Subgroups — C₁₃₉×#36396 #48030992

Order 35584.

2602 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2565×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2560×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2557×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2543×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2436×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2364×C₁₃₉	C₂	1	4	yes	maximal, complemented
16	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	#553×C₁₃₉	—	2	8	no	—
23	#548×C₁₃₉	—	2	8	no	—
24	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
50	#398×C₁₃₉	C₂²	1	4	yes	—
51	#397×C₁₃₉	C₂²	1	4	yes	—
52	#397×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#393×C₁₃₉	C₂²	1	4	yes	—
55	#392×C₁₃₉	C₂²	1	4	yes	—
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	4	yes	—
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic
62	#391×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	4	yes	—
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#388×C₁₃₉	C₂²	1	4	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#387×C₁₃₉	C₂²	1	4	yes	—
73	#387×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#386×C₁₃₉	C₂²	1	4	yes	—
76	#386×C₁₃₉	C₂²	1	4	yes	—
77	#386×C₁₃₉	C₂²	1	4	yes	—
78	#386×C₁₃₉	C₂²	1	4	yes	—
79	#386×C₁₃₉	C₂²	1	4	yes	—
80	#384×C₁₃₉	C₂²	1	1	yes	characteristic
81	#382×C₁₃₉	C₂²	1	1	yes	characteristic
82	#382×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
91	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₃₉	—	2	4	no	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	4	2	no	—
96	C₂²×Q₈×C₁₃₉	—	2	4	no	—
97	C₂²×Q₈×C₁₃₉	—	2	4	no	—
98	C₂²×Q₈×C₁₃₉	—	4	2	no	—
99	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
101	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×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	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	#127×C₁₃₉	—	4	2	no	—
119	#126×C₁₃₉	—	2	8	no	—
120	#125×C₁₃₉	—	2	4	no	—
121	#124×C₁₃₉	—	2	4	no	—
122	#124×C₁₃₉	—	2	8	no	—
123	#124×C₁₃₉	—	2	4	no	—
124	#124×C₁₃₉	—	4	2	no	—
125	#123×C₁₃₉	—	2	8	no	—
126	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
127	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
128	#121×C₁₃₉	—	2	8	no	—
129	#121×C₁₃₉	—	2	8	no	—
130	#121×C₁₃₉	—	2	4	no	—
131	#121×C₁₃₉	—	2	4	no	—
132	#121×C₁₃₉	—	2	4	no	—
133	#121×C₁₃₉	—	2	16	no	—
134	C₄×Q₈×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	—	2	8	no	—
136	C₄×D₄×C₁₃₉	—	2	8	no	—
137	C₄×D₄×C₁₃₉	—	2	8	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
140	#117×C₁₃₉	—	2	4	no	—
141	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	—	4	2	no	—
173	C₂×C₄²×C₁₃₉	—	4	2	no	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	#95×C₁₃₉	C₂³	1	4	yes	—
188	#95×C₁₃₉	C₂³	1	4	yes	—
189	#95×C₁₃₉	C₂³	1	4	yes	—
190	#95×C₁₃₉	C₂³	1	4	yes	—
191	#95×C₁₃₉	C₂³	1	4	yes	—
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	4	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
198	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	#41×C₁₃₉	—	4	16	no	—
201	C₂×Q₈×C₁₃₉	—	2	2	no	—
202	C₂×Q₈×C₁₃₉	—	2	4	no	—
203	C₂×Q₈×C₁₃₉	—	2	2	no	—
204	C₂×Q₈×C₁₃₉	—	2	4	no	—
205	C₂×Q₈×C₁₃₉	—	2	2	no	—
206	C₂×Q₈×C₁₃₉	—	2	2	no	—
207	C₂×Q₈×C₁₃₉	—	2	2	no	—
208	C₂×Q₈×C₁₃₉	—	4	2	no	—
209	C₂×Q₈×C₁₃₉	—	4	16	no	—
210	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
211	C₂×D₄×C₁₃₉	—	2	4	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	8	no	—
216	C₂×D₄×C₁₃₉	—	2	8	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	2	2	no	—
219	C₂×D₄×C₁₃₉	—	2	2	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	2	no	—
223	C₂×D₄×C₁₃₉	—	2	8	no	—
224	C₂×D₄×C₁₃₉	—	2	2	no	—
225	C₂×D₄×C₁₃₉	—	2	2	no	—
226	C₂×D₄×C₁₃₉	—	4	2	no	—
227	C₂×D₄×C₁₃₉	—	4	4	no	—
228	C₂×D₄×C₁₃₉	—	4	4	no	—
229	C₂×D₄×C₁₃₉	—	4	4	no	—
