Subgroups — D₄×#123×C₁₃₉ #48030691

Order 35584.

3742 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#123×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2443×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2418×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2412×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2405×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	complemented
22	D₄²×C₁₃₉	—	2	8	no	—
23	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₃₉	—	2	16	no	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
47	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
48	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	#399×C₁₃₉	C₂²	1	4	yes	complemented
51	#398×C₁₃₉	C₂²	1	2	yes	complemented
52	#397×C₁₃₉	C₂²	1	4	yes	complemented
53	#397×C₁₃₉	C₂²	1	2	yes	complemented
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#394×C₁₃₉	C₂²	1	4	yes	complemented
57	#390×C₁₃₉	C₂²	1	2	yes	complemented
58	#390×C₁₃₉	C₂²	1	2	yes	complemented
59	#390×C₁₃₉	C₂²	1	2	yes	complemented
60	#389×C₁₃₉	C₂²	1	2	yes	complemented
61	#389×C₁₃₉	C₂²	1	2	yes	complemented
62	#388×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	4	yes	complemented
64	#387×C₁₃₉	C₂²	1	2	yes	complemented
65	#386×C₁₃₉	C₂²	1	1	yes	characteristic
66	#386×C₁₃₉	C₂²	1	4	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	complemented
68	#386×C₁₃₉	C₂²	1	4	yes	complemented
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#386×C₁₃₉	C₂²	1	2	yes	complemented
71	#385×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#385×C₁₃₉	C₂²	1	4	yes	complemented
74	#385×C₁₃₉	C₂²	1	4	yes	complemented
75	#384×C₁₃₉	C₂²	1	2	yes	complemented
76	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#381×C₁₃₉	C₂²	1	2	yes	complemented
78	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#380×C₁₃₉	C₂²	1	2	yes	complemented
80	#380×C₁₃₉	C₂²	1	4	yes	complemented
81	#379×C₁₃₉	C₂²	1	2	yes	complemented
82	#379×C₁₃₉	C₂²	1	4	yes	complemented
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
87	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	—	2	8	no	—
89	C₂²×D₄×C₁₃₉	—	2	8	no	—
90	C₂²×D₄×C₁₃₉	—	2	8	no	—
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	—	2	8	no	—
93	C₂²×D₄×C₁₃₉	—	4	4	no	—
94	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	—	2	8	no	—
106	C₂³×C₄×C₁₃₉	—	2	8	no	—
107	C₂³×C₄×C₁₃₉	—	4	4	no	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	#127×C₁₃₉	—	2	4	no	—
118	#123×C₁₃₉	—	2	8	no	—
119	#123×C₁₃₉	—	2	8	no	—
120	#123×C₁₃₉	—	2	16	no	—
121	#123×C₁₃₉	—	2	16	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#123×C₁₃₉	—	4	4	no	—
124	#123×C₁₃₉	D₄	1	8	yes	direct product factor
125	#121×C₁₃₉	—	2	4	no	—
126	#121×C₁₃₉	—	2	8	no	—
127	#121×C₁₃₉	—	2	4	no	—
128	#120×C₁₃₉	—	2	8	no	—
129	#120×C₁₃₉	—	2	8	no	—
130	C₄×D₄×C₁₃₉	—	2	8	no	—
131	C₄×D₄×C₁₃₉	—	2	16	no	—
132	C₄×D₄×C₁₃₉	—	2	8	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	C₄×D₄×C₁₃₉	—	2	8	no	—
135	C₄×D₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
150	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
151	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
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	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	—	2	4	no	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	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	C₂⁴×C₁₃₉	—	2	4	no	—
187	C₂⁴×C₁₃₉	—	2	8	no	—
188	C₂⁴×C₁₃₉	—	2	4	no	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	—	2	4	no	—
191	C₂⁴×C₁₃₉	—	2	8	no	—
192	C₂⁴×C₁₃₉	—	4	4	no	—
193	C₂⁴×C₁₃₉	—	4	2	no	—
194	C₂⁴×C₁₃₉	—	4	4	no	—
195	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
196	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	8	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	2	32	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	4	no	—
208	C₂×D₄×C₁₃₉	—	2	4	no	—
209	C₂×D₄×C₁₃₉	—	2	4	no	—
