Subgroups — C₁₃₉×#36213 #48030809

Order 35584.

5420 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2430×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2410×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2409×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2406×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2405×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#385×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	—	2	16	no	—
19	C₂²×#41×C₁₃₉	—	2	8	no	—
20	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
21	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
22	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
23	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	#547×C₁₃₉	—	2	16	no	—
30	#546×C₁₃₉	—	2	8	no	—
31	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
34	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
35	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
39	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
42	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
51	#395×C₁₃₉	C₂²	1	2	yes	complemented
52	#395×C₁₃₉	C₂²	1	4	yes	complemented
53	#394×C₁₃₉	C₂²	1	4	yes	complemented
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#393×C₁₃₉	C₂²	1	2	yes	complemented
57	#392×C₁₃₉	C₂²	1	4	yes	complemented
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#391×C₁₃₉	C₂²	1	2	yes	complemented
60	#390×C₁₃₉	C₂²	1	2	yes	complemented
61	#386×C₁₃₉	C₂²	1	1	yes	characteristic
62	#386×C₁₃₉	C₂²	1	2	yes	—
63	#386×C₁₃₉	C₂²	1	2	yes	complemented
64	#386×C₁₃₉	C₂²	1	4	yes	complemented
65	#386×C₁₃₉	C₂²	1	4	yes	complemented
66	#386×C₁₃₉	C₂²	1	4	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	complemented
68	#385×C₁₃₉	C₂²	1	1	yes	characteristic
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	4	yes	complemented
74	#385×C₁₃₉	C₂²	1	4	yes	complemented
75	#385×C₁₃₉	C₂²	1	2	yes	complemented
76	#385×C₁₃₉	C₂²	1	4	yes	complemented
77	#385×C₁₃₉	C₂²	1	4	yes	complemented
78	#381×C₁₃₉	C₂²	1	4	yes	complemented
79	#380×C₁₃₉	C₂²	1	1	yes	characteristic
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#379×C₁₃₉	C₂²	1	1	yes	characteristic
82	#379×C₁₃₉	C₂²	1	2	yes	—
83	#379×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
86	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
87	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
89	C₂×#41×C₁₃₉	—	2	128	no	—
90	C₂×#41×C₁₃₉	—	2	8	no	—
91	C₂×#41×C₁₃₉	—	2	16	no	—
92	C₂×#41×C₁₃₉	—	2	16	no	—
93	C₂×#41×C₁₃₉	—	2	8	no	—
94	C₂×#41×C₁₃₉	—	2	8	no	—
95	C₂×#41×C₁₃₉	—	2	8	no	—
96	C₂×#41×C₁₃₉	—	2	4	no	—
97	C₂×#41×C₁₃₉	—	2	8	no	—
98	C₂×#41×C₁₃₉	—	2	16	no	—
99	C₂×#41×C₁₃₉	—	2	8	no	—
100	C₂×#41×C₁₃₉	D₄	1	16	yes	complemented
101	C₂²×Q₈×C₁₃₉	—	2	8	no	—
102	C₂²×Q₈×C₁₃₉	—	2	4	no	—
103	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
104	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃₉	—	2	8	no	—
107	C₂²×D₄×C₁₃₉	—	2	16	no	—
108	C₂²×D₄×C₁₃₉	—	2	8	no	—
109	C₂²×D₄×C₁₃₉	D₄	1	8	yes	complemented
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	—	2	8	no	—
120	C₂³×C₄×C₁₃₉	—	2	4	no	—
121	C₂³×C₄×C₁₃₉	—	2	16	no	—
122	C₂³×C₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
127	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
135	#124×C₁₃₉	—	2	4	no	—
136	#123×C₁₃₉	—	2	8	no	—
137	#123×C₁₃₉	—	2	16	no	—
138	#123×C₁₃₉	—	2	16	no	—
139	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
140	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
141	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
142	#121×C₁₃₉	—	2	4	no	—
143	#121×C₁₃₉	—	2	8	no	—
