Subgroups — C₇₃×#59941 #32969345

Order 18688.

1990 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2799	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2745	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2605	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2586	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2572	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2527	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2493	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2477	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2438	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2419	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2409	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2406	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2368	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2359	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2339	C₂	1	2	yes	maximal
18	C₂×#391×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#123×C₇₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
27	C₂×#117×C₇₃	C₂²	1	2	yes	—
28	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
31	#401×C₇₃	C₂²	1	2	yes	—
32	#400×C₇₃	C₂²	1	2	yes	—
33	#400×C₇₃	C₂²	1	2	yes	—
34	#400×C₇₃	C₂²	1	1	yes	characteristic
35	#400×C₇₃	C₂²	1	1	yes	characteristic
36	#400×C₇₃	C₂²	1	2	yes	—
37	#400×C₇₃	C₂²	1	2	yes	—
38	#398×C₇₃	C₂²	1	1	yes	characteristic
39	#398×C₇₃	C₂²	1	1	yes	characteristic
40	#398×C₇₃	C₂²	1	2	yes	—
41	#397×C₇₃	C₂²	1	2	yes	—
42	#397×C₇₃	C₂²	1	2	yes	—
43	#395×C₇₃	C₂²	1	2	yes	—
44	#395×C₇₃	C₂²	1	1	yes	characteristic
45	#395×C₇₃	C₂²	1	1	yes	characteristic
46	#395×C₇₃	C₂²	1	2	yes	—
47	#394×C₇₃	C₂²	1	1	yes	characteristic
48	#394×C₇₃	C₂²	1	1	yes	characteristic
49	#393×C₇₃	C₂²	1	2	yes	—
50	#393×C₇₃	C₂²	1	2	yes	—
51	#391×C₇₃	C₂²	1	1	yes	characteristic
52	#391×C₇₃	C₂²	1	2	yes	—
53	#391×C₇₃	C₂²	1	1	yes	characteristic
54	#391×C₇₃	C₂²	1	2	yes	—
55	#391×C₇₃	C₂²	1	2	yes	—
56	#391×C₇₃	C₂²	1	2	yes	—
57	#391×C₇₃	C₂²	1	2	yes	—
58	#391×C₇₃	C₂²	1	1	yes	characteristic
59	#391×C₇₃	C₂²	1	1	yes	characteristic
60	#391×C₇₃	C₂²	1	2	yes	—
61	#389×C₇₃	C₂²	1	2	yes	—
62	#388×C₇₃	C₂²	1	2	yes	—
63	#388×C₇₃	C₂²	1	2	yes	—
64	#388×C₇₃	C₂²	1	2	yes	—
65	#388×C₇₃	C₂²	1	2	yes	—
66	#387×C₇₃	C₂²	1	2	yes	—
67	#387×C₇₃	C₂²	1	2	yes	—
68	#387×C₇₃	C₂²	1	2	yes	—
69	#387×C₇₃	C₂²	1	2	yes	—
70	#387×C₇₃	C₂²	1	2	yes	—
71	#387×C₇₃	C₂²	1	2	yes	—
72	#387×C₇₃	C₂²	1	2	yes	—
73	#387×C₇₃	C₂²	1	2	yes	—
74	#387×C₇₃	C₂²	1	2	yes	—
75	#387×C₇₃	C₂²	1	2	yes	—
76	#387×C₇₃	C₂²	1	2	yes	—
77	#386×C₇₃	C₂²	1	2	yes	—
78	#386×C₇₃	C₂²	1	2	yes	—
79	#386×C₇₃	C₂²	1	2	yes	—
80	#386×C₇₃	C₂²	1	2	yes	—
