Subgroups — C₇₃×#59938 #32969342

Order 18688.

1696 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2742	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2692	C₂	1	2	yes	maximal
3	C₇₃×#2677	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2607	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2607	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2589	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2588	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2586	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2580	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#2564	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#2522	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2520	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2492	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2465	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2374	C₂	1	2	yes	maximal
16	C₇₃×#2368	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2365	C₂	1	2	yes	maximal, complemented
18	C₄×C₂²⋊Q₈×C₇₃	C₂	1	2	yes	maximal, complemented
19	C₄×#123×C₇₃	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×#123×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
29	#400×C₇₃	C₂²	1	2	yes	—
30	#400×C₇₃	C₂²	1	2	yes	—
31	#400×C₇₃	C₂²	1	1	yes	characteristic
32	#399×C₇₃	C₂²	1	1	yes	characteristic
33	#399×C₇₃	C₂²	1	1	yes	characteristic
34	#399×C₇₃	C₂²	1	1	yes	characteristic
35	#399×C₇₃	C₂²	1	2	yes	—
36	#398×C₇₃	C₂²	1	2	yes	—
37	#398×C₇₃	C₂²	1	2	yes	—
38	#398×C₇₃	C₂²	1	2	yes	—
39	#396×C₇₃	C₂²	1	2	yes	—
40	#395×C₇₃	C₂²	1	2	yes	—
41	#395×C₇₃	C₂²	1	2	yes	—
42	#395×C₇₃	C₂²	1	2	yes	—
43	#395×C₇₃	C₂²	1	1	yes	characteristic
44	#393×C₇₃	C₂²	1	2	yes	—
45	#393×C₇₃	C₂²	1	1	yes	characteristic
46	#393×C₇₃	C₂²	1	1	yes	characteristic
47	#393×C₇₃	C₂²	1	1	yes	characteristic
48	#393×C₇₃	C₂²	1	2	yes	—
49	#391×C₇₃	C₂²	1	2	yes	—
50	#391×C₇₃	C₂²	1	2	yes	—
51	#391×C₇₃	C₂²	1	2	yes	—
52	#391×C₇₃	C₂²	1	2	yes	—
53	#391×C₇₃	C₂²	1	2	yes	—
54	#391×C₇₃	C₂²	1	2	yes	—
55	#391×C₇₃	C₂²	1	2	yes	—
56	#391×C₇₃	C₂²	1	2	yes	—
57	#390×C₇₃	C₂²	1	2	yes	—
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	2	yes	—
60	#389×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	#388×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	#387×C₇₃	C₂²	1	2	yes	—
78	#387×C₇₃	C₂²	1	2	yes	—
79	#387×C₇₃	C₂²	1	2	yes	—
80	#387×C₇₃	C₂²	1	2	yes	—
81	#387×C₇₃	C₂²	1	2	yes	—
82	#386×C₇₃	C₂²	1	1	yes	characteristic
83	#386×C₇₃	C₂²	1	2	yes	—
84	#385×C₇₃	C₂²	1	2	yes	—
85	#385×C₇₃	C₂²	1	1	yes	characteristic
86	#385×C₇₃	C₂²	1	2	yes	—
87	#385×C₇₃	C₂²	1	2	yes	—
88	#385×C₇₃	C₂²	1	2	yes	—