144	#121×C₁₃₉	—	2	16	no	—
145	#120×C₁₃₉	—	2	8	no	—
146	#120×C₁₃₉	—	2	4	no	—
147	C₄×D₄×C₁₃₉	—	2	4	no	—
148	C₄×D₄×C₁₃₉	—	2	8	no	—
149	C₄×D₄×C₁₃₉	—	2	4	no	—
150	C₄×D₄×C₁₃₉	—	2	8	no	—
151	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
162	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	4	yes	—
189	#95×C₁₃₉	C₂³	1	4	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	4	yes	—
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	C₂⁴×C₁₃₉	—	2	4	no	—
195	C₂⁴×C₁₃₉	—	2	8	no	—
196	C₂⁴×C₁₃₉	—	2	2	no	—
197	C₂⁴×C₁₃₉	—	2	4	no	—
198	C₂⁴×C₁₃₉	—	2	4	no	—
199	C₂⁴×C₁₃₉	—	2	2	no	—
200	C₂⁴×C₁₃₉	—	2	2	no	—
201	C₂⁴×C₁₃₉	—	4	4	no	—
202	C₂⁴×C₁₃₉	—	4	2	no	—
203	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
204	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	#41×C₁₃₉	—	2	128	no	—
210	#41×C₁₃₉	—	2	64	no	—
211	#41×C₁₃₉	—	2	64	no	—
212	#41×C₁₃₉	—	4	16	no	—
213	C₂×Q₈×C₁₃₉	—	2	32	no	—
214	C₂×Q₈×C₁₃₉	—	2	8	no	—
215	C₂×Q₈×C₁₃₉	—	2	4	no	—
216	C₂×Q₈×C₁₃₉	—	2	4	no	—
217	C₂×Q₈×C₁₃₉	—	2	4	no	—
218	C₂×Q₈×C₁₃₉	—	2	2	no	—
219	C₂×Q₈×C₁₃₉	—	2	4	no	—
220	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
221	C₂×D₄×C₁₃₉	—	2	64	no	—
222	C₂×D₄×C₁₃₉	—	2	8	no	—
223	C₂×D₄×C₁₃₉	—	2	8	no	—
224	C₂×D₄×C₁₃₉	—	2	8	no	—
225	C₂×D₄×C₁₃₉	—	2	8	no	—
226	C₂×D₄×C₁₃₉	—	2	8	no	—
227	C₂×D₄×C₁₃₉	—	2	32	no	—
228	C₂×D₄×C₁₃₉	—	2	2	no	—
229	C₂×D₄×C₁₃₉	—	2	4	no	—
230	C₂×D₄×C₁₃₉	—	2	4	no	—
231	C₂×D₄×C₁₃₉	—	2	8	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	2	2	no	—
234	C₂×D₄×C₁₃₉	—	2	4	no	—
235	C₂×D₄×C₁₃₉	—	2	8	no	—
236	C₂×D₄×C₁₃₉	—	2	4	no	—
237	C₂×D₄×C₁₃₉	—	2	4	no	—
238	C₂×D₄×C₁₃₉	—	4	2	no	—
239	C₂×D₄×C₁₃₉	—	4	4	no	—
240	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
241	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
242	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
243	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
244	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃₉	—	2	64	no	—
246	C₂²×C₄×C₁₃₉	—	2	32	no	—
247	C₂²×C₄×C₁₃₉	—	2	2	no	—
248	C₂²×C₄×C₁₃₉	—	2	4	no	—
249	C₂²×C₄×C₁₃₉	—	2	8	no	—
250	C₂²×C₄×C₁₃₉	—	2	4	no	—
251	C₂²×C₄×C₁₃₉	—	2	8	no	—
252	C₂²×C₄×C₁₃₉	—	2	8	no	—
253	C₂²×C₄×C₁₃₉	—	2	4	no	—
254	C₂²×C₄×C₁₃₉	—	2	8	no	—
255	C₂²×C₄×C₁₃₉	—	2	4	no	—
256	C₂²×C₄×C₁₃₉	—	2	8	no	—
257	C₂²×C₄×C₁₃₉	—	2	4	no	—
258	C₂²×C₄×C₁₃₉	—	2	8	no	—
259	C₂²×C₄×C₁₃₉	—	2	4	no	—
260	C₂²×C₄×C₁₃₉	—	2	4	no	—
261	C₂²×C₄×C₁₃₉	—	2	4	no	—
262	C₂²×C₄×C₁₃₉	—	2	4	no	—
263	C₂²×C₄×C₁₃₉	—	2	8	no	—
264	C₂²×C₄×C₁₃₉	—	2	8	no	—
265	C₂²×C₄×C₁₃₉	—	2	4	no	—
266	C₂²×C₄×C₁₃₉	—	2	2	no	—
267	C₂²×C₄×C₁₃₉	—	2	4	no	—
268	C₂²×C₄×C₁₃₉	—	2	8	no	—
269	C₂²×C₄×C₁₃₉	—	4	4	no	—
270	C₂²×C₄×C₁₃₉	—	4	4	no	—
271	C₂²×C₄×C₁₃₉	C₂×D₄	1	16	yes	—
272	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	2	8	no	—
288	C₄⋊C₄×C₁₃₉	—	2	8	no	—
289	C₄⋊C₄×C₁₃₉	—	2	8	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	4	no	—
292	C₄⋊C₄×C₁₃₉	—	2	2	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	8	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
314	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	complemented
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	4	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	4	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	8	no	—
323	C₂³×C₁₃₉	—	2	16	no	—
324	C₂³×C₁₃₉	—	2	16	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	4	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	4	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	1	no	—
337	C₂³×C₁₃₉	—	2	1	no	—
338	C₂³×C₁₃₉	—	2	1	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	4	8	no	—
341	C₂³×C₁₃₉	—	4	16	no	—