210	C₂×D₄×C₁₃₉	—	2	4	no	—
211	C₂×D₄×C₁₃₉	—	2	8	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	2	no	—
215	C₂×D₄×C₁₃₉	—	2	4	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	4	2	no	—
219	C₂×D₄×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	4	4	no	—
221	C₂×D₄×C₁₃₉	—	4	32	no	—
222	C₂×D₄×C₁₃₉	—	4	16	no	—
223	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
224	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
226	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₁₃₉	#41	1	8	yes	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	8	no	—
234	C₂²×C₄×C₁₃₉	—	2	8	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	8	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	8	no	—
240	C₂²×C₄×C₁₃₉	—	2	8	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	2	8	no	—
244	C₂²×C₄×C₁₃₉	—	2	4	no	—
245	C₂²×C₄×C₁₃₉	—	4	4	no	—
246	C₂²×C₄×C₁₃₉	—	4	4	no	—
247	C₂²×C₄×C₁₃₉	—	4	4	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	32	no	—
251	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	4	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	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	8	no	—
268	C₄⋊C₄×C₁₃₉	—	2	8	no	—
269	C₄⋊C₄×C₁₃₉	—	2	8	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	4	no	—
275	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
276	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
294	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
295	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
296	C₄²×C₁₃₉	—	2	4	no	—
297	C₄²×C₁₃₉	—	2	4	no	—
298	C₄²×C₁₃₉	—	2	2	no	—
299	C₄²×C₁₃₉	—	2	4	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	4	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	16	no	—
306	C₂³×C₁₃₉	—	2	16	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	4	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	1	no	—
313	C₂³×C₁₃₉	—	2	4	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	4	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	4	no	—
320	C₂³×C₁₃₉	—	4	8	no	—
321	C₂³×C₁₃₉	—	4	16	no	—
322	C₂³×C₁₃₉	—	4	16	no	—
323	C₂³×C₁₃₉	—	4	8	no	—
324	C₂³×C₁₃₉	—	4	16	no	—
325	C₂³×C₁₃₉	—	4	8	no	—
326	C₂³×C₁₃₉	—	8	4	no	—
327	C₂³×C₁₃₉	—	8	8	no	—
328	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
329	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
330	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
331	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
332	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
333	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
334	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
336	D₄×C₁₃₉	—	2	16	no	—
337	D₄×C₁₃₉	—	2	8	no	—
338	D₄×C₁₃₉	—	2	8	no	—
339	D₄×C₁₃₉	—	4	8	no	—
340	D₄×C₁₃₉	—	4	8	no	—
341	D₄×C₁₃₉	—	4	8	no	—
342	D₄×C₁₃₉	—	4	8	no	—
343	D₄×C₁₃₉	—	4	4	no	—
344	D₄×C₁₃₉	—	8	4	no	—
345	D₄×C₁₃₉	#123	1	16	yes	direct product factor
346	C₂×C₄×C₁₃₉	—	2	8	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	8	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	4	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	4	no	—
361	C₂×C₄×C₁₃₉	—	2	4	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	4	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	4	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	4	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	—	4	16	no	—
375	C₂×C₄×C₁₃₉	—	4	16	no	—
376	C₂×C₄×C₁₃₉	—	4	16	no	—
377	C₂×C₄×C₁₃₉	—	4	8	no	—
378	C₂×C₄×C₁₃₉	—	4	4	no	—
379	C₂×C₄×C₁₃₉	—	4	8	no	—
380	C₂×C₄×C₁₃₉	—	4	4	no	—
381	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
387	C₂²×C₁₃₉	—	2	2	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	2	8	no	—
390	C₂²×C₁₃₉	—	2	4	no	—
391	C₂²×C₁₃₉	—	2	2	no	—
392	C₂²×C₁₃₉	—	2	4	no	—
393	C₂²×C₁₃₉	—	2	4	no	—
394	C₂²×C₁₃₉	—	2	8	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	2	no	—
398	C₂²×C₁₃₉	—	2	4	no	—
399	C₂²×C₁₃₉	—	2	4	no	—
400	C₂²×C₁₃₉	—	4	32	no	—
