Subgroups — D₄×#104×C₁₃₁ #45708317

Order 33536.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	C₄²×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1980×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1962×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1896×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1871×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1806×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1789×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	C₄×#104×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	complemented
14	#550×C₁₃₁	C₄	1	1	yes	characteristic, complemented
15	D₄×Q₈×C₁₃₁	C₄	1	1	yes	characteristic, complemented
16	#548×C₁₃₁	C₄	1	2	yes	complemented
17	#547×C₁₃₁	—	2	1	no	—
18	#547×C₁₃₁	C₄	1	1	yes	characteristic, complemented
19	#546×C₁₃₁	—	2	2	no	—
20	#546×C₁₃₁	C₄	1	2	yes	complemented
21	D₄²×C₁₃₁	—	2	1	no	—
22	D₄²×C₁₃₁	C₄	1	1	yes	characteristic, complemented
23	#532×C₁₃₁	—	2	1	no	—
24	#532×C₁₃₁	C₂²	1	1	yes	characteristic
25	#525×C₁₃₁	—	2	2	no	—
26	#525×C₁₃₁	C₂²	1	2	yes	—
27	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₁	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃₁	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	complemented
32	#436×C₁₃₁	—	2	1	no	—
33	#435×C₁₃₁	—	2	2	no	—
34	C₈×D₄×C₁₃₁	—	2	1	no	—
35	#423×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×#104×C₁₃₁	—	2	8	no	—
37	C₂×#104×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
39	C₂×#104×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×#104×C₁₃₁	C₂²	1	2	yes	complemented
41	C₂×#104×C₁₃₁	C₂²	1	2	yes	complemented
42	C₂×#104×C₁₃₁	C₂²	1	2	yes	complemented
43	C₂×#104×C₁₃₁	C₂²	1	2	yes	complemented
44	#407×C₁₃₁	C₂²	1	2	yes	complemented
45	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₄⋊C₄×C₁₃₁	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
49	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
50	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
51	#339×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
52	#339×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
53	#339×C₁₃₁	C₂²	1	2	yes	complemented
54	C₂×#41×C₁₃₁	—	2	2	no	—
55	C₂×#41×C₁₃₁	—	2	2	no	—
56	C₂×#41×C₁₃₁	—	2	4	no	—
57	C₂×#41×C₁₃₁	—	2	4	no	—
58	C₂×#41×C₁₃₁	—	4	2	no	—
59	C₂×#41×C₁₃₁	—	4	2	no	—
60	C₂×#41×C₁₃₁	C₂×C₄	1	2	yes	complemented
61	C₂×#41×C₁₃₁	C₂×C₄	1	2	yes	complemented
62	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
63	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃₁	C₂×C₄	1	2	yes	complemented
65	C₂²×D₄×C₁₃₁	—	2	2	no	—
66	C₂²×D₄×C₁₃₁	—	2	1	no	—
67	C₂²×D₄×C₁₃₁	C₂×C₄	1	2	yes	complemented
68	C₂²×D₄×C₁₃₁	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₁	—	2	2	no	—
70	C₂³×C₄×C₁₃₁	—	2	2	no	—
71	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
72	C₂×M₁₆×C₁₃₁	—	2	2	no	—
73	C₂×M₁₆×C₁₃₁	—	2	4	no	—
74	C₂×M₁₆×C₁₃₁	—	4	2	no	—
75	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃₁	—	2	2	no	—
79	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
80	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
81	#127×C₁₃₁	—	2	1	no	—
82	#127×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
