Subgroups — C₇₃×#25793 #32935197

Order 18688.

1688 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#468×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#452×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
19	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
21	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
37	#496×C₇₃	—	2	4	no	—
38	#495×C₇₃	—	2	4	no	—
39	#468×C₇₃	—	2	4	no	—
40	#452×C₇₃	—	2	4	no	—
41	#447×C₇₃	—	2	4	no	—
42	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
52	#394×C₇₃	—	2	2	no	—
53	#392×C₇₃	—	2	2	no	—
54	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	#390×C₇₃	C₂²	1	1	yes	characteristic
56	#390×C₇₃	C₂²	1	1	yes	characteristic
57	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
58	#386×C₇₃	—	2	2	no	—
59	#379×C₇₃	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
61	#336×C₇₃	C₂²	1	1	yes	characteristic, complemented
62	#336×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₇₃	—	2	1	no	—
64	C₂×#41×C₇₃	—	2	2	no	—
65	C₂×#41×C₇₃	—	2	2	no	—
66	C₂×#41×C₇₃	—	2	2	no	—
67	C₂×#41×C₇₃	—	2	2	no	—
68	C₂×#41×C₇₃	—	4	1	no	—
69	C₂×#41×C₇₃	—	4	1	no	—
70	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₇₃	—	2	2	no	—
73	C₂²×D₄×C₇₃	—	2	2	no	—
74	C₂²×D₄×C₇₃	—	2	1	no	—
75	C₂²×D₄×C₇₃	—	2	1	no	—
76	C₂²×D₄×C₇₃	—	2	2	no	—
77	C₂²×D₄×C₇₃	—	2	2	no	—
78	C₂²×D₄×C₇₃	—	2	1	no	—
79	C₂²×D₄×C₇₃	—	2	2	no	—
80	C₂²×D₄×C₇₃	—	4	1	no	—
81	C₂²×D₄×C₇₃	—	4	1	no	—
82	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇₃	—	2	1	no	—
87	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
88	AGL(1,ℤ/8)×C₇₃	—	2	32	no	—
89	C₂×Q₁₆×C₇₃	—	2	2	no	—
90	C₂×Q₁₆×C₇₃	—	2	2	no	—
91	C₂×Q₁₆×C₇₃	—	4	1	no	—
92	C₂×SD₁₆×C₇₃	—	2	2	no	—
93	C₂×SD₁₆×C₇₃	—	2	2	no	—
94	C₂×SD₁₆×C₇₃	—	2	2	no	—
95	C₂×SD₁₆×C₇₃	—	2	2	no	—
96	C₂×SD₁₆×C₇₃	—	2	2	no	—
97	C₂×SD₁₆×C₇₃	—	2	2	no	—
98	C₂×SD₁₆×C₇₃	—	2	2	no	—
99	C₂×SD₁₆×C₇₃	—	2	2	no	—
100	C₂×SD₁₆×C₇₃	—	2	2	no	—
101	C₂×SD₁₆×C₇₃	—	2	2	no	—
102	C₂×SD₁₆×C₇₃	—	4	1	no	—
103	C₂×SD₁₆×C₇₃	D₄	1	4	yes	complemented
104	C₂×D₈×C₇₃	—	2	2	no	—
105	C₂×D₈×C₇₃	—	2	2	no	—
106	C₂×D₈×C₇₃	—	2	2	no	—
107	C₂×D₈×C₇₃	—	2	2	no	—
108	C₂×D₈×C₇₃	—	2	2	no	—
109	C₂×D₈×C₇₃	—	2	2	no	—
110	C₂×D₈×C₇₃	—	2	2	no	—
111	C₂×D₈×C₇₃	—	2	2	no	—
112	C₂×D₈×C₇₃	—	2	2	no	—
113	C₂×D₈×C₇₃	—	4	1	no	—
114	C₂×D₈×C₇₃	—	4	1	no	—
115	C₂×D₈×C₇₃	D₄	1	4	yes	complemented
116	C₂×M₁₆×C₇₃	—	2	2	no	—
117	C₂×M₁₆×C₇₃	—	2	2	no	—
118	C₂×M₁₆×C₇₃	D₄	1	4	yes	complemented
119	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
123	#127×C₇₃	—	2	2	no	—
124	#127×C₇₃	—	4	1	no	—
125	#124×C₇₃	—	2	2	no	—
126	#124×C₇₃	—	2	2	no	—
127	#124×C₇₃	—	2	2	no	—
