Subgroups — C₁₃₉×#36150 #48030746

Order 35584.

2666 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2540×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2448×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₄×C₄⋊Q₈×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	2	yes	—
21	#533×C₁₃₉	—	2	8	no	—
22	#532×C₁₃₉	—	2	8	no	—
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
49	#399×C₁₃₉	C₂²	1	4	yes	—
50	#397×C₁₃₉	C₂²	1	4	yes	—
51	#396×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#392×C₁₃₉	C₂²	1	4	yes	—
55	#391×C₁₃₉	C₂²	1	2	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	4	yes	—
58	#390×C₁₃₉	C₂²	1	4	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	4	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#390×C₁₃₉	C₂²	1	2	yes	—
66	#390×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#388×C₁₃₉	C₂²	1	4	yes	—
73	#388×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#384×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	4	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₃₉	—	2	8	no	—
94	C₂×#41×C₁₃₉	—	2	8	no	—
95	C₂×#41×C₁₃₉	—	4	4	no	—
96	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
112	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
113	#127×C₁₃₉	—	2	4	no	—
114	#125×C₁₃₉	—	2	8	no	—
115	#124×C₁₃₉	—	2	8	no	—
116	#124×C₁₃₉	—	2	8	no	—
117	#124×C₁₃₉	—	4	4	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
120	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
121	#121×C₁₃₉	—	2	8	no	—
122	#121×C₁₃₉	—	2	8	no	—
123	#121×C₁₃₉	—	2	8	no	—
124	#121×C₁₃₉	—	4	4	no	—
125	#121×C₁₃₉	—	4	4	no	—
126	C₄×Q₈×C₁₃₉	—	2	8	no	—
127	C₄×Q₈×C₁₃₉	—	2	8	no	—
128	C₄×Q₈×C₁₃₉	—	4	4	no	—
129	C₄×D₄×C₁₃₉	—	2	4	no	—
130	C₄×D₄×C₁₃₉	—	2	4	no	—
131	C₄×D₄×C₁₃₉	—	2	8	no	—
132	C₄×D₄×C₁₃₉	—	2	8	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	#117×C₁₃₉	—	2	8	no	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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×C₄²×C₁₃₉	—	2	4	no	—
167	C₂×C₄²×C₁₃₉	—	2	4	no	—
168	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	#95×C₁₃₉	C₂³	1	1	yes	characteristic
184	#95×C₁₃₉	C₂³	1	1	yes	characteristic
185	#95×C₁₃₉	C₂³	1	4	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	#95×C₁₃₉	C₂³	1	4	yes	—
188	#95×C₁₃₉	C₂³	1	1	yes	characteristic
189	#95×C₁₃₉	C₂³	1	1	yes	characteristic
190	#95×C₁₃₉	C₂³	1	1	yes	characteristic
191	#95×C₁₃₉	C₂³	1	1	yes	characteristic
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
194	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	#41×C₁₃₉	—	4	32	no	—
197	C₂×Q₈×C₁₃₉	—	2	4	no	—
198	C₂×Q₈×C₁₃₉	—	2	4	no	—
199	C₂×Q₈×C₁₃₉	—	2	4	no	—
200	C₂×Q₈×C₁₃₉	—	2	4	no	—
201	C₂×Q₈×C₁₃₉	—	2	4	no	—
202	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	2	8	no	—
206	C₂×D₄×C₁₃₉	—	2	8	no	—
207	C₂×D₄×C₁₃₉	—	2	4	no	—
208	C₂×D₄×C₁₃₉	—	2	4	no	—
209	C₂×D₄×C₁₃₉	—	2	8	no	—
210	C₂×D₄×C₁₃₉	—	2	4	no	—
211	C₂×D₄×C₁₃₉	—	2	2	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	4	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	4	4	no	—
220	C₂×D₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	8	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	8	no	—
235	C₂²×C₄×C₁₃₉	—	2	2	no	—
236	C₂²×C₄×C₁₃₉	—	2	2	no	—
237	C₂²×C₄×C₁₃₉	—	2	2	no	—
238	C₂²×C₄×C₁₃₉	—	2	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	4	no	—
240	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
