Subgroups — C₁₃₉×#36236 #48030832

Order 35584.

3426 conjugacy classes of subgroups.

The subgroup lattice has 864 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×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2444×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2418×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2412×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2405×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2349×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#386×C₁₃₉	C₂	1	2	yes	maximal, 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	C₂²	1	1	yes	characteristic
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
44	#400×C₁₃₉	C₂²	1	2	yes	complemented
45	#399×C₁₃₉	C₂²	1	2	yes	complemented
46	#397×C₁₃₉	C₂²	1	4	yes	complemented
47	#397×C₁₃₉	C₂²	1	4	yes	complemented
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#394×C₁₃₉	C₂²	1	4	yes	complemented
50	#394×C₁₃₉	C₂²	1	4	yes	complemented
51	#390×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	complemented
53	#390×C₁₃₉	C₂²	1	2	yes	complemented
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	2	yes	complemented
56	#388×C₁₃₉	C₂²	1	2	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#387×C₁₃₉	C₂²	1	2	yes	complemented
59	#386×C₁₃₉	C₂²	1	1	yes	characteristic
60	#386×C₁₃₉	C₂²	1	2	yes	—
61	#386×C₁₃₉	C₂²	1	2	yes	complemented
62	#386×C₁₃₉	C₂²	1	2	yes	complemented
63	#386×C₁₃₉	C₂²	1	4	yes	complemented
64	#386×C₁₃₉	C₂²	1	4	yes	complemented
65	#386×C₁₃₉	C₂²	1	4	yes	complemented
66	#386×C₁₃₉	C₂²	1	2	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	complemented
68	#386×C₁₃₉	C₂²	1	4	yes	complemented
69	#385×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	2	yes	complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#382×C₁₃₉	C₂²	1	2	yes	complemented
74	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#381×C₁₃₉	C₂²	1	4	yes	complemented
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#380×C₁₃₉	C₂²	1	2	yes	complemented
78	#380×C₁₃₉	C₂²	1	4	yes	complemented
79	#379×C₁₃₉	C₂²	1	2	yes	complemented
80	#379×C₁₃₉	C₂²	1	4	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	—	2	8	no	—
88	C₂²×D₄×C₁₃₉	—	2	8	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	—	2	8	no	—
91	C₂²×D₄×C₁₃₉	—	2	8	no	—
92	C₂²×D₄×C₁₃₉	—	4	4	no	—
93	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	—	2	8	no	—
105	C₂³×C₄×C₁₃₉	—	4	8	no	—
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	#127×C₁₃₉	—	2	4	no	—
116	#123×C₁₃₉	—	2	4	no	—
117	#123×C₁₃₉	—	4	8	no	—
118	#123×C₁₃₉	—	4	4	no	—
119	#121×C₁₃₉	—	2	4	no	—
120	#121×C₁₃₉	—	2	8	no	—
121	#121×C₁₃₉	—	2	4	no	—
122	#120×C₁₃₉	—	2	8	no	—
123	#120×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	8	no	—
125	C₄×D₄×C₁₃₉	—	2	16	no	—
126	C₄×D₄×C₁₃₉	—	2	8	no	—
127	C₄×D₄×C₁₃₉	—	2	4	no	—
128	C₄×D₄×C₁₃₉	—	2	8	no	—
129	C₄×D₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
141	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
142	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃₉	—	2	4	no	—
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	C₂⁴×C₁₃₉	—	2	8	no	—
180	C₂⁴×C₁₃₉	—	2	4	no	—
181	C₂⁴×C₁₃₉	—	2	4	no	—
182	C₂⁴×C₁₃₉	—	2	4	no	—
183	C₂⁴×C₁₃₉	—	2	4	no	—
184	C₂⁴×C₁₃₉	—	2	8	no	—
185	C₂⁴×C₁₃₉	—	4	4	no	—
186	C₂⁴×C₁₃₉	—	4	4	no	—
187	C₂⁴×C₁₃₉	—	4	2	no	—
188	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
189	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
191	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
193	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂×D₄×C₁₃₉	—	2	2	no	—
195	C₂×D₄×C₁₃₉	—	2	8	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	2	32	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	2	8	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	2	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	—	4	2	no	—
212	C₂×D₄×C₁₃₉	—	4	2	no	—
213	C₂×D₄×C₁₃₉	—	4	4	no	—
214	C₂×D₄×C₁₃₉	—	4	32	no	—
215	C₂×D₄×C₁₃₉	—	4	16	no	—
216	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
217	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
218	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
219	C₂×D₄×C₁₃₉	#41	1	4	yes	—
220	C₂×D₄×C₁₃₉	#41	1	8	yes	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	4	no	—
