Subgroups — D₄×C₂²⋊Q₈×C₁₃₉ #48030690

Order 35584.

3488 conjugacy classes of subgroups.

The subgroup lattice has 882 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	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2449×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2440×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2437×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2409×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
17	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	D₄×Q₈×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
47	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
48	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
49	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
50	#399×C₁₃₉	C₂²	1	4	yes	complemented
51	#398×C₁₃₉	C₂²	1	4	yes	complemented
52	#396×C₁₃₉	C₂²	1	4	yes	complemented
53	#396×C₁₃₉	C₂²	1	4	yes	complemented
54	#395×C₁₃₉	C₂²	1	4	yes	complemented
55	#393×C₁₃₉	C₂²	1	4	yes	complemented
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#391×C₁₃₉	C₂²	1	2	yes	complemented
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	complemented
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#389×C₁₃₉	C₂²	1	2	yes	complemented
64	#389×C₁₃₉	C₂²	1	2	yes	complemented
65	#387×C₁₃₉	C₂²	1	2	yes	complemented
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	2	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#385×C₁₃₉	C₂²	1	4	yes	complemented
74	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#384×C₁₃₉	C₂²	1	2	yes	complemented
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	complemented
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#380×C₁₃₉	C₂²	1	4	yes	complemented
82	#379×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, 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	C₂²×Q₈×C₁₃₉	—	2	8	no	—
88	C₂²×Q₈×C₁₃₉	—	2	8	no	—
89	C₂²×Q₈×C₁₃₉	—	4	4	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	—	2	4	no	—
94	C₂²×D₄×C₁₃₉	—	2	4	no	—
95	C₂²×D₄×C₁₃₉	Q₈	1	8	yes	complemented
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	—	2	8	no	—
100	C₂³×C₄×C₁₃₉	—	2	8	no	—
101	C₂³×C₄×C₁₃₉	—	4	4	no	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
112	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
113	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
116	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
120	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
121	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
122	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	direct product factor
123	C₄×Q₈×C₁₃₉	—	2	4	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	C₄×D₄×C₁₃₉	—	2	8	no	—
127	C₄×D₄×C₁₃₉	—	2	8	no	—
128	C₄×D₄×C₁₃₉	—	2	4	no	—
129	C₄×D₄×C₁₃₉	—	2	8	no	—
130	C₄×D₄×C₁₃₉	—	2	4	no	—
131	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
156	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	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	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	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	—	2	4	no	—
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	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	C₂⁴×C₁₃₉	—	2	4	no	—
187	C₂⁴×C₁₃₉	—	2	4	no	—
188	C₂⁴×C₁₃₉	—	2	4	no	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	—	4	2	no	—
191	C₂⁴×C₁₃₉	—	4	2	no	—
192	C₂⁴×C₁₃₉	C₂×Q₈	1	8	yes	complemented
193	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
194	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂×Q₈×C₁₃₉	—	2	2	no	—
197	C₂×Q₈×C₁₃₉	—	2	8	no	—
198	C₂×Q₈×C₁₃₉	—	2	4	no	—
199	C₂×Q₈×C₁₃₉	—	2	8	no	—
200	C₂×Q₈×C₁₃₉	—	2	4	no	—
201	C₂×Q₈×C₁₃₉	—	2	2	no	—
202	C₂×Q₈×C₁₃₉	—	2	4	no	—
203	C₂×Q₈×C₁₃₉	—	4	4	no	—
204	C₂×Q₈×C₁₃₉	—	4	32	no	—
205	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	4	no	—
208	C₂×D₄×C₁₃₉	—	2	32	no	—
209	C₂×D₄×C₁₃₉	—	2	2	no	—
210	C₂×D₄×C₁₃₉	—	2	2	no	—
211	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
212	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
213	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
214	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
215	C₂×D₄×C₁₃₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	2	no	—
220	C₂²×C₄×C₁₃₉	—	2	2	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	8	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	8	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	8	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	1	no	—
241	C₂²×C₄×C₁₃₉	—	4	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	4	no	—
