Subgroups — C₇₃×#62603 #32972007

Order 18688.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3316	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3312	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3306	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3298	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3225	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3173	C₂	1	2	yes	maximal, complemented
17	C₇₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₇₃	—	2	2	no	—
21	#563×C₇₃	—	2	1	no	—
22	#562×C₇₃	—	2	1	no	—
23	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
24	#556×C₇₃	C₂²	1	2	yes	—
25	#555×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	#552×C₇₃	—	2	1	no	—
29	#552×C₇₃	C₂²	1	2	yes	—
30	#551×C₇₃	—	2	2	no	—
31	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
32	#548×C₇₃	C₂²	1	2	yes	—
33	#547×C₇₃	—	2	1	no	—
34	#547×C₇₃	C₂²	1	2	yes	—
35	#546×C₇₃	C₂²	1	2	yes	—
36	#544×C₇₃	—	2	1	no	—
37	#544×C₇₃	C₂²	1	2	yes	complemented
38	#543×C₇₃	—	2	1	no	—
39	#542×C₇₃	—	2	2	no	—
40	#542×C₇₃	—	2	1	no	—
41	#542×C₇₃	C₂²	1	2	yes	—
42	#542×C₇₃	C₂²	1	2	yes	complemented
43	#538×C₇₃	—	2	1	no	—
44	#536×C₇₃	—	2	2	no	—
45	#536×C₇₃	C₂²	1	2	yes	—
46	#533×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
48	#529×C₇₃	C₂²	1	1	yes	characteristic
49	#529×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
51	#501×C₇₃	C₂²	1	1	yes	characteristic, complemented
52	#498×C₇₃	C₂²	1	2	yes	complemented
53	#497×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	#495×C₇₃	C₂²	1	2	yes	—
55	#491×C₇₃	C₂²	1	2	yes	complemented
56	#491×C₇₃	C₂²	1	1	yes	characteristic, complemented
57	#489×C₇₃	C₂²	1	2	yes	—
58	#489×C₇₃	C₂²	1	2	yes	—
59	#489×C₇₃	C₂²	1	2	yes	—
60	#489×C₇₃	C₂²	1	2	yes	—
61	#489×C₇₃	C₂²	1	2	yes	—
62	#489×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#488×C₇₃	C₂²	1	2	yes	—
64	#488×C₇₃	C₂²	1	2	yes	—
65	#487×C₇₃	C₂²	1	2	yes	complemented
66	#487×C₇₃	C₂²	1	2	yes	complemented
67	#485×C₇₃	C₂²	1	2	yes	complemented
68	#483×C₇₃	C₂²	1	2	yes	—
69	#483×C₇₃	C₂²	1	2	yes	—
70	#483×C₇₃	C₂²	1	2	yes	complemented
71	#482×C₇₃	C₂²	1	2	yes	—
72	#481×C₇₃	C₂²	1	2	yes	—
73	#479×C₇₃	C₂²	1	2	yes	complemented
74	#478×C₇₃	C₂²	1	2	yes	—
75	#476×C₇₃	C₂²	1	2	yes	—
76	#475×C₇₃	C₂²	1	2	yes	complemented
77	#475×C₇₃	C₂²	1	2	yes	complemented
78	#475×C₇₃	C₂²	1	2	yes	complemented
79	#470×C₇₃	C₂²	1	2	yes	complemented
80	#469×C₇₃	C₂²	1	2	yes	—
81	#467×C₇₃	C₂²	1	2	yes	—
82	#465×C₇₃	C₂²	1	2	yes	—
83	#465×C₇₃	C₂²	1	2	yes	—
84	#465×C₇₃	C₂²	1	2	yes	complemented
85	#464×C₇₃	C₂²	1	2	yes	—
86	#464×C₇₃	C₂²	1	2	yes	—
87	#463×C₇₃	C₂²	1	2	yes	—
88	#463×C₇₃	C₂²	1	2	yes	—
89	#462×C₇₃	C₂²	1	2	yes	complemented
