Subgroups — C₇₃×#25790 #32935194

Order 18688.

1544 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#497×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#492×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×#448×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2431	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1969	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×Q₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#137×C₇₃	—	2	4	no	—
19	C₂×#137×C₇₃	—	2	4	no	—
20	C₂×#137×C₇₃	—	2	4	no	—
21	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
37	#497×C₇₃	—	2	4	no	—
38	#492×C₇₃	—	2	4	no	—
39	#468×C₇₃	—	2	4	no	—
40	#452×C₇₃	—	2	4	no	—
41	#448×C₇₃	—	2	4	no	—
42	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
52	#395×C₇₃	—	2	2	no	—
53	#392×C₇₃	—	2	2	no	—
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	1	yes	characteristic
56	#391×C₇₃	C₂²	1	1	yes	characteristic
57	#390×C₇₃	C₂²	1	1	yes	characteristic
58	#386×C₇₃	—	2	2	no	—
59	#385×C₇₃	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
61	#336×C₇₃	C₂²	1	1	yes	characteristic
62	#336×C₇₃	C₂²	1	1	yes	characteristic
63	C₂×#41×C₇₃	—	2	2	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	—	4	1	no	—
68	C₂×#41×C₇₃	—	4	1	no	—
69	C₂²×Q₈×C₇₃	—	2	1	no	—
70	C₂²×Q₈×C₇₃	—	2	2	no	—
71	C₂²×Q₈×C₇₃	—	2	2	no	—
72	C₂²×Q₈×C₇₃	—	2	2	no	—
73	C₂²×Q₈×C₇₃	—	2	2	no	—
74	C₂²×Q₈×C₇₃	—	4	1	no	—
75	C₂²×Q₈×C₇₃	—	4	1	no	—
76	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₇₃	—	2	1	no	—
81	C₂²×D₄×C₇₃	—	2	1	no	—
82	C₂²×D₄×C₇₃	—	2	2	no	—
83	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇₃	—	2	1	no	—
86	C₂³×C₄×C₇₃	—	2	1	no	—
87	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
88	#137×C₇₃	—	2	32	no	—
89	C₂×Q₁₆×C₇₃	—	2	2	no	—
90	C₂×Q₁₆×C₇₃	—	2	2	no	—
91	C₂×Q₁₆×C₇₃	—	2	2	no	—
92	C₂×Q₁₆×C₇₃	—	2	2	no	—
93	C₂×Q₁₆×C₇₃	—	2	2	no	—
94	C₂×Q₁₆×C₇₃	—	2	2	no	—
95	C₂×Q₁₆×C₇₃	—	2	2	no	—
96	C₂×Q₁₆×C₇₃	—	4	1	no	—
97	C₂×Q₁₆×C₇₃	D₄	1	4	yes	complemented
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	—	2	2	no	—
103	C₂×SD₁₆×C₇₃	—	2	2	no	—
104	C₂×SD₁₆×C₇₃	—	2	2	no	—
105	C₂×SD₁₆×C₇₃	—	2	2	no	—
106	C₂×SD₁₆×C₇₃	—	2	2	no	—
107	C₂×SD₁₆×C₇₃	—	2	2	no	—
108	C₂×SD₁₆×C₇₃	—	2	2	no	—
109	C₂×SD₁₆×C₇₃	—	2	2	no	—
110	C₂×SD₁₆×C₇₃	—	2	2	no	—
111	C₂×SD₁₆×C₇₃	—	2	2	no	—
112	C₂×SD₁₆×C₇₃	—	4	1	no	—
113	C₂×SD₁₆×C₇₃	—	4	1	no	—
114	C₂×SD₁₆×C₇₃	—	4	1	no	—
115	C₂×SD₁₆×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	C₄⋊Q₈×C₇₃	—	2	2	no	—
124	C₄⋊Q₈×C₇₃	—	2	2	no	—
125	C₄⋊Q₈×C₇₃	—	4	1	no	—
126	C₄⋊Q₈×C₇₃	—	4	1	no	—
127	#127×C₇₃	—	2	2	no	—
128	#127×C₇₃	—	4	1	no	—
129	#124×C₇₃	—	2	2	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	2	no	—
136	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₇₃	—	2	1	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	D₄	1	2	yes	—
145	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
147	#107×C₇₃	—	2	2	no	—
148	#103×C₇₃	—	2	2	no	—
