Subgroups — C₁₃₉×#36012 #48030608

Order 35584.

2282 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2663×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2617×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2549×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2521×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2499×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2488×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2412×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₂×#397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2364×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2273×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#551×C₁₃₉	—	2	16	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	#400×C₁₃₉	C₂²	1	2	yes	complemented
42	#400×C₁₃₉	C₂²	1	2	yes	complemented
43	#399×C₁₃₉	C₂²	1	2	yes	complemented
44	#399×C₁₃₉	C₂²	1	2	yes	complemented
45	#398×C₁₃₉	C₂²	1	2	yes	complemented
46	#397×C₁₃₉	C₂²	1	1	yes	characteristic
47	#397×C₁₃₉	C₂²	1	1	yes	characteristic
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	1	yes	characteristic
51	#397×C₁₃₉	C₂²	1	1	yes	characteristic
52	#397×C₁₃₉	C₂²	1	1	yes	characteristic
53	#397×C₁₃₉	C₂²	1	1	yes	characteristic
54	#397×C₁₃₉	C₂²	1	2	yes	—
55	#397×C₁₃₉	C₂²	1	2	yes	—
56	#397×C₁₃₉	C₂²	1	2	yes	complemented
57	#395×C₁₃₉	C₂²	1	2	yes	complemented
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#394×C₁₃₉	C₂²	1	2	yes	—
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#393×C₁₃₉	C₂²	1	2	yes	complemented
63	#392×C₁₃₉	C₂²	1	1	yes	characteristic
64	#392×C₁₃₉	C₂²	1	1	yes	characteristic
65	#391×C₁₃₉	C₂²	1	2	yes	complemented
66	#391×C₁₃₉	C₂²	1	2	yes	complemented
67	#390×C₁₃₉	C₂²	1	2	yes	complemented
68	#389×C₁₃₉	C₂²	1	2	yes	complemented
69	#389×C₁₃₉	C₂²	1	2	yes	complemented
70	#389×C₁₃₉	C₂²	1	2	yes	complemented
71	#388×C₁₃₉	C₂²	1	2	yes	complemented
72	#388×C₁₃₉	C₂²	1	2	yes	complemented
73	#388×C₁₃₉	C₂²	1	2	yes	complemented
74	#388×C₁₃₉	C₂²	1	2	yes	complemented
75	#388×C₁₃₉	C₂²	1	2	yes	complemented
76	#387×C₁₃₉	C₂²	1	2	yes	complemented
77	#387×C₁₃₉	C₂²	1	2	yes	complemented
78	#387×C₁₃₉	C₂²	1	2	yes	complemented
79	#387×C₁₃₉	C₂²	1	2	yes	complemented
80	#387×C₁₃₉	C₂²	1	2	yes	complemented
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#386×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	2	yes	complemented
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	2	yes	complemented
88	#384×C₁₃₉	C₂²	1	2	yes	complemented
89	#382×C₁₃₉	C₂²	1	2	yes	complemented
90	#381×C₁₃₉	C₂²	1	2	yes	—
91	#380×C₁₃₉	C₂²	1	2	yes	—
92	#380×C₁₃₉	C₂²	1	1	yes	characteristic
93	#380×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
108	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×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	1	yes	characteristic
121	#126×C₁₃₉	—	2	8	no	—
122	#126×C₁₃₉	—	2	8	no	—
123	#124×C₁₃₉	—	2	8	no	—
124	#123×C₁₃₉	—	2	8	no	—
125	#123×C₁₃₉	—	2	8	no	—
126	#123×C₁₃₉	—	2	8	no	—
127	#123×C₁₃₉	—	2	8	no	—
128	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
129	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
130	#121×C₁₃₉	—	2	4	no	—
131	#120×C₁₃₉	—	2	8	no	—
132	C₄×D₄×C₁₃₉	—	2	8	no	—
133	C₄×D₄×C₁₃₉	—	2	8	no	—
134	#117×C₁₃₉	—	2	8	no	—
135	#117×C₁₃₉	—	2	8	no	—
136	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
155	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
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	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×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	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	#95×C₁₃₉	C₂³	1	1	yes	characteristic
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	C₂⁴×C₁₃₉	—	2	2	no	—