81	#386×C₇₃	C₂²	1	2	yes	—
82	#385×C₇₃	C₂²	1	2	yes	—
83	#385×C₇₃	C₂²	1	2	yes	—
84	#385×C₇₃	C₂²	1	2	yes	—
85	#385×C₇₃	C₂²	1	2	yes	—
86	#385×C₇₃	C₂²	1	2	yes	—
87	#385×C₇₃	C₂²	1	2	yes	—
88	#385×C₇₃	C₂²	1	2	yes	—
89	#383×C₇₃	C₂²	1	2	yes	—
90	#381×C₇₃	C₂²	1	2	yes	—
91	#381×C₇₃	C₂²	1	1	yes	characteristic
92	#381×C₇₃	C₂²	1	2	yes	—
93	#381×C₇₃	C₂²	1	1	yes	characteristic
94	#381×C₇₃	C₂²	1	2	yes	—
95	#380×C₇₃	C₂²	1	2	yes	—
96	#380×C₇₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
103	#376×C₇₃	C₂²	1	2	yes	—
104	C₂×#95×C₇₃	C₂²	1	2	yes	—
105	C₂×#95×C₇₃	C₂²	1	2	yes	—
106	C₂×#95×C₇₃	C₂²	1	2	yes	—
107	C₂×#41×C₇₃	—	2	8	no	—
108	C₂×#41×C₇₃	—	4	2	no	—
109	C₂²×Q₈×C₇₃	—	2	4	no	—
110	C₂²×Q₈×C₇₃	—	4	2	no	—
111	C₂²×Q₈×C₇₃	—	4	2	no	—
112	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
114	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
126	#123×C₇₃	—	2	8	no	—
127	C₂²⋊Q₈×C₇₃	—	2	8	no	—
128	C₂²⋊Q₈×C₇₃	—	4	4	no	—
129	C₄×D₄×C₇₃	—	2	8	no	—
130	C₄×D₄×C₇₃	—	4	4	no	—
131	#117×C₇₃	—	4	4	no	—
132	#117×C₇₃	—	4	2	no	—
133	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₇₃	—	4	2	no	—
166	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
174	#95×C₇₃	C₂³	1	2	yes	—
175	#95×C₇₃	C₂³	1	2	yes	—
176	#95×C₇₃	C₂³	1	2	yes	—
177	#95×C₇₃	C₂³	1	2	yes	—
178	#95×C₇₃	C₂³	1	2	yes	—
179	#95×C₇₃	C₂³	1	2	yes	—
180	#95×C₇₃	C₂³	1	2	yes	—
181	#95×C₇₃	C₂³	1	2	yes	—
182	#95×C₇₃	C₂³	1	2	yes	—
183	#95×C₇₃	C₂³	1	2	yes	—
184	#95×C₇₃	C₂³	1	2	yes	—
185	#95×C₇₃	C₂³	1	2	yes	—
186	#95×C₇₃	C₂³	1	2	yes	—
187	#95×C₇₃	C₂³	1	2	yes	—
188	#95×C₇₃	C₂³	1	1	yes	characteristic
189	#95×C₇₃	C₂³	1	1	yes	characteristic
190	#95×C₇₃	C₂³	1	2	yes	—
191	#95×C₇₃	C₂³	1	2	yes	—
192	#95×C₇₃	C₂³	1	2	yes	—
193	#95×C₇₃	C₂³	1	2	yes	—
194	#95×C₇₃	C₂³	1	2	yes	—
195	#95×C₇₃	C₂³	1	2	yes	—
196	#95×C₇₃	C₂³	1	1	yes	characteristic
197	#95×C₇₃	C₂³	1	1	yes	characteristic
198	#95×C₇₃	C₂³	1	2	yes	—
199	#95×C₇₃	C₂³	1	2	yes	—
200	#95×C₇₃	C₂³	1	2	yes	—
201	#95×C₇₃	C₂³	1	2	yes	—
202	#95×C₇₃	C₂³	1	2	yes	—
203	#95×C₇₃	C₂³	1	2	yes	—
204	#95×C₇₃	C₂³	1	2	yes	—
205	#95×C₇₃	C₂³	1	2	yes	—
206	#95×C₇₃	C₂³	1	2	yes	—
207	#95×C₇₃	C₂³	1	2	yes	—
208	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
209	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
210	#41×C₇₃	—	4	16	no	—
211	C₂×Q₈×C₇₃	—	2	4	no	—
212	C₂×Q₈×C₇₃	—	2	2	no	—
213	C₂×Q₈×C₇₃	—	2	4	no	—
214	C₂×Q₈×C₇₃	—	2	4	no	—
215	C₂×Q₈×C₇₃	—	4	1	no	—
216	C₂×Q₈×C₇₃	—	4	1	no	—
217	C₂×Q₈×C₇₃	—	4	1	no	—
218	C₂×Q₈×C₇₃	—	4	2	no	—
219	C₂×Q₈×C₇₃	—	4	1	no	—
220	C₂×Q₈×C₇₃	—	4	1	no	—
221	C₂×Q₈×C₇₃	—	4	16	no	—
222	C₂×Q₈×C₇₃	#41	1	4	yes	complemented
223	C₂×D₄×C₇₃	—	2	4	no	—
224	C₂×D₄×C₇₃	—	2	4	no	—