401	C₂²×C₁₃₉	—	4	1	no	—
402	C₂²×C₁₃₉	—	4	4	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	4	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	4	no	—
409	C₂²×C₁₃₉	—	4	2	no	—
410	C₂²×C₁₃₉	—	4	4	no	—
411	C₂²×C₁₃₉	—	8	16	no	—
412	C₂²×C₁₃₉	C₂×#123	1	8	yes	complemented
413	C₂²×C₁₃₉	D₄²	1	4	yes	—
414	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
415	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
416	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
417	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₁₃₉	#585	1	2	yes	—
419	C₄×C₁₃₉	—	2	2	no	—
420	C₄×C₁₃₉	—	2	4	no	—
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	2	4	no	—
423	C₄×C₁₃₉	—	4	1	no	—
424	C₄×C₁₃₉	—	4	4	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	4	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	1	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₄×C₁₃₉	C₂×#123	1	4	yes	complemented
431	C₂×C₁₃₉	—	2	4	no	—
432	C₂×C₁₃₉	—	2	8	no	—
433	C₂×C₁₃₉	—	4	4	no	—
434	C₂×C₁₃₉	—	4	2	no	—
435	C₂×C₁₃₉	—	8	2	no	—
436	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
437	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
438	C₂×C₁₃₉	D₄×#41	1	2	yes	—
439	C₂×C₁₃₉	#3485	1	1	yes	characteristic
440	C₂×C₁₃₉	#3513	1	2	yes	—
441	D₄×#123	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₁₃₉	D₄×#123	1	1	yes	characteristic, direct product factor, Sylow
443	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic
444	C₂²×#123	C₂×C₁₃₉	1	2	yes	complemented
445	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	#2849	C₂×C₁₃₉	1	2	yes	complemented
448	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2445	C₂×C₁₃₉	1	2	yes	complemented
451	#2443	C₂×C₁₃₉	1	4	yes	complemented
452	#2422	C₂×C₁₃₉	1	2	yes	complemented
453	#2418	C₂×C₁₃₉	1	4	yes	complemented
454	#2412	C₂×C₁₃₉	1	2	yes	complemented
455	#2405	C₂×C₁₃₉	1	2	yes	complemented
456	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
457	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
459	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
462	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	complemented
464	D₄²	—	2	8	no	—
465	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₂×#123	—	2	16	no	—
467	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
470	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
471	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
472	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
473	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
474	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
479	C₂×C₄×D₄	—	2	8	no	—
480	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
485	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
486	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
487	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
488	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
489	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
490	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
491	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
492	#399	C₂²×C₁₃₉	1	4	yes	complemented
493	#398	C₂²×C₁₃₉	1	2	yes	complemented
494	#397	C₂²×C₁₃₉	1	4	yes	complemented
495	#397	C₂²×C₁₃₉	1	2	yes	complemented
496	#394	C₂²×C₁₃₉	1	4	yes	complemented
497	#394	C₂²×C₁₃₉	1	4	yes	complemented
498	#394	C₂²×C₁₃₉	1	4	yes	complemented
499	#390	C₂²×C₁₃₉	1	2	yes	complemented
500	#390	C₂²×C₁₃₉	1	2	yes	complemented
501	#390	C₂²×C₁₃₉	1	2	yes	complemented
502	#389	C₂²×C₁₃₉	1	2	yes	complemented
503	#389	C₂²×C₁₃₉	1	2	yes	complemented
504	#388	C₂²×C₁₃₉	1	4	yes	complemented
505	#388	C₂²×C₁₃₉	1	2	yes	complemented
506	#387	C₂²×C₁₃₉	1	2	yes	complemented
507	#386	C₂²×C₁₃₉	1	1	yes	characteristic
508	#386	C₂²×C₁₃₉	1	4	yes	complemented
509	#386	C₂²×C₁₃₉	1	4	yes	complemented
510	#386	C₂²×C₁₃₉	1	4	yes	complemented
511	#386	C₂²×C₁₃₉	1	4	yes	complemented
