Subgroups — C₁₃₉×#36376 #48030972

Order 35584.

2506 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×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	#2556×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2521×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
15	#2359×C₁₃₉	C₂	1	4	yes	maximal, complemented
16	C₄×C₄⋊Q₈×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	#552×C₁₃₉	—	2	8	no	—
23	#548×C₁₃₉	—	2	8	no	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
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	#399×C₁₃₉	C₂²	1	4	yes	—
51	#398×C₁₃₉	C₂²	1	4	yes	—
52	#397×C₁₃₉	C₂²	1	4	yes	—
53	#396×C₁₃₉	C₂²	1	4	yes	—
54	#395×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#391×C₁₃₉	C₂²	1	4	yes	—
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
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	#391×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	4	yes	—
68	#389×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	#388×C₁₃₉	C₂²	1	4	yes	—
73	#387×C₁₃₉	C₂²	1	4	yes	—
74	#387×C₁₃₉	C₂²	1	4	yes	—
75	#386×C₁₃₉	C₂²	1	4	yes	—
76	#386×C₁₃₉	C₂²	1	4	yes	—
77	#385×C₁₃₉	C₂²	1	4	yes	—
78	#385×C₁₃₉	C₂²	1	4	yes	—
79	#384×C₁₃₉	C₂²	1	1	yes	characteristic
80	#384×C₁₃₉	C₂²	1	1	yes	characteristic
81	#382×C₁₃₉	C₂²	1	1	yes	characteristic
82	#380×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
101	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	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	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
115	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
116	#126×C₁₃₉	—	2	8	no	—
117	#125×C₁₃₉	—	2	8	no	—
118	#125×C₁₃₉	—	2	4	no	—
119	#124×C₁₃₉	—	2	8	no	—
120	#124×C₁₃₉	—	2	4	no	—
121	#124×C₁₃₉	—	4	2	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#123×C₁₃₉	—	2	16	no	—
124	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
125	C₂²⋊Q₈×C₁₃₉	—	2	4	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	4	no	—
130	C₄×Q₈×C₁₃₉	—	2	4	no	—
131	C₄×Q₈×C₁₃₉	—	2	4	no	—
132	C₄×D₄×C₁₃₉	—	2	8	no	—
133	C₄×D₄×C₁₃₉	—	2	8	no	—
134	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
135	#117×C₁₃₉	—	2	4	no	—
136	#117×C₁₃₉	—	2	8	no	—
137	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	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	4	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	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	4	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	4	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	—	4	2	no	—
172	C₂×C₄²×C₁₃₉	—	4	2	no	—
173	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	4	yes	—
196	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	#41×C₁₃₉	—	4	16	no	—
200	C₂×Q₈×C₁₃₉	—	2	2	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	2	no	—
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	2	no	—
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	4	2	no	—
211	C₂×Q₈×C₁₃₉	—	4	16	no	—
212	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	4	no	—
216	C₂×D₄×C₁₃₉	—	2	8	no	—
217	C₂×D₄×C₁₃₉	—	2	2	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	2	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	4	2	no	—
222	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	2	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	8	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	4	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
259	C₄⋊C₄×C₁₃₉	—	2	2	no	—
260	C₄⋊C₄×C₁₃₉	—	2	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	2	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	8	no	—
273	C₄⋊C₄×C₁₃₉	—	2	8	no	—
274	C₄⋊C₄×C₁₃₉	—	2	8	no	—
275	C₄⋊C₄×C₁₃₉	—	4	4	no	—
276	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
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	8	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
289	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	complemented
292	C₄²×C₁₃₉	—	2	4	no	—
293	C₄²×C₁₃₉	—	2	4	no	—
294	C₄²×C₁₃₉	—	2	4	no	—
295	C₄²×C₁₃₉	—	2	4	no	—
296	C₄²×C₁₃₉	—	2	2	no	—
297	C₄²×C₁₃₉	—	2	2	no	—
298	C₄²×C₁₃₉	—	2	2	no	—
299	C₄²×C₁₃₉	—	2	2	no	—
300	C₄²×C₁₃₉	—	2	4	no	—
301	C₄²×C₁₃₉	—	4	2	no	—
302	C₄²×C₁₃₉	—	4	2	no	—
303	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
304	C₂³×C₁₃₉	—	2	1	no	—
305	C₂³×C₁₃₉	—	2	1	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	4	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	4	no	—
316	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
318	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
319	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
320	Q₈×C₁₃₉	—	2	8	no	—
321	Q₈×C₁₃₉	—	4	8	no	—
322	Q₈×C₁₃₉	—	4	4	no	—
323	Q₈×C₁₃₉	—	4	4	no	—
324	D₄×C₁₃₉	—	2	8	no	—
325	D₄×C₁₃₉	—	4	8	no	—
326	D₄×C₁₃₉	—	4	8	no	—
327	D₄×C₁₃₉	—	4	4	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	1	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	1	no	—
337	C₂×C₄×C₁₃₉	—	2	1	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	8	no	—
343	C₂×C₄×C₁₃₉	—	2	8	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
