Subgroups — C₇₃×#62575 #32971979

Order 18688.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3546	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3368	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3333	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3323	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3317	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3315	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3314	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3310	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3222	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3178	C₂	1	2	yes	maximal, complemented
17	C₇₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#3136	C₂	1	2	yes	maximal, complemented
19	C₇₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	#564×C₇₃	—	2	1	no	—
21	#563×C₇₃	—	2	1	no	—
22	#560×C₇₃	—	2	2	no	—
23	#557×C₇₃	C₂²	1	2	yes	complemented
24	#556×C₇₃	C₂²	1	1	yes	characteristic
25	#554×C₇₃	C₂²	1	2	yes	complemented
26	#553×C₇₃	—	2	1	no	—
27	#552×C₇₃	—	2	2	no	—
28	#552×C₇₃	C₂²	1	2	yes	—
29	#552×C₇₃	C₂²	1	2	yes	complemented
30	#550×C₇₃	C₂²	1	2	yes	—
31	#550×C₇₃	C₂²	1	1	yes	characteristic
32	#547×C₇₃	C₂²	1	1	yes	characteristic
33	#546×C₇₃	—	2	1	no	—
34	#546×C₇₃	C₂²	1	2	yes	—
35	D₄²×C₇₃	C₂²	1	1	yes	characteristic
36	#544×C₇₃	—	2	1	no	—
37	#544×C₇₃	C₂²	1	2	yes	complemented
38	#542×C₇₃	C₂²	1	2	yes	—
39	#541×C₇₃	—	2	2	no	—
40	#541×C₇₃	C₂²	1	2	yes	complemented
41	#539×C₇₃	—	2	1	no	—
42	#538×C₇₃	—	2	2	no	—
43	#537×C₇₃	—	2	1	no	—
44	#535×C₇₃	—	2	1	no	—
45	#535×C₇₃	C₂²	1	2	yes	—
46	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	#532×C₇₃	C₂²	1	1	yes	characteristic
48	#532×C₇₃	C₂²	1	1	yes	characteristic
49	#529×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#501×C₇₃	C₂²	1	2	yes	complemented
52	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	#497×C₇₃	C₂²	1	2	yes	complemented
54	#492×C₇₃	C₂²	1	1	yes	characteristic
55	#491×C₇₃	C₂²	1	2	yes	complemented
56	#490×C₇₃	C₂²	1	2	yes	—
57	#490×C₇₃	C₂²	1	2	yes	—
58	#490×C₇₃	C₂²	1	2	yes	complemented
59	#489×C₇₃	C₂²	1	2	yes	—
60	#489×C₇₃	C₂²	1	2	yes	complemented
61	#488×C₇₃	C₂²	1	2	yes	—
62	#488×C₇₃	C₂²	1	2	yes	complemented
63	#488×C₇₃	C₂²	1	2	yes	complemented
64	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#486×C₇₃	C₂²	1	1	yes	characteristic
66	#486×C₇₃	C₂²	1	2	yes	complemented
67	#485×C₇₃	C₂²	1	2	yes	complemented
68	#484×C₇₃	C₂²	1	2	yes	complemented
69	#482×C₇₃	C₂²	1	2	yes	—
70	#481×C₇₃	C₂²	1	1	yes	characteristic
71	#481×C₇₃	C₂²	1	1	yes	characteristic, complemented
72	#480×C₇₃	C₂²	1	1	yes	characteristic
73	#480×C₇₃	C₂²	1	2	yes	—
74	#480×C₇₃	C₂²	1	1	yes	characteristic, complemented
75	#479×C₇₃	C₂²	1	2	yes	complemented
76	#478×C₇₃	C₂²	1	2	yes	—
77	#478×C₇₃	C₂²	1	2	yes	complemented
78	#478×C₇₃	C₂²	1	2	yes	complemented
79	#477×C₇₃	C₂²	1	2	yes	complemented
80	#474×C₇₃	C₂²	1	2	yes	complemented
81	#470×C₇₃	C₂²	1	2	yes	complemented
82	#468×C₇₃	C₂²	1	2	yes	—
83	#468×C₇₃	C₂²	1	2	yes	—
84	#468×C₇₃	C₂²	1	2	yes	complemented
85	#467×C₇₃	C₂²	1	2	yes	complemented
86	#465×C₇₃	C₂²	1	2	yes	—
87	#464×C₇₃	C₂²	1	2	yes	—
88	#464×C₇₃	C₂²	1	2	yes	—
89	#462×C₇₃	C₂²	1	2	yes	complemented
90	#460×C₇₃	C₂²	1	2	yes	—
91	#460×C₇₃	C₂²	1	2	yes	complemented
92	#460×C₇₃	C₂²	1	2	yes	complemented
93	#452×C₇₃	C₂²	1	2	yes	complemented
94	#452×C₇₃	C₂²	1	2	yes	complemented
95	#452×C₇₃	C₂²	1	2	yes	complemented
96	#452×C₇₃	C₂²	1	2	yes	complemented
97	#450×C₇₃	C₂²	1	2	yes	—
98	#450×C₇₃	C₂²	1	2	yes	—
99	#446×C₇₃	C₂²	1	2	yes	complemented
100	#441×C₇₃	C₂²	1	2	yes	complemented