241	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
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	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	8	no	—
260	C₄⋊C₄×C₁₃₉	—	2	8	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	no	—
263	C₄⋊C₄×C₁₃₉	—	2	2	no	—
264	C₄⋊C₄×C₁₃₉	—	2	2	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	4	4	no	—
269	C₄⋊C₄×C₁₃₉	—	4	4	no	—
270	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
271	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
272	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
289	C₄²×C₁₃₉	—	2	2	no	—
290	C₄²×C₁₃₉	—	2	2	no	—
291	C₄²×C₁₃₉	—	2	2	no	—
292	C₄²×C₁₃₉	—	2	2	no	—
293	C₄²×C₁₃₉	—	2	2	no	—
294	C₄²×C₁₃₉	—	2	2	no	—
295	C₄²×C₁₃₉	—	2	8	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	2	no	—
301	C₄²×C₁₃₉	—	4	4	no	—
302	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
303	C₄²×C₁₃₉	#41	1	4	yes	complemented
304	C₂³×C₁₃₉	—	2	1	no	—
305	C₂³×C₁₃₉	—	2	1	no	—
306	C₂³×C₁₃₉	—	2	1	no	—
307	C₂³×C₁₃₉	—	2	1	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	no	—
311	C₂³×C₁₃₉	—	2	1	no	—
312	C₂³×C₁₃₉	—	2	1	no	—
313	C₂³×C₁₃₉	—	2	1	no	—
314	C₂³×C₁₃₉	—	2	1	no	—
315	C₂³×C₁₃₉	—	2	1	no	—
316	C₂³×C₁₃₉	—	2	4	no	—
317	C₂³×C₁₃₉	—	2	4	no	—
318	C₂³×C₁₃₉	—	2	4	no	—
319	C₂³×C₁₃₉	—	2	4	no	—
320	C₂³×C₁₃₉	—	2	4	no	—
321	C₂³×C₁₃₉	—	2	4	no	—
322	C₂³×C₁₃₉	—	2	4	no	—
323	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃₉	—	2	16	no	—
327	Q₈×C₁₃₉	—	4	8	no	—
328	D₄×C₁₃₉	—	2	8	no	—
329	D₄×C₁₃₉	—	4	16	no	—
330	D₄×C₁₃₉	—	4	8	no	—
331	D₄×C₁₃₉	—	4	8	no	—
332	D₄×C₁₃₉	—	4	8	no	—
333	D₄×C₁₃₉	—	8	8	no	—
334	C₂×C₄×C₁₃₉	—	2	1	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	4	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	4	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	8	no	—
345	C₂×C₄×C₁₃₉	—	2	8	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	4	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	4	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	4	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	4	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	4	no	—
366	C₂×C₄×C₁₃₉	—	2	4	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	4	16	no	—
371	C₂×C₄×C₁₃₉	—	4	4	no	—
372	C₂×C₄×C₁₃₉	—	4	4	no	—
373	C₂×C₄×C₁₃₉	—	4	4	no	—
374	C₂×C₄×C₁₃₉	—	4	4	no	—
375	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
383	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
385	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
386	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
389	C₂²×C₁₃₉	—	2	2	no	—
390	C₂²×C₁₃₉	—	2	2	no	—
391	C₂²×C₁₃₉	—	2	2	no	—
392	C₂²×C₁₃₉	—	2	2	no	—
393	C₂²×C₁₃₉	—	2	2	no	—
394	C₂²×C₁₃₉	—	2	2	no	—
395	C₂²×C₁₃₉	—	4	1	no	—
396	C₂²×C₁₃₉	—	4	1	no	—
397	C₂²×C₁₃₉	—	4	1	no	—
398	C₂²×C₁₃₉	—	4	1	no	—
399	C₂²×C₁₃₉	—	4	1	no	—
400	C₂²×C₁₃₉	—	4	1	no	—
401	C₂²×C₁₃₉	—	4	1	no	—
402	C₂²×C₁₃₉	—	4	1	no	—
403	C₂²×C₁₃₉	—	4	4	no	—
404	C₂²×C₁₃₉	—	4	4	no	—
405	C₂²×C₁₃₉	—	4	4	no	—
406	C₂²×C₁₃₉	—	4	4	no	—
407	C₂²×C₁₃₉	—	4	4	no	—
408	C₂²×C₁₃₉	—	4	4	no	—
409	C₂²×C₁₃₉	—	4	4	no	—
410	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
414	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₄×C₁₃₉	—	2	2	no	—
418	C₄×C₁₃₉	—	2	2	no	—
419	C₄×C₁₃₉	—	2	8	no	—
420	C₄×C₁₃₉	—	2	2	no	—
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	4	1	no	—
423	C₄×C₁₃₉	—	4	1	no	—
424	C₄×C₁₃₉	—	4	1	no	—
425	C₄×C₁₃₉	—	4	1	no	—