512	#386	C₂²×C₁₃₉	1	2	yes	complemented
513	#385	C₂²×C₁₃₉	1	4	yes	complemented
514	#385	C₂²×C₁₃₉	1	4	yes	complemented
515	#385	C₂²×C₁₃₉	1	4	yes	complemented
516	#385	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
517	#384	C₂²×C₁₃₉	1	2	yes	complemented
518	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
519	#381	C₂²×C₁₃₉	1	2	yes	complemented
520	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
521	#380	C₂²×C₁₃₉	1	2	yes	complemented
522	#380	C₂²×C₁₃₉	1	4	yes	complemented
523	#379	C₂²×C₁₃₉	1	2	yes	complemented
524	#379	C₂²×C₁₃₉	1	4	yes	complemented
525	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
528	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
529	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
530	C₂²×D₄	—	2	8	no	—
531	C₂²×D₄	—	2	8	no	—
532	C₂²×D₄	—	2	8	no	—
533	C₂²×D₄	—	2	4	no	—
534	C₂²×D₄	—	2	8	no	—
535	C₂²×D₄	—	4	4	no	—
536	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
537	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂³×C₄	—	2	8	no	—
548	C₂³×C₄	—	2	8	no	—
549	C₂³×C₄	—	4	4	no	—
550	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
559	#127	—	2	4	no	—
560	#123	—	2	8	no	—
561	#123	—	2	8	no	—
562	#123	—	2	16	no	—
563	#123	—	2	16	no	—
564	#123	—	2	8	no	—
565	#123	—	4	4	no	—
566	#123	D₄×C₁₃₉	1	8	yes	direct product factor
567	#121	—	2	4	no	—
568	#121	—	2	8	no	—
569	#121	—	2	4	no	—
570	#120	—	2	8	no	—
571	#120	—	2	8	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	2	16	no	—
574	C₄×D₄	—	2	8	no	—
575	C₄×D₄	—	2	4	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	2	4	no	—
578	C₂×C₄⋊C₄	—	2	4	no	—
579	C₂×C₄⋊C₄	—	2	16	no	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	—	2	8	no	—
592	C₂×C₂²⋊C₄	—	2	8	no	—
593	C₂×C₂²⋊C₄	—	2	16	no	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄²	—	2	4	no	—
615	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	4	yes	—
625	#95	C₂³×C₁₃₉	1	4	yes	—
626	#95	C₂³×C₁₃₉	1	4	yes	—
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	C₂⁴	—	2	4	no	—
629	C₂⁴	—	2	8	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	2	4	no	—
633	C₂⁴	—	2	8	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	4	no	—
637	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
638	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
642	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	8	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	32	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	32	no	—
664	C₂×D₄	—	4	16	no	—
665	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
666	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
667	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
668	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
669	C₂×D₄	#41×C₁₃₉	1	8	yes	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	8	no	—
676	C₂²×C₄	—	2	8	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	8	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	8	no	—
682	C₂²×C₄	—	2	8	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	8	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	4	4	no	—
688	C₂²×C₄	—	4	4	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	32	no	—
693	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
694	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
695	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
700	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	8	no	—
710	C₄⋊C₄	—	2	8	no	—
711	C₄⋊C₄	—	2	8	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	4	no	—
717	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
718	C₂²⋊C₄	—	2	8	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	2	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	8	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	8	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	4	no	—
735	C₂²⋊C₄	—	4	4	no	—
736	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