101	#440×C₇₃	C₂²	1	2	yes	—
102	#440×C₇₃	C₂²	1	2	yes	complemented
103	#440×C₇₃	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
106	#436×C₇₃	C₂²	1	2	yes	complemented
107	#435×C₇₃	C₂²	1	2	yes	—
108	#435×C₇₃	C₂²	1	2	yes	complemented
109	#433×C₇₃	C₂²	1	2	yes	complemented
110	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
111	#418×C₇₃	C₂²	1	2	yes	—
112	#417×C₇₃	C₂²	1	2	yes	complemented
113	#417×C₇₃	C₂²	1	2	yes	complemented
114	#417×C₇₃	C₂²	1	2	yes	complemented
115	#416×C₇₃	C₂²	1	2	yes	complemented
116	C₂×#102×C₇₃	C₂²	1	2	yes	—
117	#405×C₇₃	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₇₃	—	2	1	no	—
120	C₂×#41×C₇₃	—	2	1	no	—
121	C₂×#41×C₇₃	C₂³	1	2	yes	—
122	C₂×#41×C₇₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₇₃	—	2	1	no	—
124	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₇₃	—	2	2	no	—
135	C₄⋊Q₈×C₇₃	—	2	2	no	—
136	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
141	#127×C₇₃	—	2	2	no	—
142	#127×C₇₃	C₂³	1	1	yes	characteristic
143	#127×C₇₃	C₂³	1	2	yes	—
144	#127×C₇₃	C₂³	1	1	yes	characteristic
145	#126×C₇₃	—	2	2	no	—
146	#126×C₇₃	—	2	2	no	—
147	#126×C₇₃	—	2	2	no	—
148	#126×C₇₃	—	2	2	no	—
149	#126×C₇₃	—	2	2	no	—
150	#126×C₇₃	—	2	2	no	—
151	#126×C₇₃	D₄	1	2	yes	—
152	#125×C₇₃	—	2	2	no	—
153	#125×C₇₃	—	2	2	no	—
154	#125×C₇₃	—	2	2	no	—
155	#125×C₇₃	—	2	2	no	—
156	#125×C₇₃	—	2	2	no	—
157	#125×C₇₃	—	2	2	no	—
158	#125×C₇₃	—	2	2	no	—
159	#125×C₇₃	—	2	2	no	—
160	#125×C₇₃	—	2	1	no	—
161	#125×C₇₃	—	2	1	no	—
162	#125×C₇₃	—	2	1	no	—
163	#125×C₇₃	D₄	1	1	yes	characteristic
164	#125×C₇₃	C₂³	1	2	yes	—
165	#125×C₇₃	C₂³	1	2	yes	—
166	#125×C₇₃	C₂³	1	2	yes	—
167	#124×C₇₃	—	2	2	no	—
168	#124×C₇₃	—	2	1	no	—
169	#124×C₇₃	D₄	1	1	yes	characteristic
170	#124×C₇₃	C₂³	1	2	yes	—
171	#124×C₇₃	C₂³	1	2	yes	—
172	#123×C₇₃	—	2	2	no	—
173	#123×C₇₃	—	2	2	no	—
174	#123×C₇₃	—	2	2	no	—
175	#123×C₇₃	—	2	2	no	—
176	#123×C₇₃	—	2	2	no	—
177	#123×C₇₃	D₄	1	2	yes	—
178	C₂²⋊Q₈×C₇₃	—	2	1	no	—
179	C₂²⋊Q₈×C₇₃	—	2	1	no	—
180	C₂²⋊Q₈×C₇₃	—	2	2	no	—
181	C₂²⋊Q₈×C₇₃	—	2	2	no	—
182	C₂²⋊Q₈×C₇₃	—	2	2	no	—
183	C₂²⋊Q₈×C₇₃	—	2	2	no	—
184	C₂²⋊Q₈×C₇₃	—	2	2	no	—
185	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
186	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
190	#121×C₇₃	—	2	1	no	—
191	#121×C₇₃	—	2	1	no	—
192	#121×C₇₃	—	2	1	no	—
193	#121×C₇₃	—	2	1	no	—
194	#121×C₇₃	—	2	1	no	—
195	#121×C₇₃	—	2	2	no	—
196	#121×C₇₃	—	2	2	no	—
197	#121×C₇₃	—	2	1	no	—
198	#121×C₇₃	—	2	2	no	—
199	#121×C₇₃	—	2	2	no	—
200	#121×C₇₃	—	2	2	no	—
201	#121×C₇₃	—	2	2	no	—
202	#121×C₇₃	D₄	1	1	yes	characteristic
203	#121×C₇₃	C₂³	1	2	yes	—
204	#121×C₇₃	C₂³	1	1	yes	characteristic
205	#121×C₇₃	C₂³	1	1	yes	characteristic
206	#120×C₇₃	—	2	2	no	—
207	#120×C₇₃	—	2	2	no	—
208	#120×C₇₃	—	2	2	no	—
209	#120×C₇₃	—	2	2	no	—
210	C₄×Q₈×C₇₃	—	2	2	no	—
211	C₄×Q₈×C₇₃	—	2	1	no	—
212	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₇₃	—	2	2	no	—
218	C₄×D₄×C₇₃	—	2	2	no	—
219	C₄×D₄×C₇₃	—	2	1	no	—
220	C₄×D₄×C₇₃	—	2	1	no	—
221	C₄×D₄×C₇₃	—	2	1	no	—
222	C₄×D₄×C₇₃	C₂³	1	2	yes	—
223	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₇₃	C₂³	1	2	yes	—
227	#117×C₇₃	—	2	1	no	—
228	#117×C₇₃	—	2	1	no	—
229	#117×C₇₃	—	2	2	no	—
230	#117×C₇₃	—	2	2	no	—
231	#117×C₇₃	C₂³	1	2	yes	—
232	#117×C₇₃	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
235	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
236	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
240	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
241	#107×C₇₃	C₂³	1	2	yes	—
242	#107×C₇₃	C₂³	1	2	yes	—
243	#107×C₇₃	C₂³	1	2	yes	—