426	C₄×C₁₃₉	—	4	4	no	—
427	C₄×C₁₃₉	—	4	1	no	—
428	C₄×C₁₃₉	—	4	4	no	—
429	C₄×C₁₃₉	—	4	1	no	—
430	C₄×C₁₃₉	#546	1	4	yes	—
431	C₄×C₁₃₉	#548	1	4	yes	—
432	C₄×C₁₃₉	#550	1	4	yes	—
433	C₂×C₁₃₉	—	4	2	no	—
434	C₂×C₁₃₉	—	4	2	no	—
435	C₂×C₁₃₉	—	8	4	no	—
436	C₂×C₁₃₉	#3444	1	1	yes	characteristic
437	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
438	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
439	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
440	C₂×C₁₃₉	#3508	1	1	yes	characteristic
441	C₂×C₁₃₉	#3511	1	1	yes	characteristic
442	C₂×C₁₃₉	#3511	1	1	yes	characteristic
443	#36150	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₁₃₉	#36150	1	1	yes	characteristic, direct product factor, Sylow
445	C₂×#533	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2540	C₂×C₁₃₉	1	2	yes	complemented
451	#2490	C₂×C₁₃₉	1	2	yes	complemented
452	#2454	C₂×C₁₃₉	1	2	yes	complemented
453	#2448	C₂×C₁₃₉	1	2	yes	complemented
454	#2427	C₂×C₁₃₉	1	2	yes	complemented
455	#2426	C₂×C₁₃₉	1	2	yes	complemented
456	#2426	C₂×C₁₃₉	1	2	yes	complemented
457	#2414	C₂×C₁₃₉	1	2	yes	complemented
458	#2407	C₂×C₁₃₉	1	2	yes	complemented
459	#2367	C₂×C₁₃₉	1	2	yes	complemented
460	#2363	C₂×C₁₃₉	1	2	yes	complemented
461	#2341	C₂×C₁₃₉	1	2	yes	complemented
462	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
463	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
464	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
465	#533	—	2	8	no	—
466	#532	—	2	8	no	—
467	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
471	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
472	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
473	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
474	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
475	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
477	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
479	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
480	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
481	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
483	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
484	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
485	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
491	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
493	#399	C₂²×C₁₃₉	1	4	yes	—
494	#397	C₂²×C₁₃₉	1	4	yes	—
495	#396	C₂²×C₁₃₉	1	4	yes	—
496	#394	C₂²×C₁₃₉	1	4	yes	—
497	#394	C₂²×C₁₃₉	1	4	yes	—
498	#392	C₂²×C₁₃₉	1	4	yes	—
499	#391	C₂²×C₁₃₉	1	2	yes	—
500	#391	C₂²×C₁₃₉	1	2	yes	—
501	#390	C₂²×C₁₃₉	1	2	yes	—
502	#390	C₂²×C₁₃₉	1	2	yes	—
503	#390	C₂²×C₁₃₉	1	4	yes	—
504	#390	C₂²×C₁₃₉	1	4	yes	—
505	#390	C₂²×C₁₃₉	1	2	yes	—
506	#390	C₂²×C₁₃₉	1	2	yes	—
507	#390	C₂²×C₁₃₉	1	2	yes	—
508	#390	C₂²×C₁₃₉	1	2	yes	—
509	#390	C₂²×C₁₃₉	1	2	yes	—
510	#390	C₂²×C₁₃₉	1	4	yes	—
511	#389	C₂²×C₁₃₉	1	2	yes	—
512	#389	C₂²×C₁₃₉	1	2	yes	—
513	#389	C₂²×C₁₃₉	1	2	yes	—
514	#389	C₂²×C₁₃₉	1	2	yes	—
515	#388	C₂²×C₁₃₉	1	4	yes	—
516	#388	C₂²×C₁₃₉	1	4	yes	—
517	#388	C₂²×C₁₃₉	1	4	yes	—
518	#386	C₂²×C₁₃₉	1	4	yes	—
519	#385	C₂²×C₁₃₉	1	4	yes	—
520	#384	C₂²×C₁₃₉	1	1	yes	characteristic
521	#380	C₂²×C₁₃₉	1	2	yes	—
522	#380	C₂²×C₁₃₉	1	4	yes	—
523	#380	C₂²×C₁₃₉	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
525	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
532	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
533	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