149	#103×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	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
155	#97×C₇₃	—	2	2	no	—
156	C₄×C₈×C₇₃	—	2	2	no	—
157	#95×C₇₃	—	2	2	no	—
158	#95×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	C₂×D₄	1	1	yes	characteristic
164	#41×C₇₃	—	2	8	no	—
165	#41×C₇₃	—	4	4	no	—
166	#41×C₇₃	—	4	4	no	—
167	#41×C₇₃	—	4	4	no	—
168	C₂×Q₈×C₇₃	—	2	1	no	—
169	C₂×Q₈×C₇₃	—	2	1	no	—
170	C₂×Q₈×C₇₃	—	2	1	no	—
171	C₂×Q₈×C₇₃	—	2	8	no	—
172	C₂×Q₈×C₇₃	—	2	1	no	—
173	C₂×Q₈×C₇₃	—	2	1	no	—
174	C₂×Q₈×C₇₃	—	2	1	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	—	2	1	no	—
187	C₂×Q₈×C₇₃	—	2	1	no	—
188	C₂×Q₈×C₇₃	—	2	1	no	—
189	C₂×Q₈×C₇₃	—	2	1	no	—
190	C₂×Q₈×C₇₃	—	4	2	no	—
191	C₂×Q₈×C₇₃	—	4	2	no	—
192	C₂×Q₈×C₇₃	—	4	4	no	—
193	C₂×Q₈×C₇₃	—	4	4	no	—
194	C₂×Q₈×C₇₃	—	4	4	no	—
195	C₂×Q₈×C₇₃	—	4	2	no	—
196	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
197	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
198	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
210	C₂×D₄×C₇₃	—	4	2	no	—
211	C₂×D₄×C₇₃	—	4	4	no	—
212	C₂×D₄×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	—	4	2	no	—
214	C₂×D₄×C₇₃	—	4	2	no	—
215	C₂×D₄×C₇₃	—	4	4	no	—
216	C₂×D₄×C₇₃	—	8	2	no	—
217	C₂×D₄×C₇₃	—	8	2	no	—
218	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₇₃	—	2	1	no	—
220	C₂²×C₄×C₇₃	—	2	1	no	—
221	C₂²×C₄×C₇₃	—	2	1	no	—
222	C₂²×C₄×C₇₃	—	2	1	no	—
223	C₂²×C₄×C₇₃	—	2	1	no	—
224	C₂²×C₄×C₇₃	—	2	1	no	—
225	C₂²×C₄×C₇₃	—	2	1	no	—
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	—	4	2	no	—
230	C₂²×C₄×C₇₃	—	4	2	no	—
231	C₂²×C₄×C₇₃	—	4	2	no	—
232	C₂²×C₄×C₇₃	—	4	2	no	—
233	C₂²×C₄×C₇₃	—	4	2	no	—
234	C₂²×C₄×C₇₃	—	4	2	no	—
235	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
240	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
241	Q₁₆×C₇₃	—	2	8	no	—
242	Q₁₆×C₇₃	—	2	8	no	—
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	SD₁₆×C₇₃	—	4	4	no	—
249	SD₁₆×C₇₃	—	4	4	no	—
250	M₁₆×C₇₃	—	2	8	no	—
251	C₂×C₈×C₇₃	—	2	1	no	—
252	C₂×C₈×C₇₃	—	2	1	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	C₂×D₄	1	2	yes	—
258	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₇₃	—	2	1	no	—
264	C₄⋊C₄×C₇₃	—	2	1	no	—
265	C₄⋊C₄×C₇₃	—	2	1	no	—
266	C₄⋊C₄×C₇₃	—	2	1	no	—
267	C₄⋊C₄×C₇₃	—	4	4	no	—
268	C₄⋊C₄×C₇₃	—	4	4	no	—
269	C₄⋊C₄×C₇₃	—	4	2	no	—
270	C₂²⋊C₄×C₇₃	—	2	4	no	—
271	C₂²⋊C₄×C₇₃	—	4	4	no	—
272	C₂²⋊C₄×C₇₃	—	4	2	no	—
273	C₂²⋊C₄×C₇₃	—	4	2	no	—
274	C₂²⋊C₄×C₇₃	—	8	2	no	—
275	C₄²×C₇₃	—	2	1	no	—
276	C₄²×C₇₃	—	2	1	no	—
277	C₄²×C₇₃	—	2	1	no	—
278	C₄²×C₇₃	—	2	1	no	—
279	C₂³×C₇₃	—	2	1	no	—
280	C₂³×C₇₃	—	2	1	no	—
281	C₂³×C₇₃	—	2	2	no	—
282	C₂³×C₇₃	—	2	2	no	—
283	C₂³×C₇₃	—	2	2	no	—
284	C₂³×C₇₃	—	4	1	no	—
285	C₂³×C₇₃	—	4	1	no	—
286	C₂³×C₇₃	—	4	2	no	—
287	C₂³×C₇₃	—	4	2	no	—
288	C₂³×C₇₃	—	4	1	no	—
289	C₂³×C₇₃	—	4	1	no	—
290	C₂³×C₇₃	—	4	1	no	—
291	C₂³×C₇₃	—	4	2	no	—
292	C₂³×C₇₃	—	4	2	no	—
293	C₂³×C₇₃	#127	1	2	yes	—
294	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₇₃	—	2	2	no	—
296	Q₈×C₇₃	—	2	2	no	—
297	Q₈×C₇₃	—	2	2	no	—
298	Q₈×C₇₃	—	2	2	no	—