216	C₂⁴×C₁₃₉	—	2	2	no	—
217	C₂⁴×C₁₃₉	—	4	2	no	—
218	C₂⁴×C₁₃₉	—	4	2	no	—
219	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
220	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂×Q₈×C₁₃₉	—	2	4	no	—
225	C₂×Q₈×C₁₃₉	—	4	2	no	—
226	C₂×Q₈×C₁₃₉	—	4	2	no	—
227	C₂×D₄×C₁₃₉	—	2	4	no	—
228	C₂×D₄×C₁₃₉	—	2	4	no	—
229	C₂×D₄×C₁₃₉	—	2	4	no	—
230	C₂×D₄×C₁₃₉	—	2	4	no	—
231	C₂×D₄×C₁₃₉	—	2	4	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	4	2	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂×D₄×C₁₃₉	—	4	2	no	—
236	C₂×D₄×C₁₃₉	—	4	2	no	—
237	C₂×D₄×C₁₃₉	—	4	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	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	2	4	no	—
244	C₂²×C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
254	C₂²×C₄×C₁₃₉	—	4	2	no	—
255	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
256	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	4	no	—
275	C₄⋊C₄×C₁₃₉	—	2	4	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	4	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	no	—
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	2	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	2	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
313	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
314	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
315	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
316	C₄²×C₁₃₉	—	2	4	no	—
317	C₄²×C₁₃₉	—	2	4	no	—
318	C₄²×C₁₃₉	—	2	4	no	—
319	C₄²×C₁₃₉	—	4	2	no	—
320	C₄²×C₁₃₉	—	4	2	no	—
321	C₄²×C₁₃₉	—	4	2	no	—
322	C₄²×C₁₃₉	—	4	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	1	no	—
327	C₂³×C₁₃₉	—	2	1	no	—
328	C₂³×C₁₃₉	—	2	1	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	8	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	4	8	no	—
342	C₂³×C₁₃₉	—	8	2	no	—
343	C₂³×C₁₃₉	—	8	2	no	—
344	C₂³×C₁₃₉	—	8	4	no	—
345	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
348	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃₉	—	8	4	no	—
352	D₄×C₁₃₉	—	4	8	no	—
353	D₄×C₁₃₉	—	4	8	no	—
354	D₄×C₁₃₉	—	8	2	no	—
355	D₄×C₁₃₉	—	8	4	no	—
356	C₂×C₄×C₁₃₉	—	2	2	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	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	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	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	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	4	8	no	—
393	C₂×C₄×C₁₃₉	—	4	4	no	—
394	C₂×C₄×C₁₃₉	—	4	8	no	—
395	C₂×C₄×C₁₃₉	—	8	4	no	—
396	C₂×C₄×C₁₃₉	—	8	4	no	—
397	C₂×C₄×C₁₃₉	—	8	4	no	—
398	C₂×C₄×C₁₃₉	—	8	2	no	—
399	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
400	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
401	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
403	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
404	C₂²×C₁₃₉	—	2	4	no	—
405	C₂²×C₁₃₉	—	2	2	no	—
406	C₂²×C₁₃₉	—	2	2	no	—
407	C₂²×C₁₃₉	—	2	4	no	—
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	2	no	—
410	C₂²×C₁₃₉	—	2	4	no	—
411	C₂²×C₁₃₉	—	2	4	no	—
412	C₂²×C₁₃₉	—	4	1	no	—
413	C₂²×C₁₃₉	—	4	1	no	—
414	C₂²×C₁₃₉	—	4	1	no	—
415	C₂²×C₁₃₉	—	4	1	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	—	4	2	no	—
420	C₂²×C₁₃₉	—	4	2	no	—
421	C₂²×C₁₃₉	—	4	2	no	—
422	C₂²×C₁₃₉	—	4	2	no	—
423	C₂²×C₁₃₉	—	4	2	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	8	8	no	—
426	C₂²×C₁₃₉	#532	1	4	yes	—
427	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
428	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₁₃₉	#585	1	2	yes	—
431	C₂²×C₁₃₉	#585	1	2	yes	—
432	C₄×C₁₃₉	—	2	4	no	—
433	C₄×C₁₃₉	—	2	4	no	—
434	C₄×C₁₃₉	—	2	2	no	—
435	C₄×C₁₃₉	—	2	2	no	—
436	C₄×C₁₃₉	—	2	4	no	—
437	C₄×C₁₃₉	—	4	2	no	—
438	C₄×C₁₃₉	—	4	2	no	—
439	C₄×C₁₃₉	—	4	2	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	2	no	—