89	#382×C₇₃	C₂²	1	1	yes	characteristic
90	#381×C₇₃	C₂²	1	1	yes	characteristic
91	#380×C₇₃	C₂²	1	2	yes	—
92	#380×C₇₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×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×C₄⋊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	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
106	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₇₃	—	2	8	no	—
118	#123×C₇₃	Q₈	1	8	yes	complemented
119	C₂²⋊Q₈×C₇₃	—	2	8	no	—
120	C₂²⋊Q₈×C₇₃	—	2	8	no	—
121	C₂²⋊Q₈×C₇₃	—	4	2	no	—
122	C₄×Q₈×C₇₃	—	4	4	no	—
123	C₄×Q₈×C₇₃	—	4	2	no	—
124	C₄×D₄×C₇₃	—	4	2	no	—
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₇₃	—	4	2	no	—
161	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
170	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
172	#95×C₇₃	C₂³	1	2	yes	—
173	#95×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
189	#95×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
194	#95×C₇₃	C₂³	1	1	yes	characteristic
195	#95×C₇₃	C₂³	1	2	yes	—
196	#95×C₇₃	C₂³	1	1	yes	characteristic
197	#95×C₇₃	C₂³	1	2	yes	—
198	#95×C₇₃	C₂³	1	2	yes	—
199	#95×C₇₃	C₂³	1	2	yes	—
200	#95×C₇₃	C₂³	1	1	yes	characteristic
201	#95×C₇₃	C₂³	1	2	yes	—
202	#95×C₇₃	C₂³	1	2	yes	—
203	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
204	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₇₃	—	2	4	no	—
206	C₂×Q₈×C₇₃	—	2	4	no	—
207	C₂×Q₈×C₇₃	—	2	4	no	—
208	C₂×Q₈×C₇₃	—	2	4	no	—
209	C₂×Q₈×C₇₃	—	4	2	no	—
210	C₂×Q₈×C₇₃	—	4	1	no	—
211	C₂×Q₈×C₇₃	—	4	1	no	—
212	C₂×Q₈×C₇₃	—	4	2	no	—
213	C₂×Q₈×C₇₃	—	4	2	no	—
214	C₂×Q₈×C₇₃	—	4	2	no	—
215	C₂×D₄×C₇₃	—	4	1	no	—
216	C₂×D₄×C₇₃	—	4	1	no	—
217	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
218	C₂²×C₄×C₇₃	—	2	4	no	—
219	C₂²×C₄×C₇₃	—	2	2	no	—
220	C₂²×C₄×C₇₃	—	2	4	no	—
221	C₂²×C₄×C₇₃	—	2	2	no	—
222	C₂²×C₄×C₇₃	—	4	1	no	—
223	C₂²×C₄×C₇₃	—	4	1	no	—
224	C₂²×C₄×C₇₃	—	4	1	no	—
225	C₂²×C₄×C₇₃	—	4	2	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	C₂×Q₈	1	4	yes	—
230	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₇₃	—	2	4	no	—
248	C₄⋊C₄×C₇₃	—	2	4	no	—
249	C₄⋊C₄×C₇₃	—	2	4	no	—
250	C₄⋊C₄×C₇₃	—	2	4	no	—
251	C₄⋊C₄×C₇₃	—	2	4	no	—
252	C₄⋊C₄×C₇₃	—	2	4	no	—
253	C₄⋊C₄×C₇₃	—	2	4	no	—
254	C₄⋊C₄×C₇₃	—	2	4	no	—
255	C₄⋊C₄×C₇₃	—	2	4	no	—
256	C₄⋊C₄×C₇₃	—	4	2	no	—
257	C₄⋊C₄×C₇₃	—	4	2	no	—
258	C₄⋊C₄×C₇₃	—	4	2	no	—
259	C₄⋊C₄×C₇₃	—	4	2	no	—
260	C₄⋊C₄×C₇₃	—	4	2	no	—
261	C₄⋊C₄×C₇₃	—	4	2	no	—
262	C₄⋊C₄×C₇₃	—	4	2	no	—
263	C₄⋊C₄×C₇₃	—	4	1	no	—
264	C₄⋊C₄×C₇₃	—	4	2	no	—
265	C₄⋊C₄×C₇₃	—	4	1	no	—
266	C₄⋊C₄×C₇₃	—	4	1	no	—
267	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
268	C₄⋊C₄×C₇₃	#41	1	8	yes	—
269	C₂²⋊C₄×C₇₃	—	2	4	no	—
