Subgroups — C₇₃×#25792 #32935196

Order 18688.

1512 conjugacy classes of subgroups.

The subgroup lattice has 806 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×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#468×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#451×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2012	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×Q₁₆×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×D₈×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×#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
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	#495×C₇₃	—	2	4	no	—
39	#468×C₇₃	—	2	4	no	—
40	#451×C₇₃	—	2	4	no	—
41	#449×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	#394×C₇₃	—	2	2	no	—
53	#393×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	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇₃	—	2	1	no	—
85	C₂³×C₄×C₇₃	—	2	1	no	—
86	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
87	#137×C₇₃	—	2	32	no	—
88	C₂×Q₁₆×C₇₃	—	2	2	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	—	2	2	no	—
97	C₂×Q₁₆×C₇₃	—	4	1	no	—
98	C₂×Q₁₆×C₇₃	—	4	1	no	—
99	C₂×Q₁₆×C₇₃	D₄	1	4	yes	complemented
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	—	4	1	no	—
111	C₂×SD₁₆×C₇₃	D₄	1	4	yes	complemented
112	C₂×D₈×C₇₃	—	2	2	no	—
113	C₂×D₈×C₇₃	—	2	2	no	—
114	C₂×D₈×C₇₃	—	4	1	no	—
115	C₂×M₁₆×C₇₃	—	2	2	no	—
116	C₂×M₁₆×C₇₃	—	2	2	no	—
117	C₂×M₁₆×C₇₃	D₄	1	4	yes	—
118	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₇₃	—	2	2	no	—
123	C₄⋊Q₈×C₇₃	—	4	1	no	—
124	#124×C₇₃	—	2	2	no	—
125	#124×C₇₃	—	2	2	no	—
126	#124×C₇₃	—	2	2	no	—
127	#124×C₇₃	—	4	1	no	—
128	#124×C₇₃	—	4	1	no	—
129	#124×C₇₃	—	4	1	no	—
130	C₂²⋊Q₈×C₇₃	—	2	2	no	—
131	C₂²⋊Q₈×C₇₃	—	2	2	no	—
132	#121×C₇₃	—	2	2	no	—
133	#121×C₇₃	—	2	2	no	—
134	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₇₃	—	2	2	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	2	no	—
142	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₇₃	—	2	1	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	—
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	2	no	—
212	C₂×D₄×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	—	4	4	no	—
214	C₂×D₄×C₇₃	—	4	2	no	—
215	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₇₃	—	2	1	no	—
217	C₂²×C₄×C₇₃	—	2	1	no	—
218	C₂²×C₄×C₇₃	—	2	1	no	—
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	—	4	2	no	—
227	C₂²×C₄×C₇₃	—	4	2	no	—
228	C₂²×C₄×C₇₃	—	4	2	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	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
238	Q₁₆×C₇₃	—	2	8	no	—
239	Q₁₆×C₇₃	—	2	8	no	—
240	Q₁₆×C₇₃	—	4	4	no	—
241	Q₁₆×C₇₃	—	4	4	no	—
242	SD₁₆×C₇₃	—	2	8	no	—
243	SD₁₆×C₇₃	—	2	8	no	—
244	SD₁₆×C₇₃	—	4	4	no	—
245	SD₁₆×C₇₃	—	4	4	no	—
246	D₈×C₇₃	—	4	4	no	—
247	M₁₆×C₇₃	—	2	8	no	—
248	C₂×C₈×C₇₃	—	2	1	no	—
249	C₂×C₈×C₇₃	—	2	1	no	—
250	C₂×C₈×C₇₃	—	2	1	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	C₂×D₄	1	2	yes	—
255	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
256	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₇₃	—	2	1	no	—
261	C₄⋊C₄×C₇₃	—	2	1	no	—
262	C₄⋊C₄×C₇₃	—	2	1	no	—
263	C₄⋊C₄×C₇₃	—	2	1	no	—
264	C₄⋊C₄×C₇₃	—	4	4	no	—
265	C₄⋊C₄×C₇₃	—	4	2	no	—
266	C₂²⋊C₄×C₇₃	—	4	2	no	—
267	C₂²⋊C₄×C₇₃	—	4	4	no	—
268	C₂²⋊C₄×C₇₃	—	4	4	no	—
269	C₂²⋊C₄×C₇₃	—	4	4	no	—
270	C₂²⋊C₄×C₇₃	—	4	4	no	—
271	C₂²⋊C₄×C₇₃	—	4	2	no	—
272	C₂²⋊C₄×C₇₃	—	4	2	no	—
273	C₄²×C₇₃	—	2	1	no	—
274	C₄²×C₇₃	—	2	1	no	—
275	C₄²×C₇₃	—	2	1	no	—
276	C₄²×C₇₃	—	2	1	no	—
277	C₂³×C₇₃	—	2	1	no	—
278	C₂³×C₇₃	—	2	1	no	—
279	C₂³×C₇₃	—	2	2	no	—
280	C₂³×C₇₃	—	2	2	no	—
281	C₂³×C₇₃	—	2	2	no	—
282	C₂³×C₇₃	—	4	1	no	—
283	C₂³×C₇₃	—	4	1	no	—
284	C₂³×C₇₃	—	4	2	no	—
285	C₂³×C₇₃	—	4	2	no	—