90	#461×C₇₃	C₂²	1	2	yes	complemented
91	#452×C₇₃	C₂²	1	2	yes	—
92	#451×C₇₃	C₂²	1	1	yes	characteristic
93	#451×C₇₃	C₂²	1	2	yes	complemented
94	#450×C₇₃	C₂²	1	1	yes	characteristic
95	#449×C₇₃	C₂²	1	2	yes	—
96	#448×C₇₃	C₂²	1	1	yes	characteristic
97	#448×C₇₃	C₂²	1	2	yes	complemented
98	#447×C₇₃	C₂²	1	1	yes	characteristic
99	#446×C₇₃	C₂²	1	2	yes	complemented
100	#442×C₇₃	C₂²	1	2	yes	—
101	#441×C₇₃	C₂²	1	2	yes	complemented
102	#441×C₇₃	C₂²	1	2	yes	complemented
103	#440×C₇₃	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
106	#435×C₇₃	C₂²	1	2	yes	—
107	#435×C₇₃	C₂²	1	2	yes	complemented
108	C₈×D₄×C₇₃	C₂²	1	2	yes	—
109	#433×C₇₃	C₂²	1	2	yes	complemented
110	#431×C₇₃	C₂²	1	1	yes	characteristic
111	#419×C₇₃	C₂²	1	2	yes	complemented
112	#417×C₇₃	C₂²	1	2	yes	—
113	#416×C₇₃	C₂²	1	2	yes	—
114	C₂×#103×C₇₃	C₂²	1	2	yes	—
115	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
116	C₂×#102×C₇₃	C₂²	1	2	yes	—
117	#405×C₇₃	C₂²	1	2	yes	complemented
118	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₃	—	2	2	no	—
120	C₂×#41×C₇₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₇₃	—	2	1	no	—
122	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
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×D₈×C₇₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
132	C₂²×C₈×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	—	2	2	no	—
137	C₄⋊Q₈×C₇₃	—	2	1	no	—
138	C₄⋊Q₈×C₇₃	—	2	1	no	—
139	C₄⋊Q₈×C₇₃	—	2	1	no	—
140	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
152	#126×C₇₃	—	2	1	no	—
153	#126×C₇₃	D₄	1	2	yes	—
154	#125×C₇₃	—	2	1	no	—
155	#125×C₇₃	—	2	2	no	—
156	#125×C₇₃	—	2	2	no	—
157	#125×C₇₃	—	2	1	no	—
158	#125×C₇₃	D₄	1	1	yes	characteristic
159	#125×C₇₃	C₂³	1	2	yes	—
160	#125×C₇₃	C₂³	1	1	yes	characteristic
161	#124×C₇₃	—	2	2	no	—
162	#124×C₇₃	—	2	2	no	—
163	#124×C₇₃	—	2	2	no	—
164	#124×C₇₃	—	2	2	no	—
165	#124×C₇₃	—	2	1	no	—
166	#124×C₇₃	—	2	1	no	—
167	#124×C₇₃	D₄	1	1	yes	characteristic
168	#124×C₇₃	C₂³	1	2	yes	—
169	#124×C₇₃	C₂³	1	2	yes	—
170	#124×C₇₃	C₂³	1	2	yes	—
171	#124×C₇₃	C₂³	1	1	yes	characteristic
172	#123×C₇₃	—	2	2	no	—
173	#123×C₇₃	—	2	1	no	—
174	#123×C₇₃	—	2	2	no	—
175	#123×C₇₃	—	2	2	no	—
176	#123×C₇₃	—	2	2	no	—
177	#123×C₇₃	—	2	2	no	—
178	#123×C₇₃	—	2	2	no	—
179	#123×C₇₃	—	2	2	no	—
180	#123×C₇₃	—	2	2	no	—
181	#123×C₇₃	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₇₃	—	2	1	no	—
183	C₂²⋊Q₈×C₇₃	—	2	2	no	—
184	C₂²⋊Q₈×C₇₃	—	2	1	no	—
185	C₂²⋊Q₈×C₇₃	—	2	2	no	—
186	C₂²⋊Q₈×C₇₃	—	2	2	no	—
187	C₂²⋊Q₈×C₇₃	—	2	2	no	—
188	C₂²⋊Q₈×C₇₃	—	2	2	no	—
189	C₂²⋊Q₈×C₇₃	—	2	2	no	—
190	C₂²⋊Q₈×C₇₃	—	2	2	no	—
191	C₂²⋊Q₈×C₇₃	—	2	2	no	—
192	C₂²⋊Q₈×C₇₃	—	2	2	no	—
