Subgroups — C₁₃₉×#35939 #48030535

Order 35584.

2794 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2640×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2639×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2592×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2492×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2491×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2488×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2436×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#393×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
20	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	D₄×Q₈×C₁₃₉	—	2	8	no	—
22	#546×C₁₃₉	—	2	8	no	—
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
41	#400×C₁₃₉	C₂²	1	4	yes	complemented
42	#400×C₁₃₉	C₂²	1	2	yes	complemented
43	#397×C₁₃₉	C₂²	1	1	yes	characteristic
44	#397×C₁₃₉	C₂²	1	2	yes	complemented
45	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	#397×C₁₃₉	C₂²	1	4	yes	complemented
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#393×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#393×C₁₃₉	C₂²	1	4	yes	—
52	#393×C₁₃₉	C₂²	1	2	yes	complemented
53	#393×C₁₃₉	C₂²	1	2	yes	complemented
54	#393×C₁₃₉	C₂²	1	2	yes	complemented
55	#393×C₁₃₉	C₂²	1	2	yes	complemented
56	#393×C₁₃₉	C₂²	1	4	yes	complemented
57	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#391×C₁₃₉	C₂²	1	2	yes	complemented
60	#391×C₁₃₉	C₂²	1	4	yes	complemented
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#386×C₁₃₉	C₂²	1	4	yes	complemented
71	#382×C₁₃₉	C₂²	1	2	yes	complemented
72	#381×C₁₃₉	C₂²	1	4	yes	complemented
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#379×C₁₃₉	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂²×Q₈×C₁₃₉	—	2	8	no	—
89	C₂²×Q₈×C₁₃₉	—	4	8	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	—	2	4	no	—
95	C₂²×D₄×C₁₃₉	—	2	8	no	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
110	#124×C₁₃₉	—	2	4	no	—
111	#124×C₁₃₉	—	4	8	no	—
112	#123×C₁₃₉	—	2	8	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
116	#121×C₁₃₉	—	2	8	no	—
117	#121×C₁₃₉	—	2	4	no	—
118	#120×C₁₃₉	—	2	8	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	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	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	1	yes	characteristic
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	C₂⁴×C₁₃₉	—	2	4	no	—
175	C₂⁴×C₁₃₉	—	2	4	no	—
176	C₂⁴×C₁₃₉	—	2	8	no	—
177	C₂⁴×C₁₃₉	—	4	4	no	—
178	C₂⁴×C₁₃₉	—	4	2	no	—
179	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	#41×C₁₃₉	—	4	16	no	—
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	2	no	—
186	C₂×Q₈×C₁₃₉	—	2	8	no	—
187	C₂×Q₈×C₁₃₉	—	2	4	no	—
188	C₂×Q₈×C₁₃₉	—	2	4	no	—
189	C₂×Q₈×C₁₃₉	—	2	4	no	—
190	C₂×Q₈×C₁₃₉	—	2	8	no	—
191	C₂×Q₈×C₁₃₉	—	4	4	no	—
192	C₂×Q₈×C₁₃₉	—	4	4	no	—
193	C₂×Q₈×C₁₃₉	—	4	32	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	8	no	—
197	C₂×D₄×C₁₃₉	—	2	8	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	2	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	4	1	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	—	4	16	no	—
206	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
207	C₂×D₄×C₁₃₉	#41	1	8	yes	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	8	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	2	8	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	8	no	—
217	C₂²×C₄×C₁₃₉	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	—	4	4	no	—
220	C₂²×C₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	8	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	4	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	2	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
260	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
262	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
263	C₄²×C₁₃₉	—	2	4	no	—
264	C₄²×C₁₃₉	—	2	4	no	—
265	C₄²×C₁₃₉	—	4	2	no	—
266	C₄²×C₁₃₉	—	4	4	no	—
267	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	1	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	4	8	no	—
286	C₂³×C₁₃₉	—	4	16	no	—
287	C₂³×C₁₃₉	—	4	8	no	—
288	C₂³×C₁₃₉	—	8	4	no	—
289	C₂³×C₁₃₉	—	8	8	no	—
290	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
