Subgroups — C₇₃×#59656 #32969060

Order 18688.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#552×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2719	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2674	C₂	1	2	yes	maximal
5	C₇₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2558	C₂	1	2	yes	maximal
7	C₇₃×#2550	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2536	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#2519	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2475	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2469	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2362	C₂	1	2	yes	maximal, complemented
20	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic
24	#557×C₇₃	—	2	8	no	—
25	#552×C₇₃	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
28	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#126×C₇₃	C₂²	1	2	yes	—
30	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#125×C₇₃	C₂²	1	2	yes	—
32	C₂×#125×C₇₃	C₂²	1	2	yes	—
33	C₂×#125×C₇₃	C₂²	1	2	yes	—
34	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#123×C₇₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₇₃	C₂²	1	2	yes	—
51	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
52	#400×C₇₃	C₂²	1	2	yes	—
53	#400×C₇₃	C₂²	1	2	yes	—
54	#400×C₇₃	C₂²	1	2	yes	—
55	#399×C₇₃	C₂²	1	2	yes	—
56	#398×C₇₃	C₂²	1	2	yes	—
57	#398×C₇₃	C₂²	1	2	yes	—
58	#398×C₇₃	C₂²	1	2	yes	—
59	#398×C₇₃	C₂²	1	2	yes	—
60	#397×C₇₃	C₂²	1	2	yes	—
61	#396×C₇₃	C₂²	1	2	yes	—
62	#396×C₇₃	C₂²	1	2	yes	—
63	#396×C₇₃	C₂²	1	2	yes	—
64	#395×C₇₃	C₂²	1	2	yes	—
65	#395×C₇₃	C₂²	1	2	yes	—
66	#394×C₇₃	C₂²	1	2	yes	—
67	#393×C₇₃	C₂²	1	2	yes	—
68	#391×C₇₃	C₂²	1	1	yes	characteristic
69	#391×C₇₃	C₂²	1	1	yes	characteristic
70	#391×C₇₃	C₂²	1	2	yes	—
71	#391×C₇₃	C₂²	1	1	yes	characteristic
72	#391×C₇₃	C₂²	1	1	yes	characteristic
73	#391×C₇₃	C₂²	1	1	yes	characteristic
74	#390×C₇₃	C₂²	1	1	yes	characteristic
75	#389×C₇₃	C₂²	1	1	yes	characteristic
76	#389×C₇₃	C₂²	1	1	yes	characteristic
77	#389×C₇₃	C₂²	1	2	yes	—
78	#389×C₇₃	C₂²	1	1	yes	characteristic
79	#389×C₇₃	C₂²	1	1	yes	characteristic
80	#389×C₇₃	C₂²	1	2	yes	—
81	#389×C₇₃	C₂²	1	2	yes	—
82	#389×C₇₃	C₂²	1	2	yes	—
83	#389×C₇₃	C₂²	1	2	yes	—
84	#389×C₇₃	C₂²	1	2	yes	—
85	#388×C₇₃	C₂²	1	1	yes	characteristic
86	#388×C₇₃	C₂²	1	2	yes	—
87	#388×C₇₃	C₂²	1	2	yes	—
88	#388×C₇₃	C₂²	1	2	yes	—
89	#388×C₇₃	C₂²	1	1	yes	characteristic
90	#388×C₇₃	C₂²	1	2	yes	—
91	#388×C₇₃	C₂²	1	2	yes	—
92	#388×C₇₃	C₂²	1	2	yes	—
93	#388×C₇₃	C₂²	1	1	yes	characteristic
94	#388×C₇₃	C₂²	1	2	yes	—
95	#388×C₇₃	C₂²	1	1	yes	characteristic
96	#388×C₇₃	C₂²	1	2	yes	—
97	#387×C₇₃	C₂²	1	2	yes	—
98	#387×C₇₃	C₂²	1	2	yes	—
99	#387×C₇₃	C₂²	1	2	yes	—
100	#387×C₇₃	C₂²	1	2	yes	—
101	#387×C₇₃	C₂²	1	2	yes	—