342	C₂³×C₁₃₉	—	4	8	no	—
343	C₂³×C₁₃₉	—	4	16	no	—
344	C₂³×C₁₃₉	—	4	8	no	—
345	C₂³×C₁₃₉	—	4	4	no	—
346	C₂³×C₁₃₉	—	4	4	no	—
347	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
348	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
349	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
350	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
351	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
352	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
353	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
354	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
355	Q₈×C₁₃₉	—	2	16	no	—
356	Q₈×C₁₃₉	—	2	16	no	—
357	Q₈×C₁₃₉	—	4	4	no	—
358	D₄×C₁₃₉	—	2	32	no	—
359	D₄×C₁₃₉	—	2	32	no	—
360	D₄×C₁₃₉	—	2	16	no	—
361	D₄×C₁₃₉	—	2	8	no	—
362	D₄×C₁₃₉	—	4	8	no	—
363	D₄×C₁₃₉	—	4	8	no	—
364	D₄×C₁₃₉	—	4	4	no	—
365	D₄×C₁₃₉	—	8	4	no	—
366	D₄×C₁₃₉	#120	1	16	yes	complemented
367	C₂×C₄×C₁₃₉	—	2	8	no	—
368	C₂×C₄×C₁₃₉	—	2	16	no	—
369	C₂×C₄×C₁₃₉	—	2	32	no	—
370	C₂×C₄×C₁₃₉	—	2	16	no	—
371	C₂×C₄×C₁₃₉	—	2	32	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	4	no	—
376	C₂×C₄×C₁₃₉	—	2	4	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	8	no	—
380	C₂×C₄×C₁₃₉	—	2	16	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	4	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	4	no	—
390	C₂×C₄×C₁₃₉	—	2	4	no	—
391	C₂×C₄×C₁₃₉	—	2	1	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	2	4	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	4	no	—
398	C₂×C₄×C₁₃₉	—	4	16	no	—
399	C₂×C₄×C₁₃₉	—	4	8	no	—
400	C₂×C₄×C₁₃₉	—	4	4	no	—
401	C₂×C₄×C₁₃₉	—	8	4	no	—
402	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
403	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
404	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
406	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	complemented
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	4	no	—
410	C₂²×C₁₃₉	—	2	8	no	—
411	C₂²×C₁₃₉	—	2	4	no	—
412	C₂²×C₁₃₉	—	2	4	no	—
413	C₂²×C₁₃₉	—	2	2	no	—
414	C₂²×C₁₃₉	—	2	4	no	—
415	C₂²×C₁₃₉	—	2	8	no	—
416	C₂²×C₁₃₉	—	2	4	no	—
417	C₂²×C₁₃₉	—	2	4	no	—
418	C₂²×C₁₃₉	—	2	4	no	—
419	C₂²×C₁₃₉	—	2	4	no	—
420	C₂²×C₁₃₉	—	2	4	no	—
421	C₂²×C₁₃₉	—	2	4	no	—
422	C₂²×C₁₃₉	—	4	32	no	—
423	C₂²×C₁₃₉	—	4	16	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	4	no	—
426	C₂²×C₁₃₉	—	4	2	no	—
427	C₂²×C₁₃₉	—	4	2	no	—
428	C₂²×C₁₃₉	—	4	4	no	—
429	C₂²×C₁₃₉	—	4	2	no	—
430	C₂²×C₁₃₉	—	4	1	no	—
431	C₂²×C₁₃₉	—	4	1	no	—
432	C₂²×C₁₃₉	—	4	2	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	2	no	—
435	C₂²×C₁₃₉	C₂×#120	1	8	yes	—
436	C₂²×C₁₃₉	#547	1	4	yes	complemented
437	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
438	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
439	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂²×C₁₃₉	#585	1	2	yes	—
442	C₄×C₁₃₉	—	2	4	no	—
443	C₄×C₁₃₉	—	2	8	no	—
444	C₄×C₁₃₉	—	2	2	no	—
445	C₄×C₁₃₉	—	2	4	no	—
446	C₄×C₁₃₉	—	4	1	no	—
447	C₄×C₁₃₉	—	4	2	no	—
448	C₄×C₁₃₉	—	4	1	no	—
449	C₄×C₁₃₉	—	4	4	no	—
450	C₄×C₁₃₉	—	4	1	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₄×C₁₃₉	—	4	2	no	—
453	C₄×C₁₃₉	C₂×#120	1	4	yes	—
454	C₂×C₁₃₉	—	2	4	no	—
455	C₂×C₁₃₉	—	2	8	no	—
456	C₂×C₁₃₉	—	4	4	no	—
457	C₂×C₁₃₉	—	4	4	no	—
458	C₂×C₁₃₉	—	8	1	no	—
459	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
460	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
461	C₂×C₁₃₉	D₄×#41	1	2	yes	—
462	C₂×C₁₃₉	#3485	1	1	yes	characteristic
463	C₂×C₁₃₉	#3489	1	2	yes	—
464	#36213	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₁₃₉	#36213	1	1	yes	characteristic, direct product factor, Sylow