444	C₄×C₁₃₉	—	4	1	no	—
445	C₄×C₁₃₉	—	4	1	no	—
446	C₄×C₁₃₉	—	4	2	no	—
447	C₂×C₁₃₉	—	2	4	no	—
448	C₂×C₁₃₉	—	4	2	no	—
449	C₂×C₁₃₉	—	4	2	no	—
450	C₂×C₁₃₉	—	8	2	no	—
451	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
452	C₂×C₁₃₉	#3485	1	2	yes	—
453	C₂×C₁₃₉	#3491	1	1	yes	characteristic
454	C₂×C₁₃₉	#3510	1	1	yes	characteristic
455	C₂×C₁₃₉	#3521	1	2	yes	—
456	#36012	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₁₃₉	#36012	1	1	yes	characteristic, direct product factor, Sylow
458	C₂×#551	C₂×C₁₃₉	1	2	yes	complemented
459	#2663	C₂×C₁₃₉	1	2	yes	complemented
460	#2617	C₂×C₁₃₉	1	1	yes	characteristic
461	#2602	C₂×C₁₃₉	1	2	yes	complemented
462	#2557	C₂×C₁₃₉	1	2	yes	complemented
463	#2553	C₂×C₁₃₉	1	2	yes	complemented
464	#2549	C₂×C₁₃₉	1	1	yes	characteristic, complemented
465	#2521	C₂×C₁₃₉	1	2	yes	complemented
466	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2499	C₂×C₁₃₉	1	2	yes	complemented
468	#2496	C₂×C₁₃₉	1	2	yes	complemented
469	#2488	C₂×C₁₃₉	1	2	yes	complemented
470	#2412	C₂×C₁₃₉	1	2	yes	complemented
471	#2395	C₂×C₁₃₉	1	2	yes	complemented
472	C₂×#397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	#2364	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2359	C₂×C₁₃₉	1	2	yes	complemented
475	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2273	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#551	—	2	16	no	—
478	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
480	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
481	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
482	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
483	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
484	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
487	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
488	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
489	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
490	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
491	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
492	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
493	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
495	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
496	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
498	#400	C₂²×C₁₃₉	1	2	yes	complemented
499	#400	C₂²×C₁₃₉	1	2	yes	complemented
500	#399	C₂²×C₁₃₉	1	2	yes	complemented
501	#399	C₂²×C₁₃₉	1	2	yes	complemented
502	#398	C₂²×C₁₃₉	1	2	yes	complemented
503	#397	C₂²×C₁₃₉	1	2	yes	—
504	#397	C₂²×C₁₃₉	1	1	yes	characteristic
505	#397	C₂²×C₁₃₉	1	1	yes	characteristic
506	#397	C₂²×C₁₃₉	1	1	yes	characteristic
507	#397	C₂²×C₁₃₉	1	1	yes	characteristic
508	#397	C₂²×C₁₃₉	1	2	yes	—
509	#397	C₂²×C₁₃₉	1	1	yes	characteristic
510	#397	C₂²×C₁₃₉	1	1	yes	characteristic
511	#397	C₂²×C₁₃₉	1	2	yes	—
512	#397	C₂²×C₁₃₉	1	2	yes	—
513	#397	C₂²×C₁₃₉	1	2	yes	complemented
514	#395	C₂²×C₁₃₉	1	2	yes	complemented
515	#394	C₂²×C₁₃₉	1	2	yes	—
516	#394	C₂²×C₁₃₉	1	2	yes	—
517	#394	C₂²×C₁₃₉	1	2	yes	—
518	#394	C₂²×C₁₃₉	1	2	yes	—
519	#393	C₂²×C₁₃₉	1	2	yes	complemented
520	#392	C₂²×C₁₃₉	1	1	yes	characteristic
521	#392	C₂²×C₁₃₉	1	1	yes	characteristic
522	#391	C₂²×C₁₃₉	1	2	yes	complemented
523	#391	C₂²×C₁₃₉	1	2	yes	complemented
524	#390	C₂²×C₁₃₉	1	2	yes	complemented
525	#389	C₂²×C₁₃₉	1	2	yes	complemented
526	#389	C₂²×C₁₃₉	1	2	yes	complemented
527	#389	C₂²×C₁₃₉	1	2	yes	complemented
528	#388	C₂²×C₁₃₉	1	2	yes	complemented
529	#388	C₂²×C₁₃₉	1	2	yes	complemented
530	#388	C₂²×C₁₃₉	1	2	yes	complemented
531	#388	C₂²×C₁₃₉	1	2	yes	complemented
532	#388	C₂²×C₁₃₉	1	2	yes	complemented
533	#387	C₂²×C₁₃₉	1	2	yes	complemented
534	#387	C₂²×C₁₃₉	1	2	yes	complemented
535	#387	C₂²×C₁₃₉	1	2	yes	complemented