193	C₂²⋊Q₈×C₇₃	—	2	2	no	—
194	C₂²⋊Q₈×C₇₃	—	2	2	no	—
195	C₂²⋊Q₈×C₇₃	—	2	2	no	—
196	C₂²⋊Q₈×C₇₃	—	2	2	no	—
197	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
199	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
202	#121×C₇₃	—	2	2	no	—
203	#121×C₇₃	—	2	1	no	—
204	#121×C₇₃	—	2	2	no	—
205	#121×C₇₃	D₄	1	1	yes	characteristic
206	#121×C₇₃	C₂³	1	1	yes	characteristic
207	#121×C₇₃	C₂³	1	2	yes	—
208	#121×C₇₃	C₂³	1	2	yes	—
209	#120×C₇₃	—	2	2	no	—
210	C₄×Q₈×C₇₃	—	2	1	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	1	yes	characteristic
216	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₇₃	—	2	2	no	—
218	C₄×D₄×C₇₃	—	2	1	no	—
219	C₄×D₄×C₇₃	—	2	1	no	—
220	C₄×D₄×C₇₃	—	2	2	no	—
221	C₄×D₄×C₇₃	C₂³	1	2	yes	—
222	C₄×D₄×C₇₃	C₂³	1	2	yes	—
223	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₇₃	C₂³	1	2	yes	—
225	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
226	#117×C₇₃	—	2	1	no	—
227	#117×C₇₃	—	2	2	no	—
228	#117×C₇₃	—	2	1	no	—
229	#117×C₇₃	—	2	2	no	—
230	#117×C₇₃	—	2	1	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	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
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	#106×C₇₃	C₂³	1	2	yes	—
243	#106×C₇₃	C₂³	1	2	yes	—
244	#106×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	#103×C₇₃	C₂³	1	2	yes	—
259	#103×C₇₃	C₂³	1	2	yes	—
260	#103×C₇₃	C₂³	1	2	yes	—
261	#103×C₇₃	C₂³	1	2	yes	—
262	#103×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	1	yes	characteristic
275	#97×C₇₃	C₂³	1	1	yes	characteristic
276	#97×C₇₃	C₂³	1	2	yes	—
277	#97×C₇₃	C₂³	1	2	yes	—
278	C₄×C₈×C₇₃	C₂³	1	2	yes	—
279	C₄×C₈×C₇₃	C₂³	1	2	yes	—
280	C₂⁴×C₇₃	—	2	1	no	—
281	#41×C₇₃	—	4	2	no	—
282	#41×C₇₃	—	4	2	no	—
283	#41×C₇₃	—	8	4	no	—
284	C₂×Q₈×C₇₃	—	2	1	no	—
285	C₂×Q₈×C₇₃	—	2	2	no	—
286	C₂×Q₈×C₇₃	—	2	1	no	—
287	C₂×Q₈×C₇₃	—	2	1	no	—
288	C₂×Q₈×C₇₃	—	2	2	no	—
289	C₂×Q₈×C₇₃	—	2	2	no	—
290	C₂×Q₈×C₇₃	—	2	1	no	—
291	C₂×Q₈×C₇₃	—	4	2	no	—
292	C₂×Q₈×C₇₃	—	4	2	no	—
293	C₂×Q₈×C₇₃	—	4	2	no	—
294	C₂×Q₈×C₇₃	—	8	2	no	—
295	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
299	C₂×D₄×C₇₃	—	2	1	no	—
300	C₂×D₄×C₇₃	—	2	2	no	—
301	C₂×D₄×C₇₃	—	2	2	no	—
302	C₂×D₄×C₇₃	—	2	2	no	—
303	C₂×D₄×C₇₃	—	2	1	no	—
304	C₂×D₄×C₇₃	—	4	2	no	—
305	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
306	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
307	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
308	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇₃	—	2	2	no	—
310	C₂²×C₄×C₇₃	—	2	1	no	—
311	C₂²×C₄×C₇₃	—	2	2	no	—
312	C₂²×C₄×C₇₃	—	2	2	no	—
313	C₂²×C₄×C₇₃	—	2	1	no	—
314	C₂²×C₄×C₇₃	—	2	2	no	—
315	C₂²×C₄×C₇₃	—	2	2	no	—
316	C₂²×C₄×C₇₃	—	2	2	no	—