243	C₂²×C₄×C₁₃₉	—	4	32	no	—
244	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
245	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	no	—
263	C₄⋊C₄×C₁₃₉	—	2	8	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	8	no	—
266	C₄⋊C₄×C₁₃₉	—	2	8	no	—
267	C₄⋊C₄×C₁₃₉	—	2	8	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	2	no	—
271	C₄⋊C₄×C₁₃₉	—	2	8	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	4	no	—
278	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
280	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
292	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
293	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
294	C₄²×C₁₃₉	—	2	2	no	—
295	C₄²×C₁₃₉	—	2	2	no	—
296	C₄²×C₁₃₉	—	2	2	no	—
297	C₄²×C₁₃₉	—	2	4	no	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	1	no	—
302	C₂³×C₁₃₉	—	2	1	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	1	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	1	no	—
308	C₂³×C₁₃₉	—	2	16	no	—
309	C₂³×C₁₃₉	—	2	16	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	4	8	no	—
317	C₂³×C₁₃₉	—	4	8	no	—
318	C₂³×C₁₃₉	—	4	8	no	—
319	C₂³×C₁₃₉	—	4	8	no	—
320	C₂³×C₁₃₉	—	4	8	no	—
321	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
322	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
324	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
325	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
326	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
327	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
328	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
329	Q₈×C₁₃₉	—	2	8	no	—
330	Q₈×C₁₃₉	—	4	16	no	—
331	Q₈×C₁₃₉	—	4	8	no	—
332	D₄×C₁₃₉	—	2	16	no	—
333	D₄×C₁₃₉	—	2	8	no	—
334	D₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	direct product factor
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	8	no	—
348	C₂×C₄×C₁₃₉	—	2	8	no	—
349	C₂×C₄×C₁₃₉	—	2	16	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	4	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	4	no	—
355	C₂×C₄×C₁₃₉	—	2	4	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	4	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	4	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	4	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	4	8	no	—
369	C₂×C₄×C₁₃₉	—	4	16	no	—
370	C₂×C₄×C₁₃₉	—	4	4	no	—
371	C₂×C₄×C₁₃₉	—	4	8	no	—
372	C₂×C₄×C₁₃₉	—	4	8	no	—
373	C₂×C₄×C₁₃₉	—	4	16	no	—
374	C₂×C₄×C₁₃₉	—	4	8	no	—
375	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
379	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
384	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
385	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
386	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₁₃₉	—	2	2	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	2	2	no	—
390	C₂²×C₁₃₉	—	2	4	no	—
391	C₂²×C₁₃₉	—	2	4	no	—
392	C₂²×C₁₃₉	—	2	2	no	—
393	C₂²×C₁₃₉	—	2	2	no	—
394	C₂²×C₁₃₉	—	2	4	no	—
395	C₂²×C₁₃₉	—	2	2	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	2	2	no	—
398	C₂²×C₁₃₉	—	2	4	no	—
399	C₂²×C₁₃₉	—	2	4	no	—
400	C₂²×C₁₃₉	—	2	4	no	—
401	C₂²×C₁₃₉	—	2	4	no	—
402	C₂²×C₁₃₉	—	4	32	no	—
403	C₂²×C₁₃₉	—	4	2	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	complemented
408	C₂²×C₁₃₉	D₄×Q₈	1	4	yes	complemented
409	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
410	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
412	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂²×C₁₃₉	#585	1	1	yes	characteristic
416	C₄×C₁₃₉	—	2	2	no	—
417	C₄×C₁₃₉	—	2	2	no	—
418	C₄×C₁₃₉	—	2	4	no	—
419	C₄×C₁₃₉	—	2	4	no	—
420	C₄×C₁₃₉	—	2	4	no	—
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	4	no	—
424	C₄×C₁₃₉	—	4	4	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	1	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	complemented
429	C₄×C₁₃₉	D₄²	1	4	yes	—
430	C₂×C₁₃₉	—	2	4	no	—
431	C₂×C₁₃₉	—	2	8	no	—
432	C₂×C₁₃₉	—	4	4	no	—
433	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
434	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
435	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
436	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
437	C₂×C₁₃₉	#3489	1	1	yes	characteristic
438	C₂×C₁₃₉	#3501	1	1	yes	characteristic
439	C₂×C₁₃₉	#3520	1	1	yes	characteristic
440	D₄×C₂²⋊Q₈	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₁₃₉	D₄×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
442	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
444	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