102	#387×C₇₃	C₂²	1	2	yes	—
103	#387×C₇₃	C₂²	1	2	yes	—
104	#385×C₇₃	C₂²	1	2	yes	—
105	#385×C₇₃	C₂²	1	2	yes	—
106	#384×C₇₃	C₂²	1	1	yes	characteristic
107	#382×C₇₃	C₂²	1	1	yes	characteristic
108	#382×C₇₃	C₂²	1	2	yes	—
109	#382×C₇₃	C₂²	1	1	yes	characteristic
110	#380×C₇₃	C₂²	1	1	yes	characteristic
111	#380×C₇₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
124	C₄³×C₇₃	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
127	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₇₃	—	2	4	no	—
134	C₄⋊Q₈×C₇₃	—	2	8	no	—
135	C₄⋊Q₈×C₇₃	—	2	4	no	—
136	#126×C₇₃	—	2	8	no	—
137	#125×C₇₃	—	2	8	no	—
138	#125×C₇₃	—	2	8	no	—
139	#125×C₇₃	—	2	4	no	—
140	#125×C₇₃	—	2	8	no	—
141	#125×C₇₃	D₄	1	8	yes	—
142	#124×C₇₃	—	2	4	no	—
143	#123×C₇₃	—	2	8	no	—
144	C₂²⋊Q₈×C₇₃	—	2	4	no	—
145	C₂²⋊Q₈×C₇₃	—	2	4	no	—
146	C₂²⋊Q₈×C₇₃	—	2	4	no	—
147	C₂²⋊Q₈×C₇₃	—	2	4	no	—
148	C₂²⋊Q₈×C₇₃	—	2	8	no	—
149	C₄×Q₈×C₇₃	—	2	4	no	—
150	C₄×Q₈×C₇₃	—	2	8	no	—
151	C₄×Q₈×C₇₃	—	2	4	no	—
152	C₄×Q₈×C₇₃	—	2	4	no	—
153	C₄×Q₈×C₇₃	—	2	4	no	—
154	C₄×Q₈×C₇₃	—	2	4	no	—
155	C₄×D₄×C₇₃	—	2	4	no	—
156	#117×C₇₃	—	2	4	no	—
157	#117×C₇₃	—	2	8	no	—
158	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
224	#95×C₇₃	C₂³	1	2	yes	—
225	#95×C₇₃	C₂³	1	1	yes	characteristic
226	#95×C₇₃	C₂³	1	1	yes	characteristic
227	#95×C₇₃	C₂³	1	1	yes	characteristic
228	#95×C₇₃	C₂³	1	1	yes	characteristic
229	#95×C₇₃	C₂³	1	1	yes	characteristic
230	#95×C₇₃	C₂³	1	1	yes	characteristic
231	#95×C₇₃	C₂³	1	2	yes	—
232	#95×C₇₃	C₂³	1	1	yes	characteristic
233	#95×C₇₃	C₂³	1	1	yes	characteristic
234	#95×C₇₃	C₂³	1	2	yes	—
235	#95×C₇₃	C₂³	1	2	yes	—
236	#95×C₇₃	C₂³	1	2	yes	—
237	#95×C₇₃	C₂³	1	2	yes	—
238	#95×C₇₃	C₂³	1	2	yes	—
239	#95×C₇₃	C₂³	1	2	yes	—
240	#95×C₇₃	C₂³	1	2	yes	—
241	#95×C₇₃	C₂³	1	2	yes	—
242	#95×C₇₃	C₂³	1	2	yes	—
243	#95×C₇₃	C₂³	1	2	yes	—
244	#95×C₇₃	C₂³	1	2	yes	—
245	#95×C₇₃	C₂³	1	2	yes	—
246	#95×C₇₃	C₂³	1	2	yes	—
247	#95×C₇₃	C₂³	1	2	yes	—
248	#95×C₇₃	C₂³	1	2	yes	—
249	#95×C₇₃	C₂³	1	2	yes	—
250	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₇₃	—	2	2	no	—
253	C₂×Q₈×C₇₃	—	2	2	no	—
254	C₂×Q₈×C₇₃	—	2	4	no	—
255	C₂×Q₈×C₇₃	—	2	2	no	—
256	C₂×Q₈×C₇₃	—	2	4	no	—
257	C₂×Q₈×C₇₃	—	2	2	no	—
258	C₂×Q₈×C₇₃	—	2	2	no	—
259	C₂×Q₈×C₇₃	—	2	2	no	—
260	C₂×Q₈×C₇₃	—	2	2	no	—
261	C₂×Q₈×C₇₃	—	4	2	no	—
262	C₂×Q₈×C₇₃	—	4	1	no	—
263	C₂×Q₈×C₇₃	#41	1	4	yes	—
264	C₂×D₄×C₇₃	—	2	2	no	—
265	C₂×D₄×C₇₃	—	2	2	no	—
266	C₂×D₄×C₇₃	—	4	1	no	—
267	C₂²×C₄×C₇₃	—	2	4	no	—
268	C₂²×C₄×C₇₃	—	2	4	no	—
269	C₂²×C₄×C₇₃	—	2	2	no	—
270	C₂²×C₄×C₇₃	—	2	2	no	—
271	C₂²×C₄×C₇₃	—	2	2	no	—
272	C₂²×C₄×C₇₃	—	2	2	no	—
273	C₂²×C₄×C₇₃	—	2	2	no	—
274	C₂²×C₄×C₇₃	—	2	2	no	—
275	C₂²×C₄×C₇₃	—	4	2	no	—
276	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₇₃	—	2	2	no	—
298	C₄⋊C₄×C₇₃	—	2	4	no	—