536	#387	C₂²×C₁₃₉	1	2	yes	complemented
537	#387	C₂²×C₁₃₉	1	2	yes	complemented
538	#386	C₂²×C₁₃₉	1	2	yes	—
539	#386	C₂²×C₁₃₉	1	2	yes	—
540	#386	C₂²×C₁₃₉	1	2	yes	—
541	#386	C₂²×C₁₃₉	1	2	yes	—
542	#386	C₂²×C₁₃₉	1	2	yes	complemented
543	#385	C₂²×C₁₃₉	1	2	yes	—
544	#385	C₂²×C₁₃₉	1	2	yes	complemented
545	#384	C₂²×C₁₃₉	1	2	yes	complemented
546	#382	C₂²×C₁₃₉	1	2	yes	complemented
547	#381	C₂²×C₁₃₉	1	2	yes	—
548	#380	C₂²×C₁₃₉	1	1	yes	characteristic
549	#380	C₂²×C₁₃₉	1	2	yes	—
550	#380	C₂²×C₁₃₉	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
552	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
553	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
558	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
562	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
563	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
564	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
567	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	#126	—	2	8	no	—
579	#126	—	2	8	no	—
580	#124	—	2	8	no	—
581	#123	—	2	8	no	—
582	#123	—	2	8	no	—
583	#123	—	2	8	no	—
584	#123	—	2	8	no	—
585	C₂²⋊Q₈	—	2	8	no	—
586	C₂²⋊Q₈	—	2	8	no	—
587	#121	—	2	4	no	—
588	#120	—	2	8	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	2	8	no	—
591	#117	—	2	8	no	—
592	#117	—	2	8	no	—
593	C₂×C₄⋊C₄	—	2	4	no	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	—	2	8	no	—
612	C₂×C₂²⋊C₄	—	2	4	no	—
613	C₂×C₂²⋊C₄	—	2	4	no	—
614	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
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	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
643	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	#95	C₂³×C₁₃₉	1	1	yes	characteristic
668	#95	C₂³×C₁₃₉	1	1	yes	characteristic
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	4	2	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
677	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
680	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
713	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
770	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
771	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
772	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	4	8	no	—
799	C₂³	—	8	2	no	—
800	C₂³	—	8	2	no	—
801	C₂³	—	8	4	no	—
802	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
803	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
804	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
805	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
806	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
807	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
808	Q₈	—	8	4	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	8	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	4	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	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	8	4	no	—
853	C₂×C₄	—	8	4	no	—
854	C₂×C₄	—	8	4	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
857	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
858	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
859	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
860	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	8	8	no	—
883	C₂²	#532×C₁₃₉	1	4	yes	—
884	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
886	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
887	C₂²	#585×C₁₃₉	1	2	yes	—
888	C₂²	#585×C₁₃₉	1	2	yes	—
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₂	—	2	4	no	—
905	C₂	—	4	2	no	—
906	C₂	—	4	2	no	—
907	C₂	—	8	2	no	—
908	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
909	C₂	#3485×C₁₃₉	1	2	yes	—
910	C₂	#3491×C₁₃₉	1	1	yes	characteristic
911	C₂	#3510×C₁₃₉	1	1	yes	characteristic