351	C₂×C₄×C₁₃₉	—	2	4	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	4	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	4	8	no	—
362	C₂×C₄×C₁₃₉	—	4	8	no	—
363	C₂×C₄×C₁₃₉	—	4	8	no	—
364	C₂×C₄×C₁₃₉	—	4	8	no	—
365	C₂×C₄×C₁₃₉	—	4	8	no	—
366	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
372	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
373	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
374	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
377	C₂²×C₁₃₉	—	2	2	no	—
378	C₂²×C₁₃₉	—	2	4	no	—
379	C₂²×C₁₃₉	—	2	2	no	—
380	C₂²×C₁₃₉	—	2	4	no	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	2	no	—
383	C₂²×C₁₃₉	—	2	2	no	—
384	C₂²×C₁₃₉	—	4	2	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	—	4	2	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	4	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	4	no	—
391	C₂²×C₁₃₉	#532	1	4	yes	—
392	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
393	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
394	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
397	C₄×C₁₃₉	—	2	2	no	—
398	C₄×C₁₃₉	—	2	2	no	—
399	C₄×C₁₃₉	—	2	2	no	—
400	C₄×C₁₃₉	—	2	4	no	—
401	C₄×C₁₃₉	—	2	4	no	—
402	C₄×C₁₃₉	—	2	2	no	—
403	C₄×C₁₃₉	—	2	4	no	—
404	C₄×C₁₃₉	—	2	4	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	—	4	2	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	2	no	—
412	C₄×C₁₃₉	#546	1	4	yes	—
413	C₂×C₁₃₉	—	2	4	no	—
414	C₂×C₁₃₉	—	4	2	no	—
415	C₂×C₁₃₉	—	8	2	no	—
416	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
417	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
418	C₂×C₁₃₉	#3482	1	2	yes	—
419	C₂×C₁₃₉	#3499	1	1	yes	characteristic
420	C₂×C₁₃₉	#3520	1	2	yes	—
421	#36376	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₁₃₉	#36376	1	1	yes	characteristic, direct product factor, Sylow
423	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
424	C₂×#548	C₂×C₁₃₉	1	1	yes	characteristic
425	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
427	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	#2565	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2556	C₂×C₁₃₉	1	4	yes	complemented
430	#2545	C₂×C₁₃₉	1	1	yes	characteristic, complemented
431	#2521	C₂×C₁₃₉	1	4	yes	complemented
432	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	#2434	C₂×C₁₃₉	1	1	yes	characteristic, complemented
435	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	#2425	C₂×C₁₃₉	1	4	yes	complemented
437	#2359	C₂×C₁₃₉	1	4	yes	complemented
438	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
441	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
444	#552	—	2	8	no	—
445	#548	—	2	8	no	—
446	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
451	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
453	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
455	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
456	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
459	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
460	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
462	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
465	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
472	#399	C₂²×C₁₃₉	1	4	yes	—
473	#398	C₂²×C₁₃₉	1	4	yes	—
474	#397	C₂²×C₁₃₉	1	4	yes	—
475	#396	C₂²×C₁₃₉	1	4	yes	—
476	#395	C₂²×C₁₃₉	1	4	yes	—
477	#394	C₂²×C₁₃₉	1	4	yes	—
478	#391	C₂²×C₁₃₉	1	1	yes	characteristic
479	#391	C₂²×C₁₃₉	1	1	yes	characteristic
480	#391	C₂²×C₁₃₉	1	1	yes	characteristic
481	#391	C₂²×C₁₃₉	1	1	yes	characteristic
482	#391	C₂²×C₁₃₉	1	1	yes	characteristic
483	#391	C₂²×C₁₃₉	1	1	yes	characteristic
484	#391	C₂²×C₁₃₉	1	1	yes	characteristic
485	#391	C₂²×C₁₃₉	1	4	yes	—
486	#390	C₂²×C₁₃₉	1	1	yes	characteristic
487	#390	C₂²×C₁₃₉	1	1	yes	characteristic
488	#390	C₂²×C₁₃₉	1	1	yes	characteristic
489	#389	C₂²×C₁₃₉	1	4	yes	—
490	#389	C₂²×C₁₃₉	1	4	yes	—
491	#388	C₂²×C₁₃₉	1	4	yes	—
492	#388	C₂²×C₁₃₉	1	4	yes	—
493	#388	C₂²×C₁₃₉	1	4	yes	—
494	#388	C₂²×C₁₃₉	1	4	yes	—
495	#387	C₂²×C₁₃₉	1	4	yes	—
496	#387	C₂²×C₁₃₉	1	4	yes	—
497	#386	C₂²×C₁₃₉	1	4	yes	—
498	#386	C₂²×C₁₃₉	1	4	yes	—
499	#385	C₂²×C₁₃₉	1	4	yes	—
500	#385	C₂²×C₁₃₉	1	4	yes	—
501	#384	C₂²×C₁₃₉	1	1	yes	characteristic
502	#384	C₂²×C₁₃₉	1	1	yes	characteristic
503	#382	C₂²×C₁₃₉	1	1	yes	characteristic
504	#380	C₂²×C₁₃₉	1	4	yes	—
505	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
506	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
510	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
511	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
512	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
513	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
514	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
515	C₂×#41	—	2	4	no	—
516	C₂×#41	—	2	4	no	—
517	C₂×#41	—	4	2	no	—
518	C₂²×Q₈	—	2	4	no	—
519	C₂²×Q₈	—	2	4	no	—
520	C₂²×Q₈	—	4	2	no	—
521	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
524	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₄⋊Q₈	—	2	4	no	—