244	#107×C₇₃	C₂³	1	2	yes	—
245	#106×C₇₃	C₂³	1	2	yes	—
246	#106×C₇₃	C₂³	1	2	yes	—
247	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
248	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
249	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
250	#103×C₇₃	C₂³	1	2	yes	—
251	#103×C₇₃	C₂³	1	2	yes	—
252	#103×C₇₃	C₂³	1	2	yes	—
253	#103×C₇₃	C₂³	1	2	yes	—
254	#103×C₇₃	C₂³	1	2	yes	—
255	#103×C₇₃	C₂³	1	2	yes	—
256	#103×C₇₃	C₂³	1	2	yes	—
257	#103×C₇₃	C₂³	1	2	yes	—
258	#102×C₇₃	C₂³	1	2	yes	—
259	#102×C₇₃	C₂³	1	2	yes	—
260	#102×C₇₃	C₂³	1	2	yes	—
261	#102×C₇₃	C₂³	1	2	yes	—
262	#102×C₇₃	C₂³	1	2	yes	—
263	#102×C₇₃	C₂³	1	2	yes	—
264	#102×C₇₃	C₂³	1	2	yes	—
265	#102×C₇₃	C₂³	1	2	yes	—
266	#102×C₇₃	C₂³	1	2	yes	—
267	#102×C₇₃	C₂³	1	2	yes	—
268	#102×C₇₃	C₂³	1	2	yes	—
269	#102×C₇₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
274	#97×C₇₃	C₂³	1	2	yes	—
275	#97×C₇₃	C₂³	1	2	yes	—
276	#97×C₇₃	C₂³	1	2	yes	—
277	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₇₃	C₂³	1	2	yes	—
280	C₂⁴×C₇₃	—	2	2	no	—
281	#41×C₇₃	—	4	2	no	—
282	#41×C₇₃	—	4	2	no	—
283	#41×C₇₃	—	4	2	no	—
284	#41×C₇₃	—	4	2	no	—
285	#41×C₇₃	—	8	2	no	—
286	#41×C₇₃	—	8	2	no	—
287	C₂×Q₈×C₇₃	—	2	1	no	—
288	C₂×Q₈×C₇₃	—	2	2	no	—
289	C₂×Q₈×C₇₃	—	2	1	no	—
290	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
293	C₂×D₄×C₇₃	—	2	1	no	—
294	C₂×D₄×C₇₃	—	2	2	no	—
295	C₂×D₄×C₇₃	—	2	2	no	—
296	C₂×D₄×C₇₃	—	2	2	no	—
297	C₂×D₄×C₇₃	—	2	1	no	—
298	C₂×D₄×C₇₃	—	2	1	no	—
299	C₂×D₄×C₇₃	—	2	1	no	—
300	C₂×D₄×C₇₃	—	2	1	no	—
301	C₂×D₄×C₇₃	—	2	2	no	—
302	C₂×D₄×C₇₃	—	2	1	no	—
303	C₂×D₄×C₇₃	—	2	2	no	—
304	C₂×D₄×C₇₃	—	2	2	no	—
305	C₂×D₄×C₇₃	—	4	2	no	—
306	C₂×D₄×C₇₃	—	4	2	no	—
307	C₂×D₄×C₇₃	—	8	2	no	—
308	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
310	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
311	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
312	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇₃	—	2	1	no	—
314	C₂²×C₄×C₇₃	—	2	1	no	—
315	C₂²×C₄×C₇₃	—	2	2	no	—
316	C₂²×C₄×C₇₃	—	2	1	no	—
317	C₂²×C₄×C₇₃	—	2	1	no	—
318	C₂²×C₄×C₇₃	—	2	2	no	—
319	C₂²×C₄×C₇₃	—	2	2	no	—
320	C₂²×C₄×C₇₃	—	2	2	no	—
321	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
325	Q₁₆×C₇₃	—	4	2	no	—
326	Q₁₆×C₇₃	—	4	2	no	—
327	SD₁₆×C₇₃	—	4	2	no	—
328	SD₁₆×C₇₃	—	4	2	no	—
329	SD₁₆×C₇₃	—	4	2	no	—
330	SD₁₆×C₇₃	—	4	2	no	—
331	M₁₆×C₇₃	—	4	2	no	—
332	M₁₆×C₇₃	—	4	2	no	—
333	C₂×C₈×C₇₃	—	4	2	no	—
334	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₇₃	—	2	1	no	—
339	C₄⋊C₄×C₇₃	—	2	2	no	—
340	C₄⋊C₄×C₇₃	—	2	2	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	2	no	—
343	C₄⋊C₄×C₇₃	—	2	2	no	—
344	C₄⋊C₄×C₇₃	—	2	1	no	—
345	C₄⋊C₄×C₇₃	—	2	2	no	—
346	C₄⋊C₄×C₇₃	—	2	1	no	—
347	C₄⋊C₄×C₇₃	—	2	1	no	—
348	C₄⋊C₄×C₇₃	—	2	2	no	—
349	C₄⋊C₄×C₇₃	—	2	2	no	—
350	C₄⋊C₄×C₇₃	—	2	2	no	—
351	C₄⋊C₄×C₇₃	—	2	1	no	—
352	C₄⋊C₄×C₇₃	—	2	1	no	—
353	C₄⋊C₄×C₇₃	—	2	1	no	—
354	C₄⋊C₄×C₇₃	—	2	2	no	—
355	C₄⋊C₄×C₇₃	—	2	2	no	—
356	C₄⋊C₄×C₇₃	—	2	2	no	—
357	C₄⋊C₄×C₇₃	—	2	1	no	—
358	C₄⋊C₄×C₇₃	—	2	2	no	—
359	C₄⋊C₄×C₇₃	—	2	2	no	—
360	C₄⋊C₄×C₇₃	—	2	2	no	—
361	C₄⋊C₄×C₇₃	—	2	2	no	—
362	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
373	C₂²⋊C₄×C₇₃	—	2	2	no	—
374	C₂²⋊C₄×C₇₃	—	2	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	2	no	—
376	C₂²⋊C₄×C₇₃	—	2	2	no	—
377	C₂²⋊C₄×C₇₃	—	2	2	no	—
378	C₂²⋊C₄×C₇₃	—	2	1	no	—
379	C₂²⋊C₄×C₇₃	—	2	2	no	—
380	C₂²⋊C₄×C₇₃	—	2	2	no	—
381	C₂²⋊C₄×C₇₃	—	2	1	no	—
382	C₂²⋊C₄×C₇₃	—	2	2	no	—
383	C₂²⋊C₄×C₇₃	—	2	2	no	—
384	C₂²⋊C₄×C₇₃	—	2	2	no	—
385	C₂²⋊C₄×C₇₃	—	2	1	no	—
386	C₂²⋊C₄×C₇₃	—	2	2	no	—
387	C₂²⋊C₄×C₇₃	—	2	1	no	—