270	C₂²⋊C₄×C₇₃	—	2	4	no	—
271	C₂²⋊C₄×C₇₃	—	2	4	no	—
272	C₂²⋊C₄×C₇₃	—	2	4	no	—
273	C₂²⋊C₄×C₇₃	—	4	2	no	—
274	C₂²⋊C₄×C₇₃	—	4	2	no	—
275	C₂²⋊C₄×C₇₃	—	4	2	no	—
276	C₂²⋊C₄×C₇₃	—	4	1	no	—
277	C₂²⋊C₄×C₇₃	—	4	1	no	—
278	C₂²⋊C₄×C₇₃	—	4	1	no	—
279	C₂²⋊C₄×C₇₃	—	4	2	no	—
280	C₂²⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
281	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
282	C₄²×C₇₃	—	2	4	no	—
283	C₄²×C₇₃	—	2	4	no	—
284	C₄²×C₇₃	—	2	2	no	—
285	C₄²×C₇₃	—	4	2	no	—
286	C₄²×C₇₃	—	4	2	no	—
287	C₄²×C₇₃	—	4	2	no	—
288	C₄²×C₇₃	—	4	2	no	—
289	C₄²×C₇₃	—	4	2	no	—
290	C₄²×C₇₃	—	4	2	no	—
291	C₄²×C₇₃	—	4	2	no	—
292	C₄²×C₇₃	—	4	2	no	—
293	C₂³×C₇₃	—	2	2	no	—
294	C₂³×C₇₃	—	2	2	no	—
295	C₂³×C₇₃	—	2	1	no	—
296	C₂³×C₇₃	—	2	1	no	—
297	C₂³×C₇₃	—	2	2	no	—
298	C₂³×C₇₃	—	2	2	no	—
299	C₂³×C₇₃	—	2	1	no	—
300	C₂³×C₇₃	—	2	1	no	—
301	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
302	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
303	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
304	Q₈×C₇₃	—	4	8	no	—
305	Q₈×C₇₃	—	4	4	no	—
306	Q₈×C₇₃	—	8	4	no	—
307	Q₈×C₇₃	—	8	2	no	—
308	D₄×C₇₃	—	4	4	no	—
309	C₂×C₄×C₇₃	—	2	2	no	—
310	C₂×C₄×C₇₃	—	2	2	no	—
311	C₂×C₄×C₇₃	—	2	2	no	—
312	C₂×C₄×C₇₃	—	2	2	no	—
313	C₂×C₄×C₇₃	—	2	1	no	—
314	C₂×C₄×C₇₃	—	2	2	no	—
315	C₂×C₄×C₇₃	—	2	2	no	—
316	C₂×C₄×C₇₃	—	2	2	no	—
317	C₂×C₄×C₇₃	—	2	2	no	—
318	C₂×C₄×C₇₃	—	2	2	no	—
319	C₂×C₄×C₇₃	—	2	2	no	—
320	C₂×C₄×C₇₃	—	2	1	no	—
321	C₂×C₄×C₇₃	—	2	2	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	1	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	2	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	—	4	4	no	—
350	C₂×C₄×C₇₃	—	4	4	no	—
351	C₂×C₄×C₇₃	—	4	4	no	—
352	C₂×C₄×C₇₃	—	8	4	no	—
353	C₂×C₄×C₇₃	—	8	2	no	—
354	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
355	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
356	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
357	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
358	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₇₃	—	2	4	no	—
362	C₂²×C₇₃	—	2	4	no	—
363	C₂²×C₇₃	—	2	2	no	—
364	C₂²×C₇₃	—	2	2	no	—
365	C₂²×C₇₃	—	4	1	no	—
366	C₂²×C₇₃	—	4	1	no	—
367	C₂²×C₇₃	—	4	2	no	—
368	C₂²×C₇₃	—	4	2	no	—
369	C₂²×C₇₃	—	4	1	no	—
370	C₂²×C₇₃	—	4	1	no	—
371	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
372	C₂²×C₇₃	C₂²×#41	1	2	yes	—
373	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₇₃	#585	1	2	yes	—
375	C₂²×C₇₃	#585	1	1	yes	characteristic
376	C₄×C₇₃	—	2	4	no	—
377	C₄×C₇₃	—	2	4	no	—
378	C₄×C₇₃	—	2	4	no	—
379	C₄×C₇₃	—	2	4	no	—
380	C₄×C₇₃	—	2	2	no	—
381	C₄×C₇₃	—	2	4	no	—
382	C₄×C₇₃	—	2	2	no	—
383	C₄×C₇₃	—	4	2	no	—