128	#124×C₇₃	—	4	1	no	—
129	#124×C₇₃	—	4	1	no	—
130	#124×C₇₃	—	4	1	no	—
131	C₂²⋊Q₈×C₇₃	—	2	2	no	—
132	C₂²⋊Q₈×C₇₃	—	2	2	no	—
133	#121×C₇₃	—	2	2	no	—
134	#121×C₇₃	—	2	2	no	—
135	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
140	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
141	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
145	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
146	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
147	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
149	#107×C₇₃	—	2	2	no	—
150	#103×C₇₃	—	2	2	no	—
151	#103×C₇₃	—	2	2	no	—
152	#102×C₇₃	—	2	2	no	—
153	#102×C₇₃	—	2	2	no	—
154	#102×C₇₃	—	2	2	no	—
155	#102×C₇₃	—	2	2	no	—
156	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
157	#97×C₇₃	—	2	2	no	—
158	C₄×C₈×C₇₃	—	2	2	no	—
159	#95×C₇₃	—	2	2	no	—
160	#95×C₇₃	D₄	1	2	yes	—
161	C₂⁴×C₇₃	—	2	1	no	—
162	C₂⁴×C₇₃	—	2	1	no	—
163	C₂⁴×C₇₃	—	2	1	no	—
164	C₂⁴×C₇₃	—	2	1	no	—
165	C₂⁴×C₇₃	—	4	2	no	—
166	C₂⁴×C₇₃	—	4	2	no	—
167	C₂⁴×C₇₃	—	4	4	no	—
168	C₂⁴×C₇₃	—	4	2	no	—
169	C₂⁴×C₇₃	—	8	2	no	—
170	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
171	#41×C₇₃	—	2	8	no	—
172	#41×C₇₃	—	4	4	no	—
173	#41×C₇₃	—	4	4	no	—
174	#41×C₇₃	—	4	4	no	—
175	C₂×Q₈×C₇₃	—	2	1	no	—
176	C₂×Q₈×C₇₃	—	2	1	no	—
177	C₂×Q₈×C₇₃	—	2	1	no	—
178	C₂×Q₈×C₇₃	—	2	1	no	—
179	C₂×Q₈×C₇₃	—	2	1	no	—
180	C₂×Q₈×C₇₃	—	2	1	no	—
181	C₂×Q₈×C₇₃	—	2	1	no	—
182	C₂×Q₈×C₇₃	—	2	1	no	—
183	C₂×Q₈×C₇₃	—	2	1	no	—
184	C₂×Q₈×C₇₃	—	2	1	no	—
185	C₂×Q₈×C₇₃	—	2	1	no	—
186	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₇₃	—	2	8	no	—
188	C₂×D₄×C₇₃	—	2	1	no	—
189	C₂×D₄×C₇₃	—	2	1	no	—
190	C₂×D₄×C₇₃	—	2	1	no	—
191	C₂×D₄×C₇₃	—	2	1	no	—
192	C₂×D₄×C₇₃	—	2	1	no	—
193	C₂×D₄×C₇₃	—	2	1	no	—
194	C₂×D₄×C₇₃	—	2	1	no	—
195	C₂×D₄×C₇₃	—	2	1	no	—
196	C₂×D₄×C₇₃	—	2	1	no	—
197	C₂×D₄×C₇₃	—	2	1	no	—
198	C₂×D₄×C₇₃	—	2	1	no	—
199	C₂×D₄×C₇₃	—	2	1	no	—
200	C₂×D₄×C₇₃	—	2	1	no	—
201	C₂×D₄×C₇₃	—	2	1	no	—
202	C₂×D₄×C₇₃	—	2	1	no	—
203	C₂×D₄×C₇₃	—	2	1	no	—
204	C₂×D₄×C₇₃	—	2	1	no	—
205	C₂×D₄×C₇₃	—	2	1	no	—
206	C₂×D₄×C₇₃	—	2	1	no	—
207	C₂×D₄×C₇₃	—	2	1	no	—
208	C₂×D₄×C₇₃	—	2	1	no	—
209	C₂×D₄×C₇₃	—	4	4	no	—
210	C₂×D₄×C₇₃	—	4	4	no	—
211	C₂×D₄×C₇₃	—	4	2	no	—
212	C₂×D₄×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	—	4	2	no	—
214	C₂×D₄×C₇₃	—	4	4	no	—
215	C₂×D₄×C₇₃	—	4	4	no	—
216	C₂×D₄×C₇₃	—	4	4	no	—
217	C₂×D₄×C₇₃	—	4	2	no	—
218	C₂×D₄×C₇₃	—	4	2	no	—
219	C₂×D₄×C₇₃	—	4	2	no	—
220	C₂×D₄×C₇₃	—	4	2	no	—
221	C₂×D₄×C₇₃	—	8	2	no	—
222	C₂×D₄×C₇₃	—	8	2	no	—
223	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₇₃	—	2	1	no	—
227	C₂²×C₄×C₇₃	—	2	1	no	—
