Subgroups — C₁₃₉×#36101 #48030697

Order 35584.

3712 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2847×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2456×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2433×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2424×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	#550×C₁₃₉	—	2	8	no	—
22	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	#525×C₁₃₉	—	2	16	no	—
26	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
37	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	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	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
49	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
53	#396×C₁₃₉	C₂²	1	4	yes	complemented
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#392×C₁₃₉	C₂²	1	4	yes	—
57	#392×C₁₃₉	C₂²	1	4	yes	—
58	#392×C₁₃₉	C₂²	1	4	yes	complemented
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	complemented
63	#390×C₁₃₉	C₂²	1	2	yes	complemented
64	#390×C₁₃₉	C₂²	1	2	yes	complemented
65	#390×C₁₃₉	C₂²	1	2	yes	complemented
66	#390×C₁₃₉	C₂²	1	4	yes	complemented
67	#389×C₁₃₉	C₂²	1	2	yes	complemented
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
69	#388×C₁₃₉	C₂²	1	4	yes	complemented
70	#388×C₁₃₉	C₂²	1	4	yes	complemented
71	#387×C₁₃₉	C₂²	1	2	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#386×C₁₃₉	C₂²	1	4	yes	complemented
76	#385×C₁₃₉	C₂²	1	2	yes	—
77	#385×C₁₃₉	C₂²	1	4	yes	complemented
78	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#380×C₁₃₉	C₂²	1	1	yes	characteristic
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#380×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
86	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	4	4	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	—	2	4	no	—
93	C₂²×D₄×C₁₃₉	—	2	4	no	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	—	2	8	no	—
106	C₂³×C₄×C₁₃₉	—	2	8	no	—
107	C₂³×C₄×C₁₃₉	—	4	4	no	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	#127×C₁₃₉	—	2	8	no	—
118	#127×C₁₃₉	—	2	8	no	—
119	#127×C₁₃₉	—	2	4	no	—
120	#123×C₁₃₉	—	2	16	no	—
121	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
122	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
123	#121×C₁₃₉	—	2	8	no	—
124	#121×C₁₃₉	—	2	8	no	—
125	#121×C₁₃₉	—	2	8	no	—
126	#121×C₁₃₉	—	2	8	no	—
127	#121×C₁₃₉	—	2	16	no	—
128	#121×C₁₃₉	—	4	4	no	—
129	#121×C₁₃₉	—	4	4	no	—
130	#120×C₁₃₉	—	2	16	no	—
131	#120×C₁₃₉	—	4	8	no	—
132	C₄×Q₈×C₁₃₉	—	2	4	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	C₄×D₄×C₁₃₉	—	2	8	no	—
135	C₄×D₄×C₁₃₉	—	2	4	no	—
136	C₄×D₄×C₁₃₉	—	2	8	no	—
137	C₄×D₄×C₁₃₉	—	2	16	no	—
138	C₄×D₄×C₁₃₉	—	2	8	no	—
139	C₄×D₄×C₁₃₉	—	2	16	no	—
140	C₄×D₄×C₁₃₉	—	2	4	no	—
141	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
142	#117×C₁₃₉	—	2	8	no	—
143	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
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	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	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	2	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	4	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	—	2	4	no	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	#95×C₁₃₉	C₂³	1	4	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	4	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	—	2	4	no	—
191	C₂⁴×C₁₃₉	—	2	4	no	—
192	C₂⁴×C₁₃₉	—	2	4	no	—
193	C₂⁴×C₁₃₉	—	2	4	no	—
194	C₂⁴×C₁₃₉	—	4	2	no	—
195	C₂⁴×C₁₃₉	—	4	2	no	—
196	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
197	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
198	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	#41×C₁₃₉	—	4	32	no	—
201	C₂×Q₈×C₁₃₉	—	2	2	no	—
202	C₂×Q₈×C₁₃₉	—	2	2	no	—
203	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
204	C₂×D₄×C₁₃₉	—	2	32	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	8	no	—
208	C₂×D₄×C₁₃₉	—	2	8	no	—
209	C₂×D₄×C₁₃₉	—	2	8	no	—
210	C₂×D₄×C₁₃₉	—	2	8	no	—
211	C₂×D₄×C₁₃₉	—	2	8	no	—
