Subgroups — C₁₃₉×#35706 #48030302

Order 35584.

2038 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2653×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2617×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2572×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2569×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2527×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2523×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2510×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2459×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2458×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2436×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2412×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₂×#393×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2364×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2358×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2353×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2273×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
32	#401×C₁₃₉	C₂²	1	2	yes	complemented
33	#400×C₁₃₉	C₂²	1	2	yes	complemented
34	#400×C₁₃₉	C₂²	1	2	yes	complemented
35	#398×C₁₃₉	C₂²	1	2	yes	complemented
36	#397×C₁₃₉	C₂²	1	1	yes	characteristic
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	1	yes	characteristic
40	#397×C₁₃₉	C₂²	1	2	yes	complemented
41	#397×C₁₃₉	C₂²	1	2	yes	complemented
42	#394×C₁₃₉	C₂²	1	2	yes	—
43	#394×C₁₃₉	C₂²	1	2	yes	—
44	#394×C₁₃₉	C₂²	1	2	yes	—
45	#394×C₁₃₉	C₂²	1	2	yes	—
46	#393×C₁₃₉	C₂²	1	2	yes	—
47	#393×C₁₃₉	C₂²	1	2	yes	—
48	#393×C₁₃₉	C₂²	1	1	yes	characteristic
49	#393×C₁₃₉	C₂²	1	1	yes	characteristic
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#393×C₁₃₉	C₂²	1	1	yes	characteristic
52	#393×C₁₃₉	C₂²	1	2	yes	complemented
53	#393×C₁₃₉	C₂²	1	2	yes	complemented
54	#392×C₁₃₉	C₂²	1	1	yes	characteristic
55	#392×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	2	yes	complemented
57	#391×C₁₃₉	C₂²	1	2	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	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	complemented
64	#388×C₁₃₉	C₂²	1	2	yes	complemented
65	#388×C₁₃₉	C₂²	1	2	yes	complemented
66	#388×C₁₃₉	C₂²	1	2	yes	complemented
67	#388×C₁₃₉	C₂²	1	2	yes	complemented
68	#387×C₁₃₉	C₂²	1	2	yes	complemented
69	#387×C₁₃₉	C₂²	1	2	yes	complemented
70	#387×C₁₃₉	C₂²	1	2	yes	complemented
71	#387×C₁₃₉	C₂²	1	2	yes	complemented
72	#387×C₁₃₉	C₂²	1	2	yes	complemented
73	#387×C₁₃₉	C₂²	1	2	yes	complemented
74	#386×C₁₃₉	C₂²	1	2	yes	—
75	#386×C₁₃₉	C₂²	1	2	yes	—
76	#386×C₁₃₉	C₂²	1	2	yes	—
77	#386×C₁₃₉	C₂²	1	2	yes	—
78	#386×C₁₃₉	C₂²	1	2	yes	—
79	#386×C₁₃₉	C₂²	1	2	yes	—
80	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	complemented
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#385×C₁₃₉	C₂²	1	2	yes	—
84	#385×C₁₃₉	C₂²	1	2	yes	—
85	#383×C₁₃₉	C₂²	1	2	yes	complemented
86	#383×C₁₃₉	C₂²	1	2	yes	complemented
87	#381×C₁₃₉	C₂²	1	2	yes	—
88	#381×C₁₃₉	C₂²	1	2	yes	complemented