299	C₄⋊C₄×C₇₃	—	2	4	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	2	no	—
302	C₄⋊C₄×C₇₃	—	2	4	no	—
303	C₄⋊C₄×C₇₃	—	2	4	no	—
304	C₄⋊C₄×C₇₃	—	2	2	no	—
305	C₄⋊C₄×C₇₃	—	2	4	no	—
306	C₄⋊C₄×C₇₃	—	2	2	no	—
307	C₄⋊C₄×C₇₃	—	2	4	no	—
308	C₄⋊C₄×C₇₃	—	2	4	no	—
309	C₄⋊C₄×C₇₃	—	2	2	no	—
310	C₄⋊C₄×C₇₃	—	2	4	no	—
311	C₄⋊C₄×C₇₃	—	2	4	no	—
312	C₄⋊C₄×C₇₃	—	2	4	no	—
313	C₄⋊C₄×C₇₃	—	2	4	no	—
314	C₄⋊C₄×C₇₃	—	2	2	no	—
315	C₄⋊C₄×C₇₃	—	2	2	no	—
316	C₄⋊C₄×C₇₃	—	2	4	no	—
317	C₄⋊C₄×C₇₃	—	2	4	no	—
318	C₄⋊C₄×C₇₃	—	2	4	no	—
319	C₄⋊C₄×C₇₃	—	2	4	no	—
320	C₄⋊C₄×C₇₃	—	2	4	no	—
321	C₄⋊C₄×C₇₃	—	2	4	no	—
322	C₄⋊C₄×C₇₃	—	2	4	no	—
323	C₄⋊C₄×C₇₃	—	4	2	no	—
324	C₄⋊C₄×C₇₃	—	4	2	no	—
325	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
326	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
327	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
328	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
329	C₂²⋊C₄×C₇₃	—	2	4	no	—
330	C₂²⋊C₄×C₇₃	—	2	2	no	—
331	C₂²⋊C₄×C₇₃	—	2	2	no	—
332	C₂²⋊C₄×C₇₃	—	2	4	no	—
333	C₂²⋊C₄×C₇₃	—	2	4	no	—
334	C₂²⋊C₄×C₇₃	—	2	2	no	—
335	C₂²⋊C₄×C₇₃	—	2	4	no	—
336	C₂²⋊C₄×C₇₃	—	2	4	no	—
337	C₂²⋊C₄×C₇₃	—	2	4	no	—
338	C₂²⋊C₄×C₇₃	—	2	2	no	—
339	C₂²⋊C₄×C₇₃	—	2	2	no	—
340	C₂²⋊C₄×C₇₃	—	2	2	no	—
341	C₂²⋊C₄×C₇₃	—	2	2	no	—
342	C₂²⋊C₄×C₇₃	—	2	2	no	—
343	C₂²⋊C₄×C₇₃	—	2	2	no	—
344	C₂²⋊C₄×C₇₃	—	4	2	no	—
345	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
346	C₄²×C₇₃	—	2	4	no	—
347	C₄²×C₇₃	—	2	4	no	—
348	C₄²×C₇₃	—	2	4	no	—
349	C₄²×C₇₃	—	2	4	no	—
350	C₄²×C₇₃	—	2	2	no	—
351	C₄²×C₇₃	—	2	4	no	—
352	C₄²×C₇₃	—	2	2	no	—
353	C₄²×C₇₃	—	2	2	no	—
354	C₄²×C₇₃	—	2	2	no	—
355	C₄²×C₇₃	—	2	2	no	—
356	C₄²×C₇₃	—	2	4	no	—
357	C₄²×C₇₃	—	2	2	no	—
358	C₄²×C₇₃	—	2	2	no	—
359	C₄²×C₇₃	—	4	1	no	—
360	C₄²×C₇₃	—	4	2	no	—
361	C₄²×C₇₃	C₂×D₄	1	4	yes	—
362	C₂³×C₇₃	—	2	1	no	—
363	C₂³×C₇₃	—	2	1	no	—
364	C₂³×C₇₃	—	2	1	no	—
365	C₂³×C₇₃	—	2	1	no	—
366	C₂³×C₇₃	—	2	1	no	—
367	C₂³×C₇₃	—	2	1	no	—
368	C₂³×C₇₃	—	2	1	no	—
369	C₂³×C₇₃	—	2	1	no	—
370	C₂³×C₇₃	—	2	1	no	—
371	C₂³×C₇₃	—	2	1	no	—
372	C₂³×C₇₃	—	2	1	no	—
373	C₂³×C₇₃	—	2	1	no	—
374	C₂³×C₇₃	—	2	1	no	—
375	C₂³×C₇₃	C₂×#41	1	2	yes	—
376	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
377	Q₈×C₇₃	—	2	8	no	—
378	Q₈×C₇₃	—	4	8	no	—
379	Q₈×C₇₃	—	4	4	no	—
380	Q₈×C₇₃	—	4	4	no	—
381	D₄×C₇₃	—	4	4	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	1	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	1	no	—
389	C₂×C₄×C₇₃	—	2	1	no	—
390	C₂×C₄×C₇₃	—	2	2	no	—
391	C₂×C₄×C₇₃	—	2	1	no	—
392	C₂×C₄×C₇₃	—	2	1	no	—
393	C₂×C₄×C₇₃	—	2	2	no	—
394	C₂×C₄×C₇₃	—	2	2	no	—
395	C₂×C₄×C₇₃	—	2	1	no	—
396	C₂×C₄×C₇₃	—	2	1	no	—
397	C₂×C₄×C₇₃	—	2	2	no	—
398	C₂×C₄×C₇₃	—	2	1	no	—
399	C₂×C₄×C₇₃	—	2	1	no	—
400	C₂×C₄×C₇₃	—	2	1	no	—
401	C₂×C₄×C₇₃	—	2	1	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	2	no	—
404	C₂×C₄×C₇₃	—	2	1	no	—