299	Q₈×C₇₃	—	2	2	no	—
300	Q₈×C₇₃	—	2	2	no	—
301	Q₈×C₇₃	—	4	8	no	—
302	Q₈×C₇₃	—	4	1	no	—
303	Q₈×C₇₃	—	4	1	no	—
304	Q₈×C₇₃	—	4	1	no	—
305	Q₈×C₇₃	—	4	1	no	—
306	Q₈×C₇₃	—	4	1	no	—
307	Q₈×C₇₃	—	4	1	no	—
308	Q₈×C₇₃	—	4	1	no	—
309	Q₈×C₇₃	—	4	1	no	—
310	Q₈×C₇₃	—	4	1	no	—
311	Q₈×C₇₃	—	4	1	no	—
312	D₄×C₇₃	—	2	2	no	—
313	D₄×C₇₃	—	2	2	no	—
314	D₄×C₇₃	—	4	8	no	—
315	D₄×C₇₃	—	4	1	no	—
316	D₄×C₇₃	—	4	1	no	—
317	D₄×C₇₃	—	4	1	no	—
318	D₄×C₇₃	—	4	1	no	—
319	D₄×C₇₃	—	4	1	no	—
320	D₄×C₇₃	—	4	1	no	—
321	D₄×C₇₃	—	8	8	no	—
322	D₄×C₇₃	—	8	4	no	—
323	C₂×C₄×C₇₃	—	2	2	no	—
324	C₂×C₄×C₇₃	—	2	1	no	—
325	C₂×C₄×C₇₃	—	2	1	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	2	no	—
328	C₂×C₄×C₇₃	—	2	2	no	—
329	C₂×C₄×C₇₃	—	2	2	no	—
330	C₂×C₄×C₇₃	—	2	2	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	2	no	—
334	C₂×C₄×C₇₃	—	2	2	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	4	8	no	—
338	C₂×C₄×C₇₃	—	4	8	no	—
339	C₂×C₄×C₇₃	—	4	1	no	—
340	C₂×C₄×C₇₃	—	4	1	no	—
341	C₂×C₄×C₇₃	—	4	1	no	—
342	C₂×C₄×C₇₃	—	4	1	no	—
343	C₂×C₄×C₇₃	—	4	1	no	—
344	C₂×C₄×C₇₃	—	4	1	no	—
345	C₂×C₄×C₇₃	—	4	1	no	—
346	C₂×C₄×C₇₃	—	4	1	no	—
347	C₂×C₄×C₇₃	—	4	1	no	—
348	C₂×C₄×C₇₃	—	4	1	no	—
349	C₂×C₄×C₇₃	—	4	1	no	—
350	C₂×C₄×C₇₃	—	4	2	no	—
351	C₂×C₄×C₇₃	—	4	2	no	—
352	C₂×C₄×C₇₃	#127	1	2	yes	—
353	C₂×C₄×C₇₃	#137	1	4	yes	complemented
354	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
360	C₈×C₇₃	—	2	2	no	—
361	C₈×C₇₃	—	2	2	no	—
362	C₈×C₇₃	—	2	2	no	—
363	C₈×C₇₃	#120	1	4	yes	—
364	C₂²×C₇₃	—	2	2	no	—
365	C₂²×C₇₃	—	2	2	no	—
366	C₂²×C₇₃	—	2	2	no	—
367	C₂²×C₇₃	—	4	2	no	—
368	C₂²×C₇₃	—	4	2	no	—
369	C₂²×C₇₃	—	4	2	no	—
370	C₂²×C₇₃	—	4	4	no	—
371	C₂²×C₇₃	—	8	1	no	—
372	C₂²×C₇₃	—	8	1	no	—
373	C₂²×C₇₃	—	8	2	no	—
374	C₂²×C₇₃	—	8	1	no	—
375	C₂²×C₇₃	—	8	1	no	—
376	C₂²×C₇₃	—	8	1	no	—
377	C₂²×C₇₃	—	8	2	no	—
378	C₂²×C₇₃	—	8	2	no	—
379	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
380	C₂²×C₇₃	D₄²	1	1	yes	characteristic
381	C₂²×C₇₃	D₄²	1	1	yes	characteristic
382	C₂²×C₇₃	C₂×#137	1	2	yes	—
383	C₂²×C₇₃	#577	1	2	yes	—
384	C₄×C₇₃	—	2	2	no	—
385	C₄×C₇₃	—	2	4	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	4	2	no	—
388	C₄×C₇₃	—	4	2	no	—
389	C₄×C₇₃	—	4	2	no	—
390	C₄×C₇₃	—	8	1	no	—
391	C₄×C₇₃	—	8	1	no	—
392	C₄×C₇₃	—	8	1	no	—
393	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
394	C₄×C₇₃	#535	1	1	yes	characteristic
395	C₄×C₇₃	D₄²	1	1	yes	characteristic
396	C₄×C₇₃	D₄²	1	1	yes	characteristic
397	#25790	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂×C₇₃	—	4	2	no	—
399	C₂×C₇₃	—	8	2	no	—
400	C₂×C₇₃	—	16	1	no	—
401	C₂×C₇₃	#2433	1	1	yes	characteristic
402	C₂×C₇₃	#3152	1	1	yes	characteristic
403	C₂×C₇₃	#3154	1	1	yes	characteristic
404	C₂×C₇₃	#3266	1	2	yes	—
405	C₂×C₇₃	#3278	1	2	yes	—
406	C₂²×#137	C₂×C₇₃	1	1	yes	characteristic, complemented
407	C₂×#497	C₂×C₇₃	1	1	yes	characteristic, complemented
408	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
409	C₂×#468	C₂×C₇₃	1	1	yes	characteristic, complemented