89	#380×C₁₃₉	C₂²	1	2	yes	—
90	#380×C₁₃₉	C₂²	1	1	yes	characteristic
91	#380×C₁₃₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
104	#376×C₁₃₉	C₂²	1	2	yes	complemented
105	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	—	2	4	no	—
109	C₂²×Q₈×C₁₃₉	—	4	4	no	—
110	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	#124×C₁₃₉	—	4	4	no	—
125	#123×C₁₃₉	—	4	4	no	—
126	#121×C₁₃₉	—	2	4	no	—
127	#120×C₁₃₉	—	2	8	no	—
128	C₄×Q₈×C₁₃₉	—	4	4	no	—
129	C₄×D₄×C₁₃₉	—	2	8	no	—
130	C₄×D₄×C₁₃₉	—	4	4	no	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	1	yes	characteristic
185	#95×C₁₃₉	C₂³	1	1	yes	characteristic
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	1	yes	characteristic
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	C₂⁴×C₁₃₉	—	2	2	no	—
208	C₂⁴×C₁₃₉	—	2	2	no	—
209	C₂⁴×C₁₃₉	—	4	2	no	—
210	C₂⁴×C₁₃₉	—	4	2	no	—
211	C₂⁴×C₁₃₉	#41	1	4	yes	—
212	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₁₃₉	—	2	2	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	—	2	4	no	—
221	C₂×Q₈×C₁₃₉	—	4	2	no	—
222	C₂×Q₈×C₁₃₉	—	4	2	no	—
223	C₂×Q₈×C₁₃₉	—	4	16	no	—
224	C₂×D₄×C₁₃₉	—	2	4	no	—
225	C₂×D₄×C₁₃₉	—	2	4	no	—
226	C₂×D₄×C₁₃₉	—	2	4	no	—
227	C₂×D₄×C₁₃₉	—	2	4	no	—
228	C₂×D₄×C₁₃₉	—	2	4	no	—
229	C₂×D₄×C₁₃₉	—	2	2	no	—
230	C₂×D₄×C₁₃₉	—	4	2	no	—
231	C₂×D₄×C₁₃₉	—	4	2	no	—
232	C₂×D₄×C₁₃₉	—	4	2	no	—
233	C₂×D₄×C₁₃₉	—	4	2	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	2	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	2	no	—
245	C₂²×C₄×C₁₃₉	—	4	2	no	—
246	C₂²×C₄×C₁₃₉	—	4	2	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	—	4	2	no	—
253	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
305	C₄²×C₁₃₉	—	2	4	no	—
306	C₄²×C₁₃₉	—	2	4	no	—
307	C₄²×C₁₃₉	—	4	2	no	—
308	C₄²×C₁₃₉	—	4	2	no	—
309	C₄²×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₄²×C₁₃₉	—	4	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	1	no	—
315	C₂³×C₁₃₉	—	2	1	no	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	1	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	8	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	4	8	no	—
331	C₂³×C₁₃₉	—	8	2	no	—
332	C₂³×C₁₃₉	—	8	2	no	—
333	C₂³×C₁₃₉	—	8	4	no	—
334	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
335	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
336	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
337	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
338	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
339	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
340	Q₈×C₁₃₉	—	2	8	no	—
341	Q₈×C₁₃₉	—	4	8	no	—
342	Q₈×C₁₃₉	—	4	4	no	—
343	D₄×C₁₃₉	—	4	8	no	—
344	D₄×C₁₃₉	—	4	8	no	—
345	D₄×C₁₃₉	—	8	2	no	—
346	D₄×C₁₃₉	—	8	4	no	—
347	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	4	4	no	—
385	C₂×C₄×C₁₃₉	—	4	8	no	—
386	C₂×C₄×C₁₃₉	—	8	4	no	—
387	C₂×C₄×C₁₃₉	—	8	4	no	—
388	C₂×C₄×C₁₃₉	—	8	4	no	—
389	C₂×C₄×C₁₃₉	—	8	2	no	—
390	C₂×C₄×C₁₃₉	—	8	4	no	—