384	C₄×C₇₃	—	4	1	no	—
385	C₄×C₇₃	—	4	2	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	—	4	1	no	—
391	C₄×C₇₃	—	4	1	no	—
392	C₄×C₇₃	—	4	2	no	—
393	#59938	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂×C₇₃	—	4	2	no	—
395	C₂×C₇₃	—	4	2	no	—
396	C₂×C₇₃	Q₈×#41	1	2	yes	—
397	C₂×C₇₃	#3481	1	1	yes	characteristic
398	C₂×C₇₃	#3501	1	1	yes	characteristic
399	C₂×C₇₃	#3510	1	2	yes	—
400	C₂×C₇₃	#3533	1	1	yes	characteristic
401	#2742	C₂×C₇₃	1	1	yes	characteristic, complemented
402	#2692	C₂×C₇₃	1	2	yes	—
403	#2677	C₂×C₇₃	1	1	yes	characteristic, complemented
404	#2607	C₂×C₇₃	1	1	yes	characteristic, complemented
405	#2607	C₂×C₇₃	1	1	yes	characteristic, complemented
406	#2589	C₂×C₇₃	1	2	yes	complemented
407	#2588	C₂×C₇₃	1	2	yes	complemented
408	#2586	C₂×C₇₃	1	2	yes	complemented
409	#2580	C₂×C₇₃	1	1	yes	characteristic
410	#2564	C₂×C₇₃	1	1	yes	characteristic
411	#2522	C₂×C₇₃	1	2	yes	complemented
412	#2520	C₂×C₇₃	1	2	yes	complemented
413	#2492	C₂×C₇₃	1	2	yes	complemented
414	#2465	C₂×C₇₃	1	2	yes	complemented
415	#2374	C₂×C₇₃	1	2	yes	—
416	#2368	C₂×C₇₃	1	2	yes	complemented
417	#2365	C₂×C₇₃	1	2	yes	complemented
418	C₄×C₂²⋊Q₈	C₂×C₇₃	1	2	yes	complemented
419	C₄×#123	C₂×C₇₃	1	1	yes	characteristic
420	C₇₃	#59938	1	1	yes	characteristic, direct product factor, Sylow
421	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
422	C₂×#123	C₂²×C₇₃	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
429	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
430	#400	C₂²×C₇₃	1	1	yes	characteristic
431	#400	C₂²×C₇₃	1	2	yes	—
432	#400	C₂²×C₇₃	1	2	yes	—
433	#399	C₂²×C₇₃	1	1	yes	characteristic
434	#399	C₂²×C₇₃	1	1	yes	characteristic
435	#399	C₂²×C₇₃	1	1	yes	characteristic
436	#399	C₂²×C₇₃	1	2	yes	—
437	#398	C₂²×C₇₃	1	2	yes	—
438	#398	C₂²×C₇₃	1	2	yes	—
439	#398	C₂²×C₇₃	1	2	yes	—
440	#396	C₂²×C₇₃	1	2	yes	—
441	#395	C₂²×C₇₃	1	1	yes	characteristic
442	#395	C₂²×C₇₃	1	2	yes	—
443	#395	C₂²×C₇₃	1	2	yes	—
444	#395	C₂²×C₇₃	1	2	yes	—
445	#393	C₂²×C₇₃	1	1	yes	characteristic
446	#393	C₂²×C₇₃	1	1	yes	characteristic
447	#393	C₂²×C₇₃	1	1	yes	characteristic
448	#393	C₂²×C₇₃	1	2	yes	—
449	#393	C₂²×C₇₃	1	2	yes	—
450	#391	C₂²×C₇₃	1	2	yes	—
451	#391	C₂²×C₇₃	1	2	yes	—
452	#391	C₂²×C₇₃	1	2	yes	—
453	#391	C₂²×C₇₃	1	2	yes	—
454	#391	C₂²×C₇₃	1	2	yes	—
455	#391	C₂²×C₇₃	1	2	yes	—
456	#391	C₂²×C₇₃	1	2	yes	—
457	#391	C₂²×C₇₃	1	2	yes	—
458	#390	C₂²×C₇₃	1	2	yes	—
459	#389	C₂²×C₇₃	1	2	yes	—
460	#389	C₂²×C₇₃	1	2	yes	—
461	#389	C₂²×C₇₃	1	2	yes	—
462	#389	C₂²×C₇₃	1	2	yes	—
463	#388	C₂²×C₇₃	1	2	yes	—
464	#388	C₂²×C₇₃	1	2	yes	—
465	#388	C₂²×C₇₃	1	2	yes	—
466	#388	C₂²×C₇₃	1	2	yes	—
467	#388	C₂²×C₇₃	1	2	yes	—