466	C₂³×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	C₂×#547	C₂×C₁₃₉	1	2	yes	complemented
468	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2849	C₂×C₁₃₉	1	2	yes	complemented
470	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
471	#2434	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	#2432	C₂×C₁₃₉	1	2	yes	complemented
473	#2430	C₂×C₁₃₉	1	4	yes	complemented
474	#2410	C₂×C₁₃₉	1	2	yes	complemented
475	#2409	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2407	C₂×C₁₃₉	1	2	yes	complemented
477	#2406	C₂×C₁₃₉	1	4	yes	complemented
478	#2405	C₂×C₁₃₉	1	2	yes	complemented
479	#2339	C₂×C₁₃₉	1	2	yes	complemented
480	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	C₂×#385	C₂×C₁₃₉	1	2	yes	complemented
483	C₂²×#41	—	2	16	no	—
484	C₂²×#41	—	2	8	no	—
485	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
486	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
487	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
488	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
489	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
491	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
494	#547	—	2	16	no	—
495	#546	—	2	8	no	—
496	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
497	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
498	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
499	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
500	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
501	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
503	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
504	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
505	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
506	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
507	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
508	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
511	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
512	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
513	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
514	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
515	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
516	#395	C₂²×C₁₃₉	1	2	yes	complemented
517	#395	C₂²×C₁₃₉	1	4	yes	complemented
518	#394	C₂²×C₁₃₉	1	4	yes	complemented
519	#394	C₂²×C₁₃₉	1	4	yes	complemented
520	#394	C₂²×C₁₃₉	1	4	yes	complemented
521	#393	C₂²×C₁₃₉	1	2	yes	complemented
522	#392	C₂²×C₁₃₉	1	4	yes	complemented
523	#391	C₂²×C₁₃₉	1	2	yes	complemented
524	#391	C₂²×C₁₃₉	1	2	yes	complemented
525	#390	C₂²×C₁₃₉	1	2	yes	complemented
526	#386	C₂²×C₁₃₉	1	1	yes	characteristic
527	#386	C₂²×C₁₃₉	1	2	yes	—
528	#386	C₂²×C₁₃₉	1	4	yes	complemented
529	#386	C₂²×C₁₃₉	1	4	yes	complemented
530	#386	C₂²×C₁₃₉	1	4	yes	complemented
531	#386	C₂²×C₁₃₉	1	4	yes	complemented
532	#386	C₂²×C₁₃₉	1	2	yes	complemented
533	#385	C₂²×C₁₃₉	1	2	yes	—
534	#385	C₂²×C₁₃₉	1	2	yes	—
535	#385	C₂²×C₁₃₉	1	2	yes	—
536	#385	C₂²×C₁₃₉	1	2	yes	—
537	#385	C₂²×C₁₃₉	1	1	yes	characteristic
538	#385	C₂²×C₁₃₉	1	4	yes	complemented
539	#385	C₂²×C₁₃₉	1	4	yes	complemented
540	#385	C₂²×C₁₃₉	1	2	yes	complemented
541	#385	C₂²×C₁₃₉	1	4	yes	complemented
542	#385	C₂²×C₁₃₉	1	4	yes	complemented
543	#381	C₂²×C₁₃₉	1	4	yes	complemented
544	#380	C₂²×C₁₃₉	1	1	yes	characteristic
545	#380	C₂²×C₁₃₉	1	2	yes	complemented
546	#379	C₂²×C₁₃₉	1	2	yes	—
547	#379	C₂²×C₁₃₉	1	2	yes	—
548	#379	C₂²×C₁₃₉	1	1	yes	characteristic
549	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
550	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