537	C₄⋊Q₈	—	4	2	no	—
538	#126	—	2	8	no	—
539	#125	—	2	8	no	—
540	#125	—	2	4	no	—
541	#124	—	2	8	no	—
542	#124	—	2	4	no	—
543	#124	—	4	2	no	—
544	#123	—	2	8	no	—
545	#123	—	2	16	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	—	2	8	no	—
550	#121	—	2	8	no	—
551	#121	—	2	4	no	—
552	C₄×Q₈	—	2	4	no	—
553	C₄×Q₈	—	2	4	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	8	no	—
556	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
557	#117	—	2	4	no	—
558	#117	—	2	8	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄²	—	4	2	no	—
594	C₂×C₄²	—	4	2	no	—
595	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
607	#95	C₂³×C₁₃₉	1	4	yes	—
608	#95	C₂³×C₁₃₉	1	4	yes	—
609	#95	C₂³×C₁₃₉	1	4	yes	—
610	#95	C₂³×C₁₃₉	1	4	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	4	yes	—
615	#95	C₂³×C₁₃₉	1	4	yes	—
616	#95	C₂³×C₁₃₉	1	4	yes	—
617	#95	C₂³×C₁₃₉	1	4	yes	—
618	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	#41	—	4	16	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	4	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	16	no	—
634	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	8	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	8	no	—
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	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	8	no	—
695	C₄⋊C₄	—	2	8	no	—
696	C₄⋊C₄	—	2	8	no	—
697	C₄⋊C₄	—	4	4	no	—
698	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	8	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
712	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
713	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	complemented
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	4	2	no	—
724	C₄²	—	4	2	no	—
725	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	4	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	4	no	—
738	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
739	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
740	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
741	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
742	Q₈	—	2	8	no	—
743	Q₈	—	4	8	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	4	4	no	—
746	D₄	—	2	8	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	8	no	—
749	D₄	—	4	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	8	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
792	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
793	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
794	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
795	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
796	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
797	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
798	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	#532×C₁₃₉	1	4	yes	—
814	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
816	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
817	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
818	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	#546×C₁₃₉	1	4	yes	—
835	C₂	—	2	4	no	—
836	C₂	—	4	2	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
839	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
840	C₂	#3482×C₁₃₉	1	2	yes	—
841	C₂	#3499×C₁₃₉	1	1	yes	characteristic
842	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#548×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×#552×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2565×C₁₃₉	C₂	semidirect
7. #2556×C₁₃₉	C₂	semidirect
8. #2545×C₁₃₉	C₂	semidirect
9. #2521×C₁₃₉	C₂	semidirect
10. #2501×C₁₃₉	C₂	semidirect
11. #2499×C₁₃₉	C₂	semidirect
12. #2434×C₁₃₉	C₂	semidirect
13. #2432×C₁₃₉	C₂	semidirect
14. #2425×C₁₃₉	C₂	semidirect
15. #2359×C₁₃₉	C₂	semidirect
16. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
18. C₂×#391×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
291. C₂²⋊C₄×C₁₃₉	#41	semidirect
421. #36376	C₁₃₉	direct (N × H)
422. C₁₃₉	#36376	direct (N × H)
423. C₂×#552	C₂×C₁₃₉	semidirect
425. #2861	C₂×C₁₃₉	semidirect
426. #2857	C₂×C₁₃₉	semidirect
427. #2850	C₂×C₁₃₉	semidirect
428. #2565	C₂×C₁₃₉	semidirect
429. #2556	C₂×C₁₃₉	semidirect
430. #2545	C₂×C₁₃₉	semidirect
431. #2521	C₂×C₁₃₉	semidirect
432. #2501	C₂×C₁₃₉	semidirect
433. #2499	C₂×C₁₃₉	semidirect
434. #2434	C₂×C₁₃₉	semidirect
435. #2432	C₂×C₁₃₉	semidirect
436. #2425	C₂×C₁₃₉	semidirect
437. #2359	C₂×C₁₃₉	semidirect
438. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
439. #2297	C₂×C₁₃₉	semidirect
440. C₂×#391	C₂×C₁₃₉	semidirect
441. C₄²×D₄	C₂×C₁₃₉	semidirect
713. 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×#552×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2861×C₁₃₉	2
#2857×C₁₃₉	2
#2850×C₁₃₉	2
#2565×C₁₃₉	2
#2556×C₁₃₉	2
#2545×C₁₃₉	2
#2521×C₁₃₉	2
#2501×C₁₃₉	2
#2499×C₁₃₉	2
#2434×C₁₃₉	2
#2432×C₁₃₉	2
#2425×C₁₃₉	2
#2359×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36376	139

Subgroups — C139×#36376 #48030972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36376 #48030972