388	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
393	C₄²×C₇₃	—	2	2	no	—
394	C₄²×C₇₃	—	2	2	no	—
395	C₄²×C₇₃	—	2	2	no	—
396	C₄²×C₇₃	—	2	2	no	—
397	C₄²×C₇₃	—	2	2	no	—
398	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₇₃	C₂⁴	1	2	yes	—
402	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₂³×C₇₃	—	2	1	no	—
404	C₂³×C₇₃	—	2	2	no	—
405	C₂³×C₇₃	—	2	1	no	—
406	C₂³×C₇₃	—	8	2	no	—
407	C₂³×C₇₃	—	8	2	no	—
408	C₂³×C₇₃	—	8	2	no	—
409	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
410	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₇₃	—	2	2	no	—
412	Q₈×C₇₃	—	2	2	no	—
413	Q₈×C₇₃	—	2	2	no	—
414	Q₈×C₇₃	—	2	2	no	—
415	Q₈×C₇₃	—	4	1	no	—
416	Q₈×C₇₃	—	8	1	no	—
417	Q₈×C₇₃	—	8	2	no	—
418	Q₈×C₇₃	—	8	1	no	—
419	D₄×C₇₃	—	2	2	no	—
420	D₄×C₇₃	—	2	2	no	—
421	D₄×C₇₃	—	2	2	no	—
422	D₄×C₇₃	—	2	2	no	—
423	D₄×C₇₃	—	4	1	no	—
424	D₄×C₇₃	—	4	2	no	—
425	D₄×C₇₃	—	4	2	no	—
426	D₄×C₇₃	—	8	1	no	—
427	D₄×C₇₃	—	8	1	no	—
428	D₄×C₇₃	—	8	2	no	—
429	D₄×C₇₃	—	8	2	no	—
430	D₄×C₇₃	—	8	1	no	—
431	D₄×C₇₃	—	8	2	no	—
432	D₄×C₇₃	—	8	2	no	—
433	D₄×C₇₃	—	8	2	no	—
434	D₄×C₇₃	—	8	2	no	—
435	D₄×C₇₃	—	8	1	no	—
436	D₄×C₇₃	—	8	1	no	—
437	C₂×C₄×C₇₃	—	2	2	no	—
438	C₂×C₄×C₇₃	—	2	2	no	—
439	C₂×C₄×C₇₃	—	2	2	no	—
440	C₂×C₄×C₇₃	—	2	2	no	—
441	C₂×C₄×C₇₃	—	2	1	no	—
442	C₂×C₄×C₇₃	—	2	2	no	—
443	C₂×C₄×C₇₃	—	2	2	no	—
444	C₂×C₄×C₇₃	—	2	2	no	—
445	C₂×C₄×C₇₃	—	2	2	no	—
446	C₂×C₄×C₇₃	—	2	1	no	—
447	C₂×C₄×C₇₃	—	4	1	no	—
448	C₂×C₄×C₇₃	—	4	1	no	—
449	C₂×C₄×C₇₃	—	4	2	no	—
450	C₂×C₄×C₇₃	—	4	2	no	—
451	C₂×C₄×C₇₃	—	4	2	no	—
452	C₂×C₄×C₇₃	—	8	2	no	—
453	C₂×C₄×C₇₃	—	8	2	no	—
454	C₂×C₄×C₇₃	—	8	2	no	—
455	C₂×C₄×C₇₃	—	8	1	no	—
456	C₂×C₄×C₇₃	—	8	2	no	—
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
466	C₈×C₇₃	—	2	2	no	—
467	C₈×C₇₃	—	2	2	no	—
468	C₈×C₇₃	—	2	2	no	—
469	C₈×C₇₃	—	2	2	no	—
470	C₂²×C₇₃	—	2	1	no	—
471	C₂²×C₇₃	—	2	2	no	—
472	C₂²×C₇₃	—	2	1	no	—
473	C₂²×C₇₃	—	2	2	no	—
474	C₂²×C₇₃	—	2	1	no	—
475	C₂²×C₇₃	—	2	2	no	—
476	C₂²×C₇₃	—	4	1	no	—
477	C₂²×C₇₃	—	4	1	no	—
478	C₂²×C₇₃	—	4	2	no	—
479	C₂²×C₇₃	—	4	1	no	—
480	C₂²×C₇₃	—	4	2	no	—
481	C₂²×C₇₃	—	4	1	no	—
482	C₂²×C₇₃	—	4	1	no	—
483	C₂²×C₇₃	—	4	2	no	—
484	C₂²×C₇₃	—	4	1	no	—
485	C₂²×C₇₃	—	16	4	no	—
486	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
487	C₄×C₇₃	—	2	1	no	—
488	C₄×C₇₃	—	2	1	no	—
489	C₄×C₇₃	—	2	2	no	—
490	C₄×C₇₃	—	2	1	no	—
491	C₄×C₇₃	—	2	1	no	—
492	C₄×C₇₃	—	2	2	no	—
493	C₄×C₇₃	—	2	1	no	—
494	C₄×C₇₃	—	2	2	no	—
495	C₄×C₇₃	—	4	1	no	—
496	C₄×C₇₃	—	4	1	no	—
497	C₄×C₇₃	—	4	2	no	—
498	C₄×C₇₃	—	4	2	no	—
499	C₄×C₇₃	—	4	2	no	—
500	C₄×C₇₃	—	4	2	no	—
501	C₄×C₇₃	—	4	2	no	—
502	C₄×C₇₃	#585	1	2	yes	—
503	#62575	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
504	C₂×C₇₃	—	4	1	no	—
505	C₂×C₇₃	—	4	2	no	—
506	C₂×C₇₃	—	8	1	no	—
507	C₂×C₇₃	—	8	2	no	—
508	C₂×C₇₃	—	8	1	no	—
509	C₂×C₇₃	#3500	1	1	yes	characteristic
510	C₂×C₇₃	#3585	1	1	yes	characteristic
511	C₂×C₇₃	#3586	1	1	yes	characteristic
512	#3563	C₂×C₇₃	1	1	yes	characteristic, complemented
513	#3546	C₂×C₇₃	1	1	yes	characteristic
514	#3377	C₂×C₇₃	1	2	yes	complemented
515	#3368	C₂×C₇₃	1	2	yes	complemented
516	#3333	C₂×C₇₃	1	2	yes	complemented
517	#3323	C₂×C₇₃	1	2	yes	complemented
518	#3317	C₂×C₇₃	1	2	yes	complemented
519	#3315	C₂×C₇₃	1	2	yes	complemented
520	#3314	C₂×C₇₃	1	2	yes	complemented
521	#3310	C₂×C₇₃	1	2	yes	complemented
522	#3243	C₂×C₇₃	1	2	yes	complemented
523	#3234	C₂×C₇₃	1	1	yes	characteristic, complemented
524	#3222	C₂×C₇₃	1	2	yes	complemented
525	#3216	C₂×C₇₃	1	1	yes	characteristic, complemented
526	#3182	C₂×C₇₃	1	1	yes	characteristic, complemented
527	#3178	C₂×C₇₃	1	2	yes	complemented