212	C₂×D₄×C₁₃₉	—	2	8	no	—
213	C₂×D₄×C₁₃₉	—	2	8	no	—
214	C₂×D₄×C₁₃₉	—	2	2	no	—
215	C₂×D₄×C₁₃₉	—	2	8	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	8	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	2	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	2	2	no	—
225	C₂×D₄×C₁₃₉	—	2	4	no	—
226	C₂×D₄×C₁₃₉	—	2	4	no	—
227	C₂×D₄×C₁₃₉	—	2	4	no	—
228	C₂×D₄×C₁₃₉	—	4	4	no	—
229	C₂×D₄×C₁₃₉	—	4	4	no	—
230	C₂×D₄×C₁₃₉	—	4	4	no	—
231	C₂×D₄×C₁₃₉	—	4	4	no	—
232	C₂×D₄×C₁₃₉	—	4	2	no	—
233	C₂×D₄×C₁₃₉	—	4	4	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂×D₄×C₁₃₉	—	4	4	no	—
236	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	2	2	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
246	C₂²×C₄×C₁₃₉	—	2	2	no	—
247	C₂²×C₄×C₁₃₉	—	2	2	no	—
248	C₂²×C₄×C₁₃₉	—	2	4	no	—
249	C₂²×C₄×C₁₃₉	—	2	4	no	—
250	C₂²×C₄×C₁₃₉	—	2	4	no	—
251	C₂²×C₄×C₁₃₉	—	2	4	no	—
252	C₂²×C₄×C₁₃₉	—	2	8	no	—
253	C₂²×C₄×C₁₃₉	—	2	8	no	—
254	C₂²×C₄×C₁₃₉	—	2	4	no	—
255	C₂²×C₄×C₁₃₉	—	2	4	no	—
256	C₂²×C₄×C₁₃₉	—	2	4	no	—
257	C₂²×C₄×C₁₃₉	—	4	2	no	—
258	C₂²×C₄×C₁₃₉	—	4	2	no	—
259	C₂²×C₄×C₁₃₉	—	4	2	no	—
260	C₂²×C₄×C₁₃₉	—	4	1	no	—
261	C₂²×C₄×C₁₃₉	—	4	4	no	—
262	C₂²×C₄×C₁₃₉	—	4	32	no	—
263	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
264	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
265	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	4	no	—
282	C₄⋊C₄×C₁₃₉	—	2	8	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	2	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
290	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
291	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
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	8	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
306	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
307	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
308	C₄²×C₁₃₉	—	2	2	no	—
309	C₄²×C₁₃₉	—	2	2	no	—
310	C₄²×C₁₃₉	—	2	2	no	—
311	C₄²×C₁₃₉	—	2	8	no	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	4	no	—
314	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
315	C₂³×C₁₃₉	—	2	1	no	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	1	no	—
318	C₂³×C₁₃₉	—	2	1	no	—
319	C₂³×C₁₃₉	—	2	16	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	4	no	—
333	C₂³×C₁₃₉	—	2	4	no	—
334	C₂³×C₁₃₉	—	2	4	no	—
335	C₂³×C₁₃₉	—	2	4	no	—
336	C₂³×C₁₃₉	—	2	4	no	—
337	C₂³×C₁₃₉	—	2	4	no	—
338	C₂³×C₁₃₉	—	2	4	no	—
339	C₂³×C₁₃₉	—	4	8	no	—
340	C₂³×C₁₃₉	—	4	8	no	—
341	C₂³×C₁₃₉	—	4	8	no	—
342	C₂³×C₁₃₉	—	4	8	no	—
343	C₂³×C₁₃₉	—	4	8	no	—
344	C₂³×C₁₃₉	—	4	8	no	—
345	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
346	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
348	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
350	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃₉	—	2	8	no	—
352	D₄×C₁₃₉	—	2	16	no	—
353	D₄×C₁₃₉	—	2	8	no	—
354	D₄×C₁₃₉	—	2	8	no	—
355	D₄×C₁₃₉	—	4	16	no	—
356	D₄×C₁₃₉	—	4	16	no	—
357	D₄×C₁₃₉	—	4	16	no	—
358	D₄×C₁₃₉	—	4	8	no	—
359	D₄×C₁₃₉	—	4	8	no	—
360	D₄×C₁₃₉	—	8	4	no	—
361	D₄×C₁₃₉	—	8	8	no	—
362	D₄×C₁₃₉	—	8	8	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	8	no	—
376	C₂×C₄×C₁₃₉	—	2	8	no	—
377	C₂×C₄×C₁₃₉	—	2	16	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	4	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	1	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	4	8	no	—
394	C₂×C₄×C₁₃₉	—	4	16	no	—
395	C₂×C₄×C₁₃₉	—	4	4	no	—
396	C₂×C₄×C₁₃₉	—	4	8	no	—
397	C₂×C₄×C₁₃₉	—	4	8	no	—
398	C₂×C₄×C₁₃₉	—	4	8	no	—
399	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
400	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
403	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
404	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
408	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
411	C₂²×C₁₃₉	—	2	2	no	—
412	C₂²×C₁₃₉	—	2	2	no	—
413	C₂²×C₁₃₉	—	2	2	no	—
414	C₂²×C₁₃₉	—	2	2	no	—
415	C₂²×C₁₃₉	—	2	2	no	—
416	C₂²×C₁₃₉	—	2	2	no	—
417	C₂²×C₁₃₉	—	2	4	no	—
418	C₂²×C₁₃₉	—	2	4	no	—