551	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
552	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
554	C₂×#41	—	2	128	no	—
555	C₂×#41	—	2	8	no	—
556	C₂×#41	—	2	16	no	—
557	C₂×#41	—	2	16	no	—
558	C₂×#41	—	2	8	no	—
559	C₂×#41	—	2	8	no	—
560	C₂×#41	—	2	8	no	—
561	C₂×#41	—	2	4	no	—
562	C₂×#41	—	2	8	no	—
563	C₂×#41	—	2	16	no	—
564	C₂×#41	—	2	8	no	—
565	C₂×#41	D₄×C₁₃₉	1	16	yes	complemented
566	C₂²×Q₈	—	2	8	no	—
567	C₂²×Q₈	—	2	4	no	—
568	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
571	C₂²×D₄	—	2	8	no	—
572	C₂²×D₄	—	2	16	no	—
573	C₂²×D₄	—	2	8	no	—
574	C₂²×D₄	D₄×C₁₃₉	1	8	yes	complemented
575	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
580	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂³×C₄	—	2	8	no	—
585	C₂³×C₄	—	2	4	no	—
586	C₂³×C₄	—	2	16	no	—
587	C₂³×C₄	—	2	8	no	—
588	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
594	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
595	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
596	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₄⋊Q₈	—	2	8	no	—
600	#124	—	2	4	no	—
601	#123	—	2	8	no	—
602	#123	—	2	16	no	—
603	#123	—	2	16	no	—
604	C₂²⋊Q₈	—	2	8	no	—
605	C₂²⋊Q₈	—	2	4	no	—
606	C₂²⋊Q₈	—	2	8	no	—
607	#121	—	2	4	no	—
608	#121	—	2	8	no	—
609	#121	—	2	16	no	—
610	#120	—	2	8	no	—
611	#120	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	8	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	2	8	no	—
616	C₂×C₄⋊C₄	—	2	16	no	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
626	C₂×C₂²⋊C₄	—	2	8	no	—
627	C₂×C₂²⋊C₄	—	2	8	no	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	4	yes	—
652	#95	C₂³×C₁₃₉	1	4	yes	—
653	#95	C₂³×C₁₃₉	1	4	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	4	yes	—
658	#95	C₂³×C₁₃₉	1	4	yes	—
659	C₂⁴	—	2	4	no	—
660	C₂⁴	—	2	8	no	—
661	C₂⁴	—	2	2	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	2	4	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	4	4	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
669	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	#41	—	2	128	no	—
675	#41	—	2	64	no	—
676	#41	—	2	64	no	—
677	#41	—	4	16	no	—
678	C₂×Q₈	—	2	32	no	—
679	C₂×Q₈	—	2	8	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
686	C₂×D₄	—	2	64	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	8	no	—
689	C₂×D₄	—	2	8	no	—
690	C₂×D₄	—	2	8	no	—
691	C₂×D₄	—	2	8	no	—
692	C₂×D₄	—	2	32	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	8	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
706	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
707	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
708	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
709	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
710	C₂²×C₄	—	2	64	no	—
711	C₂²×C₄	—	2	32	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	8	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	8	no	—
717	C₂²×C₄	—	2	8	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	8	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	8	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	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	4	4	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	C₂×D₄×C₁₃₉	1	16	yes	—
737	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
738	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	8	no	—
753	C₄⋊C₄	—	2	8	no	—
754	C₄⋊C₄	—	2	8	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	8	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	8	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	8	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	8	no	—