405	C₂×C₄×C₇₃	—	2	1	no	—
406	C₂×C₄×C₇₃	—	2	2	no	—
407	C₂×C₄×C₇₃	—	2	1	no	—
408	C₂×C₄×C₇₃	—	2	1	no	—
409	C₂×C₄×C₇₃	—	2	1	no	—
410	C₂×C₄×C₇₃	—	2	2	no	—
411	C₂×C₄×C₇₃	—	2	2	no	—
412	C₂×C₄×C₇₃	—	2	2	no	—
413	C₂×C₄×C₇₃	—	2	2	no	—
414	C₂×C₄×C₇₃	—	2	1	no	—
415	C₂×C₄×C₇₃	—	2	1	no	—
416	C₂×C₄×C₇₃	—	2	2	no	—
417	C₂×C₄×C₇₃	—	2	2	no	—
418	C₂×C₄×C₇₃	—	2	2	no	—
419	C₂×C₄×C₇₃	—	2	1	no	—
420	C₂×C₄×C₇₃	—	2	1	no	—
421	C₂×C₄×C₇₃	—	2	1	no	—
422	C₂×C₄×C₇₃	—	2	1	no	—
423	C₂×C₄×C₇₃	—	2	1	no	—
424	C₂×C₄×C₇₃	—	2	1	no	—
425	C₂×C₄×C₇₃	—	2	2	no	—
426	C₂×C₄×C₇₃	—	2	1	no	—
427	C₂×C₄×C₇₃	—	2	1	no	—
428	C₂×C₄×C₇₃	—	2	2	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	2	2	no	—
431	C₂×C₄×C₇₃	—	2	2	no	—
432	C₂×C₄×C₇₃	—	2	1	no	—
433	C₂×C₄×C₇₃	—	4	8	no	—
434	C₂×C₄×C₇₃	—	4	4	no	—
435	C₂×C₄×C₇₃	—	4	4	no	—
436	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
438	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
439	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
443	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
445	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
446	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
447	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
448	C₂²×C₇₃	—	2	2	no	—
449	C₂²×C₇₃	—	2	2	no	—
450	C₂²×C₇₃	—	2	2	no	—
451	C₂²×C₇₃	—	4	1	no	—
452	C₂²×C₇₃	—	4	1	no	—
453	C₂²×C₇₃	—	4	1	no	—
454	C₂²×C₇₃	—	4	1	no	—
455	C₂²×C₇₃	—	4	1	no	—
456	C₂²×C₇₃	—	4	1	no	—
457	C₂²×C₇₃	—	4	1	no	—
458	C₂²×C₇₃	—	4	1	no	—
459	C₂²×C₇₃	—	4	1	no	—
460	C₂²×C₇₃	—	4	1	no	—
461	C₂²×C₇₃	—	4	1	no	—
462	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
463	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
466	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×C₇₃	#585	1	1	yes	characteristic
469	C₄×C₇₃	—	2	4	no	—
470	C₄×C₇₃	—	2	4	no	—
471	C₄×C₇₃	—	2	2	no	—
472	C₄×C₇₃	—	2	2	no	—
473	C₄×C₇₃	—	2	2	no	—
474	C₄×C₇₃	—	2	2	no	—
475	C₄×C₇₃	—	2	4	no	—
476	C₄×C₇₃	—	2	2	no	—
477	C₄×C₇₃	—	2	2	no	—
478	C₄×C₇₃	—	4	1	no	—
479	C₄×C₇₃	—	4	1	no	—
480	C₄×C₇₃	—	4	2	no	—
481	C₄×C₇₃	—	4	2	no	—
482	C₄×C₇₃	—	4	1	no	—
483	C₄×C₇₃	—	4	2	no	—
484	C₄×C₇₃	—	4	2	no	—
485	C₄×C₇₃	—	4	1	no	—
486	C₄×C₇₃	—	4	1	no	—
487	C₄×C₇₃	—	4	1	no	—
488	C₄×C₇₃	—	4	2	no	—
489	C₄×C₇₃	#548	1	4	yes	—
490	#59656	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₇₃	—	4	2	no	—
492	C₂×C₇₃	—	8	1	no	—
493	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
494	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
495	C₂×C₇₃	#3482	1	1	yes	characteristic
496	C₂×C₇₃	#3499	1	1	yes	characteristic
497	C₂×C₇₃	#3509	1	1	yes	characteristic
498	C₂×C₇₃	#3516	1	1	yes	characteristic
499	C₂×C₇₃	#3563	1	1	yes	characteristic
500	C₂×#557	C₂×C₇₃	1	1	yes	characteristic, complemented
501	C₂×#552	C₂×C₇₃	1	1	yes	characteristic