228	C₂²×C₄×C₇₃	—	2	1	no	—
229	C₂²×C₄×C₇₃	—	2	1	no	—
230	C₂²×C₄×C₇₃	—	2	1	no	—
231	C₂²×C₄×C₇₃	—	2	1	no	—
232	C₂²×C₄×C₇₃	—	2	1	no	—
233	C₂²×C₄×C₇₃	—	2	1	no	—
234	C₂²×C₄×C₇₃	—	4	2	no	—
235	C₂²×C₄×C₇₃	—	4	2	no	—
236	C₂²×C₄×C₇₃	—	4	2	no	—
237	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₇₃	—	4	4	no	—
244	SD₁₆×C₇₃	—	2	8	no	—
245	SD₁₆×C₇₃	—	2	8	no	—
246	SD₁₆×C₇₃	—	4	4	no	—
247	SD₁₆×C₇₃	—	4	4	no	—
248	D₈×C₇₃	—	2	8	no	—
249	D₈×C₇₃	—	2	8	no	—
250	D₈×C₇₃	—	4	4	no	—
251	D₈×C₇₃	—	4	4	no	—
252	M₁₆×C₇₃	—	2	8	no	—
253	C₂×C₈×C₇₃	—	2	1	no	—
254	C₂×C₈×C₇₃	—	2	1	no	—
255	C₂×C₈×C₇₃	—	2	1	no	—
256	C₂×C₈×C₇₃	—	2	1	no	—
257	C₂×C₈×C₇₃	—	2	1	no	—
258	C₂×C₈×C₇₃	—	2	1	no	—
259	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
262	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
263	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
264	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₇₃	—	2	1	no	—
266	C₄⋊C₄×C₇₃	—	2	1	no	—
267	C₄⋊C₄×C₇₃	—	2	1	no	—
268	C₄⋊C₄×C₇₃	—	2	1	no	—
269	C₄⋊C₄×C₇₃	—	4	2	no	—
270	C₂²⋊C₄×C₇₃	—	4	2	no	—
271	C₂²⋊C₄×C₇₃	—	4	4	no	—
272	C₂²⋊C₄×C₇₃	—	4	4	no	—
273	C₂²⋊C₄×C₇₃	—	4	4	no	—
274	C₂²⋊C₄×C₇₃	—	4	2	no	—
275	C₂²⋊C₄×C₇₃	—	4	2	no	—
276	C₂²⋊C₄×C₇₃	—	8	2	no	—
277	C₂²⋊C₄×C₇₃	—	8	2	no	—
278	C₂²⋊C₄×C₇₃	—	8	2	no	—
279	C₄²×C₇₃	—	2	1	no	—
280	C₄²×C₇₃	—	2	1	no	—
281	C₄²×C₇₃	—	2	1	no	—
282	C₄²×C₇₃	—	2	1	no	—
283	C₂³×C₇₃	—	2	1	no	—
284	C₂³×C₇₃	—	2	1	no	—
285	C₂³×C₇₃	—	2	2	no	—
286	C₂³×C₇₃	—	2	2	no	—
287	C₂³×C₇₃	—	2	2	no	—
288	C₂³×C₇₃	—	2	2	no	—
289	C₂³×C₇₃	—	2	2	no	—
290	C₂³×C₇₃	—	4	8	no	—
291	C₂³×C₇₃	—	4	1	no	—
292	C₂³×C₇₃	—	4	1	no	—
293	C₂³×C₇₃	—	4	1	no	—
294	C₂³×C₇₃	—	4	1	no	—
295	C₂³×C₇₃	—	4	1	no	—
296	C₂³×C₇₃	—	4	1	no	—
297	C₂³×C₇₃	—	4	2	no	—
298	C₂³×C₇₃	—	4	2	no	—
299	C₂³×C₇₃	—	4	2	no	—
300	C₂³×C₇₃	—	4	2	no	—
301	C₂³×C₇₃	—	4	2	no	—
302	C₂³×C₇₃	—	4	2	no	—
303	C₂³×C₇₃	—	4	1	no	—
304	C₂³×C₇₃	—	4	1	no	—
305	C₂³×C₇₃	—	4	1	no	—
306	C₂³×C₇₃	—	4	2	no	—
307	C₂³×C₇₃	—	4	2	no	—
308	C₂³×C₇₃	—	8	4	no	—
309	C₂³×C₇₃	—	8	4	no	—
310	C₂³×C₇₃	—	8	8	no	—
311	C₂³×C₇₃	—	8	8	no	—
312	C₂³×C₇₃	#127	1	2	yes	—
313	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₇₃	—	2	2	no	—
315	Q₈×C₇₃	—	2	2	no	—
316	Q₈×C₇₃	—	4	1	no	—
317	Q₈×C₇₃	—	4	1	no	—
318	Q₈×C₇₃	—	4	1	no	—
319	Q₈×C₇₃	—	4	1	no	—
320	Q₈×C₇₃	—	4	1	no	—
321	Q₈×C₇₃	—	4	1	no	—
322	D₄×C₇₃	—	2	2	no	—
323	D₄×C₇₃	—	2	2	no	—
324	D₄×C₇₃	—	2	2	no	—
325	D₄×C₇₃	—	2	2	no	—
326	D₄×C₇₃	—	2	2	no	—
327	D₄×C₇₃	—	2	2	no	—
328	D₄×C₇₃	—	4	8	no	—
329	D₄×C₇₃	—	4	8	no	—
330	D₄×C₇₃	—	4	1	no	—
331	D₄×C₇₃	—	4	1	no	—
332	D₄×C₇₃	—	4	1	no	—
333	D₄×C₇₃	—	4	1	no	—
334	D₄×C₇₃	—	4	1	no	—
335	D₄×C₇₃	—	4	1	no	—