317	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
321	Q₁₆×C₇₃	—	4	2	no	—
322	Q₁₆×C₇₃	—	4	2	no	—
323	SD₁₆×C₇₃	—	4	2	no	—
324	SD₁₆×C₇₃	—	4	2	no	—
325	SD₁₆×C₇₃	—	4	2	no	—
326	D₈×C₇₃	—	4	2	no	—
327	M₁₆×C₇₃	—	4	2	no	—
328	C₂×C₈×C₇₃	—	4	2	no	—
329	C₂×C₈×C₇₃	—	4	2	no	—
330	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
331	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₇₃	—	2	1	no	—
335	C₄⋊C₄×C₇₃	—	2	1	no	—
336	C₄⋊C₄×C₇₃	—	2	2	no	—
337	C₄⋊C₄×C₇₃	—	2	2	no	—
338	C₄⋊C₄×C₇₃	—	2	2	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	1	no	—
344	C₄⋊C₄×C₇₃	—	2	1	no	—
345	C₄⋊C₄×C₇₃	—	2	1	no	—
346	C₄⋊C₄×C₇₃	—	2	1	no	—
347	C₄⋊C₄×C₇₃	—	2	2	no	—
348	C₄⋊C₄×C₇₃	—	2	1	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	2	no	—
353	C₄⋊C₄×C₇₃	—	2	2	no	—
354	C₄⋊C₄×C₇₃	—	2	2	no	—
355	C₄⋊C₄×C₇₃	—	2	1	no	—
356	C₄⋊C₄×C₇₃	—	2	2	no	—
357	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₇₃	—	2	2	no	—
369	C₂²⋊C₄×C₇₃	—	2	1	no	—
370	C₂²⋊C₄×C₇₃	—	2	2	no	—
371	C₂²⋊C₄×C₇₃	—	2	2	no	—
372	C₂²⋊C₄×C₇₃	—	2	2	no	—
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	2	no	—
379	C₂²⋊C₄×C₇₃	—	2	2	no	—
380	C₂²⋊C₄×C₇₃	—	2	1	no	—
381	C₂²⋊C₄×C₇₃	—	2	2	no	—
382	C₂²⋊C₄×C₇₃	—	2	1	no	—
383	C₂²⋊C₄×C₇₃	—	2	1	no	—
384	C₂²⋊C₄×C₇₃	—	2	2	no	—
385	C₂²⋊C₄×C₇₃	—	2	2	no	—
386	C₂²⋊C₄×C₇₃	—	2	1	no	—
387	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
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	C₄²×C₇₃	—	2	2	no	—
393	C₄²×C₇₃	—	2	2	no	—
394	C₄²×C₇₃	—	2	1	no	—
395	C₄²×C₇₃	—	2	2	no	—
396	C₄²×C₇₃	—	2	2	no	—
397	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
400	C₄²×C₇₃	C₂⁴	1	2	yes	—
401	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂³×C₇₃	—	2	1	no	—
403	C₂³×C₇₃	—	2	2	no	—
404	C₂³×C₇₃	—	4	2	no	—
405	C₂³×C₇₃	—	8	1	no	—
406	C₂³×C₇₃	—	8	1	no	—
407	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
408	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
409	Q₈×C₇₃	—	2	2	no	—
410	Q₈×C₇₃	—	2	2	no	—
411	Q₈×C₇₃	—	2	2	no	—
412	Q₈×C₇₃	—	2	2	no	—
413	Q₈×C₇₃	—	2	2	no	—
414	Q₈×C₇₃	—	4	1	no	—
415	Q₈×C₇₃	—	8	1	no	—
416	Q₈×C₇₃	—	8	2	no	—
417	Q₈×C₇₃	—	8	1	no	—
418	Q₈×C₇₃	—	8	1	no	—
419	Q₈×C₇₃	—	8	2	no	—
420	Q₈×C₇₃	—	8	1	no	—
421	Q₈×C₇₃	—	8	2	no	—
422	D₄×C₇₃	—	2	4	no	—
423	D₄×C₇₃	—	2	2	no	—
424	D₄×C₇₃	—	2	2	no	—
425	D₄×C₇₃	—	2	2	no	—
426	D₄×C₇₃	—	4	1	no	—
427	D₄×C₇₃	—	4	2	no	—
428	D₄×C₇₃	—	8	1	no	—
429	D₄×C₇₃	—	8	2	no	—
430	D₄×C₇₃	—	8	2	no	—
431	D₄×C₇₃	—	8	2	no	—
432	C₂×C₄×C₇₃	—	2	2	no	—
433	C₂×C₄×C₇₃	—	2	2	no	—
434	C₂×C₄×C₇₃	—	2	2	no	—
435	C₂×C₄×C₇₃	—	2	2	no	—
436	C₂×C₄×C₇₃	—	2	1	no	—
437	C₂×C₄×C₇₃	—	2	1	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	2	no	—
442	C₂×C₄×C₇₃	—	2	1	no	—
443	C₂×C₄×C₇₃	—	2	2	no	—