502	#2719	C₂×C₇₃	1	2	yes	complemented
503	#2674	C₂×C₇₃	1	2	yes	—
504	#2581	C₂×C₇₃	1	1	yes	characteristic, complemented
505	#2558	C₂×C₇₃	1	2	yes	—
506	#2550	C₂×C₇₃	1	2	yes	complemented
507	#2536	C₂×C₇₃	1	1	yes	characteristic
508	#2519	C₂×C₇₃	1	2	yes	complemented
509	#2492	C₂×C₇₃	1	1	yes	characteristic, complemented
510	#2489	C₂×C₇₃	1	1	yes	characteristic, complemented
511	#2475	C₂×C₇₃	1	2	yes	complemented
512	#2469	C₂×C₇₃	1	2	yes	complemented
513	#2441	C₂×C₇₃	1	1	yes	characteristic, complemented
514	#2440	C₂×C₇₃	1	1	yes	characteristic, complemented
515	#2429	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#2429	C₂×C₇₃	1	1	yes	characteristic, complemented
517	#2362	C₂×C₇₃	1	1	yes	characteristic, complemented
518	#2362	C₂×C₇₃	1	2	yes	complemented
519	#2360	C₂×C₇₃	1	1	yes	characteristic, complemented
520	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
521	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
522	C₄×#124	C₂×C₇₃	1	1	yes	characteristic
523	C₇₃	#59656	1	1	yes	characteristic, direct product factor, Sylow
524	#557	—	2	8	no	—
525	#552	—	2	8	no	—
526	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
527	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
528	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
529	C₂×#126	C₂²×C₇₃	1	2	yes	—
530	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×#125	C₂²×C₇₃	1	2	yes	—
532	C₂×#125	C₂²×C₇₃	1	2	yes	—
533	C₂×#125	C₂²×C₇₃	1	2	yes	—
534	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
535	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
536	C₂×#123	C₂²×C₇₃	1	2	yes	—
537	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
538	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
539	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
541	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
542	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
543	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
544	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
545	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
546	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
547	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
548	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
549	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
550	C₂×#117	C₂²×C₇₃	1	2	yes	—
551	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
552	#400	C₂²×C₇₃	1	2	yes	—
553	#400	C₂²×C₇₃	1	2	yes	—
554	#400	C₂²×C₇₃	1	2	yes	—
555	#399	C₂²×C₇₃	1	2	yes	—
556	#398	C₂²×C₇₃	1	2	yes	—
557	#398	C₂²×C₇₃	1	2	yes	—
558	#398	C₂²×C₇₃	1	2	yes	—
559	#398	C₂²×C₇₃	1	2	yes	—
560	#397	C₂²×C₇₃	1	2	yes	—
561	#396	C₂²×C₇₃	1	2	yes	—
562	#396	C₂²×C₇₃	1	2	yes	—
563	#396	C₂²×C₇₃	1	2	yes	—
564	#395	C₂²×C₇₃	1	2	yes	—