336	D₄×C₇₃	—	4	1	no	—
337	D₄×C₇₃	—	4	1	no	—
338	D₄×C₇₃	—	4	1	no	—
339	D₄×C₇₃	—	4	1	no	—
340	D₄×C₇₃	—	8	8	no	—
341	D₄×C₇₃	—	8	4	no	—
342	C₂×C₄×C₇₃	—	2	1	no	—
343	C₂×C₄×C₇₃	—	2	1	no	—
344	C₂×C₄×C₇₃	—	2	2	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	2	2	no	—
349	C₂×C₄×C₇₃	—	2	2	no	—
350	C₂×C₄×C₇₃	—	2	2	no	—
351	C₂×C₄×C₇₃	—	2	2	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	2	no	—
354	C₂×C₄×C₇₃	—	2	2	no	—
355	C₂×C₄×C₇₃	—	4	8	no	—
356	C₂×C₄×C₇₃	—	4	1	no	—
357	C₂×C₄×C₇₃	—	4	1	no	—
358	C₂×C₄×C₇₃	—	4	1	no	—
359	C₂×C₄×C₇₃	—	4	1	no	—
360	C₂×C₄×C₇₃	—	4	1	no	—
361	C₂×C₄×C₇₃	—	4	1	no	—
362	C₂×C₄×C₇₃	—	4	1	no	—
363	C₂×C₄×C₇₃	—	4	2	no	—
364	C₂×C₄×C₇₃	—	4	2	no	—
365	C₂×C₄×C₇₃	#127	1	2	yes	—
366	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
372	C₈×C₇₃	—	2	2	no	—
373	C₈×C₇₃	—	2	2	no	—
374	C₈×C₇₃	—	2	2	no	—
375	C₈×C₇₃	#120	1	4	yes	—
376	C₂²×C₇₃	—	2	2	no	—
377	C₂²×C₇₃	—	2	2	no	—
378	C₂²×C₇₃	—	2	2	no	—
379	C₂²×C₇₃	—	4	2	no	—
380	C₂²×C₇₃	—	4	2	no	—
381	C₂²×C₇₃	—	4	2	no	—
382	C₂²×C₇₃	—	4	2	no	—
383	C₂²×C₇₃	—	4	2	no	—
384	C₂²×C₇₃	—	4	4	no	—
385	C₂²×C₇₃	—	4	4	no	—
386	C₂²×C₇₃	—	4	4	no	—
387	C₂²×C₇₃	—	8	16	no	—
388	C₂²×C₇₃	—	8	1	no	—
389	C₂²×C₇₃	—	8	1	no	—
390	C₂²×C₇₃	—	8	1	no	—
391	C₂²×C₇₃	—	8	1	no	—
392	C₂²×C₇₃	—	8	1	no	—
393	C₂²×C₇₃	—	8	1	no	—
394	C₂²×C₇₃	—	8	2	no	—
395	C₂²×C₇₃	—	8	2	no	—
396	C₂²×C₇₃	—	8	2	no	—
397	C₂²×C₇₃	—	8	1	no	—
398	C₂²×C₇₃	—	8	1	no	—
399	C₂²×C₇₃	—	8	1	no	—
400	C₂²×C₇₃	—	8	2	no	—
401	C₂²×C₇₃	—	8	2	no	—
402	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
403	C₂²×C₇₃	D₄²	1	1	yes	characteristic
404	C₂²×C₇₃	D₄²	1	1	yes	characteristic
405	C₂²×C₇₃	#575	1	2	yes	—
406	C₂²×C₇₃	#576	1	2	yes	—
407	C₄×C₇₃	—	2	2	no	—
408	C₄×C₇₃	—	4	2	no	—
409	C₄×C₇₃	—	4	2	no	—
410	C₄×C₇₃	—	4	2	no	—
411	C₄×C₇₃	—	8	1	no	—
412	C₄×C₇₃	—	8	1	no	—
413	C₄×C₇₃	—	8	1	no	—
414	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
415	C₄×C₇₃	#535	1	1	yes	characteristic
416	C₄×C₇₃	D₄²	1	1	yes	characteristic
417	C₄×C₇₃	D₄²	1	1	yes	characteristic
418	#25793	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂×C₇₃	—	4	2	no	—
420	C₂×C₇₃	—	8	2	no	—
421	C₂×C₇₃	—	8	2	no	—
422	C₂×C₇₃	—	8	2	no	—
423	C₂×C₇₃	—	16	1	no	—
424	C₂×C₇₃	#2433	1	1	yes	characteristic
425	C₂×C₇₃	#3153	1	1	yes	characteristic
426	C₂×C₇₃	#3155	1	1	yes	characteristic
427	C₂×C₇₃	#3268	1	2	yes	—
428	C₂×C₇₃	#3273	1	2	yes	—
429	C₂²×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic, complemented
430	C₂×#496	C₂×C₇₃	1	1	yes	characteristic, complemented
431	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
432	C₂×#468	C₂×C₇₃	1	1	yes	characteristic, complemented