230	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	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	4	no	—
249	C₂²×C₄×C₁₃₉	—	4	4	no	—
250	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
268	C₄⋊C₄×C₁₃₉	—	2	2	no	—
269	C₄⋊C₄×C₁₃₉	—	2	2	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
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	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	4	no	—
278	C₄⋊C₄×C₁₃₉	—	2	8	no	—
279	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	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	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
296	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₄²×C₁₃₉	—	2	4	no	—
300	C₄²×C₁₃₉	—	2	4	no	—
301	C₄²×C₁₃₉	—	2	2	no	—
302	C₄²×C₁₃₉	—	2	2	no	—
303	C₄²×C₁₃₉	—	2	2	no	—
304	C₄²×C₁₃₉	—	2	2	no	—
305	C₄²×C₁₃₉	—	4	2	no	—
306	C₄²×C₁₃₉	—	4	2	no	—
307	C₄²×C₁₃₉	—	4	2	no	—
308	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	1	no	—
314	C₂³×C₁₃₉	—	2	1	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	4	no	—
320	C₂³×C₁₃₉	—	2	4	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	4	no	—
325	C₂³×C₁₃₉	—	2	4	no	—
326	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
328	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
329	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
330	Q₈×C₁₃₉	—	2	8	no	—
331	Q₈×C₁₃₉	—	4	8	no	—
332	Q₈×C₁₃₉	—	4	4	no	—
333	D₄×C₁₃₉	—	2	8	no	—
334	D₄×C₁₃₉	—	4	8	no	—
335	D₄×C₁₃₉	—	4	8	no	—
336	D₄×C₁₃₉	—	4	8	no	—
337	D₄×C₁₃₉	—	4	4	no	—
338	D₄×C₁₃₉	—	4	4	no	—
339	D₄×C₁₃₉	—	8	8	no	—
340	D₄×C₁₃₉	—	8	4	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	8	no	—
354	C₂×C₄×C₁₃₉	—	2	8	no	—
355	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
364	C₂×C₄×C₁₃₉	—	2	4	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	4	no	—
371	C₂×C₄×C₁₃₉	—	2	4	no	—
372	C₂×C₄×C₁₃₉	—	4	8	no	—
373	C₂×C₄×C₁₃₉	—	4	8	no	—
374	C₂×C₄×C₁₃₉	—	4	8	no	—
375	C₂×C₄×C₁₃₉	—	4	8	no	—
376	C₂×C₄×C₁₃₉	—	8	4	no	—
377	C₂×C₄×C₁₃₉	—	8	4	no	—
378	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
384	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
386	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
388	C₂²×C₁₃₉	—	2	2	no	—
389	C₂²×C₁₃₉	—	2	4	no	—
390	C₂²×C₁₃₉	—	2	2	no	—
391	C₂²×C₁₃₉	—	2	4	no	—
392	C₂²×C₁₃₉	—	2	2	no	—
393	C₂²×C₁₃₉	—	2	2	no	—
394	C₂²×C₁₃₉	—	2	2	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	—	4	2	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	4	no	—
402	C₂²×C₁₃₉	—	4	4	no	—
403	C₂²×C₁₃₉	—	4	2	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	4	no	—
406	C₂²×C₁₃₉	—	4	4	no	—
407	C₂²×C₁₃₉	#532	1	4	yes	—
408	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
409	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
410	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂²×C₁₃₉	#585	1	2	yes	—
413	C₄×C₁₃₉	—	2	2	no	—
414	C₄×C₁₃₉	—	2	2	no	—
415	C₄×C₁₃₉	—	2	2	no	—
416	C₄×C₁₃₉	—	2	4	no	—
417	C₄×C₁₃₉	—	2	2	no	—
418	C₄×C₁₃₉	—	2	4	no	—
419	C₄×C₁₃₉	—	2	4	no	—
420	C₄×C₁₃₉	—	4	2	no	—
421	C₄×C₁₃₉	—	4	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	2	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	2	no	—
427	C₄×C₁₃₉	#546	1	4	yes	—
428	C₂×C₁₃₉	—	2	4	no	—
429	C₂×C₁₃₉	—	4	2	no	—
430	C₂×C₁₃₉	—	8	2	no	—
431	C₂×C₁₃₉	—	8	2	no	—
432	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
433	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
434	C₂×C₁₃₉	#3480	1	2	yes	—
435	C₂×C₁₃₉	#3500	1	1	yes	characteristic
436	C₂×C₁₃₉	#3505	1	2	yes	—
437	#36396	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₁₃₉	#36396	1	1	yes	characteristic, direct product factor, Sylow
439	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	C₂×#548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
441	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