528	#3142	C₂×C₇₃	1	1	yes	characteristic, complemented
529	#3136	C₂×C₇₃	1	2	yes	complemented
530	#2967	C₂×C₇₃	1	1	yes	characteristic, complemented
531	C₇₃	#62575	1	1	yes	characteristic, direct product factor, Sylow
532	#564	—	2	1	no	—
533	#563	—	2	1	no	—
534	#560	—	2	2	no	—
535	#557	C₂²×C₇₃	1	2	yes	complemented
536	#556	C₂²×C₇₃	1	1	yes	characteristic
537	#554	C₂²×C₇₃	1	2	yes	complemented
538	#553	—	2	1	no	—
539	#552	—	2	2	no	—
540	#552	C₂²×C₇₃	1	2	yes	—
541	#552	C₂²×C₇₃	1	2	yes	complemented
542	#550	C₂²×C₇₃	1	2	yes	—
543	#550	C₂²×C₇₃	1	1	yes	characteristic
544	#547	C₂²×C₇₃	1	1	yes	characteristic
545	#546	—	2	1	no	—
546	#546	C₂²×C₇₃	1	2	yes	—
547	D₄²	C₂²×C₇₃	1	1	yes	characteristic
548	#544	—	2	1	no	—
549	#544	C₂²×C₇₃	1	2	yes	complemented
550	#542	C₂²×C₇₃	1	2	yes	—
551	#541	—	2	2	no	—
552	#541	C₂²×C₇₃	1	2	yes	complemented
553	#539	—	2	1	no	—
554	#538	—	2	2	no	—
555	#537	—	2	1	no	—
556	#535	—	2	1	no	—
557	#535	C₂²×C₇₃	1	2	yes	—
558	#533	C₂²×C₇₃	1	1	yes	characteristic, complemented
559	#532	C₂²×C₇₃	1	1	yes	characteristic
560	#532	C₂²×C₇₃	1	1	yes	characteristic
561	#529	C₂²×C₇₃	1	1	yes	characteristic
562	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic, complemented
563	#501	C₂²×C₇₃	1	2	yes	complemented
564	#500	C₂²×C₇₃	1	1	yes	characteristic, complemented
565	#497	C₂²×C₇₃	1	2	yes	complemented
566	#492	C₂²×C₇₃	1	1	yes	characteristic
567	#491	C₂²×C₇₃	1	2	yes	complemented
568	#490	C₂²×C₇₃	1	2	yes	—
569	#490	C₂²×C₇₃	1	2	yes	—
570	#490	C₂²×C₇₃	1	2	yes	complemented
571	#489	C₂²×C₇₃	1	2	yes	—
572	#489	C₂²×C₇₃	1	2	yes	complemented
573	#488	C₂²×C₇₃	1	2	yes	—
574	#488	C₂²×C₇₃	1	2	yes	complemented
575	#488	C₂²×C₇₃	1	2	yes	complemented
576	#487	C₂²×C₇₃	1	1	yes	characteristic, complemented
577	#486	C₂²×C₇₃	1	1	yes	characteristic
578	#486	C₂²×C₇₃	1	2	yes	complemented
579	#485	C₂²×C₇₃	1	2	yes	complemented
580	#484	C₂²×C₇₃	1	2	yes	complemented
581	#482	C₂²×C₇₃	1	2	yes	—
582	#481	C₂²×C₇₃	1	1	yes	characteristic
583	#481	C₂²×C₇₃	1	1	yes	characteristic, complemented
584	#480	C₂²×C₇₃	1	2	yes	—
585	#480	C₂²×C₇₃	1	1	yes	characteristic
586	#480	C₂²×C₇₃	1	1	yes	characteristic, complemented
587	#479	C₂²×C₇₃	1	2	yes	complemented
588	#478	C₂²×C₇₃	1	2	yes	—
589	#478	C₂²×C₇₃	1	2	yes	complemented
590	#478	C₂²×C₇₃	1	2	yes	complemented
591	#477	C₂²×C₇₃	1	2	yes	complemented
592	#474	C₂²×C₇₃	1	2	yes	complemented
593	#470	C₂²×C₇₃	1	2	yes	complemented
594	#468	C₂²×C₇₃	1	2	yes	—
595	#468	C₂²×C₇₃	1	2	yes	—
596	#468	C₂²×C₇₃	1	2	yes	complemented
597	#467	C₂²×C₇₃	1	2	yes	complemented
598	#465	C₂²×C₇₃	1	2	yes	—
599	#464	C₂²×C₇₃	1	2	yes	—
600	#464	C₂²×C₇₃	1	2	yes	—
601	#462	C₂²×C₇₃	1	2	yes	complemented
602	#460	C₂²×C₇₃	1	2	yes	—
603	#460	C₂²×C₇₃	1	2	yes	complemented
604	#460	C₂²×C₇₃	1	2	yes	complemented
605	#452	C₂²×C₇₃	1	2	yes	complemented
606	#452	C₂²×C₇₃	1	2	yes	complemented
607	#452	C₂²×C₇₃	1	2	yes	complemented
608	#452	C₂²×C₇₃	1	2	yes	complemented
609	#450	C₂²×C₇₃	1	2	yes	—
610	#450	C₂²×C₇₃	1	2	yes	—
611	#446	C₂²×C₇₃	1	2	yes	complemented
612	#441	C₂²×C₇₃	1	2	yes	complemented
613	#440	C₂²×C₇₃	1	2	yes	—
614	#440	C₂²×C₇₃	1	2	yes	complemented
615	#440	C₂²×C₇₃	1	2	yes	complemented
616	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
618	#436	C₂²×C₇₃	1	2	yes	complemented
619	#435	C₂²×C₇₃	1	2	yes	—
620	#435	C₂²×C₇₃	1	2	yes	complemented
621	#433	C₂²×C₇₃	1	2	yes	complemented
622	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
623	#418	C₂²×C₇₃	1	2	yes	—
624	#417	C₂²×C₇₃	1	2	yes	complemented
625	#417	C₂²×C₇₃	1	2	yes	complemented
626	#417	C₂²×C₇₃	1	2	yes	complemented