433	C₂×#452	C₂×C₇₃	1	1	yes	characteristic, complemented
434	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
435	#2435	C₂×C₇₃	1	1	yes	characteristic, complemented
436	#2431	C₂×C₇₃	1	1	yes	characteristic, complemented
437	#2015	C₂×C₇₃	1	1	yes	characteristic, complemented
438	#2012	C₂×C₇₃	1	1	yes	characteristic, complemented
439	#2012	C₂×C₇₃	1	1	yes	characteristic, complemented
440	#2011	C₂×C₇₃	1	1	yes	characteristic, complemented
441	#1973	C₂×C₇₃	1	1	yes	characteristic, complemented
442	#1970	C₂×C₇₃	1	1	yes	characteristic, complemented
443	#1753	C₂×C₇₃	1	1	yes	characteristic, complemented
444	C₇₃	#25793	1	1	yes	characteristic, direct product factor, Sylow
445	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
446	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
447	C₂×AGL(1,ℤ/8)	—	2	4	no	—
448	C₂×AGL(1,ℤ/8)	—	2	4	no	—
449	C₂×AGL(1,ℤ/8)	—	2	4	no	—
450	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
451	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
452	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
453	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
454	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
455	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
456	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
457	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
458	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
459	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
460	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic, complemented
461	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
462	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
463	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
465	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
466	#496	—	2	4	no	—
467	#495	—	2	4	no	—
468	#468	—	2	4	no	—
469	#452	—	2	4	no	—
470	#447	—	2	4	no	—
471	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
472	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
473	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
474	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
475	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
476	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
477	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
478	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
479	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic, complemented
480	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
481	#394	—	2	2	no	—
482	#392	—	2	2	no	—
483	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