83	#124×C₁₃₁	—	2	2	no	—
84	#124×C₁₃₁	C₂×C₄	1	2	yes	complemented
85	#123×C₁₃₁	—	2	2	no	—
86	#123×C₁₃₁	—	2	2	no	—
87	#123×C₁₃₁	—	2	2	no	—
88	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
89	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
90	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	complemented
91	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	complemented
92	#121×C₁₃₁	—	2	2	no	—
93	#121×C₁₃₁	—	2	1	no	—
94	#121×C₁₃₁	—	2	1	no	—
95	#121×C₁₃₁	—	2	1	no	—
96	#121×C₁₃₁	—	2	1	no	—
97	#121×C₁₃₁	—	2	2	no	—
98	#121×C₁₃₁	—	2	2	no	—
99	#121×C₁₃₁	C₂×C₄	1	2	yes	complemented
100	#121×C₁₃₁	C₂×C₄	1	2	yes	complemented
101	#120×C₁₃₁	—	2	2	no	—
102	#120×C₁₃₁	—	2	2	no	—
103	#120×C₁₃₁	—	2	2	no	—
104	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
105	C₄×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
106	C₄×D₄×C₁₃₁	—	2	8	no	—
107	C₄×D₄×C₁₃₁	—	2	1	no	—
108	C₄×D₄×C₁₃₁	—	2	2	no	—
109	C₄×D₄×C₁₃₁	—	2	1	no	—
110	C₄×D₄×C₁₃₁	—	2	1	no	—
111	C₄×D₄×C₁₃₁	—	2	2	no	—
112	C₄×D₄×C₁₃₁	—	2	1	no	—
113	C₄×D₄×C₁₃₁	—	2	2	no	—
114	C₄×D₄×C₁₃₁	—	2	1	no	—
115	C₄×D₄×C₁₃₁	—	2	1	no	—
116	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
118	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
122	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
123	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
124	#117×C₁₃₁	—	2	1	no	—
125	#117×C₁₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
132	C₂×C₄²×C₁₃₁	—	2	1	no	—
133	C₂×C₄²×C₁₃₁	—	2	1	no	—
134	C₂×C₄²×C₁₃₁	—	2	4	no	—
135	C₂×C₄²×C₁₃₁	—	2	2	no	—
136	C₂×C₄²×C₁₃₁	—	2	1	no	—
137	C₂×C₄²×C₁₃₁	—	4	2	no	—
138	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
142	C₄⋊C₈×C₁₃₁	—	2	1	no	—
143	C₄⋊C₈×C₁₃₁	—	2	1	no	—
144	#104×C₁₃₁	—	2	4	no	—
145	#104×C₁₃₁	—	2	2	no	—
146	#104×C₁₃₁	—	2	4	no	—
147	#104×C₁₃₁	—	2	4	no	—
148	#104×C₁₃₁	—	4	2	no	—
149	#104×C₁₃₁	—	4	2	no	—
150	#104×C₁₃₁	D₄	1	4	yes	direct product factor
151	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
152	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
153	#97×C₁₃₁	—	2	1	no	—
154	C₄×C₈×C₁₃₁	—	2	1	no	—
155	#95×C₁₃₁	—	2	1	no	—
156	#95×C₁₃₁	—	2	2	no	—
157	C₂⁴×C₁₃₁	—	2	2	no	—
158	C₂⁴×C₁₃₁	C₂×D₄	1	2	yes	—
159	#41×C₁₃₁	—	2	1	no	—
160	#41×C₁₃₁	—	2	1	no	—
161	#41×C₁₃₁	—	2	4	no	—
162	#41×C₁₃₁	—	2	4	no	—
163	#41×C₁₃₁	—	2	2	no	—
164	#41×C₁₃₁	—	2	2	no	—
165	#41×C₁₃₁	—	2	2	no	—
166	#41×C₁₃₁	—	2	2	no	—
167	#41×C₁₃₁	—	4	4	no	—
168	#41×C₁₃₁	—	4	4	no	—
169	#41×C₁₃₁	—	4	2	no	—
170	#41×C₁₃₁	—	4	2	no	—
171	#41×C₁₃₁	—	4	4	no	—
172	#41×C₁₃₁	—	4	4	no	—
173	#41×C₁₃₁	C₂×D₄	1	2	yes	—
174	#41×C₁₃₁	#41	1	2	yes	—
175	C₂×Q₈×C₁₃₁	—	2	2	no	—
176	C₂×Q₈×C₁₃₁	—	2	4	no	—
177	C₂×Q₈×C₁₃₁	—	4	2	no	—
178	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
179	C₂×Q₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₁₃₁	—	2	1	no	—
181	C₂×D₄×C₁₃₁	—	2	4	no	—
182	C₂×D₄×C₁₃₁	—	2	4	no	—
183	C₂×D₄×C₁₃₁	—	2	2	no	—
184	C₂×D₄×C₁₃₁	—	2	2	no	—
185	C₂×D₄×C₁₃₁	—	2	2	no	—
186	C₂×D₄×C₁₃₁	—	2	2	no	—
187	C₂×D₄×C₁₃₁	—	2	2	no	—
188	C₂×D₄×C₁₃₁	—	2	1	no	—
189	C₂×D₄×C₁₃₁	—	2	2	no	—
190	C₂×D₄×C₁₃₁	—	2	1	no	—
191	C₂×D₄×C₁₃₁	—	4	2	no	—
192	C₂×D₄×C₁₃₁	—	4	4	no	—
193	C₂×D₄×C₁₃₁	—	4	4	no	—