444	#2565	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2560	C₂×C₁₃₉	1	4	yes	complemented
446	#2557	C₂×C₁₃₉	1	4	yes	complemented
447	#2544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	#2543	C₂×C₁₃₉	1	4	yes	complemented
449	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
451	#2436	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2364	C₂×C₁₃₉	1	4	yes	complemented
454	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
455	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
456	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
457	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
459	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
460	#553	—	2	8	no	—
461	#548	—	2	8	no	—
462	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
464	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
465	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
474	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
478	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
488	#398	C₂²×C₁₃₉	1	4	yes	—
489	#397	C₂²×C₁₃₉	1	4	yes	—
490	#397	C₂²×C₁₃₉	1	4	yes	—
491	#394	C₂²×C₁₃₉	1	4	yes	—
492	#393	C₂²×C₁₃₉	1	4	yes	—
493	#392	C₂²×C₁₃₉	1	4	yes	—
494	#391	C₂²×C₁₃₉	1	4	yes	—
495	#391	C₂²×C₁₃₉	1	1	yes	characteristic
496	#391	C₂²×C₁₃₉	1	1	yes	characteristic
497	#391	C₂²×C₁₃₉	1	1	yes	characteristic
498	#391	C₂²×C₁₃₉	1	1	yes	characteristic
499	#391	C₂²×C₁₃₉	1	1	yes	characteristic
500	#391	C₂²×C₁₃₉	1	1	yes	characteristic
501	#390	C₂²×C₁₃₉	1	4	yes	—
502	#390	C₂²×C₁₃₉	1	1	yes	characteristic
503	#390	C₂²×C₁₃₉	1	1	yes	characteristic
504	#390	C₂²×C₁₃₉	1	1	yes	characteristic
505	#390	C₂²×C₁₃₉	1	1	yes	characteristic
506	#388	C₂²×C₁₃₉	1	4	yes	—
507	#388	C₂²×C₁₃₉	1	4	yes	—
508	#388	C₂²×C₁₃₉	1	4	yes	—
509	#388	C₂²×C₁₃₉	1	4	yes	—
510	#387	C₂²×C₁₃₉	1	4	yes	—
511	#387	C₂²×C₁₃₉	1	4	yes	—
512	#386	C₂²×C₁₃₉	1	4	yes	—
513	#386	C₂²×C₁₃₉	1	4	yes	—
514	#386	C₂²×C₁₃₉	1	4	yes	—
515	#386	C₂²×C₁₃₉	1	4	yes	—
516	#386	C₂²×C₁₃₉	1	4	yes	—
517	#386	C₂²×C₁₃₉	1	4	yes	—
518	#384	C₂²×C₁₃₉	1	1	yes	characteristic
519	#382	C₂²×C₁₃₉	1	1	yes	characteristic
520	#382	C₂²×C₁₃₉	1	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
523	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
529	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
530	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
531	C₂×#41	—	2	4	no	—
532	C₂×#41	—	2	4	no	—
533	C₂×#41	—	4	2	no	—
534	C₂²×Q₈	—	2	4	no	—
535	C₂²×Q₈	—	2	4	no	—
536	C₂²×Q₈	—	4	2	no	—
537	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
539	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
556	#127	—	4	2	no	—
557	#126	—	2	8	no	—
558	#125	—	2	4	no	—
559	#124	—	2	4	no	—
560	#124	—	2	8	no	—
561	#124	—	2	4	no	—
562	#124	—	4	2	no	—
563	#123	—	2	8	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	8	no	—
566	#121	—	2	8	no	—
567	#121	—	2	8	no	—
568	#121	—	2	4	no	—
569	#121	—	2	4	no	—
570	#121	—	2	4	no	—
571	#121	—	2	16	no	—
572	C₄×Q₈	—	2	4	no	—
573	C₄×D₄	—	2	8	no	—
574	C₄×D₄	—	2	8	no	—
575	C₄×D₄	—	2	8	no	—
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
578	#117	—	2	4	no	—
579	C₂×C₄⋊C₄	—	2	4	no	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄²	—	4	2	no	—
611	C₂×C₄²	—	4	2	no	—
612	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄²	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	1	yes	characteristic
623	#95	C₂³×C₁₃₉	1	4	yes	—
624	#95	C₂³×C₁₃₉	1	4	yes	—
625	#95	C₂³×C₁₃₉	1	4	yes	—
626	#95	C₂³×C₁₃₉	1	4	yes	—
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	4	yes	—
631	#95	C₂³×C₁₃₉	1	4	yes	—
632	#95	C₂³×C₁₃₉	1	4	yes	—
633	#95	C₂³×C₁₃₉	1	4	yes	—
634	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
638	#41	—	4	16	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	4	2	no	—
647	C₂×Q₈	—	4	16	no	—