737	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	4	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	16	no	—
748	C₂³	—	2	16	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	4	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	16	no	—
764	C₂³	—	4	16	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	16	no	—
767	C₂³	—	4	8	no	—
768	C₂³	—	8	4	no	—
769	C₂³	—	8	8	no	—
770	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
771	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
772	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
773	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
774	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
775	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
776	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
777	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
778	D₄	—	2	16	no	—
779	D₄	—	2	8	no	—
780	D₄	—	2	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	4	no	—
786	D₄	—	8	4	no	—
787	D₄	#123×C₁₃₉	1	16	yes	direct product factor
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	4	16	no	—
817	C₂×C₄	—	4	16	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	—	4	16	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
825	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
827	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
828	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	8	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	8	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	4	32	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	8	16	no	—
854	C₂²	C₂×#123×C₁₃₉	1	8	yes	complemented
855	C₂²	D₄²×C₁₃₉	1	4	yes	—
856	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
857	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
858	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
859	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
860	C₂²	#585×C₁₃₉	1	2	yes	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	4	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	4	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	C₂×#123×C₁₃₉	1	4	yes	complemented
873	C₂	—	2	4	no	—
874	C₂	—	2	8	no	—
875	C₂	—	4	4	no	—
876	C₂	—	4	2	no	—
877	C₂	—	8	2	no	—
878	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
879	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
880	C₂	D₄×#41×C₁₃₉	1	2	yes	—
881	C₂	#3485×C₁₃₉	1	1	yes	characteristic
882	C₂	#3513×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×D₄²×C₁₃₉	C₂
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. C₂²×#123×C₁₃₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2849×C₁₃₉	C₂	semidirect
6. #2501×C₁₃₉	C₂	semidirect
7. #2486×C₁₃₉	C₂	semidirect
8. #2445×C₁₃₉	C₂	semidirect
9. #2443×C₁₃₉	C₂	semidirect
10. #2422×C₁₃₉	C₂	semidirect
11. #2418×C₁₃₉	C₂	semidirect
12. #2412×C₁₃₉	C₂	semidirect
13. #2405×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
15. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
16. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
17. C₄×#123×C₁₃₉	C₂	semidirect
21. C₂⁴×C₄×C₁₃₉	C₂²	semidirect
27. C₂×#123×C₁₃₉	C₂²	semidirect
28. C₂×#123×C₁₃₉	C₂²	semidirect
29. C₂×#123×C₁₃₉	C₂²	semidirect
30. C₂×#123×C₁₃₉	C₂²	semidirect
31. C₂×#123×C₁₃₉	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
49. C₂²×C₄²×C₁₃₉	C₂²	semidirect
50. #399×C₁₃₉	C₂²	semidirect
51. #398×C₁₃₉	C₂²	semidirect
52. #397×C₁₃₉	C₂²	semidirect
53. #397×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
57. #390×C₁₃₉	C₂²	semidirect
58. #390×C₁₃₉	C₂²	semidirect
59. #390×C₁₃₉	C₂²	semidirect
60. #389×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #388×C₁₃₉	C₂²	semidirect
63. #388×C₁₃₉	C₂²	semidirect
64. #387×C₁₃₉	C₂²	semidirect
66. #386×C₁₃₉	C₂²	semidirect
67. #386×C₁₃₉	C₂²	semidirect
68. #386×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #385×C₁₃₉	C₂²	semidirect