391	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
392	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
393	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
394	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
395	C₂²×C₁₃₉	—	2	2	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	2	no	—
398	C₂²×C₁₃₉	—	2	4	no	—
399	C₂²×C₁₃₉	—	2	2	no	—
400	C₂²×C₁₃₉	—	2	2	no	—
401	C₂²×C₁₃₉	—	2	4	no	—
402	C₂²×C₁₃₉	—	2	4	no	—
403	C₂²×C₁₃₉	—	4	1	no	—
404	C₂²×C₁₃₉	—	4	1	no	—
405	C₂²×C₁₃₉	—	4	1	no	—
406	C₂²×C₁₃₉	—	4	1	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	—	4	2	no	—
409	C₂²×C₁₃₉	—	4	2	no	—
410	C₂²×C₁₃₉	—	4	2	no	—
411	C₂²×C₁₃₉	—	4	2	no	—
412	C₂²×C₁₃₉	—	4	2	no	—
413	C₂²×C₁₃₉	—	4	2	no	—
414	C₂²×C₁₃₉	—	4	2	no	—
415	C₂²×C₁₃₉	—	4	2	no	—
416	C₂²×C₁₃₉	—	8	8	no	—
417	C₂²×C₁₃₉	#529	1	4	yes	—
418	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
419	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
420	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
422	C₂²×C₁₃₉	#585	1	2	yes	—
423	C₄×C₁₃₉	—	2	2	no	—
424	C₄×C₁₃₉	—	2	2	no	—
425	C₄×C₁₃₉	—	2	4	no	—
426	C₄×C₁₃₉	—	2	4	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	2	no	—
430	C₄×C₁₃₉	—	4	2	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₄×C₁₃₉	—	4	2	no	—
433	C₄×C₁₃₉	—	4	1	no	—
434	C₄×C₁₃₉	—	4	1	no	—
435	C₄×C₁₃₉	—	4	2	no	—
436	C₄×C₁₃₉	—	4	2	no	—
437	C₄×C₁₃₉	—	4	2	no	—
438	C₂×C₁₃₉	—	2	4	no	—
439	C₂×C₁₃₉	—	4	2	no	—
440	C₂×C₁₃₉	—	4	2	no	—
441	C₂×C₁₃₉	—	8	2	no	—
442	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
443	C₂×C₁₃₉	#3490	1	1	yes	characteristic
444	C₂×C₁₃₉	#3505	1	2	yes	—
445	C₂×C₁₃₉	#3510	1	1	yes	characteristic
446	C₂×C₁₃₉	#3514	1	2	yes	—
447	#35706	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₁₃₉	#35706	1	1	yes	characteristic, direct product factor, Sylow
449	#2653	C₂×C₁₃₉	1	2	yes	complemented
450	#2617	C₂×C₁₃₉	1	1	yes	characteristic
451	#2572	C₂×C₁₃₉	1	2	yes	complemented
452	#2569	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2557	C₂×C₁₃₉	1	2	yes	complemented
454	#2527	C₂×C₁₃₉	1	2	yes	complemented
455	#2523	C₂×C₁₃₉	1	2	yes	complemented
456	#2510	C₂×C₁₃₉	1	2	yes	complemented
457	#2459	C₂×C₁₃₉	1	2	yes	complemented
458	#2458	C₂×C₁₃₉	1	2	yes	complemented
459	#2436	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	#2412	C₂×C₁₃₉	1	2	yes	complemented
461	#2398	C₂×C₁₃₉	1	2	yes	complemented
462	C₂×#393	C₂×C₁₃₉	1	1	yes	characteristic, complemented
463	#2364	C₂×C₁₃₉	1	1	yes	characteristic, complemented
464	#2358	C₂×C₁₃₉	1	2	yes	complemented
465	#2353	C₂×C₁₃₉	1	2	yes	complemented
466	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2273	C₂×C₁₃₉	1	1	yes	characteristic, complemented
468	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
470	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
471	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
473	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
474	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