445	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2848	C₂×C₁₃₉	1	2	yes	complemented
447	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	#2452	C₂×C₁₃₉	1	2	yes	complemented
450	#2449	C₂×C₁₃₉	1	4	yes	complemented
451	#2440	C₂×C₁₃₉	1	2	yes	complemented
452	#2437	C₂×C₁₃₉	1	4	yes	complemented
453	#2417	C₂×C₁₃₉	1	2	yes	complemented
454	#2409	C₂×C₁₃₉	1	2	yes	complemented
455	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
456	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
457	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	—
458	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
459	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
460	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
462	D₄×Q₈	—	2	8	no	—
463	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
464	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
465	C₂×C₂²⋊Q₈	—	2	16	no	—
466	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
467	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
468	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
470	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
471	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
472	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
473	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
474	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
475	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
476	C₂×C₄×D₄	—	2	8	no	—
477	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
487	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
488	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
489	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
490	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
491	#399	C₂²×C₁₃₉	1	4	yes	complemented
492	#398	C₂²×C₁₃₉	1	4	yes	complemented
493	#396	C₂²×C₁₃₉	1	4	yes	complemented
494	#396	C₂²×C₁₃₉	1	4	yes	complemented
495	#395	C₂²×C₁₃₉	1	4	yes	complemented
496	#393	C₂²×C₁₃₉	1	4	yes	complemented
497	#391	C₂²×C₁₃₉	1	2	yes	complemented
498	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
499	#390	C₂²×C₁₃₉	1	2	yes	—
500	#390	C₂²×C₁₃₉	1	2	yes	—
501	#389	C₂²×C₁₃₉	1	2	yes	complemented
502	#389	C₂²×C₁₃₉	1	2	yes	complemented
503	#389	C₂²×C₁₃₉	1	2	yes	complemented
504	#389	C₂²×C₁₃₉	1	2	yes	complemented
505	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
506	#387	C₂²×C₁₃₉	1	2	yes	complemented
507	#386	C₂²×C₁₃₉	1	4	yes	—
508	#386	C₂²×C₁₃₉	1	4	yes	—
509	#385	C₂²×C₁₃₉	1	4	yes	—
510	#385	C₂²×C₁₃₉	1	2	yes	—
511	#385	C₂²×C₁₃₉	1	4	yes	complemented
512	#385	C₂²×C₁₃₉	1	4	yes	complemented
513	#385	C₂²×C₁₃₉	1	4	yes	complemented
514	#385	C₂²×C₁₃₉	1	4	yes	complemented
515	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
516	#384	C₂²×C₁₃₉	1	2	yes	complemented
517	#380	C₂²×C₁₃₉	1	1	yes	characteristic
518	#380	C₂²×C₁₃₉	1	2	yes	—
519	#380	C₂²×C₁₃₉	1	2	yes	—
520	#380	C₂²×C₁₃₉	1	2	yes	complemented
521	#380	C₂²×C₁₃₉	1	2	yes	complemented
522	#380	C₂²×C₁₃₉	1	4	yes	complemented
523	#379	C₂²×C₁₃₉	1	4	yes	—
524	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
525	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
527	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
528	C₂²×Q₈	—	2	8	no	—
529	C₂²×Q₈	—	2	8	no	—
530	C₂²×Q₈	—	4	4	no	—
531	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
532	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
533	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂²×D₄	—	2	4	no	—
535	C₂²×D₄	—	2	4	no	—
536	C₂²×D₄	Q₈×C₁₃₉	1	8	yes	complemented
537	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂³×C₄	—	2	8	no	—
541	C₂³×C₄	—	2	8	no	—
542	C₂³×C₄	—	4	4	no	—
543	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₄⋊Q₈	—	2	8	no	—
554	C₄⋊Q₈	—	2	4	no	—
555	C₂²⋊Q₈	—	2	8	no	—
556	C₂²⋊Q₈	—	2	8	no	—
557	C₂²⋊Q₈	—	2	8	no	—
558	C₂²⋊Q₈	—	2	8	no	—
559	C₂²⋊Q₈	—	2	16	no	—
560	C₂²⋊Q₈	—	2	16	no	—
561	C₂²⋊Q₈	—	2	16	no	—
562	C₂²⋊Q₈	—	4	4	no	—
563	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	direct product factor
564	C₄×Q₈	—	2	4	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	8	no	—
567	C₄×D₄	—	2	8	no	—
568	C₄×D₄	—	2	8	no	—
569	C₄×D₄	—	2	4	no	—
570	C₄×D₄	—	2	8	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
573	C₂×C₄⋊C₄	—	2	4	no	—
574	C₂×C₄⋊C₄	—	2	8	no	—
575	C₂×C₄⋊C₄	—	2	16	no	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	—	2	8	no	—
597	C₂×C₂²⋊C₄	—	2	16	no	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	2	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	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄²	—	2	4	no	—