225	C₂×D₄×C₇₃	—	2	4	no	—
226	C₂×D₄×C₇₃	—	4	1	no	—
227	C₂×D₄×C₇₃	#41	1	8	yes	—
228	C₂²×C₄×C₇₃	—	2	2	no	—
229	C₂²×C₄×C₇₃	—	2	2	no	—
230	C₂²×C₄×C₇₃	—	2	2	no	—
231	C₂²×C₄×C₇₃	—	2	4	no	—
232	C₂²×C₄×C₇₃	—	2	4	no	—
233	C₂²×C₄×C₇₃	—	2	4	no	—
234	C₂²×C₄×C₇₃	—	2	4	no	—
235	C₂²×C₄×C₇₃	—	2	4	no	—
236	C₂²×C₄×C₇₃	—	2	2	no	—
237	C₂²×C₄×C₇₃	—	2	2	no	—
238	C₂²×C₄×C₇₃	—	2	4	no	—
239	C₂²×C₄×C₇₃	—	2	4	no	—
240	C₂²×C₄×C₇₃	—	2	4	no	—
241	C₂²×C₄×C₇₃	—	2	4	no	—
242	C₂²×C₄×C₇₃	—	2	4	no	—
243	C₂²×C₄×C₇₃	—	2	4	no	—
244	C₂²×C₄×C₇₃	—	4	2	no	—
245	C₂²×C₄×C₇₃	—	4	2	no	—
246	C₂²×C₄×C₇₃	—	4	2	no	—
247	C₂²×C₄×C₇₃	—	4	2	no	—
248	C₂²×C₄×C₇₃	—	4	2	no	—
249	C₂²×C₄×C₇₃	—	4	2	no	—
250	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₇₃	—	2	4	no	—
268	C₄⋊C₄×C₇₃	—	2	4	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	4	no	—
271	C₄⋊C₄×C₇₃	—	2	4	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	4	1	no	—
276	C₄⋊C₄×C₇₃	—	4	1	no	—
277	C₄⋊C₄×C₇₃	—	4	1	no	—
278	C₄⋊C₄×C₇₃	—	4	1	no	—
279	C₄⋊C₄×C₇₃	—	4	2	no	—
280	C₄⋊C₄×C₇₃	—	4	1	no	—
281	C₄⋊C₄×C₇₃	—	4	1	no	—
282	C₄⋊C₄×C₇₃	—	4	2	no	—
283	C₄⋊C₄×C₇₃	—	4	2	no	—
284	C₄⋊C₄×C₇₃	—	4	2	no	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	—	2	4	no	—
288	C₂²⋊C₄×C₇₃	—	2	4	no	—
289	C₂²⋊C₄×C₇₃	—	2	4	no	—
290	C₂²⋊C₄×C₇₃	—	2	4	no	—
291	C₂²⋊C₄×C₇₃	—	2	4	no	—
292	C₂²⋊C₄×C₇₃	—	2	4	no	—
293	C₂²⋊C₄×C₇₃	—	2	4	no	—
294	C₂²⋊C₄×C₇₃	—	2	4	no	—
295	C₂²⋊C₄×C₇₃	—	4	2	no	—
296	C₂²⋊C₄×C₇₃	—	4	2	no	—
297	C₂²⋊C₄×C₇₃	—	4	2	no	—
298	C₄²×C₇₃	—	2	4	no	—
299	C₄²×C₇₃	—	2	4	no	—
300	C₄²×C₇₃	—	2	4	no	—
301	C₄²×C₇₃	—	4	1	no	—
302	C₄²×C₇₃	—	4	1	no	—
303	C₄²×C₇₃	—	4	2	no	—
304	C₄²×C₇₃	—	4	2	no	—
305	C₄²×C₇₃	—	4	2	no	—
306	C₂³×C₇₃	—	2	1	no	—
307	C₂³×C₇₃	—	2	1	no	—
308	C₂³×C₇₃	—	2	2	no	—
309	C₂³×C₇₃	—	2	2	no	—
310	C₂³×C₇₃	—	2	2	no	—
311	C₂³×C₇₃	—	2	2	no	—
312	C₂³×C₇₃	—	2	2	no	—
313	C₂³×C₇₃	—	2	2	no	—
314	C₂³×C₇₃	—	2	2	no	—
315	C₂³×C₇₃	C₂×#41	1	4	yes	—
316	C₂³×C₇₃	C₂×#41	1	4	yes	—
317	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
318	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
319	Q₈×C₇₃	—	4	4	no	—
320	Q₈×C₇₃	—	4	8	no	—
321	Q₈×C₇₃	—	4	4	no	—
322	Q₈×C₇₃	—	4	4	no	—
323	D₄×C₇₃	—	2	16	no	—
324	D₄×C₇₃	—	4	4	no	—
325	C₂×C₄×C₇₃	—	2	8	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	2	no	—
328	C₂×C₄×C₇₃	—	2	1	no	—
329	C₂×C₄×C₇₃	—	2	2	no	—
330	C₂×C₄×C₇₃	—	2	1	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	1	no	—
334	C₂×C₄×C₇₃	—	2	1	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	2	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	2	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	2	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	1	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	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	2	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	1	no	—