286	C₂³×C₇₃	—	4	1	no	—
287	C₂³×C₇₃	—	4	1	no	—
288	C₂³×C₇₃	—	4	1	no	—
289	C₂³×C₇₃	—	4	2	no	—
290	C₂³×C₇₃	—	4	2	no	—
291	C₂³×C₇₃	#127	1	2	yes	—
292	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₇₃	—	2	2	no	—
294	Q₈×C₇₃	—	2	2	no	—
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	—	4	8	no	—
300	Q₈×C₇₃	—	4	1	no	—
301	Q₈×C₇₃	—	4	1	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	D₄×C₇₃	—	2	2	no	—
311	D₄×C₇₃	—	2	2	no	—
312	D₄×C₇₃	—	4	8	no	—
313	D₄×C₇₃	—	4	1	no	—
314	D₄×C₇₃	—	4	1	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	—	8	4	no	—
320	C₂×C₄×C₇₃	—	2	1	no	—
321	C₂×C₄×C₇₃	—	2	1	no	—
322	C₂×C₄×C₇₃	—	2	2	no	—
323	C₂×C₄×C₇₃	—	2	2	no	—
324	C₂×C₄×C₇₃	—	2	2	no	—
325	C₂×C₄×C₇₃	—	2	2	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	—	4	8	no	—
336	C₂×C₄×C₇₃	—	4	8	no	—
337	C₂×C₄×C₇₃	—	4	1	no	—
338	C₂×C₄×C₇₃	—	4	1	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	2	no	—
349	C₂×C₄×C₇₃	—	4	2	no	—
350	C₂×C₄×C₇₃	#127	1	2	yes	—
351	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
357	C₈×C₇₃	—	2	2	no	—
358	C₈×C₇₃	—	2	2	no	—
359	C₈×C₇₃	—	2	2	no	—
360	C₈×C₇₃	#120	1	4	yes	—
361	C₂²×C₇₃	—	2	2	no	—
362	C₂²×C₇₃	—	2	2	no	—
363	C₂²×C₇₃	—	2	2	no	—
364	C₂²×C₇₃	—	4	2	no	—
365	C₂²×C₇₃	—	4	2	no	—
366	C₂²×C₇₃	—	4	2	no	—
367	C₂²×C₇₃	—	4	4	no	—
368	C₂²×C₇₃	—	8	1	no	—
369	C₂²×C₇₃	—	8	1	no	—
370	C₂²×C₇₃	—	8	2	no	—
371	C₂²×C₇₃	—	8	1	no	—
372	C₂²×C₇₃	—	8	1	no	—
373	C₂²×C₇₃	—	8	1	no	—
374	C₂²×C₇₃	—	8	2	no	—
375	C₂²×C₇₃	—	8	2	no	—
376	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
377	C₂²×C₇₃	D₄²	1	1	yes	characteristic
378	C₂²×C₇₃	D₄²	1	1	yes	characteristic
379	C₂²×C₇₃	#575	1	2	yes	—
380	C₂²×C₇₃	#578	1	2	yes	—
381	C₄×C₇₃	—	2	2	no	—
382	C₄×C₇₃	—	4	2	no	—
383	C₄×C₇₃	—	4	2	no	—
384	C₄×C₇₃	—	4	2	no	—
385	C₄×C₇₃	—	4	2	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	8	1	no	—
388	C₄×C₇₃	—	8	1	no	—
389	C₄×C₇₃	—	8	1	no	—
390	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
391	C₄×C₇₃	#535	1	1	yes	characteristic
392	C₄×C₇₃	D₄²	1	1	yes	characteristic
393	C₄×C₇₃	D₄²	1	1	yes	characteristic
394	#25792	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂×C₇₃	—	4	2	no	—
396	C₂×C₇₃	—	8	2	no	—
397	C₂×C₇₃	—	16	1	no	—
398	C₂×C₇₃	#2433	1	1	yes	characteristic
399	C₂×C₇₃	#3153	1	1	yes	characteristic
400	C₂×C₇₃	#3156	1	1	yes	characteristic
401	C₂×C₇₃	#3269	1	2	yes	—
402	C₂×C₇₃	#3277	1	2	yes	—
403	C₂²×#137	C₂×C₇₃	1	1	yes	characteristic, complemented
404	C₂×#497	C₂×C₇₃	1	1	yes	characteristic, complemented
405	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
406	C₂×#468	C₂×C₇₃	1	1	yes	characteristic, complemented
407	C₂×#449	C₂×C₇₃	1	1	yes	characteristic
408	C₂×#451	C₂×C₇₃	1	1	yes	characteristic, complemented
409	#2436	C₂×C₇₃	1	1	yes	characteristic, complemented
410	#2432	C₂×C₇₃	1	1	yes	characteristic, complemented
411	#2016	C₂×C₇₃	1	1	yes	characteristic, complemented
412	#2015	C₂×C₇₃	1	1	yes	characteristic, complemented
413	#2015	C₂×C₇₃	1	1	yes	characteristic, complemented
414	#2012	C₂×C₇₃	1	1	yes	characteristic, complemented
415	#1973	C₂×C₇₃	1	1	yes	characteristic, complemented
416	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
417	#1753	C₂×C₇₃	1	1	yes	characteristic, complemented
418	C₇₃	#25792	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
420	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
421	C₂×#137	—	2	4	no	—
422	C₂×#137	—	2	4	no	—
423	C₂×#137	—	2	4	no	—
424	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
425	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
426	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
427	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
428	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