194	C₂×D₄×C₁₃₁	—	4	4	no	—
195	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
196	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×D₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
199	C₂×D₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₁	—	2	1	no	—
201	C₂²×C₄×C₁₃₁	—	2	2	no	—
202	C₂²×C₄×C₁₃₁	—	2	1	no	—
203	C₂²×C₄×C₁₃₁	—	2	2	no	—
204	C₂²×C₄×C₁₃₁	—	2	2	no	—
205	C₂²×C₄×C₁₃₁	—	2	2	no	—
206	C₂²×C₄×C₁₃₁	—	2	8	no	—
207	C₂²×C₄×C₁₃₁	—	2	2	no	—
208	C₂²×C₄×C₁₃₁	—	2	1	no	—
209	C₂²×C₄×C₁₃₁	—	2	2	no	—
210	C₂²×C₄×C₁₃₁	—	2	1	no	—
211	C₂²×C₄×C₁₃₁	—	2	2	no	—
212	C₂²×C₄×C₁₃₁	—	2	2	no	—
213	C₂²×C₄×C₁₃₁	—	2	2	no	—
214	C₂²×C₄×C₁₃₁	—	2	1	no	—
215	C₂²×C₄×C₁₃₁	—	4	4	no	—
216	C₂²×C₄×C₁₃₁	—	4	4	no	—
217	C₂²×C₄×C₁₃₁	—	4	4	no	—
218	C₂²×C₄×C₁₃₁	—	4	4	no	—
219	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
227	M₁₆×C₁₃₁	—	2	1	no	—
228	M₁₆×C₁₃₁	—	2	2	no	—
229	M₁₆×C₁₃₁	—	2	1	no	—
230	M₁₆×C₁₃₁	—	2	1	no	—
231	M₁₆×C₁₃₁	—	2	2	no	—
232	M₁₆×C₁₃₁	—	4	4	no	—
233	M₁₆×C₁₃₁	C₂×D₄	1	2	yes	complemented
234	C₂×C₈×C₁₃₁	—	2	1	no	—
235	C₂×C₈×C₁₃₁	—	2	1	no	—
236	C₂×C₈×C₁₃₁	—	2	2	no	—
237	C₂×C₈×C₁₃₁	—	4	4	no	—
238	C₄⋊C₄×C₁₃₁	—	2	4	no	—
239	C₄⋊C₄×C₁₃₁	—	2	1	no	—
240	C₄⋊C₄×C₁₃₁	—	2	2	no	—
241	C₄⋊C₄×C₁₃₁	—	2	1	no	—
242	C₄⋊C₄×C₁₃₁	—	2	1	no	—
243	C₄⋊C₄×C₁₃₁	—	2	1	no	—
244	C₄⋊C₄×C₁₃₁	—	2	2	no	—
245	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
246	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
247	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
248	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
251	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
252	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
253	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
254	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
255	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
256	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
257	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
258	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
259	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
260	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
261	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
262	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
263	C₂²⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
264	C₄²×C₁₃₁	—	2	4	no	—
265	C₄²×C₁₃₁	—	2	1	no	—
266	C₄²×C₁₃₁	—	2	1	no	—
267	C₄²×C₁₃₁	—	2	1	no	—
268	C₄²×C₁₃₁	—	2	1	no	—
269	C₄²×C₁₃₁	—	2	2	no	—
270	C₄²×C₁₃₁	—	2	1	no	—
271	C₄²×C₁₃₁	—	2	1	no	—
272	C₄²×C₁₃₁	—	2	2	no	—
273	C₄²×C₁₃₁	—	4	4	no	—
274	C₄²×C₁₃₁	—	4	2	no	—
275	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
276	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
277	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃₁	C₂×D₄	1	2	yes	complemented
280	C₂³×C₁₃₁	—	2	1	no	—
281	C₂³×C₁₃₁	—	2	2	no	—
282	C₂³×C₁₃₁	—	2	2	no	—
283	C₂³×C₁₃₁	—	2	4	no	—
284	C₂³×C₁₃₁	—	2	2	no	—
285	C₂³×C₁₃₁	—	4	2	no	—
286	C₂³×C₁₃₁	—	4	4	no	—
287	C₂³×C₁₃₁	—	4	4	no	—
288	C₂³×C₁₃₁	—	8	2	no	—
289	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₁₃₁	—	2	1	no	—
293	Q₈×C₁₃₁	—	2	2	no	—
294	Q₈×C₁₃₁	—	2	2	no	—
295	Q₈×C₁₃₁	—	4	4	no	—