410	C₂×#452	C₂×C₇₃	1	1	yes	characteristic, complemented
411	C₂×#448	C₂×C₇₃	1	1	yes	characteristic, complemented
412	#2434	C₂×C₇₃	1	1	yes	characteristic, complemented
413	#2431	C₂×C₇₃	1	1	yes	characteristic
414	#2016	C₂×C₇₃	1	1	yes	characteristic, complemented
415	#2015	C₂×C₇₃	1	1	yes	characteristic, complemented
416	#2014	C₂×C₇₃	1	1	yes	characteristic, complemented
417	#2013	C₂×C₇₃	1	1	yes	characteristic, complemented
418	#1973	C₂×C₇₃	1	1	yes	characteristic, complemented
419	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
420	#1753	C₂×C₇₃	1	1	yes	characteristic, complemented
421	C₇₃	#25790	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
423	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
424	C₂×#137	—	2	4	no	—
425	C₂×#137	—	2	4	no	—
426	C₂×#137	—	2	4	no	—
427	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
428	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
429	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
430	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
431	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
432	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
433	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
434	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
435	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
436	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
439	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
440	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
441	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
442	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
443	#497	—	2	4	no	—
444	#492	—	2	4	no	—
445	#468	—	2	4	no	—
446	#452	—	2	4	no	—
447	#448	—	2	4	no	—
448	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
449	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
450	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
451	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
452	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
454	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
456	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
457	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
458	#395	—	2	2	no	—
459	#392	—	2	2	no	—
460	#391	C₂²×C₇₃	1	1	yes	characteristic
461	#391	C₂²×C₇₃	1	1	yes	characteristic
462	#391	C₂²×C₇₃	1	1	yes	characteristic
463	#390	C₂²×C₇₃	1	1	yes	characteristic
464	#386	—	2	2	no	—
465	#385	—	2	2	no	—
466	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
467	#336	C₂²×C₇₃	1	1	yes	characteristic
468	#336	C₂²×C₇₃	1	1	yes	characteristic
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	4	1	no	—
474	C₂×#41	—	4	1	no	—
475	C₂²×Q₈	—	2	1	no	—
476	C₂²×Q₈	—	2	2	no	—
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	—	2	2	no	—
480	C₂²×Q₈	—	4	1	no	—
481	C₂²×Q₈	—	4	1	no	—
482	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	2	no	—
489	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
494	#137	—	2	32	no	—