419	C₂²×C₁₃₉	—	2	4	no	—
420	C₂²×C₁₃₉	—	2	4	no	—
421	C₂²×C₁₃₉	—	2	4	no	—
422	C₂²×C₁₃₉	—	2	4	no	—
423	C₂²×C₁₃₉	—	4	32	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	2	no	—
426	C₂²×C₁₃₉	—	4	2	no	—
427	C₂²×C₁₃₉	—	4	2	no	—
428	C₂²×C₁₃₉	—	4	2	no	—
429	C₂²×C₁₃₉	—	4	2	no	—
430	C₂²×C₁₃₉	—	4	2	no	—
431	C₂²×C₁₃₉	—	4	2	no	—
432	C₂²×C₁₃₉	—	4	4	no	—
433	C₂²×C₁₃₉	—	4	4	no	—
434	C₂²×C₁₃₉	—	4	4	no	—
435	C₂²×C₁₃₉	—	4	4	no	—
436	C₂²×C₁₃₉	—	4	4	no	—
437	C₂²×C₁₃₉	—	4	4	no	—
438	C₂²×C₁₃₉	—	4	4	no	—
439	C₂²×C₁₃₉	#550	1	4	yes	complemented
440	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
441	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
442	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
443	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²×C₁₃₉	#585	1	1	yes	characteristic
447	C₄×C₁₃₉	—	2	2	no	—
448	C₄×C₁₃₉	—	2	2	no	—
449	C₄×C₁₃₉	—	2	4	no	—
450	C₄×C₁₃₉	—	2	4	no	—
451	C₄×C₁₃₉	—	2	4	no	—
452	C₄×C₁₃₉	—	2	2	no	—
453	C₄×C₁₃₉	—	4	2	no	—
454	C₄×C₁₃₉	—	4	4	no	—
455	C₄×C₁₃₉	—	4	1	no	—
456	C₄×C₁₃₉	—	4	2	no	—
457	C₄×C₁₃₉	—	4	2	no	—
458	C₄×C₁₃₉	#525	1	4	yes	complemented
459	C₄×C₁₃₉	D₄²	1	4	yes	—
460	C₂×C₁₃₉	—	2	4	no	—
461	C₂×C₁₃₉	—	4	4	no	—
462	C₂×C₁₃₉	—	4	4	no	—
463	C₂×C₁₃₉	—	8	4	no	—
464	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
465	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
466	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
467	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
468	C₂×C₁₃₉	#3488	1	1	yes	characteristic
469	C₂×C₁₃₉	#3506	1	1	yes	characteristic
470	C₂×C₁₃₉	#3519	1	1	yes	characteristic
471	#36101	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₁₃₉	#36101	1	1	yes	characteristic, direct product factor, Sylow
473	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	C₂×#525	C₂×C₁₃₉	1	2	yes	complemented
475	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#2847	C₂×C₁₃₉	1	2	yes	complemented
478	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
479	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
480	#2456	C₂×C₁₃₉	1	4	yes	complemented
481	#2445	C₂×C₁₃₉	1	2	yes	complemented
482	#2433	C₂×C₁₃₉	1	2	yes	complemented
483	#2424	C₂×C₁₃₉	1	4	yes	complemented
484	#2414	C₂×C₁₃₉	1	2	yes	complemented
485	#2407	C₂×C₁₃₉	1	2	yes	complemented
486	#2366	C₂×C₁₃₉	1	2	yes	complemented
487	#2361	C₂×C₁₃₉	1	2	yes	complemented
488	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
489	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
490	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
491	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
493	#550	—	2	8	no	—
494	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
495	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
496	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
497	#525	—	2	16	no	—
498	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
500	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
501	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
502	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
503	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
504	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
505	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
506	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
507	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
508	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
509	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
510	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
511	C₂×C₄×D₄	—	2	8	no	—
512	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
513	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
517	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
521	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
522	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
523	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
524	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
525	#396	C₂²×C₁₃₉	1	4	yes	complemented