612	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	4	yes	—
624	#95	C₂³×C₁₃₉	1	4	yes	—
625	#95	C₂³×C₁₃₉	1	4	yes	—
626	#95	C₂³×C₁₃₉	1	4	yes	—
627	C₂⁴	—	2	4	no	—
628	C₂⁴	—	2	4	no	—
629	C₂⁴	—	2	4	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	C₂×Q₈×C₁₃₉	1	8	yes	complemented
634	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	8	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	2	8	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	—	4	32	no	—
646	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	complemented
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	32	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
653	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
654	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
655	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
656	C₂×D₄	#41×C₁₃₉	1	4	yes	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	8	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	8	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	4	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	—	4	32	no	—
685	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
686	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
687	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	2	no	—
704	C₄⋊C₄	—	2	8	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	8	no	—
707	C₄⋊C₄	—	2	8	no	—
708	C₄⋊C₄	—	2	8	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	8	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	4	no	—
719	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
720	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
721	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	8	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	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
734	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	16	no	—
750	C₂³	—	2	16	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	8	no	—
762	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
763	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
764	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
765	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
766	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
767	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
768	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
769	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
770	Q₈	—	2	8	no	—
771	Q₈	—	4	16	no	—
772	Q₈	—	4	8	no	—
773	D₄	—	2	16	no	—
774	D₄	—	2	8	no	—
775	D₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	direct product factor
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	8	no	—
790	C₂×C₄	—	2	16	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	16	no	—
813	C₂×C₄	—	4	16	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	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	C₂²×D₄×C₁₃₉	1	2	yes	—
824	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
825	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
826	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
827	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	32	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	complemented
849	C₂²	D₄×Q₈×C₁₃₉	1	4	yes	complemented
850	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
851	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
852	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
853	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
854	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
855	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
856	C₂²	#585×C₁₃₉	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	4	no	—
860	C₄	—	2	4	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	4	no	—
865	C₄	—	4	4	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	complemented
870	C₄	D₄²×C₁₃₉	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	2	8	no	—
873	C₂	—	4	4	no	—
874	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
875	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
876	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
877	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
878	C₂	#3489×C₁₃₉	1	1	yes	characteristic
879	C₂	#3501×C₁₃₉	1	1	yes	characteristic
880	C₂	#3520×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
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
2. C₂²×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2848×C₁₃₉	C₂	semidirect
6. #2542×C₁₃₉	C₂	semidirect