296	Q₈×C₁₃₁	C₄×D₄	1	2	yes	complemented
297	D₄×C₁₃₁	—	2	2	no	—
298	D₄×C₁₃₁	—	2	2	no	—
299	D₄×C₁₃₁	—	2	4	no	—
300	D₄×C₁₃₁	—	2	2	no	—
301	D₄×C₁₃₁	—	2	1	no	—
302	D₄×C₁₃₁	—	2	2	no	—
303	D₄×C₁₃₁	—	2	2	no	—
304	D₄×C₁₃₁	—	4	4	no	—
305	D₄×C₁₃₁	—	4	4	no	—
306	D₄×C₁₃₁	—	4	4	no	—
307	D₄×C₁₃₁	—	4	2	no	—
308	D₄×C₁₃₁	—	4	2	no	—
309	D₄×C₁₃₁	—	4	4	no	—
310	D₄×C₁₃₁	—	4	2	no	—
311	D₄×C₁₃₁	—	8	1	no	—
312	D₄×C₁₃₁	—	8	2	no	—
313	D₄×C₁₃₁	#104	1	4	yes	direct product factor
314	D₄×C₁₃₁	C₄×D₄	1	2	yes	complemented
315	C₂×C₄×C₁₃₁	—	2	2	no	—
316	C₂×C₄×C₁₃₁	—	2	2	no	—
317	C₂×C₄×C₁₃₁	—	2	1	no	—
318	C₂×C₄×C₁₃₁	—	2	2	no	—
319	C₂×C₄×C₁₃₁	—	2	2	no	—
320	C₂×C₄×C₁₃₁	—	2	2	no	—
321	C₂×C₄×C₁₃₁	—	2	2	no	—
322	C₂×C₄×C₁₃₁	—	2	2	no	—
323	C₂×C₄×C₁₃₁	—	2	2	no	—
324	C₂×C₄×C₁₃₁	—	2	2	no	—
325	C₂×C₄×C₁₃₁	—	2	2	no	—
326	C₂×C₄×C₁₃₁	—	2	2	no	—
327	C₂×C₄×C₁₃₁	—	2	2	no	—
328	C₂×C₄×C₁₃₁	—	2	2	no	—
329	C₂×C₄×C₁₃₁	—	2	2	no	—
330	C₂×C₄×C₁₃₁	—	2	2	no	—
331	C₂×C₄×C₁₃₁	—	2	2	no	—
332	C₂×C₄×C₁₃₁	—	2	2	no	—
333	C₂×C₄×C₁₃₁	—	2	4	no	—
334	C₂×C₄×C₁₃₁	—	2	1	no	—
335	C₂×C₄×C₁₃₁	—	2	1	no	—
336	C₂×C₄×C₁₃₁	—	2	2	no	—
337	C₂×C₄×C₁₃₁	—	4	1	no	—
338	C₂×C₄×C₁₃₁	—	4	4	no	—
339	C₂×C₄×C₁₃₁	—	4	4	no	—
340	C₂×C₄×C₁₃₁	—	4	4	no	—
341	C₂×C₄×C₁₃₁	—	4	16	no	—
342	C₂×C₄×C₁₃₁	—	4	1	no	—
343	C₂×C₄×C₁₃₁	—	4	2	no	—
344	C₂×C₄×C₁₃₁	—	4	2	no	—
345	C₂×C₄×C₁₃₁	—	4	1	no	—
346	C₂×C₄×C₁₃₁	—	4	2	no	—
347	C₂×C₄×C₁₃₁	—	4	2	no	—
348	C₂×C₄×C₁₃₁	—	4	2	no	—
349	C₂×C₄×C₁₃₁	—	8	1	no	—
350	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
362	C₈×C₁₃₁	—	2	2	no	—
363	C₈×C₁₃₁	—	4	2	no	—
364	C₈×C₁₃₁	—	4	1	no	—
365	C₂²×C₁₃₁	—	2	2	no	—
366	C₂²×C₁₃₁	—	2	1	no	—
367	C₂²×C₁₃₁	—	2	1	no	—
368	C₂²×C₁₃₁	—	2	2	no	—
369	C₂²×C₁₃₁	—	2	2	no	—
370	C₂²×C₁₃₁	—	2	2	no	—
371	C₂²×C₁₃₁	—	2	2	no	—
372	C₂²×C₁₃₁	—	2	2	no	—
373	C₂²×C₁₃₁	—	4	4	no	—
374	C₂²×C₁₃₁	—	4	4	no	—
375	C₂²×C₁₃₁	—	4	1	no	—
376	C₂²×C₁₃₁	—	4	1	no	—
377	C₂²×C₁₃₁	—	4	2	no	—
378	C₂²×C₁₃₁	—	4	2	no	—
379	C₂²×C₁₃₁	—	4	2	no	—
380	C₂²×C₁₃₁	—	8	8	no	—
381	C₂²×C₁₃₁	C₂×#104	1	4	yes	complemented
382	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
383	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
384	C₂²×C₁₃₁	#546	1	1	yes	characteristic
385	C₄×C₁₃₁	—	2	4	no	—
386	C₄×C₁₃₁	—	2	2	no	—
387	C₄×C₁₃₁	—	2	2	no	—
388	C₄×C₁₃₁	—	2	2	no	—
389	C₄×C₁₃₁	—	2	1	no	—
390	C₄×C₁₃₁	—	2	1	no	—
391	C₄×C₁₃₁	—	2	1	no	—
392	C₄×C₁₃₁	—	4	2	no	—
393	C₄×C₁₃₁	—	4	4	no	—
394	C₄×C₁₃₁	—	4	2	no	—
395	C₄×C₁₃₁	—	4	1	no	—
396	C₄×C₁₃₁	—	4	1	no	—
397	C₄×C₁₃₁	C₂×#104	1	2	yes	complemented
398	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
399	C₄×C₁₃₁	#518	1	1	yes	characteristic
400	C₄×C₁₃₁	D₄²	1	1	yes	characteristic
401	C₄×C₁₃₁	#546	1	1	yes	characteristic
402	C₂×C₁₃₁	—	2	1	no	—
403	C₂×C₁₃₁	—	2	1	no	—
404	C₂×C₁₃₁	—	2	4	no	—
405	C₂×C₁₃₁	—	4	2	no	—
406	C₂×C₁₃₁	—	4	2	no	—
407	C₂×C₁₃₁	—	8	2	no	—
408	C₂×C₁₃₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
409	C₂×C₁₃₁	C₂²×#104	1	1	yes	characteristic
410	C₂×C₁₃₁	#2901	1	1	yes	characteristic
411	D₄×#104	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₁₃₁	D₄×#104	1	1	yes	characteristic, direct product factor, Sylow
413	D₄×#41	C₂×C₁₃₁	1	1	yes	characteristic
414	D₄×M₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