224	C₂²×C₄×C₁₃₉	—	2	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	8	no	—
227	C₂²×C₄×C₁₃₉	—	2	8	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	8	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	4	no	—
235	C₂²×C₄×C₁₃₉	—	2	8	no	—
236	C₂²×C₄×C₁₃₉	—	2	8	no	—
237	C₂²×C₄×C₁₃₉	—	4	4	no	—
238	C₂²×C₄×C₁₃₉	—	4	4	no	—
239	C₂²×C₄×C₁₃₉	—	4	4	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	—	4	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	4	no	—
243	C₂²×C₄×C₁₃₉	—	4	32	no	—
244	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	2	no	—
260	C₄⋊C₄×C₁₃₉	—	2	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	4	4	no	—
265	C₄⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
286	C₄²×C₁₃₉	—	2	4	no	—
287	C₄²×C₁₃₉	—	2	4	no	—
288	C₄²×C₁₃₉	—	2	2	no	—
289	C₄²×C₁₃₉	—	2	4	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	4	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	16	no	—
296	C₂³×C₁₃₉	—	2	16	no	—
297	C₂³×C₁₃₉	—	2	1	no	—
298	C₂³×C₁₃₉	—	2	2	no	—
299	C₂³×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	1	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	4	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	4	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	4	8	no	—
311	C₂³×C₁₃₉	—	4	16	no	—
312	C₂³×C₁₃₉	—	4	16	no	—
313	C₂³×C₁₃₉	—	4	8	no	—
314	C₂³×C₁₃₉	—	4	16	no	—
315	C₂³×C₁₃₉	—	4	8	no	—
316	C₂³×C₁₃₉	—	8	4	no	—
317	C₂³×C₁₃₉	—	8	8	no	—
318	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
319	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
320	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
321	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
322	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
323	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	D₄×C₁₃₉	—	2	16	no	—
327	D₄×C₁₃₉	—	2	8	no	—
328	D₄×C₁₃₉	—	2	8	no	—
329	D₄×C₁₃₉	—	4	8	no	—
330	D₄×C₁₃₉	—	4	8	no	—
331	D₄×C₁₃₉	—	4	8	no	—
332	D₄×C₁₃₉	—	4	8	no	—
333	D₄×C₁₃₉	—	4	4	no	—
334	D₄×C₁₃₉	—	8	4	no	—
335	D₄×C₁₃₉	#123	1	16	yes	complemented
336	C₂×C₄×C₁₃₉	—	2	8	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	1	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	8	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	4	no	—
348	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	4	no	—
356	C₂×C₄×C₁₃₉	—	2	4	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	4	no	—
362	C₂×C₄×C₁₃₉	—	2	4	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	4	16	no	—
366	C₂×C₄×C₁₃₉	—	4	16	no	—
367	C₂×C₄×C₁₃₉	—	4	8	no	—
368	C₂×C₄×C₁₃₉	—	4	8	no	—
369	C₂×C₄×C₁₃₉	—	4	4	no	—
370	C₂×C₄×C₁₃₉	—	4	4	no	—
371	C₂×C₄×C₁₃₉	—	8	8	no	—
372	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
376	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
377	C₂²×C₁₃₉	—	2	2	no	—
378	C₂²×C₁₃₉	—	2	4	no	—
379	C₂²×C₁₃₉	—	2	4	no	—
380	C₂²×C₁₃₉	—	2	8	no	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	8	no	—
384	C₂²×C₁₃₉	—	2	4	no	—
385	C₂²×C₁₃₉	—	2	4	no	—
386	C₂²×C₁₃₉	—	2	2	no	—
387	C₂²×C₁₃₉	—	2	4	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	2	4	no	—
390	C₂²×C₁₃₉	—	4	32	no	—
391	C₂²×C₁₃₉	—	4	1	no	—
392	C₂²×C₁₃₉	—	4	4	no	—
393	C₂²×C₁₃₉	—	4	1	no	—
394	C₂²×C₁₃₉	—	4	4	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	—	4	2	no	—
398	C₂²×C₁₃₉	—	4	4	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	4	no	—
401	C₂²×C₁₃₉	—	8	16	no	—
402	C₂²×C₁₃₉	C₂×#123	1	8	yes	—
403	C₂²×C₁₃₉	#546	1	4	yes	—
404	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
405	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
406	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₄×C₁₃₉	—	2	2	no	—
410	C₄×C₁₃₉	—	2	2	no	—
411	C₄×C₁₃₉	—	2	4	no	—
412	C₄×C₁₃₉	—	4	1	no	—
413	C₄×C₁₃₉	—	4	2	no	—
414	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	4	no	—
417	C₄×C₁₃₉	—	4	1	no	—
418	C₄×C₁₃₉	—	4	4	no	—
419	C₄×C₁₃₉	—	4	2	no	—
420	C₄×C₁₃₉	C₂×#123	1	4	yes	—
421	C₂×C₁₃₉	—	2	4	no	—
422	C₂×C₁₃₉	—	2	8	no	—
423	C₂×C₁₃₉	—	4	4	no	—
424	C₂×C₁₃₉	—	4	2	no	—
425	C₂×C₁₃₉	—	8	2	no	—
426	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
427	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
428	C₂×C₁₃₉	#3481	1	2	yes	—
429	C₂×C₁₃₉	#3484	1	1	yes	characteristic
430	C₂×C₁₃₉	#3519	1	2	yes	—
431	#36236	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₁₃₉	#36236	1	1	yes	characteristic, direct product factor, Sylow