444	C₂×C₄×C₇₃	—	4	1	no	—
445	C₂×C₄×C₇₃	—	4	2	no	—
446	C₂×C₄×C₇₃	—	4	4	no	—
447	C₂×C₄×C₇₃	—	8	2	no	—
448	C₂×C₄×C₇₃	—	8	2	no	—
449	C₂×C₄×C₇₃	—	8	2	no	—
450	C₂×C₄×C₇₃	—	8	2	no	—
451	C₂×C₄×C₇₃	—	8	1	no	—
452	C₂×C₄×C₇₃	—	8	2	no	—
453	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
462	C₈×C₇₃	—	2	2	no	—
463	C₈×C₇₃	—	2	2	no	—
464	C₈×C₇₃	—	2	2	no	—
465	C₈×C₇₃	—	2	2	no	—
466	C₂²×C₇₃	—	2	1	no	—
467	C₂²×C₇₃	—	2	1	no	—
468	C₂²×C₇₃	—	2	2	no	—
469	C₂²×C₇₃	—	2	2	no	—
470	C₂²×C₇₃	—	2	2	no	—
471	C₂²×C₇₃	—	4	1	no	—
472	C₂²×C₇₃	—	4	2	no	—
473	C₂²×C₇₃	—	4	2	no	—
474	C₂²×C₇₃	—	4	1	no	—
475	C₂²×C₇₃	—	4	1	no	—
476	C₂²×C₇₃	—	4	2	no	—
477	C₂²×C₇₃	—	16	2	no	—
478	C₂²×C₇₃	#577	1	2	yes	—
479	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₇₃	—	2	1	no	—
481	C₄×C₇₃	—	2	1	no	—
482	C₄×C₇₃	—	2	2	no	—
483	C₄×C₇₃	—	2	2	no	—
484	C₄×C₇₃	—	2	1	no	—
485	C₄×C₇₃	—	2	1	no	—
486	C₄×C₇₃	—	2	1	no	—
487	C₄×C₇₃	—	2	2	no	—
488	C₄×C₇₃	—	4	1	no	—
489	C₄×C₇₃	—	4	2	no	—
490	C₄×C₇₃	—	4	2	no	—
491	C₄×C₇₃	—	4	2	no	—
492	C₄×C₇₃	—	4	1	no	—
493	C₄×C₇₃	—	4	2	no	—
494	C₄×C₇₃	—	4	2	no	—
495	C₄×C₇₃	—	4	1	no	—
496	C₄×C₇₃	#585	1	2	yes	—
497	#62603	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂×C₇₃	—	2	2	no	—
499	C₂×C₇₃	—	4	2	no	—
500	C₂×C₇₃	—	8	1	no	—
501	C₂×C₇₃	—	8	2	no	—
502	C₂×C₇₃	#3500	1	1	yes	characteristic
503	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
504	C₂×C₇₃	#3586	1	1	yes	characteristic
505	#3561	C₂×C₇₃	1	1	yes	characteristic, complemented
506	#3544	C₂×C₇₃	1	1	yes	characteristic, complemented
507	#3376	C₂×C₇₃	1	2	yes	complemented
508	#3369	C₂×C₇₃	1	2	yes	complemented
509	#3321	C₂×C₇₃	1	2	yes	complemented
510	#3316	C₂×C₇₃	1	2	yes	complemented
511	#3312	C₂×C₇₃	1	2	yes	complemented
512	#3306	C₂×C₇₃	1	2	yes	complemented
513	#3298	C₂×C₇₃	1	2	yes	complemented
514	#3296	C₂×C₇₃	1	2	yes	complemented
515	#3244	C₂×C₇₃	1	2	yes	complemented
516	#3229	C₂×C₇₃	1	1	yes	characteristic, complemented
517	#3225	C₂×C₇₃	1	2	yes	complemented
518	#3211	C₂×C₇₃	1	1	yes	characteristic, complemented
519	#3181	C₂×C₇₃	1	1	yes	characteristic, complemented
520	#3173	C₂×C₇₃	1	2	yes	complemented
521	#3137	C₂×C₇₃	1	2	yes	complemented
522	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
523	#2968	C₂×C₇₃	1	1	yes	characteristic, complemented
524	C₇₃	#62603	1	1	yes	characteristic, direct product factor, Sylow
525	#563	—	2	2	no	—
526	#563	—	2	1	no	—
527	#562	—	2	1	no	—
528	Q₈²	C₂²×C₇₃	1	1	yes	characteristic, complemented
529	#556	C₂²×C₇₃	1	2	yes	—
530	#555	C₂²×C₇₃	1	1	yes	characteristic, complemented
531	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
532	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