774	C₂²⋊C₄	—	2	8	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	4	4	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	4	no	—
779	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	complemented
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	8	no	—
788	C₂³	—	2	16	no	—
789	C₂³	—	2	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	4	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	—	2	2	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	8	no	—
806	C₂³	—	4	16	no	—
807	C₂³	—	4	8	no	—
808	C₂³	—	4	16	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
813	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
814	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
815	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
816	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
817	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
818	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
819	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
820	Q₈	—	2	16	no	—
821	Q₈	—	2	16	no	—
822	Q₈	—	4	4	no	—
823	D₄	—	2	32	no	—
824	D₄	—	2	32	no	—
825	D₄	—	2	16	no	—
826	D₄	—	2	8	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	8	no	—
829	D₄	—	4	4	no	—
830	D₄	—	8	4	no	—
831	D₄	#120×C₁₃₉	1	16	yes	complemented
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	16	no	—
834	C₂×C₄	—	2	32	no	—
835	C₂×C₄	—	2	16	no	—
836	C₂×C₄	—	2	32	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	16	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	4	16	no	—
864	C₂×C₄	—	4	8	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
868	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
869	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
872	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	complemented
873	C₂²	—	2	2	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	8	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	4	32	no	—
888	C₂²	—	4	16	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂×#120×C₁₃₉	1	8	yes	—
901	C₂²	#547×C₁₃₉	1	4	yes	complemented
902	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
903	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
904	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
905	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
906	C₂²	#585×C₁₃₉	1	2	yes	—
907	C₄	—	2	4	no	—
908	C₄	—	2	8	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	4	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	C₂×#120×C₁₃₉	1	4	yes	—
919	C₂	—	2	4	no	—
920	C₂	—	2	8	no	—
921	C₂	—	4	4	no	—
922	C₂	—	4	4	no	—
923	C₂	—	8	1	no	—
924	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
925	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
926	C₂	D₄×#41×C₁₃₉	1	2	yes	—
927	C₂	#3485×C₁₃₉	1	1	yes	characteristic
928	C₂	#3489×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. C₂×#546×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2848×C₁₃₉	C₂	semidirect
6. #2434×C₁₃₉	C₂	semidirect
7. #2432×C₁₃₉	C₂	semidirect
8. #2430×C₁₃₉	C₂	semidirect
9. #2410×C₁₃₉	C₂	semidirect
10. #2409×C₁₃₉	C₂	semidirect
11. #2407×C₁₃₉	C₂	semidirect
12. #2406×C₁₃₉	C₂	semidirect
13. #2405×C₁₃₉	C₂	semidirect
14. #2339×C₁₃₉	C₂	semidirect
15. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×#120×C₁₃₉	C₂	semidirect
17. C₂×#385×C₁₃₉	C₂	semidirect
23. C₂²×#41×C₁₃₉	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×#124×C₁₃₉	C₂²	semidirect
33. C₂×#123×C₁₃₉	C₂²	semidirect
34. C₂×#123×C₁₃₉	C₂²	semidirect
35. C₂×#123×C₁₃₉	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
39. C₂×#121×C₁₃₉	C₂²	semidirect