433	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic
434	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
435	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	#2849	C₂×C₁₃₉	1	2	yes	complemented
437	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
438	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2445	C₂×C₁₃₉	1	2	yes	complemented
440	#2444	C₂×C₁₃₉	1	4	yes	complemented
441	#2420	C₂×C₁₃₉	1	2	yes	complemented
442	#2418	C₂×C₁₃₉	1	4	yes	complemented
443	#2412	C₂×C₁₃₉	1	2	yes	complemented
444	#2405	C₂×C₁₃₉	1	2	yes	complemented
445	#2349	C₂×C₁₃₉	1	2	yes	complemented
446	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
448	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	C₂×#386	C₂×C₁₃₉	1	2	yes	complemented
450	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
452	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
453	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	complemented
454	D₄²	—	2	8	no	—
455	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
458	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
459	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
462	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
463	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
464	C₂×C₄×D₄	—	2	8	no	—
465	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
470	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
471	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
472	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
473	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
474	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
475	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
476	#400	C₂²×C₁₃₉	1	2	yes	complemented
477	#399	C₂²×C₁₃₉	1	2	yes	complemented
478	#397	C₂²×C₁₃₉	1	4	yes	complemented
479	#397	C₂²×C₁₃₉	1	4	yes	complemented
480	#394	C₂²×C₁₃₉	1	4	yes	complemented
481	#394	C₂²×C₁₃₉	1	4	yes	complemented
482	#394	C₂²×C₁₃₉	1	4	yes	complemented
483	#390	C₂²×C₁₃₉	1	2	yes	complemented
484	#390	C₂²×C₁₃₉	1	2	yes	complemented
485	#390	C₂²×C₁₃₉	1	2	yes	complemented
486	#389	C₂²×C₁₃₉	1	2	yes	complemented
487	#389	C₂²×C₁₃₉	1	2	yes	complemented
488	#388	C₂²×C₁₃₉	1	4	yes	complemented
489	#388	C₂²×C₁₃₉	1	2	yes	complemented
490	#387	C₂²×C₁₃₉	1	2	yes	complemented
491	#386	C₂²×C₁₃₉	1	2	yes	—
492	#386	C₂²×C₁₃₉	1	1	yes	characteristic
493	#386	C₂²×C₁₃₉	1	4	yes	complemented
494	#386	C₂²×C₁₃₉	1	2	yes	complemented
495	#386	C₂²×C₁₃₉	1	2	yes	complemented
496	#386	C₂²×C₁₃₉	1	4	yes	complemented
497	#386	C₂²×C₁₃₉	1	4	yes	complemented
498	#386	C₂²×C₁₃₉	1	2	yes	complemented
499	#386	C₂²×C₁₃₉	1	4	yes	complemented
500	#386	C₂²×C₁₃₉	1	4	yes	complemented
501	#385	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
502	#385	C₂²×C₁₃₉	1	4	yes	complemented
503	#385	C₂²×C₁₃₉	1	2	yes	complemented
504	#385	C₂²×C₁₃₉	1	4	yes	complemented
505	#382	C₂²×C₁₃₉	1	2	yes	complemented
506	#381	C₂²×C₁₃₉	1	4	yes	complemented
507	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
508	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
509	#380	C₂²×C₁₃₉	1	2	yes	complemented
510	#380	C₂²×C₁₃₉	1	4	yes	complemented
511	#379	C₂²×C₁₃₉	1	2	yes	complemented
512	#379	C₂²×C₁₃₉	1	4	yes	complemented
513	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
514	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
515	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
516	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
517	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
518	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
519	C₂²×D₄	—	2	8	no	—
520	C₂²×D₄	—	2	8	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	8	no	—
523	C₂²×D₄	—	2	8	no	—
524	C₂²×D₄	—	4	4	no	—
525	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
526	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂³×C₄	—	2	8	no	—
537	C₂³×C₄	—	4	8	no	—
538	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
547	#127	—	2	4	no	—
548	#123	—	2	4	no	—
549	#123	—	4	8	no	—
550	#123	—	4	4	no	—
551	#121	—	2	4	no	—
552	#121	—	2	8	no	—
553	#121	—	2	4	no	—
554	#120	—	2	8	no	—
555	#120	—	2	8	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	16	no	—