415	C₂²×#104	C₂×C₁₃₁	1	2	yes	complemented
416	C₄²×D₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
417	#1980	C₂×C₁₃₁	1	1	yes	characteristic, complemented
418	#1962	C₂×C₁₃₁	1	1	yes	characteristic, complemented
419	#1896	C₂×C₁₃₁	1	2	yes	complemented
420	#1871	C₂×C₁₃₁	1	2	yes	complemented
421	#1806	C₂×C₁₃₁	1	1	yes	characteristic, complemented
422	#1789	C₂×C₁₃₁	1	2	yes	complemented
423	C₄×#104	C₂×C₁₃₁	1	1	yes	characteristic, complemented
424	C₂²×#41	C₂²×C₁₃₁	1	2	yes	—
425	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	complemented
426	#550	C₄×C₁₃₁	1	1	yes	characteristic, complemented
427	D₄×Q₈	C₄×C₁₃₁	1	1	yes	characteristic, complemented
428	#548	C₄×C₁₃₁	1	2	yes	complemented
429	#547	—	2	1	no	—
430	#547	C₄×C₁₃₁	1	1	yes	characteristic, complemented
431	#546	—	2	2	no	—
432	#546	C₄×C₁₃₁	1	2	yes	complemented
433	D₄²	—	2	1	no	—
434	D₄²	C₄×C₁₃₁	1	1	yes	characteristic, complemented
435	#532	—	2	1	no	—
436	#532	C₂²×C₁₃₁	1	1	yes	characteristic
437	#525	—	2	2	no	—
438	#525	C₂²×C₁₃₁	1	2	yes	—
439	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
440	C₂×C₄×D₄	—	2	1	no	—
441	C₂×C₄×D₄	—	2	1	no	—
442	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
443	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	complemented
444	#436	—	2	1	no	—
445	#435	—	2	2	no	—
446	C₈×D₄	—	2	1	no	—
447	#423	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
448	C₂×#104	—	2	8	no	—
449	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
450	C₂×#104	C₂²×C₁₃₁	1	1	yes	characteristic
451	C₂×#104	C₂²×C₁₃₁	1	1	yes	characteristic
452	C₂×#104	C₂²×C₁₃₁	1	2	yes	complemented
453	C₂×#104	C₂²×C₁₃₁	1	2	yes	complemented
454	C₂×#104	C₂²×C₁₃₁	1	2	yes	complemented
455	C₂×#104	C₂²×C₁₃₁	1	2	yes	complemented
456	#407	C₂²×C₁₃₁	1	2	yes	complemented
457	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
458	C₄×C₄⋊C₄	—	2	1	no	—
459	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
460	C₄×C₂²⋊C₄	—	2	2	no	—
461	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
462	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
463	#339	C₂²×C₁₃₁	1	2	yes	complemented
464	#339	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
465	#339	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	4	2	no	—
471	C₂×#41	—	4	2	no	—
472	C₂×#41	C₂×C₄×C₁₃₁	1	2	yes	complemented
473	C₂×#41	C₂×C₄×C₁₃₁	1	2	yes	complemented
474	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
475	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
476	C₂²×Q₈	C₂×C₄×C₁₃₁	1	2	yes	complemented
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	C₂×C₄×C₁₃₁	1	2	yes	complemented
480	C₂²×D₄	D₄×C₁₃₁	1	1	yes	characteristic
481	C₂³×C₄	—	2	2	no	—
482	C₂³×C₄	—	2	2	no	—
483	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
484	C₂×M₁₆	—	2	2	no	—
485	C₂×M₁₆	—	2	4	no	—
486	C₂×M₁₆	—	4	2	no	—
487	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
488	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
490	C₂²×C₈	—	2	2	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
493	#127	—	2	1	no	—
494	#127	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
495	#124	—	2	2	no	—
496	#124	C₂×C₄×C₁₃₁	1	2	yes	complemented