912	C₂	#3521×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. C₂×#551×C₁₃₉	C₂	semidirect
2. #2663×C₁₃₉	C₂	semidirect
4. #2602×C₁₃₉	C₂	semidirect
5. #2557×C₁₃₉	C₂	semidirect
6. #2553×C₁₃₉	C₂	semidirect
7. #2549×C₁₃₉	C₂	semidirect
8. #2521×C₁₃₉	C₂	semidirect
9. #2501×C₁₃₉	C₂	semidirect
10. #2499×C₁₃₉	C₂	semidirect
11. #2496×C₁₃₉	C₂	semidirect
12. #2488×C₁₃₉	C₂	semidirect
13. #2412×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. C₂×#397×C₁₃₉	C₂	semidirect
16. #2364×C₁₃₉	C₂	semidirect
17. #2359×C₁₃₉	C₂	semidirect
18. #2344×C₁₃₉	C₂	semidirect
19. #2273×C₁₃₉	C₂	semidirect
41. #400×C₁₃₉	C₂²	semidirect
42. #400×C₁₃₉	C₂²	semidirect
43. #399×C₁₃₉	C₂²	semidirect
44. #399×C₁₃₉	C₂²	semidirect
45. #398×C₁₃₉	C₂²	semidirect
56. #397×C₁₃₉	C₂²	semidirect
57. #395×C₁₃₉	C₂²	semidirect
62. #393×C₁₃₉	C₂²	semidirect
65. #391×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
67. #390×C₁₃₉	C₂²	semidirect
68. #389×C₁₃₉	C₂²	semidirect
69. #389×C₁₃₉	C₂²	semidirect
70. #389×C₁₃₉	C₂²	semidirect
71. #388×C₁₃₉	C₂²	semidirect
72. #388×C₁₃₉	C₂²	semidirect
73. #388×C₁₃₉	C₂²	semidirect
74. #388×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
76. #387×C₁₃₉	C₂²	semidirect
77. #387×C₁₃₉	C₂²	semidirect
78. #387×C₁₃₉	C₂²	semidirect
79. #387×C₁₃₉	C₂²	semidirect
80. #387×C₁₃₉	C₂²	semidirect
85. #386×C₁₃₉	C₂²	semidirect
87. #385×C₁₃₉	C₂²	semidirect
88. #384×C₁₃₉	C₂²	semidirect
89. #382×C₁₃₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
95. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
157. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
456. #36012	C₁₃₉	direct (N × H)
457. C₁₃₉	#36012	direct (N × H)
458. C₂×#551	C₂×C₁₃₉	semidirect
459. #2663	C₂×C₁₃₉	semidirect
461. #2602	C₂×C₁₃₉	semidirect
462. #2557	C₂×C₁₃₉	semidirect
463. #2553	C₂×C₁₃₉	semidirect
464. #2549	C₂×C₁₃₉	semidirect
465. #2521	C₂×C₁₃₉	semidirect
466. #2501	C₂×C₁₃₉	semidirect
467. #2499	C₂×C₁₃₉	semidirect
468. #2496	C₂×C₁₃₉	semidirect
469. #2488	C₂×C₁₃₉	semidirect
470. #2412	C₂×C₁₃₉	semidirect
471. #2395	C₂×C₁₃₉	semidirect
472. C₂×#397	C₂×C₁₃₉	semidirect
473. #2364	C₂×C₁₃₉	semidirect
474. #2359	C₂×C₁₃₉	semidirect
475. #2344	C₂×C₁₃₉	semidirect
476. #2273	C₂×C₁₃₉	semidirect
498. #400	C₂²×C₁₃₉	semidirect
499. #400	C₂²×C₁₃₉	semidirect
500. #399	C₂²×C₁₃₉	semidirect
501. #399	C₂²×C₁₃₉	semidirect
502. #398	C₂²×C₁₃₉	semidirect
513. #397	C₂²×C₁₃₉	semidirect
514. #395	C₂²×C₁₃₉	semidirect
519. #393	C₂²×C₁₃₉	semidirect
522. #391	C₂²×C₁₃₉	semidirect
523. #391	C₂²×C₁₃₉	semidirect
524. #390	C₂²×C₁₃₉	semidirect
525. #389	C₂²×C₁₃₉	semidirect
526. #389	C₂²×C₁₃₉	semidirect
527. #389	C₂²×C₁₃₉	semidirect
528. #388	C₂²×C₁₃₉	semidirect
529. #388	C₂²×C₁₃₉	semidirect
530. #388	C₂²×C₁₃₉	semidirect
531. #388	C₂²×C₁₃₉	semidirect
532. #388	C₂²×C₁₃₉	semidirect
533. #387	C₂²×C₁₃₉	semidirect
534. #387	C₂²×C₁₃₉	semidirect
535. #387	C₂²×C₁₃₉	semidirect
536. #387	C₂²×C₁₃₉	semidirect
537. #387	C₂²×C₁₃₉	semidirect
542. #386	C₂²×C₁₃₉	semidirect
544. #385	C₂²×C₁₃₉	semidirect
545. #384	C₂²×C₁₃₉	semidirect
546. #382	C₂²×C₁₃₉	semidirect
551. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
552. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
561. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
562. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
614. C₂×C₂²⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₁₃₉	2
#2663×C₁₃₉	2
#2617×C₁₃₉	2
#2602×C₁₃₉	2
#2557×C₁₃₉	2
#2553×C₁₃₉	2
#2549×C₁₃₉	2
#2521×C₁₃₉	2
#2501×C₁₃₉	2
#2499×C₁₃₉	2
#2496×C₁₃₉	2
#2488×C₁₃₉	2
#2412×C₁₃₉	2
#2395×C₁₃₉	2
C₂×#397×C₁₃₉	2
#2364×C₁₃₉	2
#2359×C₁₃₉	2
#2344×C₁₃₉	2
#2273×C₁₃₉	2
#36012	139

Subgroups — C139×#36012 #48030608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36012 #48030608