291	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
292	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
293	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
294	Q₈×C₁₃₉	—	2	8	no	—
295	Q₈×C₁₃₉	—	4	16	no	—
296	Q₈×C₁₃₉	—	4	8	no	—
297	Q₈×C₁₃₉	—	4	4	no	—
298	D₄×C₁₃₉	—	4	4	no	—
299	D₄×C₁₃₉	—	4	8	no	—
300	D₄×C₁₃₉	—	4	8	no	—
301	D₄×C₁₃₉	—	4	4	no	—
302	D₄×C₁₃₉	—	8	4	no	—
303	D₄×C₁₃₉	#124	1	16	yes	complemented
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	4	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	4	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	4	8	no	—
332	C₂×C₄×C₁₃₉	—	4	16	no	—
333	C₂×C₄×C₁₃₉	—	4	8	no	—
334	C₂×C₄×C₁₃₉	—	4	4	no	—
335	C₂×C₄×C₁₃₉	—	4	4	no	—
336	C₂×C₄×C₁₃₉	—	8	8	no	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
343	C₂²×C₁₃₉	—	2	4	no	—
344	C₂²×C₁₃₉	—	2	4	no	—
345	C₂²×C₁₃₉	—	2	8	no	—
346	C₂²×C₁₃₉	—	2	8	no	—
347	C₂²×C₁₃₉	—	2	2	no	—
348	C₂²×C₁₃₉	—	2	4	no	—
349	C₂²×C₁₃₉	—	4	1	no	—
350	C₂²×C₁₃₉	—	4	1	no	—
351	C₂²×C₁₃₉	—	4	2	no	—
352	C₂²×C₁₃₉	—	4	1	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	4	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	4	no	—
362	C₂²×C₁₃₉	—	8	16	no	—
363	C₂²×C₁₃₉	C₂×#124	1	8	yes	—
364	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
366	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₁₃₉	#585	1	1	yes	characteristic
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	2	4	no	—
371	C₄×C₁₃₉	—	2	4	no	—
372	C₄×C₁₃₉	—	2	2	no	—
373	C₄×C₁₃₉	—	4	1	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	4	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	4	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	C₂×#124	1	4	yes	—
382	C₂×C₁₃₉	—	2	8	no	—
383	C₂×C₁₃₉	—	4	2	no	—
384	C₂×C₁₃₉	—	8	1	no	—
385	C₂×C₁₃₉	—	8	2	no	—
386	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
387	C₂×C₁₃₉	#3484	1	1	yes	characteristic
388	C₂×C₁₃₉	#3489	1	1	yes	characteristic
389	C₂×C₁₃₉	#3514	1	2	yes	—
390	C₂×C₁₃₉	#3520	1	2	yes	—
391	#35939	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₁₃₉	#35939	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic
395	#2640	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	#2639	C₂×C₁₃₉	1	2	yes	complemented
397	#2592	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2561	C₂×C₁₃₉	1	2	yes	complemented
400	#2492	C₂×C₁₃₉	1	2	yes	complemented
401	#2491	C₂×C₁₃₉	1	2	yes	complemented
402	#2488	C₂×C₁₃₉	1	4	yes	complemented
403	#2472	C₂×C₁₃₉	1	4	yes	complemented
404	#2436	C₂×C₁₃₉	1	2	yes	complemented
405	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	C₂×#393	C₂×C₁₃₉	1	2	yes	complemented
407	#2339	C₂×C₁₃₉	1	2	yes	complemented
408	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
409	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
412	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
413	D₄×Q₈	—	2	8	no	—
414	#546	—	2	8	no	—
415	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
416	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
417	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
419	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
420	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
422	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
423	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
426	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
427	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
433	#400	C₂²×C₁₃₉	1	4	yes	complemented
434	#400	C₂²×C₁₃₉	1	2	yes	complemented
435	#397	C₂²×C₁₃₉	1	1	yes	characteristic
436	#397	C₂²×C₁₃₉	1	2	yes	complemented
437	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
438	#397	C₂²×C₁₃₉	1	4	yes	complemented
439	#394	C₂²×C₁₃₉	1	2	yes	—
440	#394	C₂²×C₁₃₉	1	4	yes	complemented
441	#393	C₂²×C₁₃₉	1	2	yes	—
442	#393	C₂²×C₁₃₉	1	1	yes	characteristic
443	#393	C₂²×C₁₃₉	1	4	yes	—
444	#393	C₂²×C₁₃₉	1	2	yes	complemented
445	#393	C₂²×C₁₃₉	1	2	yes	complemented
446	#393	C₂²×C₁₃₉	1	2	yes	complemented
447	#393	C₂²×C₁₃₉	1	2	yes	complemented
448	#393	C₂²×C₁₃₉	1	4	yes	complemented
449	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
450	#391	C₂²×C₁₃₉	1	2	yes	complemented
451	#391	C₂²×C₁₃₉	1	2	yes	complemented
452	#391	C₂²×C₁₃₉	1	4	yes	complemented