534	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
535	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
536	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
537	C₂×#41	—	2	8	no	—
538	C₂×#41	—	2	8	no	—
539	C₂×#41	—	4	4	no	—
540	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
541	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
542	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₄⋊Q₈	—	2	4	no	—
556	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
557	#127	—	2	4	no	—
558	#125	—	2	8	no	—
559	#124	—	2	8	no	—
560	#124	—	2	8	no	—
561	#124	—	4	4	no	—
562	C₂²⋊Q₈	—	2	8	no	—
563	C₂²⋊Q₈	—	2	8	no	—
564	C₂²⋊Q₈	—	4	4	no	—
565	#121	—	2	8	no	—
566	#121	—	2	8	no	—
567	#121	—	2	8	no	—
568	#121	—	4	4	no	—
569	#121	—	4	4	no	—
570	C₄×Q₈	—	2	8	no	—
571	C₄×Q₈	—	2	8	no	—
572	C₄×Q₈	—	4	4	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	4	no	—
575	C₄×D₄	—	2	8	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	2	4	no	—
578	#117	—	2	8	no	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
610	C₂×C₄²	—	2	4	no	—
611	C₂×C₄²	—	2	4	no	—
612	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
613	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
625	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
627	#95	C₂³×C₁₃₉	1	1	yes	characteristic
628	#95	C₂³×C₁₃₉	1	1	yes	characteristic
629	#95	C₂³×C₁₃₉	1	1	yes	characteristic
630	#95	C₂³×C₁₃₉	1	1	yes	characteristic
631	#95	C₂³×C₁₃₉	1	1	yes	characteristic
632	#95	C₂³×C₁₃₉	1	1	yes	characteristic
633	#95	C₂³×C₁₃₉	1	4	yes	—
634	#95	C₂³×C₁₃₉	1	4	yes	—
635	#95	C₂³×C₁₃₉	1	4	yes	—
636	#95	C₂³×C₁₃₉	1	4	yes	—
637	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
638	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	#41	—	4	32	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	8	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	8	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
685	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	8	no	—
704	C₄⋊C₄	—	2	8	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	4	4	no	—
713	C₄⋊C₄	—	4	4	no	—
714	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
715	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	8	no	—
719	C₂²⋊C₄	—	2	8	no	—
720	C₂²⋊C₄	—	2	8	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	8	no	—
726	C₂²⋊C₄	—	2	8	no	—
727	C₂²⋊C₄	—	2	8	no	—
728	C₂²⋊C₄	—	4	4	no	—
729	C₂²⋊C₄	—	4	4	no	—
730	C₂²⋊C₄	—	4	4	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	8	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	4	4	no	—
746	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
747	C₄²	#41×C₁₃₉	1	4	yes	complemented
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	2	4	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	4	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	2	4	no	—
766	C₂³	—	2	4	no	—
767	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
768	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
769	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
770	Q₈	—	2	16	no	—
771	Q₈	—	4	8	no	—
772	D₄	—	2	8	no	—
773	D₄	—	4	16	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	8	no	—
777	D₄	—	8	8	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	8	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	4	16	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
823	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