476	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
480	#401	C₂²×C₁₃₉	1	2	yes	complemented
481	#400	C₂²×C₁₃₉	1	2	yes	complemented
482	#400	C₂²×C₁₃₉	1	2	yes	complemented
483	#398	C₂²×C₁₃₉	1	2	yes	complemented
484	#397	C₂²×C₁₃₉	1	1	yes	characteristic
485	#397	C₂²×C₁₃₉	1	1	yes	characteristic
486	#397	C₂²×C₁₃₉	1	2	yes	—
487	#397	C₂²×C₁₃₉	1	2	yes	—
488	#397	C₂²×C₁₃₉	1	2	yes	complemented
489	#397	C₂²×C₁₃₉	1	2	yes	complemented
490	#394	C₂²×C₁₃₉	1	2	yes	—
491	#394	C₂²×C₁₃₉	1	2	yes	—
492	#394	C₂²×C₁₃₉	1	2	yes	—
493	#394	C₂²×C₁₃₉	1	2	yes	—
494	#393	C₂²×C₁₃₉	1	1	yes	characteristic
495	#393	C₂²×C₁₃₉	1	1	yes	characteristic
496	#393	C₂²×C₁₃₉	1	1	yes	characteristic
497	#393	C₂²×C₁₃₉	1	1	yes	characteristic
498	#393	C₂²×C₁₃₉	1	2	yes	—
499	#393	C₂²×C₁₃₉	1	2	yes	—
500	#393	C₂²×C₁₃₉	1	2	yes	complemented
501	#393	C₂²×C₁₃₉	1	2	yes	complemented
502	#392	C₂²×C₁₃₉	1	1	yes	characteristic
503	#392	C₂²×C₁₃₉	1	1	yes	characteristic
504	#391	C₂²×C₁₃₉	1	2	yes	complemented
505	#391	C₂²×C₁₃₉	1	2	yes	complemented
506	#391	C₂²×C₁₃₉	1	2	yes	complemented
507	#391	C₂²×C₁₃₉	1	2	yes	complemented
508	#390	C₂²×C₁₃₉	1	2	yes	—
509	#388	C₂²×C₁₃₉	1	2	yes	—
510	#388	C₂²×C₁₃₉	1	2	yes	—
511	#388	C₂²×C₁₃₉	1	2	yes	complemented
512	#388	C₂²×C₁₃₉	1	2	yes	complemented
513	#388	C₂²×C₁₃₉	1	2	yes	complemented
514	#388	C₂²×C₁₃₉	1	2	yes	complemented
515	#388	C₂²×C₁₃₉	1	2	yes	complemented
516	#387	C₂²×C₁₃₉	1	2	yes	complemented
517	#387	C₂²×C₁₃₉	1	2	yes	complemented
518	#387	C₂²×C₁₃₉	1	2	yes	complemented
519	#387	C₂²×C₁₃₉	1	2	yes	complemented
520	#387	C₂²×C₁₃₉	1	2	yes	complemented
521	#387	C₂²×C₁₃₉	1	2	yes	complemented
522	#386	C₂²×C₁₃₉	1	2	yes	—
523	#386	C₂²×C₁₃₉	1	2	yes	—
524	#386	C₂²×C₁₃₉	1	2	yes	—
525	#386	C₂²×C₁₃₉	1	2	yes	—
526	#386	C₂²×C₁₃₉	1	2	yes	—
527	#386	C₂²×C₁₃₉	1	2	yes	—
528	#386	C₂²×C₁₃₉	1	2	yes	—
529	#386	C₂²×C₁₃₉	1	2	yes	complemented
530	#385	C₂²×C₁₃₉	1	2	yes	—
531	#385	C₂²×C₁₃₉	1	2	yes	—
532	#385	C₂²×C₁₃₉	1	2	yes	—
533	#383	C₂²×C₁₃₉	1	2	yes	complemented
534	#383	C₂²×C₁₃₉	1	2	yes	complemented
535	#381	C₂²×C₁₃₉	1	2	yes	—
536	#381	C₂²×C₁₃₉	1	2	yes	complemented
537	#380	C₂²×C₁₃₉	1	1	yes	characteristic
538	#380	C₂²×C₁₃₉	1	2	yes	—
539	#380	C₂²×C₁₃₉	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
544	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
545	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
549	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
551	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
552	#376	C₂²×C₁₃₉	1	2	yes	complemented
553	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
555	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂²×Q₈	—	2	4	no	—
557	C₂²×Q₈	—	4	4	no	—
558	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
560	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	#124	—	4	4	no	—
573	#123	—	4	4	no	—
574	#121	—	2	4	no	—
575	#120	—	2	8	no	—
576	C₄×Q₈	—	4	4	no	—
577	C₄×D₄	—	2	8	no	—