648	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	2	8	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	8	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	4	no	—
687	C₂²×C₄	—	4	4	no	—
688	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
689	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
690	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
691	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	8	no	—
717	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	—	4	4	no	—
734	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
735	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	4	no	—
764	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
765	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
766	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
767	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
768	Q₈	—	2	8	no	—
769	Q₈	—	4	8	no	—
770	Q₈	—	4	4	no	—
771	D₄	—	2	8	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	8	8	no	—
778	D₄	—	8	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	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	4	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
821	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
822	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
823	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
824	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
825	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	4	4	no	—
845	C₂²	#532×C₁₃₉	1	4	yes	—
846	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
847	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
848	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
849	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
850	C₂²	#585×C₁₃₉	1	2	yes	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	4	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	#546×C₁₃₉	1	4	yes	—
866	C₂	—	2	4	no	—
867	C₂	—	4	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
871	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
872	C₂	#3480×C₁₃₉	1	2	yes	—
873	C₂	#3500×C₁₃₉	1	1	yes	characteristic
874	C₂	#3505×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#553×C₁₃₉	C₂	semidirect
2. C₂×#548×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2565×C₁₃₉	C₂	semidirect
7. #2560×C₁₃₉	C₂	semidirect
8. #2557×C₁₃₉	C₂	semidirect
9. #2544×C₁₃₉	C₂	semidirect
10. #2543×C₁₃₉	C₂	semidirect
11. #2504×C₁₃₉	C₂	semidirect
12. #2499×C₁₃₉	C₂	semidirect
13. #2436×C₁₃₉	C₂	semidirect
14. #2431×C₁₃₉	C₂	semidirect
15. #2364×C₁₃₉	C₂	semidirect
16. C₄×#124×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
18. C₂×#391×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
139. C₄×D₄×C₁₃₉	D₄	semidirect
252. C₂²×C₄×C₁₃₉	#41	semidirect
437. #36396	C₁₃₉	direct (N × H)
438. C₁₃₉	#36396	direct (N × H)
439. C₂×#553	C₂×C₁₃₉	semidirect
440. C₂×#548	C₂×C₁₃₉	semidirect
441. #2861	C₂×C₁₃₉	semidirect
442. #2856	C₂×C₁₃₉	semidirect
443. #2850	C₂×C₁₃₉	semidirect
444. #2565	C₂×C₁₃₉	semidirect
445. #2560	C₂×C₁₃₉	semidirect
446. #2557	C₂×C₁₃₉	semidirect
447. #2544	C₂×C₁₃₉	semidirect
448. #2543	C₂×C₁₃₉	semidirect
449. #2504	C₂×C₁₃₉	semidirect
450. #2499	C₂×C₁₃₉	semidirect
451. #2436	C₂×C₁₃₉	semidirect
452. #2431	C₂×C₁₃₉	semidirect
453. #2364	C₂×C₁₃₉	semidirect
454. C₄×#124	C₂×C₁₃₉	semidirect
455. #2297	C₂×C₁₃₉	semidirect
456. C₂×#391	C₂×C₁₃₉	semidirect
457. C₄²×D₄	C₂×C₁₃₉	semidirect
577. C₄×D₄	D₄×C₁₃₉	semidirect
690. C₂²×C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2861×C₁₃₉	2
#2856×C₁₃₉	2
#2850×C₁₃₉	2
#2565×C₁₃₉	2
#2560×C₁₃₉	2
#2557×C₁₃₉	2
#2544×C₁₃₉	2
#2543×C₁₃₉	2
#2504×C₁₃₉	2
#2499×C₁₃₉	2
#2436×C₁₃₉	2
#2431×C₁₃₉	2
#2364×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36396	139

Subgroups — C139×#36396 #48030992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36396 #48030992