468	#387	C₂²×C₇₃	1	2	yes	—
469	#387	C₂²×C₇₃	1	2	yes	—
470	#387	C₂²×C₇₃	1	2	yes	—
471	#387	C₂²×C₇₃	1	2	yes	—
472	#387	C₂²×C₇₃	1	2	yes	—
473	#387	C₂²×C₇₃	1	2	yes	—
474	#387	C₂²×C₇₃	1	2	yes	—
475	#387	C₂²×C₇₃	1	2	yes	—
476	#387	C₂²×C₇₃	1	2	yes	—
477	#387	C₂²×C₇₃	1	2	yes	—
478	#387	C₂²×C₇₃	1	2	yes	—
479	#387	C₂²×C₇₃	1	2	yes	—
480	#387	C₂²×C₇₃	1	2	yes	—
481	#387	C₂²×C₇₃	1	2	yes	—
482	#387	C₂²×C₇₃	1	2	yes	—
483	#386	C₂²×C₇₃	1	2	yes	—
484	#386	C₂²×C₇₃	1	1	yes	characteristic
485	#385	C₂²×C₇₃	1	2	yes	—
486	#385	C₂²×C₇₃	1	2	yes	—
487	#385	C₂²×C₇₃	1	2	yes	—
488	#385	C₂²×C₇₃	1	2	yes	—
489	#385	C₂²×C₇₃	1	1	yes	characteristic
490	#382	C₂²×C₇₃	1	1	yes	characteristic
491	#381	C₂²×C₇₃	1	1	yes	characteristic
492	#380	C₂²×C₇₃	1	2	yes	—
493	#380	C₂²×C₇₃	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
507	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
508	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
509	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
511	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
518	C₄⋊Q₈	—	2	8	no	—
519	#123	Q₈×C₇₃	1	8	yes	complemented
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	—	2	8	no	—
522	C₂²⋊Q₈	—	4	2	no	—
523	C₄×Q₈	—	4	4	no	—
524	C₄×Q₈	—	4	2	no	—
525	C₄×D₄	—	4	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
561	C₂×C₄²	—	4	2	no	—
562	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
573	#95	C₂³×C₇₃	1	2	yes	—
574	#95	C₂³×C₇₃	1	1	yes	characteristic
575	#95	C₂³×C₇₃	1	1	yes	characteristic
576	#95	C₂³×C₇₃	1	2	yes	—
577	#95	C₂³×C₇₃	1	2	yes	—
578	#95	C₂³×C₇₃	1	2	yes	—
579	#95	C₂³×C₇₃	1	2	yes	—
580	#95	C₂³×C₇₃	1	2	yes	—
581	#95	C₂³×C₇₃	1	2	yes	—
582	#95	C₂³×C₇₃	1	2	yes	—
583	#95	C₂³×C₇₃	1	2	yes	—
584	#95	C₂³×C₇₃	1	2	yes	—
585	#95	C₂³×C₇₃	1	2	yes	—
586	#95	C₂³×C₇₃	1	2	yes	—
587	#95	C₂³×C₇₃	1	2	yes	—
588	#95	C₂³×C₇₃	1	2	yes	—
589	#95	C₂³×C₇₃	1	2	yes	—
590	#95	C₂³×C₇₃	1	2	yes	—
591	#95	C₂³×C₇₃	1	2	yes	—
592	#95	C₂³×C₇₃	1	2	yes	—
593	#95	C₂³×C₇₃	1	2	yes	—
594	#95	C₂³×C₇₃	1	2	yes	—
595	#95	C₂³×C₇₃	1	2	yes	—
596	#95	C₂³×C₇₃	1	1	yes	characteristic
597	#95	C₂³×C₇₃	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	1	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×D₄	—	4	1	no	—
617	C₂×D₄	—	4	1	no	—
618	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	4	1	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
669	C₄⋊C₄	#41×C₇₃	1	8	yes	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
682	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	2	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	2	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	2	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