824	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
825	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
826	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
827	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
828	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
829	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
830	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
831	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
832	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	4	no	—
854	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
855	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
856	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
857	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
858	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
859	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
860	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	8	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	4	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	#546×C₁₃₉	1	4	yes	—
875	C₄	#548×C₁₃₉	1	4	yes	—
876	C₄	#550×C₁₃₉	1	4	yes	—
877	C₂	—	4	2	no	—
878	C₂	—	4	2	no	—
879	C₂	—	8	4	no	—
880	C₂	#3444×C₁₃₉	1	1	yes	characteristic
881	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
882	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
883	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
884	C₂	#3508×C₁₃₉	1	1	yes	characteristic
885	C₂	#3511×C₁₃₉	1	1	yes	characteristic
886	C₂	#3511×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×#533×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2856×C₁₃₉	C₂	semidirect
6. #2540×C₁₃₉	C₂	semidirect
7. #2490×C₁₃₉	C₂	semidirect
8. #2454×C₁₃₉	C₂	semidirect
9. #2448×C₁₃₉	C₂	semidirect
10. #2427×C₁₃₉	C₂	semidirect
11. #2426×C₁₃₉	C₂	semidirect
12. #2426×C₁₃₉	C₂	semidirect
13. #2414×C₁₃₉	C₂	semidirect
14. #2407×C₁₃₉	C₂	semidirect
15. #2367×C₁₃₉	C₂	semidirect
16. #2363×C₁₃₉	C₂	semidirect
17. #2341×C₁₃₉	C₂	semidirect
18. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
112. C₄⋊Q₈×C₁₃₉	D₄	semidirect
241. C₂²×C₄×C₁₃₉	#41	semidirect
303. C₄²×C₁₃₉	#41	semidirect
443. #36150	C₁₃₉	direct (N × H)
444. C₁₃₉	#36150	direct (N × H)
445. C₂×#533	C₂×C₁₃₉	semidirect
446. C₂×#532	C₂×C₁₃₉	semidirect
447. #2858	C₂×C₁₃₉	semidirect
448. #2857	C₂×C₁₃₉	semidirect
449. #2856	C₂×C₁₃₉	semidirect
450. #2540	C₂×C₁₃₉	semidirect
451. #2490	C₂×C₁₃₉	semidirect
452. #2454	C₂×C₁₃₉	semidirect
453. #2448	C₂×C₁₃₉	semidirect
454. #2427	C₂×C₁₃₉	semidirect
455. #2426	C₂×C₁₃₉	semidirect
456. #2426	C₂×C₁₃₉	semidirect
457. #2414	C₂×C₁₃₉	semidirect
458. #2407	C₂×C₁₃₉	semidirect
459. #2367	C₂×C₁₃₉	semidirect
460. #2363	C₂×C₁₃₉	semidirect
461. #2341	C₂×C₁₃₉	semidirect
462. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
463. C₄²×D₄	C₂×C₁₃₉	semidirect
556. C₄⋊Q₈	D₄×C₁₃₉	semidirect
685. C₂²×C₄	#41×C₁₃₉	semidirect
747. C₄²	#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×#533×C₁₃₉	2
C₂×#532×C₁₃₉	2
#2858×C₁₃₉	2
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2540×C₁₃₉	2
#2490×C₁₃₉	2
#2454×C₁₃₉	2
#2448×C₁₃₉	2
#2427×C₁₃₉	2
#2426×C₁₃₉	2
#2414×C₁₃₉	2
#2407×C₁₃₉	2
#2367×C₁₃₉	2
#2363×C₁₃₉	2
#2341×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36150	139

Subgroups — C139×#36150 #48030746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36150 #48030746