Subgroups — C₁₃₉×#36002 #48030598

Order 35584.

1672 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2654×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2632×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2605×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2588×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2560×C₁₃₉	C₂	1	2	yes	maximal
6	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2532×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2529×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2474×C₁₃₉	C₂	1	2	yes	maximal
10	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2372×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2356×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2276×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#399×C₁₃₉	C₂²	1	2	yes	—
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	1	yes	characteristic
38	#398×C₁₃₉	C₂²	1	1	yes	characteristic
39	#397×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#396×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#395×C₁₃₉	C₂²	1	2	yes	—
45	#395×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	1	yes	characteristic
48	#395×C₁₃₉	C₂²	1	1	yes	characteristic
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	2	yes	—
51	#393×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	2	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#383×C₁₃₉	C₂²	1	1	yes	characteristic
88	#383×C₁₃₉	C₂²	1	1	yes	characteristic
89	#382×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	—
103	#376×C₁₃₉	C₂²	1	2	yes	—
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic
106	#376×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
114	#126×C₁₃₉	—	2	8	no	—
115	#124×C₁₃₉	—	2	4	no	—
116	#124×C₁₃₉	—	4	2	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₄×Q₈×C₁₃₉	—	2	8	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	C₄×Q₈×C₁₃₉	—	4	4	no	—
122	#117×C₁₃₉	—	4	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	1	yes	characteristic
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	1	yes	characteristic
177	#95×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	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₁₃₉	—	2	4	no	—
206	C₂×Q₈×C₁₃₉	—	2	2	no	—
207	C₂×Q₈×C₁₃₉	—	2	2	no	—
208	C₂×Q₈×C₁₃₉	—	2	4	no	—
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	2	2	no	—
211	C₂×Q₈×C₁₃₉	—	2	4	no	—
212	C₂×Q₈×C₁₃₉	—	4	2	no	—
213	C₂×Q₈×C₁₃₉	—	4	1	no	—
214	C₂×Q₈×C₁₃₉	—	4	1	no	—
215	C₂×Q₈×C₁₃₉	—	4	1	no	—
216	C₂×D₄×C₁₃₉	—	2	2	no	—
217	C₂×D₄×C₁₃₉	—	4	1	no	—
218	C₂×D₄×C₁₃₉	—	4	1	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	4	2	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	4	no	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	4	no	—
283	C₄²×C₁₃₉	—	2	4	no	—
284	C₄²×C₁₃₉	—	4	2	no	—
285	C₄²×C₁₃₉	—	4	2	no	—
286	C₄²×C₁₃₉	—	4	2	no	—
287	C₄²×C₁₃₉	—	4	1	no	—
288	C₄²×C₁₃₉	—	4	1	no	—
289	C₄²×C₁₃₉	#41	1	4	yes	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
298	Q₈×C₁₃₉	—	2	8	no	—
299	Q₈×C₁₃₉	—	4	4	no	—
300	Q₈×C₁₃₉	—	4	8	no	—
301	Q₈×C₁₃₉	—	8	2	no	—
302	D₄×C₁₃₉	—	8	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
345	C₂×C₄×C₁₃₉	—	4	8	no	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
353	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
363	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
365	C₂²×C₁₃₉	#585	1	1	yes	characteristic
366	C₄×C₁₃₉	—	2	4	no	—
367	C₄×C₁₃₉	—	2	2	no	—
368	C₄×C₁₃₉	—	2	2	no	—
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	2	2	no	—