360	C₂×C₄×C₇₃	—	2	1	no	—
361	C₂×C₄×C₇₃	—	2	2	no	—
362	C₂×C₄×C₇₃	—	2	2	no	—
363	C₂×C₄×C₇₃	—	2	2	no	—
364	C₂×C₄×C₇₃	—	2	2	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	2	no	—
368	C₂×C₄×C₇₃	—	4	8	no	—
369	C₂×C₄×C₇₃	—	4	8	no	—
370	C₂×C₄×C₇₃	—	4	8	no	—
371	C₂×C₄×C₇₃	—	4	8	no	—
372	C₂×C₄×C₇₃	—	4	4	no	—
373	C₂×C₄×C₇₃	—	4	4	no	—
374	C₂×C₄×C₇₃	—	8	4	no	—
375	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
378	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₇₃	2₋¹⁺⁴	1	4	yes	—
380	C₂²×C₇₃	—	2	4	no	—
381	C₂²×C₇₃	—	2	2	no	—
382	C₂²×C₇₃	—	2	4	no	—
383	C₂²×C₇₃	—	2	2	no	—
384	C₂²×C₇₃	—	2	4	no	—
385	C₂²×C₇₃	—	2	4	no	—
386	C₂²×C₇₃	—	2	4	no	—
387	C₂²×C₇₃	—	4	2	no	—
388	C₂²×C₇₃	—	4	2	no	—
389	C₂²×C₇₃	—	4	2	no	—
390	C₂²×C₇₃	—	4	2	no	—
391	C₂²×C₇₃	#551	1	4	yes	—
392	C₂²×C₇₃	C₂²×#41	1	2	yes	—
393	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	2	yes	—
397	C₄×C₇₃	—	2	4	no	—
398	C₄×C₇₃	—	2	2	no	—
399	C₄×C₇₃	—	2	2	no	—
400	C₄×C₇₃	—	2	4	no	—
401	C₄×C₇₃	—	2	4	no	—
402	C₄×C₇₃	—	4	1	no	—
403	C₄×C₇₃	—	4	1	no	—
404	C₄×C₇₃	—	4	1	no	—
405	C₄×C₇₃	—	4	1	no	—
406	C₄×C₇₃	—	4	2	no	—
407	C₄×C₇₃	—	4	2	no	—
408	C₄×C₇₃	—	4	2	no	—
409	C₄×C₇₃	—	4	2	no	—
410	C₄×C₇₃	—	4	2	no	—
411	C₄×C₇₃	—	4	2	no	—
412	C₄×C₇₃	—	4	2	no	—
413	C₄×C₇₃	—	4	2	no	—
414	#59941	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₇₃	—	2	4	no	—
416	C₂×C₇₃	—	4	4	no	—
417	C₂×C₇₃	C₂×#551	1	1	yes	characteristic
418	C₂×C₇₃	#3482	1	2	yes	—
419	C₂×C₇₃	#3490	1	1	yes	characteristic
420	C₂×C₇₃	#3520	1	2	yes	—
421	C₂×C₇₃	#3544	1	1	yes	characteristic
422	#2799	C₂×C₇₃	1	1	yes	characteristic, complemented
423	#2745	C₂×C₇₃	1	2	yes	complemented
424	#2728	C₂×C₇₃	1	1	yes	characteristic, complemented
425	#2605	C₂×C₇₃	1	2	yes	complemented
426	#2586	C₂×C₇₃	1	1	yes	characteristic, complemented
427	#2572	C₂×C₇₃	1	1	yes	characteristic, complemented
428	#2527	C₂×C₇₃	1	2	yes	complemented
429	#2493	C₂×C₇₃	1	2	yes	complemented
430	#2484	C₂×C₇₃	1	1	yes	characteristic, complemented
431	#2477	C₂×C₇₃	1	2	yes	complemented
432	#2438	C₂×C₇₃	1	2	yes	complemented
433	#2419	C₂×C₇₃	1	2	yes	complemented
434	#2409	C₂×C₇₃	1	2	yes	complemented
435	#2406	C₂×C₇₃	1	1	yes	characteristic
436	#2368	C₂×C₇₃	1	2	yes	complemented
437	#2359	C₂×C₇₃	1	2	yes	complemented
438	#2339	C₂×C₇₃	1	2	yes	—
439	C₂×#391	C₂×C₇₃	1	1	yes	characteristic, complemented
440	#2290	C₂×C₇₃	1	2	yes	complemented
441	C₇₃	#59941	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
443	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