74. #385×C₁₃₉	C₂²	semidirect
75. #384×C₁₃₉	C₂²	semidirect
76. #381×C₁₃₉	C₂²	semidirect
77. #381×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #379×C₁₃₉	C₂²	semidirect
82. #379×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. #123×C₁₃₉	D₄	direct (N × H)
252. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
275. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
294. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
295. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
345. D₄×C₁₃₉	#123	direct (N × H)
412. C₂²×C₁₃₉	C₂×#123	semidirect
430. C₄×C₁₃₉	C₂×#123	semidirect
441. D₄×#123	C₁₃₉	direct (N × H)
442. C₁₃₉	D₄×#123	direct (N × H)
444. C₂²×#123	C₂×C₁₃₉	semidirect
445. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
446. #2854	C₂×C₁₃₉	semidirect
447. #2849	C₂×C₁₃₉	semidirect
448. #2501	C₂×C₁₃₉	semidirect
449. #2486	C₂×C₁₃₉	semidirect
450. #2445	C₂×C₁₃₉	semidirect
451. #2443	C₂×C₁₃₉	semidirect
452. #2422	C₂×C₁₃₉	semidirect
453. #2418	C₂×C₁₃₉	semidirect
454. #2412	C₂×C₁₃₉	semidirect
455. #2405	C₂×C₁₃₉	semidirect
456. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
457. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
458. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
459. C₄×#123	C₂×C₁₃₉	semidirect
463. C₂⁴×C₄	C₂²×C₁₃₉	semidirect
469. C₂×#123	C₂²×C₁₃₉	semidirect
470. C₂×#123	C₂²×C₁₃₉	semidirect
471. C₂×#123	C₂²×C₁₃₉	semidirect
472. C₂×#123	C₂²×C₁₃₉	semidirect
473. C₂×#123	C₂²×C₁₃₉	semidirect
484. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
485. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
486. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
487. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
488. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
489. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
490. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
491. C₂²×C₄²	C₂²×C₁₃₉	semidirect
492. #399	C₂²×C₁₃₉	semidirect
493. #398	C₂²×C₁₃₉	semidirect
494. #397	C₂²×C₁₃₉	semidirect
495. #397	C₂²×C₁₃₉	semidirect
496. #394	C₂²×C₁₃₉	semidirect
497. #394	C₂²×C₁₃₉	semidirect
498. #394	C₂²×C₁₃₉	semidirect
499. #390	C₂²×C₁₃₉	semidirect
500. #390	C₂²×C₁₃₉	semidirect
501. #390	C₂²×C₁₃₉	semidirect
502. #389	C₂²×C₁₃₉	semidirect
503. #389	C₂²×C₁₃₉	semidirect
504. #388	C₂²×C₁₃₉	semidirect
505. #388	C₂²×C₁₃₉	semidirect
506. #387	C₂²×C₁₃₉	semidirect
508. #386	C₂²×C₁₃₉	semidirect
509. #386	C₂²×C₁₃₉	semidirect
510. #386	C₂²×C₁₃₉	semidirect
511. #386	C₂²×C₁₃₉	semidirect
512. #386	C₂²×C₁₃₉	semidirect
513. #385	C₂²×C₁₃₉	semidirect
514. #385	C₂²×C₁₃₉	semidirect
515. #385	C₂²×C₁₃₉	semidirect
516. #385	C₂²×C₁₃₉	semidirect
517. #384	C₂²×C₁₃₉	semidirect
518. #381	C₂²×C₁₃₉	semidirect
519. #381	C₂²×C₁₃₉	semidirect
520. #380	C₂²×C₁₃₉	semidirect
521. #380	C₂²×C₁₃₉	semidirect
522. #380	C₂²×C₁₃₉	semidirect
523. #379	C₂²×C₁₃₉	semidirect
524. #379	C₂²×C₁₃₉	semidirect
525. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
526. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
527. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
566. #123	D₄×C₁₃₉	direct (N × H)
694. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
717. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
736. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
737. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
787. D₄	#123×C₁₃₉	direct (N × H)
854. C₂²	C₂×#123×C₁₃₉	semidirect
872. C₄	C₂×#123×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₃₉	2
C₂²×#123×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2854×C₁₃₉	2
#2849×C₁₃₉	2
#2501×C₁₃₉	2
#2486×C₁₃₉	2
#2445×C₁₃₉	2
#2443×C₁₃₉	2
#2422×C₁₃₉	2
#2418×C₁₃₉	2
#2412×C₁₃₉	2
#2405×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#123×C₁₃₉	2
D₄×#123	139

Subgroups — D4×#123×C139 #48030691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#123×C₁₃₉ #48030691