578	C₄×D₄	—	4	4	no	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₂²⋊C₄	—	2	4	no	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	4	4	no	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	2	yes	—
627	#95	C₂³×C₁₃₉	1	1	yes	characteristic
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	1	yes	characteristic
633	#95	C₂³×C₁₃₉	1	2	yes	—
634	#95	C₂³×C₁₃₉	1	2	yes	—
635	#95	C₂³×C₁₃₉	1	2	yes	—
636	#95	C₂³×C₁₃₉	1	2	yes	—
637	#95	C₂³×C₁₃₉	1	2	yes	—
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	#95	C₂³×C₁₃₉	1	2	yes	—
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	1	yes	characteristic
649	#95	C₂³×C₁₃₉	1	1	yes	characteristic
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	4	2	no	—
658	C₂⁴	—	4	2	no	—
659	C₂⁴	#41×C₁₃₉	1	4	yes	—
660	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
661	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
663	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	16	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	8	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	4	no	—
782	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
783	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
784	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
785	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
786	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
787	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
788	Q₈	—	2	8	no	—
789	Q₈	—	4	8	no	—
790	Q₈	—	4	4	no	—
791	D₄	—	4	8	no	—
792	D₄	—	4	8	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
840	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
841	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
842	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	8	no	—
865	C₂²	#529×C₁₃₉	1	4	yes	—
866	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
867	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
868	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
869	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
870	C₂²	#585×C₁₃₉	1	2	yes	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	2	4	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
891	C₂	#3490×C₁₃₉	1	1	yes	characteristic
892	C₂	#3505×C₁₃₉	1	2	yes	—
893	C₂	#3510×C₁₃₉	1	1	yes	characteristic
894	C₂	#3514×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2617×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
1. #2653×C₁₃₉	C₂	semidirect
3. #2572×C₁₃₉	C₂	semidirect
4. #2569×C₁₃₉	C₂	semidirect
5. #2557×C₁₃₉	C₂	semidirect
6. #2527×C₁₃₉	C₂	semidirect
7. #2523×C₁₃₉	C₂	semidirect
8. #2510×C₁₃₉	C₂	semidirect
9. #2459×C₁₃₉	C₂	semidirect
10. #2458×C₁₃₉	C₂	semidirect
11. #2436×C₁₃₉	C₂	semidirect
12. #2412×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. C₂×#393×C₁₃₉	C₂	semidirect
15. #2364×C₁₃₉	C₂	semidirect
16. #2358×C₁₃₉	C₂	semidirect
17. #2353×C₁₃₉	C₂	semidirect
18. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
19. #2273×C₁₃₉	C₂	semidirect