429	C₂²×SD₁₆	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×D₈	C₂²×C₇₃	1	1	yes	characteristic
433	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
434	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
435	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
436	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
437	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
438	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
439	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
440	#497	—	2	4	no	—
441	#495	—	2	4	no	—
442	#468	—	2	4	no	—
443	#451	—	2	4	no	—
444	#449	—	2	4	no	—
445	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
446	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
447	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
448	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
449	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
453	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
454	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
455	#394	—	2	2	no	—
456	#393	—	2	2	no	—
457	#391	C₂²×C₇₃	1	1	yes	characteristic
458	#391	C₂²×C₇₃	1	1	yes	characteristic
459	#391	C₂²×C₇₃	1	1	yes	characteristic
460	#390	C₂²×C₇₃	1	1	yes	characteristic
461	#386	—	2	2	no	—
462	#385	—	2	2	no	—
463	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
464	#336	C₂²×C₇₃	1	1	yes	characteristic
465	#336	C₂²×C₇₃	1	1	yes	characteristic
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	4	1	no	—
471	C₂×#41	—	4	1	no	—
472	C₂²×Q₈	—	2	1	no	—
473	C₂²×Q₈	—	2	2	no	—
474	C₂²×Q₈	—	2	2	no	—
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×Q₈	—	2	2	no	—
477	C₂²×Q₈	—	4	1	no	—
478	C₂²×Q₈	—	4	1	no	—
479	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
490	#137	—	2	32	no	—
491	C₂×Q₁₆	—	2	2	no	—
492	C₂×Q₁₆	—	2	2	no	—
493	C₂×Q₁₆	—	2	2	no	—
494	C₂×Q₁₆	—	2	2	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	—	4	1	no	—
501	C₂×Q₁₆	—	4	1	no	—
502	C₂×Q₁₆	D₄×C₇₃	1	4	yes	complemented
503	C₂×SD₁₆	—	2	2	no	—
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	—	4	1	no	—
514	C₂×SD₁₆	D₄×C₇₃	1	4	yes	complemented
515	C₂×D₈	—	2	2	no	—
516	C₂×D₈	—	2	2	no	—
517	C₂×D₈	—	4	1	no	—
518	C₂×M₁₆	—	2	2	no	—
519	C₂×M₁₆	—	2	2	no	—
520	C₂×M₁₆	D₄×C₇₃	1	4	yes	—
521	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	4	1	no	—
527	#124	—	2	2	no	—
528	#124	—	2	2	no	—
529	#124	—	2	2	no	—
530	#124	—	4	1	no	—
531	#124	—	4	1	no	—
532	#124	—	4	1	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	2	no	—
544	C₂×C₂²⋊C₄	—	2	2	no	—
545	C₂×C₂²⋊C₄	—	2	2	no	—
546	C₂×C₂²⋊C₄	—	2	2	no	—
547	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
550	#107	—	2	2	no	—
551	#103	—	2	2	no	—
552	#103	—	2	2	no	—
553	#103	—	2	2	no	—
554	#103	—	2	2	no	—
555	#102	—	2	2	no	—
556	#102	—	2	2	no	—
557	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
558	#97	—	2	2	no	—
559	C₄×C₈	—	2	2	no	—
560	#95	—	2	2	no	—
561	#95	—	2	2	no	—
562	#95	—	2	2	no	—
563	#95	D₄×C₇₃	1	2	yes	—
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
567	#41	—	2	8	no	—
568	#41	—	4	4	no	—
569	#41	—	4	4	no	—
570	#41	—	4	4	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	8	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	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	—	4	2	no	—
594	C₂×Q₈	—	4	2	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	4	no	—
597	C₂×Q₈	—	4	4	no	—
598	C₂×Q₈	—	4	2	no	—
599	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
600	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
601	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
636	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
639	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
641	Q₁₆	—	2	8	no	—