484	#390	C₂²×C₇₃	1	1	yes	characteristic
485	#390	C₂²×C₇₃	1	1	yes	characteristic
486	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
487	#386	—	2	2	no	—
488	#379	—	2	2	no	—
489	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
490	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
491	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
492	C₂⁵	—	2	1	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	4	1	no	—
498	C₂×#41	—	4	1	no	—
499	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	2	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	4	1	no	—
510	C₂²×D₄	—	4	1	no	—
511	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
517	AGL(1,ℤ/8)	—	2	32	no	—
518	C₂×Q₁₆	—	2	2	no	—
519	C₂×Q₁₆	—	2	2	no	—
520	C₂×Q₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	2	2	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×SD₁₆	D₄×C₇₃	1	4	yes	complemented
533	C₂×D₈	—	2	2	no	—
534	C₂×D₈	—	2	2	no	—
535	C₂×D₈	—	2	2	no	—
536	C₂×D₈	—	2	2	no	—
537	C₂×D₈	—	2	2	no	—
538	C₂×D₈	—	2	2	no	—
539	C₂×D₈	—	2	2	no	—
540	C₂×D₈	—	2	2	no	—
541	C₂×D₈	—	2	2	no	—
542	C₂×D₈	—	4	1	no	—
543	C₂×D₈	—	4	1	no	—
544	C₂×D₈	D₄×C₇₃	1	4	yes	complemented
545	C₂×M₁₆	—	2	2	no	—
546	C₂×M₁₆	—	2	2	no	—
547	C₂×M₁₆	D₄×C₇₃	1	4	yes	complemented
548	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
552	#127	—	2	2	no	—
553	#127	—	4	1	no	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	4	1	no	—
558	#124	—	4	1	no	—
559	#124	—	4	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	2	no	—
570	C₂×C₂²⋊C₄	—	2	2	no	—
571	C₂×C₂²⋊C₄	—	2	2	no	—
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	2	2	no	—
574	C₂×C₂²⋊C₄	—	2	2	no	—
575	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
576	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
578	#107	—	2	2	no	—
579	#103	—	2	2	no	—
580	#103	—	2	2	no	—
581	#102	—	2	2	no	—
582	#102	—	2	2	no	—
583	#102	—	2	2	no	—
584	#102	—	2	2	no	—
585	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
586	#97	—	2	2	no	—
587	C₄×C₈	—	2	2	no	—
588	#95	—	2	2	no	—
589	#95	D₄×C₇₃	1	2	yes	—
590	C₂⁴	—	2	1	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	1	no	—
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	4	no	—
597	C₂⁴	—	4	2	no	—
598	C₂⁴	—	8	2	no	—
599	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
600	#41	—	2	8	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	8	2	no	—
651	C₂×D₄	—	8	2	no	—
652	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
653	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
654	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