526	#394	C₂²×C₁₃₉	1	4	yes	complemented
527	#394	C₂²×C₁₃₉	1	4	yes	complemented
528	#392	C₂²×C₁₃₉	1	4	yes	—
529	#392	C₂²×C₁₃₉	1	4	yes	—
530	#392	C₂²×C₁₃₉	1	4	yes	complemented
531	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
532	#390	C₂²×C₁₃₉	1	2	yes	—
533	#390	C₂²×C₁₃₉	1	2	yes	—
534	#390	C₂²×C₁₃₉	1	2	yes	complemented
535	#390	C₂²×C₁₃₉	1	2	yes	complemented
536	#390	C₂²×C₁₃₉	1	2	yes	complemented
537	#390	C₂²×C₁₃₉	1	2	yes	complemented
538	#390	C₂²×C₁₃₉	1	4	yes	complemented
539	#389	C₂²×C₁₃₉	1	2	yes	complemented
540	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
541	#388	C₂²×C₁₃₉	1	4	yes	complemented
542	#388	C₂²×C₁₃₉	1	4	yes	complemented
543	#387	C₂²×C₁₃₉	1	2	yes	complemented
544	#386	C₂²×C₁₃₉	1	4	yes	—
545	#386	C₂²×C₁₃₉	1	4	yes	complemented
546	#386	C₂²×C₁₃₉	1	4	yes	complemented
547	#386	C₂²×C₁₃₉	1	4	yes	complemented
548	#385	C₂²×C₁₃₉	1	2	yes	—
549	#385	C₂²×C₁₃₉	1	4	yes	complemented
550	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
551	#380	C₂²×C₁₃₉	1	1	yes	characteristic
552	#380	C₂²×C₁₃₉	1	2	yes	complemented
553	#380	C₂²×C₁₃₉	1	2	yes	complemented
554	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
555	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
556	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
557	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
558	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
559	C₂×#41	—	2	8	no	—
560	C₂×#41	—	2	8	no	—
561	C₂×#41	—	4	4	no	—
562	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	2	4	no	—
565	C₂²×D₄	—	2	4	no	—
566	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂³×C₄	—	2	8	no	—
578	C₂³×C₄	—	2	8	no	—
579	C₂³×C₄	—	4	4	no	—
580	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
586	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
589	#127	—	2	8	no	—
590	#127	—	2	8	no	—
591	#127	—	2	4	no	—
592	#123	—	2	16	no	—
593	C₂²⋊Q₈	—	2	8	no	—
594	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
595	#121	—	2	8	no	—
596	#121	—	2	8	no	—
597	#121	—	2	8	no	—
598	#121	—	2	8	no	—
599	#121	—	2	16	no	—
600	#121	—	4	4	no	—
601	#121	—	4	4	no	—
602	#120	—	2	16	no	—
603	#120	—	4	8	no	—
604	C₄×Q₈	—	2	4	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	8	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	8	no	—
609	C₄×D₄	—	2	16	no	—
610	C₄×D₄	—	2	8	no	—
611	C₄×D₄	—	2	16	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
614	#117	—	2	8	no	—
615	C₂×C₄⋊C₄	—	2	4	no	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	—	2	8	no	—
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	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄²	—	2	4	no	—
647	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	4	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	4	yes	—
661	C₂⁴	—	2	4	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	2	4	no	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	2	4	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
669	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
672	#41	—	4	32	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	complemented
676	C₂×D₄	—	2	32	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	8	no	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	2	8	no	—
685	C₂×D₄	—	2	8	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	8	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
709	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	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	8	no	—
725	C₂²×C₄	—	2	8	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	4	no	—
734	C₂²×C₄	—	4	32	no	—
735	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
736	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
737	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
738	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	8	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
762	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