7. #2538×C₁₃₉	C₂	semidirect
8. #2452×C₁₃₉	C₂	semidirect
9. #2449×C₁₃₉	C₂	semidirect
10. #2440×C₁₃₉	C₂	semidirect
11. #2437×C₁₃₉	C₂	semidirect
12. #2417×C₁₃₉	C₂	semidirect
13. #2409×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
15. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
18. C₂³×Q₈×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
46. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
50. #399×C₁₃₉	C₂²	semidirect
51. #398×C₁₃₉	C₂²	semidirect
52. #396×C₁₃₉	C₂²	semidirect
53. #396×C₁₃₉	C₂²	semidirect
54. #395×C₁₃₉	C₂²	semidirect
55. #393×C₁₃₉	C₂²	semidirect
56. #391×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
60. #389×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
63. #389×C₁₃₉	C₂²	semidirect
64. #389×C₁₃₉	C₂²	semidirect
65. #387×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #385×C₁₃₉	C₂²	semidirect
74. #384×C₁₃₉	C₂²	semidirect
75. #384×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
95. C₂²×D₄×C₁₃₉	Q₈	semidirect
122. C₂²⋊Q₈×C₁₃₉	D₄	direct (N × H)
192. C₂⁴×C₁₃₉	C₂×Q₈	semidirect
205. C₂×Q₈×C₁₃₉	C₂×D₄	semidirect
213. C₂×D₄×C₁₃₉	C₂×Q₈	semidirect
214. C₂×D₄×C₁₃₉	C₂×Q₈	semidirect
246. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
279. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
280. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
334. D₄×C₁₃₉	C₂²⋊Q₈	direct (N × H)
407. C₂²×C₁₃₉	C₂×C₂²⋊Q₈	semidirect
408. C₂²×C₁₃₉	D₄×Q₈	semidirect
428. C₄×C₁₃₉	C₂×C₂²⋊Q₈	semidirect
440. D₄×C₂²⋊Q₈	C₁₃₉	direct (N × H)
441. C₁₃₉	D₄×C₂²⋊Q₈	direct (N × H)
442. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
443. C₂²×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
445. #2857	C₂×C₁₃₉	semidirect
446. #2848	C₂×C₁₃₉	semidirect
447. #2542	C₂×C₁₃₉	semidirect
448. #2538	C₂×C₁₃₉	semidirect
449. #2452	C₂×C₁₃₉	semidirect
450. #2449	C₂×C₁₃₉	semidirect
451. #2440	C₂×C₁₃₉	semidirect
452. #2437	C₂×C₁₃₉	semidirect
453. #2417	C₂×C₁₃₉	semidirect
454. #2409	C₂×C₁₃₉	semidirect
455. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
456. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
458. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
459. C₂³×Q₈	C₂²×C₁₃₉	semidirect
463. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
469. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
470. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
471. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
472. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
473. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
474. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
475. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
486. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
487. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
491. #399	C₂²×C₁₃₉	semidirect
492. #398	C₂²×C₁₃₉	semidirect
493. #396	C₂²×C₁₃₉	semidirect
494. #396	C₂²×C₁₃₉	semidirect
495. #395	C₂²×C₁₃₉	semidirect
496. #393	C₂²×C₁₃₉	semidirect
497. #391	C₂²×C₁₃₉	semidirect
498. #391	C₂²×C₁₃₉	semidirect
501. #389	C₂²×C₁₃₉	semidirect
502. #389	C₂²×C₁₃₉	semidirect
503. #389	C₂²×C₁₃₉	semidirect
504. #389	C₂²×C₁₃₉	semidirect
505. #389	C₂²×C₁₃₉	semidirect
506. #387	C₂²×C₁₃₉	semidirect
511. #385	C₂²×C₁₃₉	semidirect
512. #385	C₂²×C₁₃₉	semidirect
513. #385	C₂²×C₁₃₉	semidirect
514. #385	C₂²×C₁₃₉	semidirect
515. #384	C₂²×C₁₃₉	semidirect
516. #384	C₂²×C₁₃₉	semidirect
520. #380	C₂²×C₁₃₉	semidirect
521. #380	C₂²×C₁₃₉	semidirect
522. #380	C₂²×C₁₃₉	semidirect
524. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
525. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
536. C₂²×D₄	Q₈×C₁₃₉	semidirect
563. C₂²⋊Q₈	D₄×C₁₃₉	direct (N × H)
633. C₂⁴	C₂×Q₈×C₁₃₉	semidirect
646. C₂×Q₈	C₂×D₄×C₁₃₉	semidirect
654. C₂×D₄	C₂×Q₈×C₁₃₉	semidirect
655. C₂×D₄	C₂×Q₈×C₁₃₉	semidirect
687. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
720. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
721. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
775. D₄	C₂²⋊Q₈×C₁₃₉	direct (N × H)
848. C₂²	C₂×C₂²⋊Q₈×C₁₃₉	semidirect
849. C₂²	D₄×Q₈×C₁₃₉	semidirect
869. C₄	C₂×C₂²⋊Q₈×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
C₂²×C₂²⋊Q₈×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2857×C₁₃₉	2
#2848×C₁₃₉	2
#2542×C₁₃₉	2
#2538×C₁₃₉	2
#2452×C₁₃₉	2
#2449×C₁₃₉	2
#2440×C₁₃₉	2
#2437×C₁₃₉	2
#2417×C₁₃₉	2
#2409×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
D₄×C₂²⋊Q₈	139

Subgroups — D4×C22⋊Q8×C139 #48030690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₂²⋊Q₈×C₁₃₉ #48030690