667	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
668	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
672	Q₁₆	—	4	4	no	—
673	SD₁₆	—	2	8	no	—
674	SD₁₆	—	2	8	no	—
675	SD₁₆	—	4	4	no	—
676	SD₁₆	—	4	4	no	—
677	D₈	—	2	8	no	—
678	D₈	—	2	8	no	—
679	D₈	—	4	4	no	—
680	D₈	—	4	4	no	—
681	M₁₆	—	2	8	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
689	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
690	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
691	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
692	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
693	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₂²⋊C₄	—	4	4	no	—
702	C₂²⋊C₄	—	4	4	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	8	2	no	—
706	C₂²⋊C₄	—	8	2	no	—
707	C₂²⋊C₄	—	8	2	no	—
708	C₄²	—	2	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	4	8	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	8	4	no	—
738	C₂³	—	8	4	no	—
739	C₂³	—	8	8	no	—
740	C₂³	—	8	8	no	—
741	C₂³	#127×C₇₃	1	2	yes	—
742	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
743	Q₈	—	2	2	no	—
744	Q₈	—	2	2	no	—
745	Q₈	—	4	1	no	—
746	Q₈	—	4	1	no	—
747	Q₈	—	4	1	no	—
748	Q₈	—	4	1	no	—
749	Q₈	—	4	1	no	—
750	Q₈	—	4	1	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	8	8	no	—
770	D₄	—	8	4	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	#127×C₇₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
799	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
800	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	2	no	—
803	C₈	—	2	2	no	—
804	C₈	#120×C₇₃	1	4	yes	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	8	16	no	—
817	C₂²	—	8	2	no	—
818	C₂²	—	8	2	no	—
819	C₂²	—	8	2	no	—
820	C₂²	—	8	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	—	8	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	2	no	—
827	C₂²	—	8	2	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
832	C₂²	D₄²×C₇₃	1	1	yes	characteristic
833	C₂²	D₄²×C₇₃	1	1	yes	characteristic
834	C₂²	#575×C₇₃	1	2	yes	—
835	C₂²	#576×C₇₃	1	2	yes	—
836	C₄	—	2	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	8	1	no	—
841	C₄	—	8	1	no	—
842	C₄	—	8	1	no	—
843	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
844	C₄	#535×C₇₃	1	1	yes	characteristic
845	C₄	D₄²×C₇₃	1	1	yes	characteristic
846	C₄	D₄²×C₇₃	1	1	yes	characteristic
847	C₂	—	4	2	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	—	8	2	no	—
851	C₂	—	16	1	no	—
852	C₂	C₇₃×#2433	1	1	yes	characteristic
853	C₂	C₇₃×#3153	1	1	yes	characteristic
854	C₂	C₇₃×#3155	1	1	yes	characteristic
855	C₂	C₇₃×#3268	1	2	yes	—