453	#390	C₂²×C₁₃₉	1	2	yes	—
454	#390	C₂²×C₁₃₉	1	2	yes	—
455	#390	C₂²×C₁₃₉	1	2	yes	—
456	#388	C₂²×C₁₃₉	1	4	yes	—
457	#388	C₂²×C₁₃₉	1	4	yes	complemented
458	#388	C₂²×C₁₃₉	1	4	yes	complemented
459	#386	C₂²×C₁₃₉	1	4	yes	—
460	#386	C₂²×C₁₃₉	1	4	yes	—
461	#386	C₂²×C₁₃₉	1	4	yes	complemented
462	#386	C₂²×C₁₃₉	1	4	yes	complemented
463	#382	C₂²×C₁₃₉	1	2	yes	complemented
464	#381	C₂²×C₁₃₉	1	4	yes	complemented
465	#380	C₂²×C₁₃₉	1	2	yes	—
466	#380	C₂²×C₁₃₉	1	2	yes	complemented
467	#379	C₂²×C₁₃₉	1	4	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
469	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
470	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
474	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
475	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
476	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
477	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	8	no	—
480	C₂²×Q₈	—	2	8	no	—
481	C₂²×Q₈	—	4	8	no	—
482	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
485	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
486	C₂²×D₄	—	2	4	no	—
487	C₂²×D₄	—	2	8	no	—
488	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₄⋊Q₈	—	2	8	no	—
501	C₄⋊Q₈	—	2	4	no	—
502	#124	—	2	4	no	—
503	#124	—	4	8	no	—
504	#123	—	2	8	no	—
505	C₂²⋊Q₈	—	2	8	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	16	no	—
508	#121	—	2	8	no	—
509	#121	—	2	4	no	—
510	#120	—	2	8	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×D₄	—	2	8	no	—
513	C₄×D₄	—	2	8	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	—	2	8	no	—
526	C₂×C₂²⋊C₄	—	4	8	no	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
551	#95	C₂³×C₁₃₉	1	1	yes	characteristic
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	2	yes	—
554	#95	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	1	yes	characteristic
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	4	no	—
568	C₂⁴	—	2	8	no	—
569	C₂⁴	—	4	4	no	—
570	C₂⁴	—	4	2	no	—
571	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
573	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
574	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
575	#41	—	4	16	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	8	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	8	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	—	4	32	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	4	1	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	16	no	—
598	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
599	C₂×D₄	#41×C₁₃₉	1	8	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	4	no	—
611	C₂²×C₄	—	4	4	no	—
612	C₂²×C₄	—	4	4	no	—
613	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	8	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	4	4	no	—
649	C₂²⋊C₄	—	4	4	no	—
650	C₂²⋊C₄	—	4	4	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	4	2	no	—
658	C₄²	—	4	4	no	—
659	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	4	8	no	—
678	C₂³	—	4	16	no	—
679	C₂³	—	4	8	no	—
680	C₂³	—	8	4	no	—
681	C₂³	—	8	8	no	—
682	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
683	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
684	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
685	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
686	Q₈	—	2	8	no	—
687	Q₈	—	4	16	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	4	no	—
690	D₄	—	4	4	no	—
691	D₄	—	4	8	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	8	4	no	—
695	D₄	#124×C₁₃₉	1	16	yes	complemented
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	4	16	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	8	no	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
733	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
734	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	8	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	8	16	no	—
755	C₂²	C₂×#124×C₁₃₉	1	8	yes	—
756	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
758	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
759	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²	#585×C₁₃₉	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	2	no	—
773	C₄	C₂×#124×C₁₃₉	1	4	yes	—