21. C₂×#124×C₁₃₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
32. #401×C₁₃₉	C₂²	semidirect
33. #400×C₁₃₉	C₂²	semidirect
34. #400×C₁₃₉	C₂²	semidirect
35. #398×C₁₃₉	C₂²	semidirect
40. #397×C₁₃₉	C₂²	semidirect
41. #397×C₁₃₉	C₂²	semidirect
52. #393×C₁₃₉	C₂²	semidirect
53. #393×C₁₃₉	C₂²	semidirect
56. #391×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
63. #388×C₁₃₉	C₂²	semidirect
64. #388×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
68. #387×C₁₃₉	C₂²	semidirect
69. #387×C₁₃₉	C₂²	semidirect
70. #387×C₁₃₉	C₂²	semidirect
71. #387×C₁₃₉	C₂²	semidirect
72. #387×C₁₃₉	C₂²	semidirect
73. #387×C₁₃₉	C₂²	semidirect
81. #386×C₁₃₉	C₂²	semidirect
85. #383×C₁₃₉	C₂²	semidirect
86. #383×C₁₃₉	C₂²	semidirect
88. #381×C₁₃₉	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
104. #376×C₁₃₉	C₂²	semidirect
447. #35706	C₁₃₉	direct (N × H)
448. C₁₃₉	#35706	direct (N × H)
449. #2653	C₂×C₁₃₉	semidirect
451. #2572	C₂×C₁₃₉	semidirect
452. #2569	C₂×C₁₃₉	semidirect
453. #2557	C₂×C₁₃₉	semidirect
454. #2527	C₂×C₁₃₉	semidirect
455. #2523	C₂×C₁₃₉	semidirect
456. #2510	C₂×C₁₃₉	semidirect
457. #2459	C₂×C₁₃₉	semidirect
458. #2458	C₂×C₁₃₉	semidirect
459. #2436	C₂×C₁₃₉	semidirect
460. #2412	C₂×C₁₃₉	semidirect
461. #2398	C₂×C₁₃₉	semidirect
462. C₂×#393	C₂×C₁₃₉	semidirect
463. #2364	C₂×C₁₃₉	semidirect
464. #2358	C₂×C₁₃₉	semidirect
465. #2353	C₂×C₁₃₉	semidirect
466. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
467. #2273	C₂×C₁₃₉	semidirect
469. C₂×#124	C₂²×C₁₃₉	semidirect
473. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
480. #401	C₂²×C₁₃₉	semidirect
481. #400	C₂²×C₁₃₉	semidirect
482. #400	C₂²×C₁₃₉	semidirect
483. #398	C₂²×C₁₃₉	semidirect
488. #397	C₂²×C₁₃₉	semidirect
489. #397	C₂²×C₁₃₉	semidirect
500. #393	C₂²×C₁₃₉	semidirect
501. #393	C₂²×C₁₃₉	semidirect
504. #391	C₂²×C₁₃₉	semidirect
505. #391	C₂²×C₁₃₉	semidirect
506. #391	C₂²×C₁₃₉	semidirect
507. #391	C₂²×C₁₃₉	semidirect
511. #388	C₂²×C₁₃₉	semidirect
512. #388	C₂²×C₁₃₉	semidirect
513. #388	C₂²×C₁₃₉	semidirect
514. #388	C₂²×C₁₃₉	semidirect
515. #388	C₂²×C₁₃₉	semidirect
516. #387	C₂²×C₁₃₉	semidirect
517. #387	C₂²×C₁₃₉	semidirect
518. #387	C₂²×C₁₃₉	semidirect
519. #387	C₂²×C₁₃₉	semidirect
520. #387	C₂²×C₁₃₉	semidirect
521. #387	C₂²×C₁₃₉	semidirect
529. #386	C₂²×C₁₃₉	semidirect
533. #383	C₂²×C₁₃₉	semidirect
534. #383	C₂²×C₁₃₉	semidirect
536. #381	C₂²×C₁₃₉	semidirect
550. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
551. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
552. #376	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2653×C₁₃₉	2
#2617×C₁₃₉	2
#2572×C₁₃₉	2
#2569×C₁₃₉	2
#2557×C₁₃₉	2
#2527×C₁₃₉	2
#2523×C₁₃₉	2
#2510×C₁₃₉	2
#2459×C₁₃₉	2
#2458×C₁₃₉	2
#2436×C₁₃₉	2
#2412×C₁₃₉	2
#2398×C₁₃₉	2
C₂×#393×C₁₃₉	2
#2364×C₁₃₉	2
#2358×C₁₃₉	2
#2353×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#2273×C₁₃₉	2
#35706	139

Subgroups — C139×#35706 #48030302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35706 #48030302