371	C₄×C₁₃₉	—	2	4	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	2	4	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	1	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	1	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₂×C₁₃₉	—	8	2	no	—
385	C₂×C₁₃₉	#3444	1	1	yes	characteristic
386	C₂×C₁₃₉	#3494	1	1	yes	characteristic
387	C₂×C₁₃₉	#3509	1	1	yes	characteristic
388	C₂×C₁₃₉	#3518	1	2	yes	—
389	C₂×C₁₃₉	#3520	1	2	yes	—
390	#36002	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₁₃₉	#36002	1	1	yes	characteristic, direct product factor, Sylow
392	#2654	C₂×C₁₃₉	1	2	yes	complemented
393	#2632	C₂×C₁₃₉	1	1	yes	characteristic
394	#2605	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2588	C₂×C₁₃₉	1	2	yes	complemented
396	#2560	C₂×C₁₃₉	1	2	yes	—
397	#2545	C₂×C₁₃₉	1	1	yes	characteristic
398	#2532	C₂×C₁₃₉	1	2	yes	complemented
399	#2529	C₂×C₁₃₉	1	2	yes	complemented
400	#2474	C₂×C₁₃₉	1	2	yes	—
401	#2469	C₂×C₁₃₉	1	2	yes	complemented
402	#2465	C₂×C₁₃₉	1	2	yes	complemented
403	#2451	C₂×C₁₃₉	1	2	yes	complemented
404	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2396	C₂×C₁₃₉	1	2	yes	complemented
406	#2373	C₂×C₁₃₉	1	2	yes	complemented
407	#2372	C₂×C₁₃₉	1	1	yes	characteristic
408	#2362	C₂×C₁₃₉	1	2	yes	complemented
409	#2356	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2276	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
419	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
420	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
421	#400	C₂²×C₁₃₉	1	2	yes	—
422	#400	C₂²×C₁₃₉	1	2	yes	—
423	#400	C₂²×C₁₃₉	1	2	yes	—
424	#399	C₂²×C₁₃₉	1	2	yes	—
425	#398	C₂²×C₁₃₉	1	2	yes	—
426	#398	C₂²×C₁₃₉	1	1	yes	characteristic
427	#398	C₂²×C₁₃₉	1	2	yes	—
428	#398	C₂²×C₁₃₉	1	1	yes	characteristic
429	#398	C₂²×C₁₃₉	1	2	yes	—
430	#397	C₂²×C₁₃₉	1	2	yes	—
431	#397	C₂²×C₁₃₉	1	2	yes	—
432	#396	C₂²×C₁₃₉	1	2	yes	—
433	#396	C₂²×C₁₃₉	1	2	yes	—
434	#396	C₂²×C₁₃₉	1	2	yes	—
435	#395	C₂²×C₁₃₉	1	2	yes	—
436	#395	C₂²×C₁₃₉	1	2	yes	—
437	#395	C₂²×C₁₃₉	1	2	yes	—
438	#395	C₂²×C₁₃₉	1	1	yes	characteristic
439	#395	C₂²×C₁₃₉	1	1	yes	characteristic
440	#394	C₂²×C₁₃₉	1	2	yes	—
441	#393	C₂²×C₁₃₉	1	2	yes	—
442	#393	C₂²×C₁₃₉	1	2	yes	—
443	#391	C₂²×C₁₃₉	1	2	yes	—
444	#391	C₂²×C₁₃₉	1	1	yes	characteristic
445	#391	C₂²×C₁₃₉	1	2	yes	—
446	#391	C₂²×C₁₃₉	1	2	yes	—
447	#391	C₂²×C₁₃₉	1	2	yes	—
448	#391	C₂²×C₁₃₉	1	2	yes	—
449	#390	C₂²×C₁₃₉	1	1	yes	characteristic
450	#389	C₂²×C₁₃₉	1	2	yes	—
451	#389	C₂²×C₁₃₉	1	2	yes	—
452	#389	C₂²×C₁₃₉	1	2	yes	—
453	#388	C₂²×C₁₃₉	1	2	yes	—
454	#388	C₂²×C₁₃₉	1	2	yes	—
455	#388	C₂²×C₁₃₉	1	2	yes	—
456	#388	C₂²×C₁₃₉	1	2	yes	—
457	#388	C₂²×C₁₃₉	1	2	yes	—
458	#388	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#388	C₂²×C₁₃₉	1	2	yes	—
461	#388	C₂²×C₁₃₉	1	2	yes	—
462	#388	C₂²×C₁₃₉	1	2	yes	—
463	#388	C₂²×C₁₃₉	1	2	yes	—
464	#388	C₂²×C₁₃₉	1	2	yes	—
465	#388	C₂²×C₁₃₉	1	2	yes	—
466	#387	C₂²×C₁₃₉	1	2	yes	—
467	#387	C₂²×C₁₃₉	1	2	yes	—
468	#387	C₂²×C₁₃₉	1	2	yes	—
469	#387	C₂²×C₁₃₉	1	2	yes	—
470	#387	C₂²×C₁₃₉	1	2	yes	—
471	#387	C₂²×C₁₃₉	1	2	yes	—
472	#387	C₂²×C₁₃₉	1	2	yes	—
473	#387	C₂²×C₁₃₉	1	2	yes	—
474	#387	C₂²×C₁₃₉	1	2	yes	—
475	#387	C₂²×C₁₃₉	1	2	yes	—
476	#386	C₂²×C₁₃₉	1	2	yes	—
477	#385	C₂²×C₁₃₉	1	2	yes	—
478	#383	C₂²×C₁₃₉	1	1	yes	characteristic
479	#383	C₂²×C₁₃₉	1	1	yes	characteristic
480	#382	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
494	#376	C₂²×C₁₃₉	1	1	yes	characteristic
495	#376	C₂²×C₁₃₉	1	1	yes	characteristic