444	C₂×#123	C₂²×C₇₃	1	2	yes	—
445	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
446	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
449	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
450	C₂×#117	C₂²×C₇₃	1	2	yes	—
451	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
452	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
453	#401	C₂²×C₇₃	1	2	yes	—
454	#400	C₂²×C₇₃	1	1	yes	characteristic
455	#400	C₂²×C₇₃	1	2	yes	—
456	#400	C₂²×C₇₃	1	2	yes	—
457	#400	C₂²×C₇₃	1	2	yes	—
458	#400	C₂²×C₇₃	1	2	yes	—
459	#400	C₂²×C₇₃	1	1	yes	characteristic
460	#398	C₂²×C₇₃	1	1	yes	characteristic
461	#398	C₂²×C₇₃	1	2	yes	—
462	#398	C₂²×C₇₃	1	1	yes	characteristic
463	#397	C₂²×C₇₃	1	2	yes	—
464	#397	C₂²×C₇₃	1	2	yes	—
465	#395	C₂²×C₇₃	1	1	yes	characteristic
466	#395	C₂²×C₇₃	1	2	yes	—
467	#395	C₂²×C₇₃	1	1	yes	characteristic
468	#395	C₂²×C₇₃	1	2	yes	—
469	#394	C₂²×C₇₃	1	1	yes	characteristic
470	#394	C₂²×C₇₃	1	1	yes	characteristic
471	#393	C₂²×C₇₃	1	2	yes	—
472	#393	C₂²×C₇₃	1	2	yes	—
473	#391	C₂²×C₇₃	1	1	yes	characteristic
474	#391	C₂²×C₇₃	1	2	yes	—
475	#391	C₂²×C₇₃	1	2	yes	—
476	#391	C₂²×C₇₃	1	2	yes	—
477	#391	C₂²×C₇₃	1	2	yes	—
478	#391	C₂²×C₇₃	1	1	yes	characteristic
479	#391	C₂²×C₇₃	1	2	yes	—
480	#391	C₂²×C₇₃	1	2	yes	—
481	#391	C₂²×C₇₃	1	1	yes	characteristic
482	#391	C₂²×C₇₃	1	1	yes	characteristic
483	#389	C₂²×C₇₃	1	2	yes	—
484	#388	C₂²×C₇₃	1	2	yes	—
485	#388	C₂²×C₇₃	1	2	yes	—
486	#388	C₂²×C₇₃	1	2	yes	—
487	#388	C₂²×C₇₃	1	2	yes	—
488	#387	C₂²×C₇₃	1	2	yes	—
489	#387	C₂²×C₇₃	1	2	yes	—
490	#387	C₂²×C₇₃	1	2	yes	—
491	#387	C₂²×C₇₃	1	2	yes	—
492	#387	C₂²×C₇₃	1	2	yes	—
493	#387	C₂²×C₇₃	1	2	yes	—
494	#387	C₂²×C₇₃	1	2	yes	—
495	#387	C₂²×C₇₃	1	2	yes	—
496	#387	C₂²×C₇₃	1	2	yes	—
497	#387	C₂²×C₇₃	1	2	yes	—
498	#387	C₂²×C₇₃	1	2	yes	—
499	#386	C₂²×C₇₃	1	2	yes	—
500	#386	C₂²×C₇₃	1	2	yes	—
501	#386	C₂²×C₇₃	1	2	yes	—
502	#386	C₂²×C₇₃	1	2	yes	—
503	#386	C₂²×C₇₃	1	2	yes	—
504	#385	C₂²×C₇₃	1	2	yes	—
505	#385	C₂²×C₇₃	1	2	yes	—
506	#385	C₂²×C₇₃	1	2	yes	—
507	#385	C₂²×C₇₃	1	2	yes	—
508	#385	C₂²×C₇₃	1	2	yes	—
509	#385	C₂²×C₇₃	1	2	yes	—
510	#385	C₂²×C₇₃	1	2	yes	—
511	#383	C₂²×C₇₃	1	2	yes	—
512	#381	C₂²×C₇₃	1	2	yes	—
513	#381	C₂²×C₇₃	1	2	yes	—
514	#381	C₂²×C₇₃	1	2	yes	—
515	#381	C₂²×C₇₃	1	1	yes	characteristic
516	#381	C₂²×C₇₃	1	1	yes	characteristic
517	#380	C₂²×C₇₃	1	2	yes	—
518	#380	C₂²×C₇₃	1	2	yes	—
519	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
525	#376	C₂²×C₇₃	1	2	yes	—
526	C₂×#95	C₂²×C₇₃	1	2	yes	—
527	C₂×#95	C₂²×C₇₃	1	2	yes	—
528	C₂×#95	C₂²×C₇₃	1	2	yes	—
529	C₂×#41	—	2	8	no	—
530	C₂×#41	—	4	2	no	—
531	C₂²×Q₈	—	2	4	no	—
532	C₂²×Q₈	—	4	2	no	—