533	#552	—	2	1	no	—
534	#552	C₂²×C₇₃	1	2	yes	—
535	#551	—	2	2	no	—
536	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
537	#548	C₂²×C₇₃	1	2	yes	—
538	#547	—	2	1	no	—
539	#547	C₂²×C₇₃	1	2	yes	—
540	#546	C₂²×C₇₃	1	2	yes	—
541	#544	—	2	1	no	—
542	#544	C₂²×C₇₃	1	2	yes	complemented
543	#543	—	2	1	no	—
544	#542	—	2	2	no	—
545	#542	—	2	1	no	—
546	#542	C₂²×C₇₃	1	2	yes	—
547	#542	C₂²×C₇₃	1	2	yes	complemented
548	#538	—	2	1	no	—
549	#536	—	2	2	no	—
550	#536	C₂²×C₇₃	1	2	yes	—
551	#533	C₂²×C₇₃	1	1	yes	characteristic
552	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
553	#529	C₂²×C₇₃	1	1	yes	characteristic
554	#529	C₂²×C₇₃	1	1	yes	characteristic
555	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
556	#501	C₂²×C₇₃	1	1	yes	characteristic, complemented
557	#498	C₂²×C₇₃	1	2	yes	complemented
558	#497	C₂²×C₇₃	1	1	yes	characteristic, complemented
559	#495	C₂²×C₇₃	1	2	yes	—
560	#491	C₂²×C₇₃	1	2	yes	complemented
561	#491	C₂²×C₇₃	1	1	yes	characteristic, complemented
562	#489	C₂²×C₇₃	1	2	yes	—
563	#489	C₂²×C₇₃	1	2	yes	—
564	#489	C₂²×C₇₃	1	2	yes	—
565	#489	C₂²×C₇₃	1	2	yes	—
566	#489	C₂²×C₇₃	1	2	yes	—
567	#489	C₂²×C₇₃	1	1	yes	characteristic, complemented
568	#488	C₂²×C₇₃	1	2	yes	—
569	#488	C₂²×C₇₃	1	2	yes	—
570	#487	C₂²×C₇₃	1	2	yes	complemented
571	#487	C₂²×C₇₃	1	2	yes	complemented
572	#485	C₂²×C₇₃	1	2	yes	complemented
573	#483	C₂²×C₇₃	1	2	yes	—
574	#483	C₂²×C₇₃	1	2	yes	—
575	#483	C₂²×C₇₃	1	2	yes	complemented
576	#482	C₂²×C₇₃	1	2	yes	—
577	#481	C₂²×C₇₃	1	2	yes	—
578	#479	C₂²×C₇₃	1	2	yes	complemented
579	#478	C₂²×C₇₃	1	2	yes	—
580	#476	C₂²×C₇₃	1	2	yes	—
581	#475	C₂²×C₇₃	1	2	yes	complemented
582	#475	C₂²×C₇₃	1	2	yes	complemented
583	#475	C₂²×C₇₃	1	2	yes	complemented
584	#470	C₂²×C₇₃	1	2	yes	complemented
585	#469	C₂²×C₇₃	1	2	yes	—
586	#467	C₂²×C₇₃	1	2	yes	—
587	#465	C₂²×C₇₃	1	2	yes	—
588	#465	C₂²×C₇₃	1	2	yes	—
589	#465	C₂²×C₇₃	1	2	yes	complemented
590	#464	C₂²×C₇₃	1	2	yes	—
591	#464	C₂²×C₇₃	1	2	yes	—
592	#463	C₂²×C₇₃	1	2	yes	—
593	#463	C₂²×C₇₃	1	2	yes	—
594	#462	C₂²×C₇₃	1	2	yes	complemented
595	#461	C₂²×C₇₃	1	2	yes	complemented
596	#452	C₂²×C₇₃	1	2	yes	—
597	#451	C₂²×C₇₃	1	1	yes	characteristic
598	#451	C₂²×C₇₃	1	2	yes	complemented
599	#450	C₂²×C₇₃	1	1	yes	characteristic
600	#449	C₂²×C₇₃	1	2	yes	—
601	#448	C₂²×C₇₃	1	1	yes	characteristic
602	#448	C₂²×C₇₃	1	2	yes	complemented
603	#447	C₂²×C₇₃	1	1	yes	characteristic
604	#446	C₂²×C₇₃	1	2	yes	complemented
605	#442	C₂²×C₇₃	1	2	yes	—
606	#441	C₂²×C₇₃	1	2	yes	complemented
607	#441	C₂²×C₇₃	1	2	yes	complemented
608	#440	C₂²×C₇₃	1	2	yes	complemented
609	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
610	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