565	#395	C₂²×C₇₃	1	2	yes	—
566	#394	C₂²×C₇₃	1	2	yes	—
567	#393	C₂²×C₇₃	1	2	yes	—
568	#391	C₂²×C₇₃	1	1	yes	characteristic
569	#391	C₂²×C₇₃	1	1	yes	characteristic
570	#391	C₂²×C₇₃	1	1	yes	characteristic
571	#391	C₂²×C₇₃	1	1	yes	characteristic
572	#391	C₂²×C₇₃	1	2	yes	—
573	#391	C₂²×C₇₃	1	1	yes	characteristic
574	#390	C₂²×C₇₃	1	1	yes	characteristic
575	#389	C₂²×C₇₃	1	1	yes	characteristic
576	#389	C₂²×C₇₃	1	1	yes	characteristic
577	#389	C₂²×C₇₃	1	2	yes	—
578	#389	C₂²×C₇₃	1	2	yes	—
579	#389	C₂²×C₇₃	1	1	yes	characteristic
580	#389	C₂²×C₇₃	1	1	yes	characteristic
581	#389	C₂²×C₇₃	1	2	yes	—
582	#389	C₂²×C₇₃	1	2	yes	—
583	#389	C₂²×C₇₃	1	2	yes	—
584	#389	C₂²×C₇₃	1	2	yes	—
585	#388	C₂²×C₇₃	1	1	yes	characteristic
586	#388	C₂²×C₇₃	1	2	yes	—
587	#388	C₂²×C₇₃	1	2	yes	—
588	#388	C₂²×C₇₃	1	2	yes	—
589	#388	C₂²×C₇₃	1	2	yes	—
590	#388	C₂²×C₇₃	1	2	yes	—
591	#388	C₂²×C₇₃	1	2	yes	—
592	#388	C₂²×C₇₃	1	1	yes	characteristic
593	#388	C₂²×C₇₃	1	2	yes	—
594	#388	C₂²×C₇₃	1	1	yes	characteristic
595	#388	C₂²×C₇₃	1	2	yes	—
596	#388	C₂²×C₇₃	1	1	yes	characteristic
597	#387	C₂²×C₇₃	1	2	yes	—
598	#387	C₂²×C₇₃	1	2	yes	—
599	#387	C₂²×C₇₃	1	2	yes	—
600	#387	C₂²×C₇₃	1	2	yes	—
601	#387	C₂²×C₇₃	1	2	yes	—
602	#387	C₂²×C₇₃	1	2	yes	—
603	#387	C₂²×C₇₃	1	2	yes	—
604	#385	C₂²×C₇₃	1	2	yes	—
605	#385	C₂²×C₇₃	1	2	yes	—
606	#384	C₂²×C₇₃	1	1	yes	characteristic
607	#382	C₂²×C₇₃	1	1	yes	characteristic
608	#382	C₂²×C₇₃	1	1	yes	characteristic
609	#382	C₂²×C₇₃	1	2	yes	—
610	#380	C₂²×C₇₃	1	1	yes	characteristic
611	#380	C₂²×C₇₃	1	1	yes	characteristic
612	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
615	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
616	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
617	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
618	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
621	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
623	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
624	C₄³	C₂²×C₇₃	1	1	yes	characteristic
625	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
626	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
627	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
628	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
629	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
633	C₄⋊Q₈	—	2	4	no	—
634	C₄⋊Q₈	—	2	8	no	—
635	C₄⋊Q₈	—	2	4	no	—
636	#126	—	2	8	no	—
637	#125	—	2	8	no	—
638	#125	—	2	8	no	—
639	#125	—	2	4	no	—
640	#125	—	2	8	no	—
641	#125	D₄×C₇₃	1	8	yes	—
642	#124	—	2	4	no	—
643	#123	—	2	8	no	—
644	C₂²⋊Q₈	—	2	4	no	—
645	C₂²⋊Q₈	—	2	4	no	—
646	C₂²⋊Q₈	—	2	4	no	—
647	C₂²⋊Q₈	—	2	4	no	—
648	C₂²⋊Q₈	—	2	8	no	—
649	C₄×Q₈	—	2	4	no	—
650	C₄×Q₈	—	2	8	no	—
651	C₄×Q₈	—	2	4	no	—
652	C₄×Q₈	—	2	4	no	—
653	C₄×Q₈	—	2	4	no	—
654	C₄×Q₈	—	2	4	no	—