533	C₂²×Q₈	—	4	2	no	—
534	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
535	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
544	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
545	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
546	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
547	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
548	#123	—	2	8	no	—
549	C₂²⋊Q₈	—	2	8	no	—
550	C₂²⋊Q₈	—	4	4	no	—
551	C₄×D₄	—	2	8	no	—
552	C₄×D₄	—	4	4	no	—
553	#117	—	4	4	no	—
554	#117	—	4	2	no	—
555	C₂×C₄⋊C₄	—	4	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
587	C₂×C₄²	—	4	2	no	—
588	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
596	#95	C₂³×C₇₃	1	2	yes	—
597	#95	C₂³×C₇₃	1	2	yes	—
598	#95	C₂³×C₇₃	1	2	yes	—
599	#95	C₂³×C₇₃	1	2	yes	—
600	#95	C₂³×C₇₃	1	2	yes	—
601	#95	C₂³×C₇₃	1	2	yes	—
602	#95	C₂³×C₇₃	1	2	yes	—
603	#95	C₂³×C₇₃	1	2	yes	—
604	#95	C₂³×C₇₃	1	2	yes	—
605	#95	C₂³×C₇₃	1	2	yes	—
606	#95	C₂³×C₇₃	1	2	yes	—
607	#95	C₂³×C₇₃	1	2	yes	—
608	#95	C₂³×C₇₃	1	2	yes	—
609	#95	C₂³×C₇₃	1	2	yes	—
610	#95	C₂³×C₇₃	1	2	yes	—
611	#95	C₂³×C₇₃	1	2	yes	—
612	#95	C₂³×C₇₃	1	2	yes	—
613	#95	C₂³×C₇₃	1	2	yes	—
614	#95	C₂³×C₇₃	1	2	yes	—
615	#95	C₂³×C₇₃	1	2	yes	—
616	#95	C₂³×C₇₃	1	2	yes	—
617	#95	C₂³×C₇₃	1	2	yes	—
618	#95	C₂³×C₇₃	1	2	yes	—
619	#95	C₂³×C₇₃	1	2	yes	—
620	#95	C₂³×C₇₃	1	1	yes	characteristic
621	#95	C₂³×C₇₃	1	1	yes	characteristic
622	#95	C₂³×C₇₃	1	2	yes	—
623	#95	C₂³×C₇₃	1	2	yes	—
624	#95	C₂³×C₇₃	1	2	yes	—
625	#95	C₂³×C₇₃	1	2	yes	—
626	#95	C₂³×C₇₃	1	2	yes	—
627	#95	C₂³×C₇₃	1	1	yes	characteristic
628	#95	C₂³×C₇₃	1	1	yes	characteristic
629	#95	C₂³×C₇₃	1	2	yes	—
630	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
631	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
632	#41	—	4	16	no	—
633	C₂×Q₈	—	2	4	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	4	no	—
636	C₂×Q₈	—	2	4	no	—
637	C₂×Q₈	—	4	1	no	—
638	C₂×Q₈	—	4	1	no	—
639	C₂×Q₈	—	4	1	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	16	no	—
644	C₂×Q₈	#41×C₇₃	1	4	yes	complemented
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	#41×C₇₃	1	8	yes	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	1	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	4	1	no	—
724	C₄²	—	4	1	no	—
725	C₄²	—	4	2	no	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	2	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	C₂×#41×C₇₃	1	4	yes	—
738	C₂³	C₂×#41×C₇₃	1	4	yes	—
739	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
740	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
741	Q₈	—	4	4	no	—
742	Q₈	—	4	8	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	4	no	—
745	D₄	—	2	16	no	—