763	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	8	no	—
769	C₂²⋊C₄	—	2	8	no	—
770	C₂²⋊C₄	—	2	8	no	—
771	C₂²⋊C₄	—	2	8	no	—
772	C₂²⋊C₄	—	2	8	no	—
773	C₂²⋊C₄	—	2	8	no	—
774	C₂²⋊C₄	—	4	4	no	—
775	C₂²⋊C₄	—	4	4	no	—
776	C₂²⋊C₄	—	4	4	no	—
777	C₂²⋊C₄	—	4	4	no	—
778	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
779	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	8	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	4	no	—
786	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	16	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	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	4	no	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	4	8	no	—
812	C₂³	—	4	8	no	—
813	C₂³	—	4	8	no	—
814	C₂³	—	4	8	no	—
815	C₂³	—	4	8	no	—
816	C₂³	—	4	8	no	—
817	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
818	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
819	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
820	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
821	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
822	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
823	Q₈	—	2	8	no	—
824	D₄	—	2	16	no	—
825	D₄	—	2	8	no	—
826	D₄	—	2	8	no	—
827	D₄	—	4	16	no	—
828	D₄	—	4	16	no	—
829	D₄	—	4	16	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	8	no	—
832	D₄	—	8	4	no	—
833	D₄	—	8	8	no	—
834	D₄	—	8	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	16	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	16	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
874	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
875	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
876	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
879	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
880	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
881	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
882	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	4	32	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	4	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	4	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	4	4	no	—
909	C₂²	—	4	4	no	—
910	C₂²	—	4	4	no	—
911	C₂²	#550×C₁₃₉	1	4	yes	complemented
912	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
913	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
914	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
915	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
916	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
917	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
918	C₂²	#585×C₁₃₉	1	1	yes	characteristic
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	4	no	—
922	C₄	—	2	4	no	—
923	C₄	—	2	4	no	—
924	C₄	—	2	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	4	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	#525×C₁₃₉	1	4	yes	complemented
931	C₄	D₄²×C₁₃₉	1	4	yes	—
932	C₂	—	2	4	no	—
933	C₂	—	4	4	no	—
934	C₂	—	4	4	no	—
935	C₂	—	8	4	no	—
936	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
937	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
938	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
939	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
940	C₂	#3488×C₁₃₉	1	1	yes	characteristic
941	C₂	#3506×C₁₃₉	1	1	yes	characteristic
942	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	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×#550×C₁₃₉	C₂	semidirect
2. C₂×#525×C₁₃₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2847×C₁₃₉	C₂	semidirect
6. #2541×C₁₃₉	C₂	semidirect
7. #2538×C₁₃₉	C₂	semidirect
8. #2456×C₁₃₉	C₂	semidirect
9. #2445×C₁₃₉	C₂	semidirect
10. #2433×C₁₃₉	C₂	semidirect
11. #2424×C₁₃₉	C₂	semidirect
12. #2414×C₁₃₉	C₂	semidirect
13. #2407×C₁₃₉	C₂	semidirect
14. #2366×C₁₃₉	C₂	semidirect
15. #2361×C₁₃₉	C₂	semidirect
16. #2354×C₁₃₉	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
18. C₂²×#41×C₁₃₉	C₂²	semidirect
24. C₂×#127×C₁₃₉	C₂²	semidirect