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	#123	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	complemented
503	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	complemented
504	#121	—	2	2	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	C₂×C₄×C₁₃₁	1	2	yes	complemented
512	#121	C₂×C₄×C₁₃₁	1	2	yes	complemented
513	#120	—	2	2	no	—
514	#120	—	2	2	no	—
515	#120	—	2	2	no	—
516	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
517	C₄×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
529	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
530	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
531	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
532	C₄×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic, complemented
533	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
534	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
535	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
536	#117	—	2	1	no	—
537	#117	C₂³×C₁₃₁	1	1	yes	characteristic
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	—	2	2	no	—
543	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	—	2	4	no	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	—	2	2	no	—
549	C₂×C₄²	—	4	2	no	—
550	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
554	C₄⋊C₈	—	2	1	no	—
555	C₄⋊C₈	—	2	1	no	—
556	#104	—	2	4	no	—
557	#104	—	2	2	no	—
558	#104	—	2	4	no	—
559	#104	—	2	4	no	—
560	#104	—	4	2	no	—
561	#104	—	4	2	no	—
562	#104	D₄×C₁₃₁	1	4	yes	direct product factor
563	C₂²⋊C₈	—	2	2	no	—
564	C₂²⋊C₈	—	2	2	no	—
565	#97	—	2	1	no	—
566	C₄×C₈	—	2	1	no	—
567	#95	—	2	1	no	—
568	#95	—	2	2	no	—
569	C₂⁴	—	2	2	no	—
570	C₂⁴	C₂×D₄×C₁₃₁	1	2	yes	—
571	#41	—	2	1	no	—
572	#41	—	2	1	no	—
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	#41	—	4	2	no	—
582	#41	—	4	2	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	C₂×D₄×C₁₃₁	1	2	yes	—
586	#41	#41×C₁₃₁	1	2	yes	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
591	C₂×Q₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
608	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
609	C₂×D₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
610	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
611	C₂×D₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	—	4	4	no	—
631	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
632	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
633	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
636	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
639	M₁₆	—	2	1	no	—
640	M₁₆	—	2	2	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	1	no	—
643	M₁₆	—	2	2	no	—
644	M₁₆	—	4	4	no	—
645	M₁₆	C₂×D₄×C₁₃₁	1	2	yes	complemented
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	4	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
658	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
659	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
660	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
661	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
673	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
674	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