558	C₄×D₄	—	2	8	no	—
559	C₄×D₄	—	2	4	no	—
560	C₄×D₄	—	2	8	no	—
561	C₄×D₄	—	2	4	no	—
562	C₂×C₄⋊C₄	—	2	4	no	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₂²⋊C₄	—	2	8	no	—
573	C₂×C₂²⋊C₄	—	4	8	no	—
574	C₂×C₂²⋊C₄	—	4	4	no	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
595	C₂×C₄²	—	2	4	no	—
596	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	4	yes	—
602	#95	C₂³×C₁₃₉	1	4	yes	—
603	#95	C₂³×C₁₃₉	1	4	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	4	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	4	yes	—
611	C₂⁴	—	2	8	no	—
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	2	4	no	—
616	C₂⁴	—	2	8	no	—
617	C₂⁴	—	4	4	no	—
618	C₂⁴	—	4	4	no	—
619	C₂⁴	—	4	2	no	—
620	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
621	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
622	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	8	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	32	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	32	no	—
647	C₂×D₄	—	4	16	no	—
648	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
649	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
650	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
651	C₂×D₄	#41×C₁₃₉	1	4	yes	—
652	C₂×D₄	#41×C₁₃₉	1	8	yes	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	8	no	—
659	C₂²×C₄	—	2	8	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	8	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	8	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	4	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	32	no	—
676	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	4	4	no	—
697	C₄⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	8	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₂²⋊C₄	—	4	4	no	—
716	C₂²⋊C₄	—	4	4	no	—
717	C₂²⋊C₄	—	4	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	16	no	—
728	C₂³	—	2	16	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	4	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	16	no	—
744	C₂³	—	4	16	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	4	16	no	—
747	C₂³	—	4	8	no	—
748	C₂³	—	8	4	no	—
749	C₂³	—	8	8	no	—
750	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
751	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
752	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
753	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
754	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
755	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
756	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
757	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
758	D₄	—	2	16	no	—
759	D₄	—	2	8	no	—
760	D₄	—	2	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	8	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	4	no	—
767	D₄	#123×C₁₃₉	1	16	yes	complemented
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	8	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	4	16	no	—
798	C₂×C₄	—	4	16	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	8	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	8	8	no	—
804	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
806	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
807	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
808	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	8	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	4	32	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	8	16	no	—
834	C₂²	C₂×#123×C₁₃₉	1	8	yes	—
835	C₂²	#546×C₁₃₉	1	4	yes	—
836	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
837	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
838	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
839	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
840	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	4	no	—
852	C₄	C₂×#123×C₁₃₉	1	4	yes	—
853	C₂	—	2	4	no	—
854	C₂	—	2	8	no	—
855	C₂	—	4	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	2	no	—
858	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
859	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
860	C₂	#3481×C₁₃₉	1	2	yes	—
861	C₂	#3484×C₁₃₉	1	1	yes	characteristic
862	C₂	#3519×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×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2504×C₁₃₉	C₂	semidirect