703	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
704	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
705	Q₈	—	4	8	no	—
706	Q₈	—	4	4	no	—
707	Q₈	—	8	4	no	—
708	Q₈	—	8	2	no	—
709	D₄	—	4	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	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	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	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
756	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
757	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
758	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
759	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
760	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
761	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
773	C₂²	C₂²×#41×C₇₃	1	2	yes	—
774	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
775	C₂²	#585×C₇₃	1	2	yes	—
776	C₂²	#585×C₇₃	1	1	yes	characteristic
777	C₄	—	2	4	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	4	2	no	—
796	C₂	Q₈×#41×C₇₃	1	2	yes	—
797	C₂	C₇₃×#3481	1	1	yes	characteristic
798	C₂	C₇₃×#3501	1	1	yes	characteristic
799	C₂	C₇₃×#3510	1	2	yes	—
800	C₂	C₇₃×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂³
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×#2742	C₂	semidirect
3. C₇₃×#2677	C₂	semidirect
4. C₇₃×#2607	C₂	semidirect
5. C₇₃×#2607	C₂	semidirect
6. C₇₃×#2589	C₂	semidirect
7. C₇₃×#2588	C₂	semidirect
8. C₇₃×#2586	C₂	semidirect
11. C₇₃×#2522	C₂	semidirect
12. C₇₃×#2520	C₂	semidirect
13. C₇₃×#2492	C₂	semidirect
14. C₇₃×#2465	C₂	semidirect
16. C₇₃×#2368	C₂	semidirect
17. C₇₃×#2365	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₇₃	C₂	semidirect
118. #123×C₇₃	Q₈	semidirect
393. #59938	C₇₃	direct (N × H)
401. #2742	C₂×C₇₃	semidirect
403. #2677	C₂×C₇₃	semidirect
404. #2607	C₂×C₇₃	semidirect
405. #2607	C₂×C₇₃	semidirect
406. #2589	C₂×C₇₃	semidirect
407. #2588	C₂×C₇₃	semidirect
408. #2586	C₂×C₇₃	semidirect
411. #2522	C₂×C₇₃	semidirect
412. #2520	C₂×C₇₃	semidirect
413. #2492	C₂×C₇₃	semidirect
414. #2465	C₂×C₇₃	semidirect
416. #2368	C₂×C₇₃	semidirect
417. #2365	C₂×C₇₃	semidirect
418. C₄×C₂²⋊Q₈	C₂×C₇₃	semidirect
420. C₇₃	#59938	direct (N × H)
519. #123	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2742	2
C₇₃×#2692	2
C₇₃×#2677	2
C₇₃×#2607	2
C₇₃×#2589	2
C₇₃×#2588	2
C₇₃×#2586	2
C₇₃×#2580	2
C₇₃×#2564	2
C₇₃×#2522	2
C₇₃×#2520	2
C₇₃×#2492	2
C₇₃×#2465	2
C₇₃×#2374	2
C₇₃×#2368	2
C₇₃×#2365	2
C₄×C₂²⋊Q₈×C₇₃	2
C₄×#123×C₇₃	2
#59938	73

Subgroups — C73×#59938 #32969342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59938 #32969342