496	#376	C₂²×C₁₃₉	1	1	yes	characteristic
497	#376	C₂²×C₁₃₉	1	2	yes	—
498	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₄⋊Q₈	—	4	2	no	—
505	#126	—	2	8	no	—
506	#124	—	2	4	no	—
507	#124	—	4	2	no	—
508	C₂²⋊Q₈	—	2	8	no	—
509	C₄×Q₈	—	2	8	no	—
510	C₄×Q₈	—	2	4	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×Q₈	—	4	4	no	—
513	#117	—	4	4	no	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
564	#95	C₂³×C₁₃₉	1	1	yes	characteristic
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	1	yes	characteristic
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	1	yes	characteristic
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	1	yes	characteristic
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	1	yes	characteristic
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	4	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	1	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	4	1	no	—
609	C₂×D₄	—	4	1	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	4	2	no	—
676	C₄²	—	4	2	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	1	no	—
679	C₄²	—	4	1	no	—
680	C₄²	#41×C₁₃₉	1	4	yes	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
689	Q₈	—	2	8	no	—
690	Q₈	—	4	4	no	—
691	Q₈	—	4	8	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	8	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
738	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
740	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
741	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
742	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
743	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
744	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
754	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
755	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
756	C₂²	#585×C₁₃₉	1	1	yes	characteristic
757	C₄	—	2	4	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	4	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₂	—	8	2	no	—
776	C₂	#3444×C₁₃₉	1	1	yes	characteristic
777	C₂	#3494×C₁₃₉	1	1	yes	characteristic
778	C₂	#3509×C₁₃₉	1	1	yes	characteristic
779	C₂	#3518×C₁₃₉	1	2	yes	—
780	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2654×C₁₃₉	C₂	semidirect
3. #2605×C₁₃₉	C₂	semidirect
4. #2588×C₁₃₉	C₂	semidirect
7. #2532×C₁₃₉	C₂	semidirect
8. #2529×C₁₃₉	C₂	semidirect
10. #2469×C₁₃₉	C₂	semidirect
11. #2465×C₁₃₉	C₂	semidirect
12. #2451×C₁₃₉	C₂	semidirect
13. #2399×C₁₃₉	C₂	semidirect
14. #2396×C₁₃₉	C₂	semidirect
15. #2373×C₁₃₉	C₂	semidirect
17. #2362×C₁₃₉	C₂	semidirect
18. #2356×C₁₃₉	C₂	semidirect
19. #2276×C₁₃₉	C₂	semidirect
390. #36002	C₁₃₉	direct (N × H)
391. C₁₃₉	#36002	direct (N × H)
392. #2654	C₂×C₁₃₉	semidirect
394. #2605	C₂×C₁₃₉	semidirect
395. #2588	C₂×C₁₃₉	semidirect
398. #2532	C₂×C₁₃₉	semidirect
399. #2529	C₂×C₁₃₉	semidirect
401. #2469	C₂×C₁₃₉	semidirect
402. #2465	C₂×C₁₃₉	semidirect
403. #2451	C₂×C₁₃₉	semidirect
404. #2399	C₂×C₁₃₉	semidirect
405. #2396	C₂×C₁₃₉	semidirect
406. #2373	C₂×C₁₃₉	semidirect
408. #2362	C₂×C₁₃₉	semidirect
409. #2356	C₂×C₁₃₉	semidirect
410. #2276	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2654×C₁₃₉	2
#2632×C₁₃₉	2
#2605×C₁₃₉	2
#2588×C₁₃₉	2
#2560×C₁₃₉	2
#2545×C₁₃₉	2
#2532×C₁₃₉	2
#2529×C₁₃₉	2
#2474×C₁₃₉	2
#2469×C₁₃₉	2
#2465×C₁₃₉	2
#2451×C₁₃₉	2
#2399×C₁₃₉	2
#2396×C₁₃₉	2
#2373×C₁₃₉	2
#2372×C₁₃₉	2
#2362×C₁₃₉	2
#2356×C₁₃₉	2
#2276×C₁₃₉	2
#36002	139

Subgroups — C139×#36002 #48030598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36002 #48030598