
#2848×C₁₃₉	2
#2547×C₁₃₉	2
#2538×C₁₃₉	2
#2485×C₁₃₉	2
#2480×C₁₃₉	2
#2466×C₁₃₉	2
#2447×C₁₃₉	2
#2435×C₁₃₉	2
#2415×C₁₃₉	2
#2367×C₁₃₉	2
#2360×C₁₃₉	2
#2354×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#2280×C₁₃₉	2
#36161	139

Subgroups — C139×#36161 #48030757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36161 #48030757