627	#416	C₂²×C₇₃	1	2	yes	complemented
628	C₂×#102	C₂²×C₇₃	1	2	yes	—
629	#405	C₂²×C₇₃	1	2	yes	complemented
630	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
631	C₂×#41	—	2	1	no	—
632	C₂×#41	—	2	1	no	—
633	C₂×#41	C₂³×C₇₃	1	2	yes	—
634	C₂×#41	C₂³×C₇₃	1	2	yes	—
635	C₂²×D₄	—	2	1	no	—
636	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
637	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
638	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
643	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
644	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
645	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
653	#127	—	2	2	no	—
654	#127	C₂³×C₇₃	1	1	yes	characteristic
655	#127	C₂³×C₇₃	1	1	yes	characteristic
656	#127	C₂³×C₇₃	1	2	yes	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	D₄×C₇₃	1	2	yes	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	2	no	—
670	#125	—	2	2	no	—
671	#125	—	2	2	no	—
672	#125	—	2	1	no	—
673	#125	—	2	1	no	—
674	#125	—	2	1	no	—
675	#125	D₄×C₇₃	1	1	yes	characteristic
676	#125	C₂³×C₇₃	1	2	yes	—
677	#125	C₂³×C₇₃	1	2	yes	—
678	#125	C₂³×C₇₃	1	2	yes	—
679	#124	—	2	2	no	—
680	#124	—	2	1	no	—
681	#124	D₄×C₇₃	1	1	yes	characteristic
682	#124	C₂³×C₇₃	1	2	yes	—
683	#124	C₂³×C₇₃	1	2	yes	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	D₄×C₇₃	1	2	yes	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	2	1	no	—
706	#121	—	2	1	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	D₄×C₇₃	1	1	yes	characteristic
715	#121	C₂³×C₇₃	1	1	yes	characteristic
716	#121	C₂³×C₇₃	1	1	yes	characteristic
717	#121	C₂³×C₇₃	1	2	yes	—
718	#120	—	2	2	no	—
719	#120	—	2	2	no	—
720	#120	—	2	2	no	—
721	#120	—	2	2	no	—
722	C₄×Q₈	—	2	2	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
725	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
726	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
727	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
728	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₇₃	1	2	yes	—
737	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
738	C₄×D₄	C₂³×C₇₃	1	2	yes	—
739	#117	—	2	1	no	—
740	#117	—	2	1	no	—
741	#117	—	2	2	no	—
742	#117	—	2	2	no	—
743	#117	C₂³×C₇₃	1	2	yes	—
744	#117	C₂³×C₇₃	1	2	yes	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
753	#107	C₂³×C₇₃	1	2	yes	—
754	#107	C₂³×C₇₃	1	2	yes	—
755	#107	C₂³×C₇₃	1	2	yes	—
756	#107	C₂³×C₇₃	1	2	yes	—
757	#106	C₂³×C₇₃	1	2	yes	—
758	#106	C₂³×C₇₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
762	#103	C₂³×C₇₃	1	2	yes	—
763	#103	C₂³×C₇₃	1	2	yes	—
764	#103	C₂³×C₇₃	1	2	yes	—
765	#103	C₂³×C₇₃	1	2	yes	—
766	#103	C₂³×C₇₃	1	2	yes	—
767	#103	C₂³×C₇₃	1	2	yes	—
768	#103	C₂³×C₇₃	1	2	yes	—
769	#103	C₂³×C₇₃	1	2	yes	—
770	#102	C₂³×C₇₃	1	2	yes	—
771	#102	C₂³×C₇₃	1	2	yes	—
772	#102	C₂³×C₇₃	1	2	yes	—
773	#102	C₂³×C₇₃	1	2	yes	—
774	#102	C₂³×C₇₃	1	2	yes	—
775	#102	C₂³×C₇₃	1	2	yes	—
776	#102	C₂³×C₇₃	1	2	yes	—
777	#102	C₂³×C₇₃	1	2	yes	—
778	#102	C₂³×C₇₃	1	2	yes	—
779	#102	C₂³×C₇₃	1	2	yes	—
780	#102	C₂³×C₇₃	1	2	yes	—
781	#102	C₂³×C₇₃	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
783	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
784	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
786	#97	C₂³×C₇₃	1	2	yes	—
787	#97	C₂³×C₇₃	1	2	yes	—
788	#97	C₂³×C₇₃	1	2	yes	—
789	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
790	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
791	C₄×C₈	C₂³×C₇₃	1	2	yes	—
792	C₂⁴	—	2	2	no	—
793	#41	—	4	2	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	8	2	no	—