26. C₂×#123×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×#121×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
35. C₂×#121×C₁₃₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
49. C₂×#117×C₁₃₉	C₂²	semidirect
53. #396×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
58. #392×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
62. #390×C₁₃₉	C₂²	semidirect
63. #390×C₁₃₉	C₂²	semidirect
64. #390×C₁₃₉	C₂²	semidirect
65. #390×C₁₃₉	C₂²	semidirect
66. #390×C₁₃₉	C₂²	semidirect
67. #389×C₁₃₉	C₂²	semidirect
68. #389×C₁₃₉	C₂²	semidirect
69. #388×C₁₃₉	C₂²	semidirect
70. #388×C₁₃₉	C₂²	semidirect
71. #387×C₁₃₉	C₂²	semidirect
73. #386×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
75. #386×C₁₃₉	C₂²	semidirect
77. #385×C₁₃₉	C₂²	semidirect
78. #384×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
82. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
122. C₂²⋊Q₈×C₁₃₉	D₄	semidirect
141. C₄×D₄×C₁₃₉	D₄	semidirect
203. C₂×Q₈×C₁₃₉	C₂×D₄	semidirect
237. C₂×D₄×C₁₃₉	#41	semidirect
265. C₂²×C₄×C₁₃₉	#41	semidirect
290. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
291. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
439. C₂²×C₁₃₉	#550	semidirect
458. C₄×C₁₃₉	#525	semidirect
471. #36101	C₁₃₉	direct (N × H)
472. C₁₃₉	#36101	direct (N × H)
473. C₂×#550	C₂×C₁₃₉	semidirect
474. C₂×#525	C₂×C₁₃₉	semidirect
475. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
476. #2856	C₂×C₁₃₉	semidirect
477. #2847	C₂×C₁₃₉	semidirect
478. #2541	C₂×C₁₃₉	semidirect
479. #2538	C₂×C₁₃₉	semidirect
480. #2456	C₂×C₁₃₉	semidirect
481. #2445	C₂×C₁₃₉	semidirect
482. #2433	C₂×C₁₃₉	semidirect
483. #2424	C₂×C₁₃₉	semidirect
484. #2414	C₂×C₁₃₉	semidirect
485. #2407	C₂×C₁₃₉	semidirect
486. #2366	C₂×C₁₃₉	semidirect
487. #2361	C₂×C₁₃₉	semidirect
488. #2354	C₂×C₁₃₉	semidirect
489. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
490. C₂²×#41	C₂²×C₁₃₉	semidirect
496. C₂×#127	C₂²×C₁₃₉	semidirect
498. C₂×#123	C₂²×C₁₃₉	semidirect
500. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
504. C₂×#121	C₂²×C₁₃₉	semidirect
505. C₂×#121	C₂²×C₁₃₉	semidirect
506. C₂×#121	C₂²×C₁₃₉	semidirect
507. C₂×#121	C₂²×C₁₃₉	semidirect
510. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
519. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
520. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
521. C₂×#117	C₂²×C₁₃₉	semidirect
525. #396	C₂²×C₁₃₉	semidirect
526. #394	C₂²×C₁₃₉	semidirect
527. #394	C₂²×C₁₃₉	semidirect
530. #392	C₂²×C₁₃₉	semidirect
531. #391	C₂²×C₁₃₉	semidirect
534. #390	C₂²×C₁₃₉	semidirect
535. #390	C₂²×C₁₃₉	semidirect
536. #390	C₂²×C₁₃₉	semidirect
537. #390	C₂²×C₁₃₉	semidirect
538. #390	C₂²×C₁₃₉	semidirect
539. #389	C₂²×C₁₃₉	semidirect
540. #389	C₂²×C₁₃₉	semidirect
541. #388	C₂²×C₁₃₉	semidirect
542. #388	C₂²×C₁₃₉	semidirect
543. #387	C₂²×C₁₃₉	semidirect
545. #386	C₂²×C₁₃₉	semidirect
546. #386	C₂²×C₁₃₉	semidirect
547. #386	C₂²×C₁₃₉	semidirect
549. #385	C₂²×C₁₃₉	semidirect
550. #384	C₂²×C₁₃₉	semidirect
552. #380	C₂²×C₁₃₉	semidirect
553. #380	C₂²×C₁₃₉	semidirect
554. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
555. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
556. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
594. C₂²⋊Q₈	D₄×C₁₃₉	semidirect
613. C₄×D₄	D₄×C₁₃₉	semidirect
675. C₂×Q₈	C₂×D₄×C₁₃₉	semidirect
709. C₂×D₄	#41×C₁₃₉	semidirect
737. C₂²×C₄	#41×C₁₃₉	semidirect
762. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
763. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
911. C₂²	#550×C₁₃₉	semidirect
930. C₄	#525×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₃₉	2
C₂×#525×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2856×C₁₃₉	2
#2847×C₁₃₉	2
#2541×C₁₃₉	2
#2538×C₁₃₉	2
#2456×C₁₃₉	2
#2445×C₁₃₉	2
#2433×C₁₃₉	2
#2424×C₁₃₉	2
#2414×C₁₃₉	2
#2407×C₁₃₉	2
#2366×C₁₃₉	2
#2361×C₁₃₉	2
#2354×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#36101	139

Subgroups — C139×#36101 #48030697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36101 #48030697