642	Q₁₆	—	2	8	no	—
643	Q₁₆	—	4	4	no	—
644	Q₁₆	—	4	4	no	—
645	SD₁₆	—	2	8	no	—
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	4	4	no	—
648	SD₁₆	—	4	4	no	—
649	D₈	—	4	4	no	—
650	M₁₆	—	2	8	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
658	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
659	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
660	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
661	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
662	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₂²⋊C₄	—	4	4	no	—
673	C₂²⋊C₄	—	4	4	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	#127×C₇₃	1	2	yes	—
695	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	2	2	no	—
702	Q₈	—	4	8	no	—
703	Q₈	—	4	1	no	—
704	Q₈	—	4	1	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	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	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	4	1	no	—
722	D₄	—	8	4	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	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	—	4	8	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	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	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	#127×C₇₃	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
758	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
759	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	2	2	no	—
763	C₈	#120×C₇₃	1	4	yes	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	8	2	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	2	no	—
775	C₂²	—	8	2	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
780	C₂²	D₄²×C₇₃	1	1	yes	characteristic
781	C₂²	D₄²×C₇₃	1	1	yes	characteristic
782	C₂²	#575×C₇₃	1	2	yes	—
783	C₂²	#578×C₇₃	1	2	yes	—
784	C₄	—	2	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	8	1	no	—
791	C₄	—	8	1	no	—
792	C₄	—	8	1	no	—
793	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
794	C₄	#535×C₇₃	1	1	yes	characteristic
795	C₄	D₄²×C₇₃	1	1	yes	characteristic
796	C₄	D₄²×C₇₃	1	1	yes	characteristic
797	C₂	—	4	2	no	—
798	C₂	—	8	2	no	—
799	C₂	—	16	1	no	—
800	C₂	C₇₃×#2433	1	1	yes	characteristic
801	C₂	C₇₃×#3153	1	1	yes	characteristic
802	C₂	C₇₃×#3156	1	1	yes	characteristic
803	C₂	C₇₃×#3269	1	2	yes	—
804	C₂	C₇₃×#3277	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#449×C₇₃	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×#495×C₇₃	C₂	semidirect
4. C₂×#468×C₇₃	C₂	semidirect
6. C₂×#451×C₇₃	C₂	semidirect
7. C₇₃×#2436	C₂	semidirect
8. C₇₃×#2432	C₂	semidirect
9. C₇₃×#2016	C₂	semidirect
10. C₇₃×#2015	C₂	semidirect
11. C₇₃×#2015	C₂	semidirect
12. C₇₃×#2012	C₂	semidirect
13. C₇₃×#1973	C₂	semidirect
14. C₇₃×#1969	C₂	semidirect
15. C₇₃×#1753	C₂	semidirect
99. C₂×Q₁₆×C₇₃	D₄	semidirect
111. C₂×SD₁₆×C₇₃	D₄	semidirect
394. #25792	C₇₃	direct (N × H)
403. C₂²×#137	C₂×C₇₃	semidirect
404. C₂×#497	C₂×C₇₃	semidirect
405. C₂×#495	C₂×C₇₃	semidirect
406. C₂×#468	C₂×C₇₃	semidirect
408. C₂×#451	C₂×C₇₃	semidirect
409. #2436	C₂×C₇₃	semidirect
410. #2432	C₂×C₇₃	semidirect
411. #2016	C₂×C₇₃	semidirect
412. #2015	C₂×C₇₃	semidirect
413. #2015	C₂×C₇₃	semidirect
414. #2012	C₂×C₇₃	semidirect
415. #1973	C₂×C₇₃	semidirect
416. #1969	C₂×C₇₃	semidirect
417. #1753	C₂×C₇₃	semidirect
418. C₇₃	#25792	direct (N × H)
502. C₂×Q₁₆	D₄×C₇₃	semidirect
514. C₂×SD₁₆	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×#137×C₇₃	2
C₂×#497×C₇₃	2
C₂×#495×C₇₃	2
C₂×#468×C₇₃	2
C₂×#449×C₇₃	2
C₂×#451×C₇₃	2
C₇₃×#2436	2
C₇₃×#2432	2
C₇₃×#2016	2
C₇₃×#2015	2
C₇₃×#2012	2
C₇₃×#1973	2
C₇₃×#1969	2
C₇₃×#1753	2
#25792	73

Subgroups — C73×#25792 #32935196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25792 #32935196