798	#41	—	8	2	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
804	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	8	2	no	—
820	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
821	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
822	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
823	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
824	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
837	Q₁₆	—	4	2	no	—
838	Q₁₆	—	4	2	no	—
839	SD₁₆	—	4	2	no	—
840	SD₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	M₁₆	—	4	2	no	—
844	M₁₆	—	4	2	no	—
845	C₂×C₈	—	4	2	no	—
846	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
847	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
848	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
849	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
876	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
901	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
902	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
911	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
912	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
913	C₄²	C₂⁴×C₇₃	1	2	yes	—
914	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
915	C₂³	—	2	1	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	8	2	no	—
919	C₂³	—	8	2	no	—
920	C₂³	—	8	2	no	—
921	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
922	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	4	1	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	1	no	—
930	Q₈	—	8	2	no	—
931	D₄	—	2	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	2	no	—
938	D₄	—	8	2	no	—
939	D₄	—	8	1	no	—
940	D₄	—	8	2	no	—
941	D₄	—	8	1	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	2	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
970	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
971	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
972	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
973	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
977	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
978	C₈	—	2	2	no	—
979	C₈	—	2	2	no	—
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	16	4	no	—
998	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	#585×C₇₃	1	2	yes	—
1015	C₂	—	4	2	no	—
1016	C₂	—	4	1	no	—
1017	C₂	—	8	1	no	—
1018	C₂	—	8	2	no	—
1019	C₂	—	8	1	no	—
1020	C₂	C₇₃×#3500	1	1	yes	characteristic
1021	C₂	C₇₃×#3585	1	1	yes	characteristic
1022	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₇₃×#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #529×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3563	C₂	semidirect
3. C₇₃×#3377	C₂	semidirect
4. C₇₃×#3368	C₂	semidirect
5. C₇₃×#3333	C₂	semidirect
6. C₇₃×#3323	C₂	semidirect
7. C₇₃×#3317	C₂	semidirect
8. C₇₃×#3315	C₂	semidirect
9. C₇₃×#3314	C₂	semidirect
10. C₇₃×#3310	C₂	semidirect
11. C₇₃×#3243	C₂	semidirect
12. C₇₃×#3234	C₂	semidirect
13. C₇₃×#3222	C₂	semidirect
14. C₇₃×#3216	C₂	semidirect
15. C₇₃×#3182	C₂	semidirect
16. C₇₃×#3178	C₂	semidirect
17. C₇₃×#3142	C₂	semidirect
18. C₇₃×#3136	C₂	semidirect
19. C₇₃×#2967	C₂	semidirect
23. #557×C₇₃	C₂²	semidirect
25. #554×C₇₃	C₂²	semidirect
29. #552×C₇₃	C₂²	semidirect
37. #544×C₇₃	C₂²	semidirect
40. #541×C₇₃	C₂²	semidirect
46. #533×C₇₃	C₂²	semidirect
50. C₂×#125×C₇₃	C₂²	semidirect
51. #501×C₇₃	C₂²	semidirect
52. #500×C₇₃	C₂²	semidirect
53. #497×C₇₃	C₂²	semidirect
55. #491×C₇₃	C₂²	semidirect
58. #490×C₇₃	C₂²	semidirect
60. #489×C₇₃	C₂²	semidirect
62. #488×C₇₃	C₂²	semidirect
63. #488×C₇₃	C₂²	semidirect
64. #487×C₇₃	C₂²	semidirect