675	C₂²⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	4	4	no	—
686	C₄²	—	4	2	no	—
687	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
688	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
691	C₄²	C₂×D₄×C₁₃₁	1	2	yes	complemented
692	C₂³	—	2	4	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
702	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
703	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	4	no	—
708	Q₈	C₄×D₄×C₁₃₁	1	2	yes	complemented
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	2	no	—
725	D₄	#104×C₁₃₁	1	4	yes	direct product factor
726	D₄	C₄×D₄×C₁₃₁	1	2	yes	complemented
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
763	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
764	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
765	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
766	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
767	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
768	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
771	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
772	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
773	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
774	C₈	—	2	2	no	—
775	C₈	—	4	2	no	—
776	C₈	—	4	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	8	no	—
793	C₂²	C₂×#104×C₁₃₁	1	4	yes	complemented
794	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
795	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
796	C₂²	#546×C₁₃₁	1	1	yes	characteristic
797	C₄	—	2	4	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	C₂×#104×C₁₃₁	1	2	yes	complemented
810	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
811	C₄	#518×C₁₃₁	1	1	yes	characteristic
812	C₄	D₄²×C₁₃₁	1	1	yes	characteristic
813	C₄	#546×C₁₃₁	1	1	yes	characteristic
814	C₂	—	2	1	no	—
815	C₂	—	2	1	no	—
816	C₂	—	2	4	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	D₄×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
821	C₂	C₂²×#104×C₁₃₁	1	1	yes	characteristic
822	C₂	#2901×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂²×C₂²⋊C₄
prime radical	D₄×#41×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄×D₄×C₁₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₃₁	C₂	semidirect
3. C₂²×#104×C₁₃₁	C₂	semidirect
4. C₄²×D₄×C₁₃₁	C₂	semidirect
5. #1980×C₁₃₁	C₂	semidirect
6. #1962×C₁₃₁	C₂	semidirect
7. #1896×C₁₃₁	C₂	semidirect
8. #1871×C₁₃₁	C₂	semidirect
9. #1806×C₁₃₁	C₂	semidirect
10. #1789×C₁₃₁	C₂	semidirect
11. C₄×#104×C₁₃₁	C₂	semidirect
13. C₂²×M₁₆×C₁₃₁	C₂²	semidirect
14. #550×C₁₃₁	C₄	semidirect
15. D₄×Q₈×C₁₃₁	C₄	semidirect
16. #548×C₁₃₁	C₄	semidirect
18. #547×C₁₃₁	C₄	semidirect
20. #546×C₁₃₁	C₄	semidirect
22. D₄²×C₁₃₁	C₄	semidirect
31. C₂²×C₄²×C₁₃₁	C₂²	semidirect
35. #423×C₁₃₁	C₂²	semidirect
40. C₂×#104×C₁₃₁	C₂²	semidirect
41. C₂×#104×C₁₃₁	C₂²	semidirect
42. C₂×#104×C₁₃₁	C₂²	semidirect
43. C₂×#104×C₁₃₁	C₂²	semidirect
44. #407×C₁₃₁	C₂²	semidirect
45. C₄×M₁₆×C₁₃₁	C₂²	semidirect
47. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
50. C₄³×C₁₃₁	C₂²	semidirect
51. #339×C₁₃₁	C₂²	semidirect
52. #339×C₁₃₁	C₂²	semidirect
53. #339×C₁₃₁	C₂²	semidirect