495	C₂×Q₁₆	—	2	2	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×Q₁₆	—	2	2	no	—
498	C₂×Q₁₆	—	2	2	no	—
499	C₂×Q₁₆	—	2	2	no	—
500	C₂×Q₁₆	—	2	2	no	—
501	C₂×Q₁₆	—	2	2	no	—
502	C₂×Q₁₆	—	4	1	no	—
503	C₂×Q₁₆	D₄×C₇₃	1	4	yes	complemented
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	D₄×C₇₃	1	4	yes	complemented
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	2	no	—
524	C₂×M₁₆	D₄×C₇₃	1	4	yes	complemented
525	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	4	1	no	—
532	C₄⋊Q₈	—	4	1	no	—
533	#127	—	2	2	no	—
534	#127	—	4	1	no	—
535	#124	—	2	2	no	—
536	#124	—	4	1	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
553	#107	—	2	2	no	—
554	#103	—	2	2	no	—
555	#103	—	2	2	no	—
556	#103	—	2	2	no	—
557	#103	—	2	2	no	—
558	#102	—	2	2	no	—
559	#102	—	2	2	no	—
560	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
561	#97	—	2	2	no	—
562	C₄×C₈	—	2	2	no	—
563	#95	—	2	2	no	—
564	#95	—	2	2	no	—
565	#95	—	2	2	no	—
566	#95	D₄×C₇₃	1	2	yes	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	—	2	1	no	—
569	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
570	#41	—	2	8	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	#41	—	4	4	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	8	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	4	2	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	—	4	4	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	4	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
603	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
604	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	8	2	no	—
623	C₂×D₄	—	8	2	no	—
624	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
642	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
644	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
645	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
647	Q₁₆	—	2	8	no	—
648	Q₁₆	—	2	8	no	—
649	Q₁₆	—	4	4	no	—
650	SD₁₆	—	2	8	no	—
651	SD₁₆	—	2	8	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	4	no	—
654	SD₁₆	—	4	4	no	—
655	SD₁₆	—	4	4	no	—
656	M₁₆	—	2	8	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
664	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
665	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
666	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
667	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
668	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	4	4	no	—
674	C₄⋊C₄	—	4	4	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	8	2	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	2	no	—
699	C₂³	#127×C₇₃	1	2	yes	—
700	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
701	Q₈	—	2	2	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	8	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	Q₈	—	4	1	no	—
713	Q₈	—	4	1	no	—
714	Q₈	—	4	1	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	1	no	—
717	Q₈	—	4	1	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	4	8	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	8	8	no	—