746	D₄	—	4	4	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	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	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	8	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	8	4	no	—
797	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
798	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
799	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
800	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
801	C₂×C₄	2₋¹⁺⁴×C₇₃	1	4	yes	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	#551×C₇₃	1	4	yes	—
814	C₂²	C₂²×#41×C₇₃	1	2	yes	—
815	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
816	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
817	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
818	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	2	yes	—
819	C₄	—	2	4	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₂	—	2	4	no	—
837	C₂	—	4	4	no	—
838	C₂	C₂×#551×C₇₃	1	1	yes	characteristic
839	C₂	C₇₃×#3482	1	2	yes	—
840	C₂	C₇₃×#3490	1	1	yes	characteristic
841	C₂	C₇₃×#3520	1	2	yes	—
842	C₂	C₇₃×#3544	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2799	C₂	semidirect
2. C₇₃×#2745	C₂	semidirect
3. C₇₃×#2728	C₂	semidirect
4. C₇₃×#2605	C₂	semidirect
5. C₇₃×#2586	C₂	semidirect
6. C₇₃×#2572	C₂	semidirect
7. C₇₃×#2527	C₂	semidirect
8. C₇₃×#2493	C₂	semidirect
9. C₇₃×#2484	C₂	semidirect
10. C₇₃×#2477	C₂	semidirect
11. C₇₃×#2438	C₂	semidirect
12. C₇₃×#2419	C₂	semidirect
13. C₇₃×#2409	C₂	semidirect
15. C₇₃×#2368	C₂	semidirect
16. C₇₃×#2359	C₂	semidirect
18. C₂×#391×C₇₃	C₂	semidirect
19. C₇₃×#2290	C₂	semidirect
222. C₂×Q₈×C₇₃	#41	semidirect
414. #59941	C₇₃	direct (N × H)
422. #2799	C₂×C₇₃	semidirect
423. #2745	C₂×C₇₃	semidirect
424. #2728	C₂×C₇₃	semidirect
425. #2605	C₂×C₇₃	semidirect
426. #2586	C₂×C₇₃	semidirect
427. #2572	C₂×C₇₃	semidirect
428. #2527	C₂×C₇₃	semidirect
429. #2493	C₂×C₇₃	semidirect
430. #2484	C₂×C₇₃	semidirect
431. #2477	C₂×C₇₃	semidirect
432. #2438	C₂×C₇₃	semidirect
433. #2419	C₂×C₇₃	semidirect
434. #2409	C₂×C₇₃	semidirect
436. #2368	C₂×C₇₃	semidirect
437. #2359	C₂×C₇₃	semidirect
439. C₂×#391	C₂×C₇₃	semidirect
440. #2290	C₂×C₇₃	semidirect
441. C₇₃	#59941	direct (N × H)
644. C₂×Q₈	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2799	2
C₇₃×#2745	2
C₇₃×#2728	2
C₇₃×#2605	2
C₇₃×#2586	2
C₇₃×#2572	2
C₇₃×#2527	2
C₇₃×#2493	2
C₇₃×#2484	2
C₇₃×#2477	2
C₇₃×#2438	2
C₇₃×#2419	2
C₇₃×#2409	2
C₇₃×#2406	2
C₇₃×#2368	2
C₇₃×#2359	2
C₇₃×#2339	2
C₂×#391×C₇₃	2
C₇₃×#2290	2
#59941	73

Subgroups — C73×#59941 #32969345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59941 #32969345