655	C₄×D₄	—	2	4	no	—
656	#117	—	2	4	no	—
657	#117	—	2	8	no	—
658	C₂×C₄⋊C₄	—	2	4	no	—
659	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
704	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
709	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
710	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
712	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
713	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
715	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
721	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
723	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
724	#95	C₂³×C₇₃	1	2	yes	—
725	#95	C₂³×C₇₃	1	1	yes	characteristic
726	#95	C₂³×C₇₃	1	1	yes	characteristic
727	#95	C₂³×C₇₃	1	1	yes	characteristic
728	#95	C₂³×C₇₃	1	1	yes	characteristic
729	#95	C₂³×C₇₃	1	1	yes	characteristic
730	#95	C₂³×C₇₃	1	1	yes	characteristic
731	#95	C₂³×C₇₃	1	2	yes	—
732	#95	C₂³×C₇₃	1	1	yes	characteristic
733	#95	C₂³×C₇₃	1	1	yes	characteristic
734	#95	C₂³×C₇₃	1	2	yes	—
735	#95	C₂³×C₇₃	1	2	yes	—
736	#95	C₂³×C₇₃	1	2	yes	—
737	#95	C₂³×C₇₃	1	2	yes	—
738	#95	C₂³×C₇₃	1	2	yes	—
739	#95	C₂³×C₇₃	1	2	yes	—
740	#95	C₂³×C₇₃	1	2	yes	—
741	#95	C₂³×C₇₃	1	2	yes	—
742	#95	C₂³×C₇₃	1	2	yes	—
743	#95	C₂³×C₇₃	1	2	yes	—
744	#95	C₂³×C₇₃	1	2	yes	—
745	#95	C₂³×C₇₃	1	2	yes	—
746	#95	C₂³×C₇₃	1	2	yes	—
747	#95	C₂³×C₇₃	1	2	yes	—
748	#95	C₂³×C₇₃	1	2	yes	—
749	#95	C₂³×C₇₃	1	2	yes	—
750	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
751	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	—	2	2	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	4	2	no	—
762	C₂×Q₈	—	4	1	no	—
763	C₂×Q₈	#41×C₇₃	1	4	yes	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	2	4	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
826	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
827	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
828	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
846	C₄²	—	2	4	no	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₄²	—	2	4	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	4	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	4	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	4	1	no	—
860	C₄²	—	4	2	no	—
861	C₄²	C₂×D₄×C₇₃	1	4	yes	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	C₂×#41×C₇₃	1	2	yes	—
876	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
877	Q₈	—	2	8	no	—
878	Q₈	—	4	8	no	—
879	Q₈	—	4	4	no	—
880	Q₈	—	4	4	no	—
881	D₄	—	4	4	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
938	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
939	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
941	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
942	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