856	C₂	C₇₃×#3273	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₇₃	C₂	semidirect
2. C₂×#496×C₇₃	C₂	semidirect
3. C₂×#495×C₇₃	C₂	semidirect
4. C₂×#468×C₇₃	C₂	semidirect
5. C₂×#452×C₇₃	C₂	semidirect
6. C₂×#447×C₇₃	C₂	semidirect
7. C₇₃×#2435	C₂	semidirect
8. C₇₃×#2431	C₂	semidirect
9. C₇₃×#2015	C₂	semidirect
10. C₇₃×#2012	C₂	semidirect
11. C₇₃×#2012	C₂	semidirect
12. C₇₃×#2011	C₂	semidirect
13. C₇₃×#1973	C₂	semidirect
14. C₇₃×#1970	C₂	semidirect
15. C₇₃×#1753	C₂	semidirect
21. C₂²×Q₁₆×C₇₃	C₂²	semidirect
24. C₂²×SD₁₆×C₇₃	C₂²	semidirect
25. C₂²×SD₁₆×C₇₃	C₂²	semidirect
31. C₂×#127×C₇₃	C₂²	semidirect
34. C₂×#124×C₇₃	C₂²	semidirect
42. C₂×#107×C₇₃	C₂²	semidirect
43. C₂×#103×C₇₃	C₂²	semidirect
44. C₂×#103×C₇₃	C₂²	semidirect
47. C₂×#102×C₇₃	C₂²	semidirect
48. C₂×#102×C₇₃	C₂²	semidirect
50. C₂×#97×C₇₃	C₂²	semidirect
51. C₂×C₄×C₈×C₇₃	C₂²	semidirect
54. #391×C₇₃	C₂²	semidirect
57. #390×C₇₃	C₂²	semidirect
61. #336×C₇₃	C₂²	semidirect
62. #336×C₇₃	C₂²	semidirect
103. C₂×SD₁₆×C₇₃	D₄	semidirect
115. C₂×D₈×C₇₃	D₄	semidirect
118. C₂×M₁₆×C₇₃	D₄	semidirect
156. C₂²⋊C₈×C₇₃	D₄	semidirect
418. #25793	C₇₃	direct (N × H)
429. C₂²×AGL(1,ℤ/8)	C₂×C₇₃	semidirect
430. C₂×#496	C₂×C₇₃	semidirect
431. C₂×#495	C₂×C₇₃	semidirect
432. C₂×#468	C₂×C₇₃	semidirect
433. C₂×#452	C₂×C₇₃	semidirect
434. C₂×#447	C₂×C₇₃	semidirect
435. #2435	C₂×C₇₃	semidirect
436. #2431	C₂×C₇₃	semidirect
437. #2015	C₂×C₇₃	semidirect
438. #2012	C₂×C₇₃	semidirect
439. #2012	C₂×C₇₃	semidirect
440. #2011	C₂×C₇₃	semidirect
441. #1973	C₂×C₇₃	semidirect
442. #1970	C₂×C₇₃	semidirect
443. #1753	C₂×C₇₃	semidirect
444. C₇₃	#25793	direct (N × H)
450. C₂²×Q₁₆	C₂²×C₇₃	semidirect
453. C₂²×SD₁₆	C₂²×C₇₃	semidirect
454. C₂²×SD₁₆	C₂²×C₇₃	semidirect
460. C₂×#127	C₂²×C₇₃	semidirect
463. C₂×#124	C₂²×C₇₃	semidirect
471. C₂×#107	C₂²×C₇₃	semidirect
472. C₂×#103	C₂²×C₇₃	semidirect
473. C₂×#103	C₂²×C₇₃	semidirect
476. C₂×#102	C₂²×C₇₃	semidirect
477. C₂×#102	C₂²×C₇₃	semidirect
479. C₂×#97	C₂²×C₇₃	semidirect
480. C₂×C₄×C₈	C₂²×C₇₃	semidirect
483. #391	C₂²×C₇₃	semidirect
486. #390	C₂²×C₇₃	semidirect
490. #336	C₂²×C₇₃	semidirect
491. #336	C₂²×C₇₃	semidirect
532. C₂×SD₁₆	D₄×C₇₃	semidirect
544. C₂×D₈	D₄×C₇₃	semidirect
547. C₂×M₁₆	D₄×C₇₃	semidirect
585. C₂²⋊C₈	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₇₃	2
C₂×#496×C₇₃	2
C₂×#495×C₇₃	2
C₂×#468×C₇₃	2
C₂×#452×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2435	2
C₇₃×#2431	2
C₇₃×#2015	2
C₇₃×#2012	2
C₇₃×#2011	2
C₇₃×#1973	2
C₇₃×#1970	2
C₇₃×#1753	2
#25793	73

Subgroups — C73×#25793 #32935197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25793 #32935197