6. #2487×C₁₃₉	C₂	semidirect
7. #2445×C₁₃₉	C₂	semidirect
8. #2444×C₁₃₉	C₂	semidirect
9. #2420×C₁₃₉	C₂	semidirect
10. #2418×C₁₃₉	C₂	semidirect
11. #2412×C₁₃₉	C₂	semidirect
12. #2405×C₁₃₉	C₂	semidirect
13. #2349×C₁₃₉	C₂	semidirect
14. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
15. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. C₂×#386×C₁₃₉	C₂	semidirect
21. C₂⁴×C₄×C₁₃₉	C₂²	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
26. C₂×#123×C₁₃₉	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
43. C₂²×C₄²×C₁₃₉	C₂²	semidirect
44. #400×C₁₃₉	C₂²	semidirect
45. #399×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
47. #397×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #394×C₁₃₉	C₂²	semidirect
50. #394×C₁₃₉	C₂²	semidirect
51. #390×C₁₃₉	C₂²	semidirect
52. #390×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #388×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #387×C₁₃₉	C₂²	semidirect
61. #386×C₁₃₉	C₂²	semidirect
62. #386×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
68. #386×C₁₃₉	C₂²	semidirect
69. #385×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #382×C₁₃₉	C₂²	semidirect
74. #381×C₁₃₉	C₂²	semidirect
75. #381×C₁₃₉	C₂²	semidirect
76. #380×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
79. #379×C₁₃₉	C₂²	semidirect
80. #379×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
335. D₄×C₁₃₉	#123	semidirect
431. #36236	C₁₃₉	direct (N × H)
432. C₁₃₉	#36236	direct (N × H)
434. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
435. #2854	C₂×C₁₃₉	semidirect
436. #2849	C₂×C₁₃₉	semidirect
437. #2504	C₂×C₁₃₉	semidirect
438. #2487	C₂×C₁₃₉	semidirect
439. #2445	C₂×C₁₃₉	semidirect
440. #2444	C₂×C₁₃₉	semidirect
441. #2420	C₂×C₁₃₉	semidirect
442. #2418	C₂×C₁₃₉	semidirect
443. #2412	C₂×C₁₃₉	semidirect
444. #2405	C₂×C₁₃₉	semidirect
445. #2349	C₂×C₁₃₉	semidirect
446. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
447. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
448. C₄×#123	C₂×C₁₃₉	semidirect
449. C₂×#386	C₂×C₁₃₉	semidirect
453. C₂⁴×C₄	C₂²×C₁₃₉	semidirect
457. C₂×#123	C₂²×C₁₃₉	semidirect
458. C₂×#123	C₂²×C₁₃₉	semidirect
469. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
470. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
471. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
472. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
473. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
474. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
475. C₂²×C₄²	C₂²×C₁₃₉	semidirect
476. #400	C₂²×C₁₃₉	semidirect
477. #399	C₂²×C₁₃₉	semidirect
478. #397	C₂²×C₁₃₉	semidirect
479. #397	C₂²×C₁₃₉	semidirect
480. #394	C₂²×C₁₃₉	semidirect
481. #394	C₂²×C₁₃₉	semidirect
482. #394	C₂²×C₁₃₉	semidirect
483. #390	C₂²×C₁₃₉	semidirect
484. #390	C₂²×C₁₃₉	semidirect
485. #390	C₂²×C₁₃₉	semidirect
486. #389	C₂²×C₁₃₉	semidirect
487. #389	C₂²×C₁₃₉	semidirect
488. #388	C₂²×C₁₃₉	semidirect
489. #388	C₂²×C₁₃₉	semidirect
490. #387	C₂²×C₁₃₉	semidirect
493. #386	C₂²×C₁₃₉	semidirect
494. #386	C₂²×C₁₃₉	semidirect
495. #386	C₂²×C₁₃₉	semidirect
496. #386	C₂²×C₁₃₉	semidirect
497. #386	C₂²×C₁₃₉	semidirect
498. #386	C₂²×C₁₃₉	semidirect
499. #386	C₂²×C₁₃₉	semidirect
500. #386	C₂²×C₁₃₉	semidirect
501. #385	C₂²×C₁₃₉	semidirect
502. #385	C₂²×C₁₃₉	semidirect
503. #385	C₂²×C₁₃₉	semidirect
504. #385	C₂²×C₁₃₉	semidirect
505. #382	C₂²×C₁₃₉	semidirect
506. #381	C₂²×C₁₃₉	semidirect
507. #381	C₂²×C₁₃₉	semidirect
508. #380	C₂²×C₁₃₉	semidirect
509. #380	C₂²×C₁₃₉	semidirect
510. #380	C₂²×C₁₃₉	semidirect
511. #379	C₂²×C₁₃₉	semidirect
512. #379	C₂²×C₁₃₉	semidirect
513. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
514. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
515. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
516. C₂×#95	C₂²×C₁₃₉	semidirect
767. D₄	#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×C₄×D₄×C₁₃₉	2
#2854×C₁₃₉	2
#2849×C₁₃₉	2
#2504×C₁₃₉	2
#2487×C₁₃₉	2
#2445×C₁₃₉	2
#2444×C₁₃₉	2
#2420×C₁₃₉	2
#2418×C₁₃₉	2
#2412×C₁₃₉	2
#2405×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×#386×C₁₃₉	2
#36236	139

Subgroups — C139×#36236 #48030832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36236 #48030832