728	D₄	—	8	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	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	—	4	8	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	#127×C₇₃	1	2	yes	—
759	C₂×C₄	#137×C₇₃	1	4	yes	complemented
760	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
764	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
765	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	#120×C₇₃	1	4	yes	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	8	2	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	8	2	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
786	C₂²	D₄²×C₇₃	1	1	yes	characteristic
787	C₂²	D₄²×C₇₃	1	1	yes	characteristic
788	C₂²	C₂×#137×C₇₃	1	2	yes	—
789	C₂²	#577×C₇₃	1	2	yes	—
790	C₄	—	2	4	no	—
791	C₄	—	2	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	8	1	no	—
797	C₄	—	8	1	no	—
798	C₄	—	8	1	no	—
799	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
800	C₄	#535×C₇₃	1	1	yes	characteristic
801	C₄	D₄²×C₇₃	1	1	yes	characteristic
802	C₄	D₄²×C₇₃	1	1	yes	characteristic
803	C₂	—	4	2	no	—
804	C₂	—	8	2	no	—
805	C₂	—	16	1	no	—
806	C₂	C₇₃×#2433	1	1	yes	characteristic
807	C₂	C₇₃×#3152	1	1	yes	characteristic
808	C₂	C₇₃×#3154	1	1	yes	characteristic
809	C₂	C₇₃×#3266	1	2	yes	—
810	C₂	C₇₃×#3278	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2431	C₂
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×#137×C₇₃	C₂	semidirect
2. C₂×#497×C₇₃	C₂	semidirect
3. C₂×#492×C₇₃	C₂	semidirect
4. C₂×#468×C₇₃	C₂	semidirect
5. C₂×#452×C₇₃	C₂	semidirect
6. C₂×#448×C₇₃	C₂	semidirect
7. C₇₃×#2434	C₂	semidirect
9. C₇₃×#2016	C₂	semidirect
10. C₇₃×#2015	C₂	semidirect
11. C₇₃×#2014	C₂	semidirect
12. C₇₃×#2013	C₂	semidirect
13. C₇₃×#1973	C₂	semidirect
14. C₇₃×#1969	C₂	semidirect
15. C₇₃×#1753	C₂	semidirect
97. C₂×Q₁₆×C₇₃	D₄	semidirect
115. C₂×SD₁₆×C₇₃	D₄	semidirect
118. C₂×M₁₆×C₇₃	D₄	semidirect
154. C₂²⋊C₈×C₇₃	D₄	semidirect
353. C₂×C₄×C₇₃	#137	semidirect
397. #25790	C₇₃	direct (N × H)
406. C₂²×#137	C₂×C₇₃	semidirect
407. C₂×#497	C₂×C₇₃	semidirect
408. C₂×#492	C₂×C₇₃	semidirect
409. C₂×#468	C₂×C₇₃	semidirect
410. C₂×#452	C₂×C₇₃	semidirect
411. C₂×#448	C₂×C₇₃	semidirect
412. #2434	C₂×C₇₃	semidirect
414. #2016	C₂×C₇₃	semidirect
415. #2015	C₂×C₇₃	semidirect
416. #2014	C₂×C₇₃	semidirect
417. #2013	C₂×C₇₃	semidirect
418. #1973	C₂×C₇₃	semidirect
419. #1969	C₂×C₇₃	semidirect
420. #1753	C₂×C₇₃	semidirect
421. C₇₃	#25790	direct (N × H)
503. C₂×Q₁₆	D₄×C₇₃	semidirect
521. C₂×SD₁₆	D₄×C₇₃	semidirect
524. C₂×M₁₆	D₄×C₇₃	semidirect
560. C₂²⋊C₈	D₄×C₇₃	semidirect
759. C₂×C₄	#137×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₇₃	2
C₂×#497×C₇₃	2
C₂×#492×C₇₃	2
C₂×#468×C₇₃	2
C₂×#452×C₇₃	2
C₂×#448×C₇₃	2
C₇₃×#2434	2
C₇₃×#2431	2
C₇₃×#2016	2
C₇₃×#2015	2
C₇₃×#2014	2
C₇₃×#2013	2
C₇₃×#1973	2
C₇₃×#1969	2
C₇₃×#1753	2
#25790	73

Subgroups — C73×#25790 #32935194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25790 #32935194