66. #486×C₇₃	C₂²	semidirect
67. #485×C₇₃	C₂²	semidirect
68. #484×C₇₃	C₂²	semidirect
71. #481×C₇₃	C₂²	semidirect
74. #480×C₇₃	C₂²	semidirect
75. #479×C₇₃	C₂²	semidirect
77. #478×C₇₃	C₂²	semidirect
78. #478×C₇₃	C₂²	semidirect
79. #477×C₇₃	C₂²	semidirect
80. #474×C₇₃	C₂²	semidirect
81. #470×C₇₃	C₂²	semidirect
84. #468×C₇₃	C₂²	semidirect
85. #467×C₇₃	C₂²	semidirect
89. #462×C₇₃	C₂²	semidirect
91. #460×C₇₃	C₂²	semidirect
92. #460×C₇₃	C₂²	semidirect
93. #452×C₇₃	C₂²	semidirect
94. #452×C₇₃	C₂²	semidirect
95. #452×C₇₃	C₂²	semidirect
96. #452×C₇₃	C₂²	semidirect
99. #446×C₇₃	C₂²	semidirect
100. #441×C₇₃	C₂²	semidirect
102. #440×C₇₃	C₂²	semidirect
103. #440×C₇₃	C₂²	semidirect
104. C₄×Q₁₆×C₇₃	C₂²	semidirect
105. C₄×SD₁₆×C₇₃	C₂²	semidirect
106. #436×C₇₃	C₂²	semidirect
108. #435×C₇₃	C₂²	semidirect
109. #433×C₇₃	C₂²	semidirect
110. #432×C₇₃	C₂²	semidirect
112. #417×C₇₃	C₂²	semidirect
113. #417×C₇₃	C₂²	semidirect
114. #417×C₇₃	C₂²	semidirect
115. #416×C₇₃	C₂²	semidirect
117. #405×C₇₃	C₂²	semidirect
118. C₄×M₁₆×C₇₃	C₂²	semidirect
503. #62575	C₇₃	direct (N × H)
512. #3563	C₂×C₇₃	semidirect
514. #3377	C₂×C₇₃	semidirect
515. #3368	C₂×C₇₃	semidirect
516. #3333	C₂×C₇₃	semidirect
517. #3323	C₂×C₇₃	semidirect
518. #3317	C₂×C₇₃	semidirect
519. #3315	C₂×C₇₃	semidirect
520. #3314	C₂×C₇₃	semidirect
521. #3310	C₂×C₇₃	semidirect
522. #3243	C₂×C₇₃	semidirect
523. #3234	C₂×C₇₃	semidirect
524. #3222	C₂×C₇₃	semidirect
525. #3216	C₂×C₇₃	semidirect
526. #3182	C₂×C₇₃	semidirect
527. #3178	C₂×C₇₃	semidirect
528. #3142	C₂×C₇₃	semidirect
529. #3136	C₂×C₇₃	semidirect
530. #2967	C₂×C₇₃	semidirect
531. C₇₃	#62575	direct (N × H)
535. #557	C₂²×C₇₃	semidirect
537. #554	C₂²×C₇₃	semidirect
541. #552	C₂²×C₇₃	semidirect
549. #544	C₂²×C₇₃	semidirect
552. #541	C₂²×C₇₃	semidirect
558. #533	C₂²×C₇₃	semidirect
562. C₂×#125	C₂²×C₇₃	semidirect
563. #501	C₂²×C₇₃	semidirect
564. #500	C₂²×C₇₃	semidirect
565. #497	C₂²×C₇₃	semidirect
567. #491	C₂²×C₇₃	semidirect
570. #490	C₂²×C₇₃	semidirect
572. #489	C₂²×C₇₃	semidirect
574. #488	C₂²×C₇₃	semidirect
575. #488	C₂²×C₇₃	semidirect
576. #487	C₂²×C₇₃	semidirect
578. #486	C₂²×C₇₃	semidirect
579. #485	C₂²×C₇₃	semidirect
580. #484	C₂²×C₇₃	semidirect
583. #481	C₂²×C₇₃	semidirect
586. #480	C₂²×C₇₃	semidirect
587. #479	C₂²×C₇₃	semidirect
589. #478	C₂²×C₇₃	semidirect
590. #478	C₂²×C₇₃	semidirect
591. #477	C₂²×C₇₃	semidirect
592. #474	C₂²×C₇₃	semidirect
593. #470	C₂²×C₇₃	semidirect
596. #468	C₂²×C₇₃	semidirect
597. #467	C₂²×C₇₃	semidirect
601. #462	C₂²×C₇₃	semidirect
603. #460	C₂²×C₇₃	semidirect
604. #460	C₂²×C₇₃	semidirect
605. #452	C₂²×C₇₃	semidirect
606. #452	C₂²×C₇₃	semidirect
607. #452	C₂²×C₇₃	semidirect
608. #452	C₂²×C₇₃	semidirect
611. #446	C₂²×C₇₃	semidirect
612. #441	C₂²×C₇₃	semidirect
614. #440	C₂²×C₇₃	semidirect
615. #440	C₂²×C₇₃	semidirect
616. C₄×Q₁₆	C₂²×C₇₃	semidirect
617. C₄×SD₁₆	C₂²×C₇₃	semidirect
618. #436	C₂²×C₇₃	semidirect
620. #435	C₂²×C₇₃	semidirect
621. #433	C₂²×C₇₃	semidirect
622. #432	C₂²×C₇₃	semidirect
624. #417	C₂²×C₇₃	semidirect
625. #417	C₂²×C₇₃	semidirect
626. #417	C₂²×C₇₃	semidirect
627. #416	C₂²×C₇₃	semidirect
629. #405	C₂²×C₇₃	semidirect
630. C₄×M₁₆	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3563	2
C₇₃×#3546	2
C₇₃×#3377	2
C₇₃×#3368	2
C₇₃×#3333	2
C₇₃×#3323	2
C₇₃×#3317	2
C₇₃×#3315	2
C₇₃×#3314	2
C₇₃×#3310	2
C₇₃×#3243	2
C₇₃×#3234	2
C₇₃×#3222	2
C₇₃×#3216	2
C₇₃×#3182	2
C₇₃×#3178	2
C₇₃×#3142	2
C₇₃×#3136	2
C₇₃×#2967	2
#62575	73

Subgroups — C73×#62575 #32971979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62575 #32971979