60. C₂×#41×C₁₃₁	C₂×C₄	semidirect
61. C₂×#41×C₁₃₁	C₂×C₄	semidirect
64. C₂²×Q₈×C₁₃₁	C₂×C₄	semidirect
67. C₂²×D₄×C₁₃₁	C₂×C₄	semidirect
80. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
82. #127×C₁₃₁	C₂×C₄	semidirect
84. #124×C₁₃₁	C₂×C₄	semidirect
90. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
91. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
99. #121×C₁₃₁	C₂×C₄	semidirect
100. #121×C₁₃₁	C₂×C₄	semidirect
104. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
105. C₄×Q₈×C₁₃₁	C₂×C₄	semidirect
119. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
120. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
150. #104×C₁₃₁	D₄	direct (N × H)
233. M₁₆×C₁₃₁	C₂×D₄	semidirect
279. C₄²×C₁₃₁	C₂×D₄	semidirect
296. Q₈×C₁₃₁	C₄×D₄	semidirect
313. D₄×C₁₃₁	#104	direct (N × H)
314. D₄×C₁₃₁	C₄×D₄	semidirect
381. C₂²×C₁₃₁	C₂×#104	semidirect
397. C₄×C₁₃₁	C₂×#104	semidirect
411. D₄×#104	C₁₃₁	direct (N × H)
412. C₁₃₁	D₄×#104	direct (N × H)
414. D₄×M₁₆	C₂×C₁₃₁	semidirect
415. C₂²×#104	C₂×C₁₃₁	semidirect
416. C₄²×D₄	C₂×C₁₃₁	semidirect
417. #1980	C₂×C₁₃₁	semidirect
418. #1962	C₂×C₁₃₁	semidirect
419. #1896	C₂×C₁₃₁	semidirect
420. #1871	C₂×C₁₃₁	semidirect
421. #1806	C₂×C₁₃₁	semidirect
422. #1789	C₂×C₁₃₁	semidirect
423. C₄×#104	C₂×C₁₃₁	semidirect
425. C₂²×M₁₆	C₂²×C₁₃₁	semidirect
426. #550	C₄×C₁₃₁	semidirect
427. D₄×Q₈	C₄×C₁₃₁	semidirect
428. #548	C₄×C₁₃₁	semidirect
430. #547	C₄×C₁₃₁	semidirect
432. #546	C₄×C₁₃₁	semidirect
434. D₄²	C₄×C₁₃₁	semidirect
443. C₂²×C₄²	C₂²×C₁₃₁	semidirect
447. #423	C₂²×C₁₃₁	semidirect
452. C₂×#104	C₂²×C₁₃₁	semidirect
453. C₂×#104	C₂²×C₁₃₁	semidirect
454. C₂×#104	C₂²×C₁₃₁	semidirect
455. C₂×#104	C₂²×C₁₃₁	semidirect
456. #407	C₂²×C₁₃₁	semidirect
457. C₄×M₁₆	C₂²×C₁₃₁	semidirect
459. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
462. C₄³	C₂²×C₁₃₁	semidirect
463. #339	C₂²×C₁₃₁	semidirect
464. #339	C₂²×C₁₃₁	semidirect
465. #339	C₂²×C₁₃₁	semidirect
472. C₂×#41	C₂×C₄×C₁₃₁	semidirect
473. C₂×#41	C₂×C₄×C₁₃₁	semidirect
476. C₂²×Q₈	C₂×C₄×C₁₃₁	semidirect
479. C₂²×D₄	C₂×C₄×C₁₃₁	semidirect
492. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
494. #127	C₂×C₄×C₁₃₁	semidirect
496. #124	C₂×C₄×C₁₃₁	semidirect
502. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
503. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
511. #121	C₂×C₄×C₁₃₁	semidirect
512. #121	C₂×C₄×C₁₃₁	semidirect
516. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
517. C₄×Q₈	C₂×C₄×C₁₃₁	semidirect
531. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
532. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
562. #104	D₄×C₁₃₁	direct (N × H)
645. M₁₆	C₂×D₄×C₁₃₁	semidirect
691. C₄²	C₂×D₄×C₁₃₁	semidirect
708. Q₈	C₄×D₄×C₁₃₁	semidirect
725. D₄	#104×C₁₃₁	direct (N × H)
726. D₄	C₄×D₄×C₁₃₁	semidirect
793. C₂²	C₂×#104×C₁₃₁	semidirect
809. C₄	C₂×#104×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₁₃₁	2
D₄×M₁₆×C₁₃₁	2
C₂²×#104×C₁₃₁	2
C₄²×D₄×C₁₃₁	2
#1980×C₁₃₁	2
#1962×C₁₃₁	2
#1896×C₁₃₁	2
#1871×C₁₃₁	2
#1806×C₁₃₁	2
#1789×C₁₃₁	2
C₄×#104×C₁₃₁	2
D₄×#104	131

Subgroups — D4×#104×C131 #45708317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#104×C₁₃₁ #45708317