774	C₂	—	2	8	no	—
775	C₂	—	4	2	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	1	no	—
778	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
779	C₂	#3484×C₁₃₉	1	1	yes	characteristic
780	C₂	#3489×C₁₃₉	1	1	yes	characteristic
781	C₂	#3514×C₁₃₉	1	2	yes	—
782	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#546×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×D₄×Q₈×C₁₃₉	C₂	semidirect
3. #2640×C₁₃₉	C₂	semidirect
4. #2639×C₁₃₉	C₂	semidirect
5. #2592×C₁₃₉	C₂	semidirect
6. #2563×C₁₃₉	C₂	semidirect
7. #2561×C₁₃₉	C₂	semidirect
8. #2492×C₁₃₉	C₂	semidirect
9. #2491×C₁₃₉	C₂	semidirect
10. #2488×C₁₃₉	C₂	semidirect
11. #2472×C₁₃₉	C₂	semidirect
12. #2436×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. C₂×#393×C₁₃₉	C₂	semidirect
15. #2339×C₁₃₉	C₂	semidirect
16. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
19. C₂³×Q₈×C₁₃₉	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×#124×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
41. #400×C₁₃₉	C₂²	semidirect
42. #400×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
45. #397×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
52. #393×C₁₃₉	C₂²	semidirect
53. #393×C₁₃₉	C₂²	semidirect
54. #393×C₁₃₉	C₂²	semidirect
55. #393×C₁₃₉	C₂²	semidirect
56. #393×C₁₃₉	C₂²	semidirect
57. #393×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
60. #391×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #382×C₁₃₉	C₂²	semidirect
72. #381×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
76. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
77. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
82. #376×C₁₃₉	C₂²	semidirect
83. C₂×#95×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
303. D₄×C₁₃₉	#124	semidirect
391. #35939	C₁₃₉	direct (N × H)
392. C₁₃₉	#35939	direct (N × H)
393. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
395. #2640	C₂×C₁₃₉	semidirect
396. #2639	C₂×C₁₃₉	semidirect
397. #2592	C₂×C₁₃₉	semidirect
398. #2563	C₂×C₁₃₉	semidirect
399. #2561	C₂×C₁₃₉	semidirect
400. #2492	C₂×C₁₃₉	semidirect
401. #2491	C₂×C₁₃₉	semidirect
402. #2488	C₂×C₁₃₉	semidirect
403. #2472	C₂×C₁₃₉	semidirect
404. #2436	C₂×C₁₃₉	semidirect
405. #2398	C₂×C₁₃₉	semidirect
406. C₂×#393	C₂×C₁₃₉	semidirect
407. #2339	C₂×C₁₃₉	semidirect
408. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
409. #2275	C₂×C₁₃₉	semidirect
411. C₂³×Q₈	C₂²×C₁₃₉	semidirect
415. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
416. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
418. C₂×#124	C₂²×C₁₃₉	semidirect
421. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
422. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
426. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
433. #400	C₂²×C₁₃₉	semidirect
434. #400	C₂²×C₁₃₉	semidirect
436. #397	C₂²×C₁₃₉	semidirect
437. #397	C₂²×C₁₃₉	semidirect
438. #397	C₂²×C₁₃₉	semidirect
440. #394	C₂²×C₁₃₉	semidirect
444. #393	C₂²×C₁₃₉	semidirect
445. #393	C₂²×C₁₃₉	semidirect
446. #393	C₂²×C₁₃₉	semidirect
447. #393	C₂²×C₁₃₉	semidirect
448. #393	C₂²×C₁₃₉	semidirect
449. #393	C₂²×C₁₃₉	semidirect
450. #391	C₂²×C₁₃₉	semidirect
451. #391	C₂²×C₁₃₉	semidirect
452. #391	C₂²×C₁₃₉	semidirect
457. #388	C₂²×C₁₃₉	semidirect
458. #388	C₂²×C₁₃₉	semidirect
461. #386	C₂²×C₁₃₉	semidirect
462. #386	C₂²×C₁₃₉	semidirect
463. #382	C₂²×C₁₃₉	semidirect
464. #381	C₂²×C₁₃₉	semidirect
466. #380	C₂²×C₁₃₉	semidirect
468. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
469. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
471. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
472. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
473. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
474. #376	C₂²×C₁₃₉	semidirect
475. C₂×#95	C₂²×C₁₃₉	semidirect
476. C₂×#95	C₂²×C₁₃₉	semidirect
695. D₄	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2640×C₁₃₉	2
#2639×C₁₃₉	2
#2592×C₁₃₉	2
#2563×C₁₃₉	2
#2561×C₁₃₉	2
#2492×C₁₃₉	2
#2491×C₁₃₉	2
#2488×C₁₃₉	2
#2472×C₁₃₉	2
#2436×C₁₃₉	2
#2398×C₁₃₉	2
C₂×#393×C₁₃₉	2
#2339×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35939	139

Subgroups — C139×#35939 #48030535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35939 #48030535