40. C₂×#121×C₁₃₉	C₂²	semidirect
41. C₂×#121×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
51. #395×C₁₃₉	C₂²	semidirect
52. #395×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #393×C₁₃₉	C₂²	semidirect
57. #392×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
63. #386×C₁₃₉	C₂²	semidirect
64. #386×C₁₃₉	C₂²	semidirect
65. #386×C₁₃₉	C₂²	semidirect
66. #386×C₁₃₉	C₂²	semidirect
67. #386×C₁₃₉	C₂²	semidirect
73. #385×C₁₃₉	C₂²	semidirect
74. #385×C₁₃₉	C₂²	semidirect
75. #385×C₁₃₉	C₂²	semidirect
76. #385×C₁₃₉	C₂²	semidirect
77. #385×C₁₃₉	C₂²	semidirect
78. #381×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
86. C₂×#95×C₁₃₉	C₂²	semidirect
100. C₂×#41×C₁₃₉	D₄	semidirect
109. C₂²×D₄×C₁₃₉	D₄	semidirect
314. C₂²⋊C₄×C₁₃₉	#41	semidirect
366. D₄×C₁₃₉	#120	semidirect
407. C₂×C₄×C₁₃₉	C₂×#41	semidirect
436. C₂²×C₁₃₉	#547	semidirect
464. #36213	C₁₃₉	direct (N × H)
465. C₁₃₉	#36213	direct (N × H)
466. C₂³×#41	C₂×C₁₃₉	semidirect
467. C₂×#547	C₂×C₁₃₉	semidirect
468. C₂×#546	C₂×C₁₃₉	semidirect
469. #2849	C₂×C₁₃₉	semidirect
470. #2848	C₂×C₁₃₉	semidirect
471. #2434	C₂×C₁₃₉	semidirect
472. #2432	C₂×C₁₃₉	semidirect
473. #2430	C₂×C₁₃₉	semidirect
474. #2410	C₂×C₁₃₉	semidirect
475. #2409	C₂×C₁₃₉	semidirect
476. #2407	C₂×C₁₃₉	semidirect
477. #2406	C₂×C₁₃₉	semidirect
478. #2405	C₂×C₁₃₉	semidirect
479. #2339	C₂×C₁₃₉	semidirect
480. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
481. C₄×#120	C₂×C₁₃₉	semidirect
482. C₂×#385	C₂×C₁₃₉	semidirect
488. C₂²×#41	C₂²×C₁₃₉	semidirect
496. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
497. C₂×#124	C₂²×C₁₃₉	semidirect
498. C₂×#123	C₂²×C₁₃₉	semidirect
499. C₂×#123	C₂²×C₁₃₉	semidirect
500. C₂×#123	C₂²×C₁₃₉	semidirect
502. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
503. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
504. C₂×#121	C₂²×C₁₃₉	semidirect
505. C₂×#121	C₂²×C₁₃₉	semidirect
506. C₂×#121	C₂²×C₁₃₉	semidirect
510. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
511. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
512. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
513. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
516. #395	C₂²×C₁₃₉	semidirect
517. #395	C₂²×C₁₃₉	semidirect
518. #394	C₂²×C₁₃₉	semidirect
519. #394	C₂²×C₁₃₉	semidirect
520. #394	C₂²×C₁₃₉	semidirect
521. #393	C₂²×C₁₃₉	semidirect
522. #392	C₂²×C₁₃₉	semidirect
523. #391	C₂²×C₁₃₉	semidirect
524. #391	C₂²×C₁₃₉	semidirect
525. #390	C₂²×C₁₃₉	semidirect
528. #386	C₂²×C₁₃₉	semidirect
529. #386	C₂²×C₁₃₉	semidirect
530. #386	C₂²×C₁₃₉	semidirect
531. #386	C₂²×C₁₃₉	semidirect
532. #386	C₂²×C₁₃₉	semidirect
538. #385	C₂²×C₁₃₉	semidirect
539. #385	C₂²×C₁₃₉	semidirect
540. #385	C₂²×C₁₃₉	semidirect
541. #385	C₂²×C₁₃₉	semidirect
542. #385	C₂²×C₁₃₉	semidirect
543. #381	C₂²×C₁₃₉	semidirect
545. #380	C₂²×C₁₃₉	semidirect
550. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
551. C₂×#95	C₂²×C₁₃₉	semidirect
565. C₂×#41	D₄×C₁₃₉	semidirect
574. C₂²×D₄	D₄×C₁₃₉	semidirect
779. C₂²⋊C₄	#41×C₁₃₉	semidirect
831. D₄	#120×C₁₃₉	semidirect
872. C₂×C₄	C₂×#41×C₁₃₉	semidirect
901. C₂²	#547×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₃₉	2
C₂×#547×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2849×C₁₃₉	2
#2848×C₁₃₉	2
#2434×C₁₃₉	2
#2432×C₁₃₉	2
#2430×C₁₃₉	2
#2410×C₁₃₉	2
#2409×C₁₃₉	2
#2407×C₁₃₉	2
#2406×C₁₃₉	2
#2405×C₁₃₉	2
#2339×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#120×C₁₃₉	2
C₂×#385×C₁₃₉	2
#36213	139

Subgroups — C139×#36213 #48030809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36213 #48030809