943	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
944	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
945	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
946	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
947	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
963	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
964	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
965	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
966	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
967	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
968	C₂²	#585×C₇₃	1	1	yes	characteristic
969	C₄	—	2	4	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	4	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	#548×C₇₃	1	4	yes	—
990	C₂	—	4	2	no	—
991	C₂	—	8	1	no	—
992	C₂	C₂×#548×C₇₃	1	1	yes	characteristic
993	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
994	C₂	C₇₃×#3482	1	1	yes	characteristic
995	C₂	C₇₃×#3499	1	1	yes	characteristic
996	C₂	C₇₃×#3509	1	1	yes	characteristic
997	C₂	C₇₃×#3516	1	1	yes	characteristic
998	C₂	C₇₃×#3563	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. C₂×#557×C₇₃	C₂	semidirect
3. C₇₃×#2719	C₂	semidirect
5. C₇₃×#2581	C₂	semidirect
7. C₇₃×#2550	C₂	semidirect
9. C₇₃×#2519	C₂	semidirect
10. C₇₃×#2492	C₂	semidirect
11. C₇₃×#2489	C₂	semidirect
12. C₇₃×#2475	C₂	semidirect
13. C₇₃×#2469	C₂	semidirect
14. C₇₃×#2441	C₂	semidirect
15. C₇₃×#2440	C₂	semidirect
16. C₇₃×#2429	C₂	semidirect
17. C₇₃×#2429	C₂	semidirect
18. C₇₃×#2362	C₂	semidirect
19. C₇₃×#2362	C₂	semidirect
20. C₇₃×#2360	C₂	semidirect
21. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
22. C₄×#125×C₇₃	C₂	semidirect
490. #59656	C₇₃	direct (N × H)
500. C₂×#557	C₂×C₇₃	semidirect
502. #2719	C₂×C₇₃	semidirect
504. #2581	C₂×C₇₃	semidirect
506. #2550	C₂×C₇₃	semidirect
508. #2519	C₂×C₇₃	semidirect
509. #2492	C₂×C₇₃	semidirect
510. #2489	C₂×C₇₃	semidirect
511. #2475	C₂×C₇₃	semidirect
512. #2469	C₂×C₇₃	semidirect
513. #2441	C₂×C₇₃	semidirect
514. #2440	C₂×C₇₃	semidirect
515. #2429	C₂×C₇₃	semidirect
516. #2429	C₂×C₇₃	semidirect
517. #2362	C₂×C₇₃	semidirect
518. #2362	C₂×C₇₃	semidirect
519. #2360	C₂×C₇₃	semidirect
520. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
521. C₄×#125	C₂×C₇₃	semidirect
523. C₇₃	#59656	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#557×C₇₃	2
C₂×#552×C₇₃	2
C₇₃×#2719	2
C₇₃×#2674	2
C₇₃×#2581	2
C₇₃×#2558	2
C₇₃×#2550	2
C₇₃×#2536	2
C₇₃×#2519	2
C₇₃×#2492	2
C₇₃×#2489	2
C₇₃×#2475	2
C₇₃×#2469	2
C₇₃×#2441	2
C₇₃×#2440	2
C₇₃×#2429	2
C₇₃×#2362	2
C₇₃×#2360	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#125×C₇₃	2
C₄×#124×C₇₃	2
#59656	73

Subgroups — C73×#59656 #32969060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59656 #32969060