611	#435	C₂²×C₇₃	1	2	yes	—
612	#435	C₂²×C₇₃	1	2	yes	complemented
613	C₈×D₄	C₂²×C₇₃	1	2	yes	—
614	#433	C₂²×C₇₃	1	2	yes	complemented
615	#431	C₂²×C₇₃	1	1	yes	characteristic
616	#419	C₂²×C₇₃	1	2	yes	complemented
617	#417	C₂²×C₇₃	1	2	yes	—
618	#416	C₂²×C₇₃	1	2	yes	—
619	C₂×#103	C₂²×C₇₃	1	2	yes	—
620	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
621	C₂×#102	C₂²×C₇₃	1	2	yes	—
622	#405	C₂²×C₇₃	1	2	yes	complemented
623	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
624	C₂×#41	—	2	2	no	—
625	C₂×#41	C₂³×C₇₃	1	2	yes	—
626	C₂²×Q₈	—	2	1	no	—
627	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
628	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
629	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
630	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
631	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
635	C₂×D₈	C₂³×C₇₃	1	2	yes	—
636	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
637	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	1	no	—
658	#126	D₄×C₇₃	1	2	yes	—
659	#125	—	2	1	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	1	no	—
663	#125	D₄×C₇₃	1	1	yes	characteristic
664	#125	C₂³×C₇₃	1	1	yes	characteristic
665	#125	C₂³×C₇₃	1	2	yes	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	1	no	—
671	#124	—	2	1	no	—
672	#124	D₄×C₇₃	1	1	yes	characteristic
673	#124	C₂³×C₇₃	1	2	yes	—
674	#124	C₂³×C₇₃	1	2	yes	—
675	#124	C₂³×C₇₃	1	1	yes	characteristic
676	#124	C₂³×C₇₃	1	2	yes	—
677	#123	—	2	2	no	—
678	#123	—	2	1	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	D₄×C₇₃	1	2	yes	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
705	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	D₄×C₇₃	1	1	yes	characteristic
711	#121	C₂³×C₇₃	1	1	yes	characteristic
712	#121	C₂³×C₇₃	1	2	yes	—
713	#121	C₂³×C₇₃	1	2	yes	—
714	#120	—	2	2	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
719	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
720	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
721	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
727	C₄×D₄	C₂³×C₇₃	1	2	yes	—
728	C₄×D₄	C₂³×C₇₃	1	2	yes	—
729	C₄×D₄	C₂³×C₇₃	1	2	yes	—
730	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
731	#117	—	2	1	no	—
732	#117	—	2	2	no	—
733	#117	—	2	1	no	—
734	#117	—	2	2	no	—
735	#117	—	2	1	no	—
736	#117	C₂³×C₇₃	1	2	yes	—
737	#117	C₂³×C₇₃	1	2	yes	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
742	C₂×C₂²⋊C₄	—	2	1	no	—
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	2	no	—
745	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
746	#107	C₂³×C₇₃	1	2	yes	—
747	#106	C₂³×C₇₃	1	2	yes	—
748	#106	C₂³×C₇₃	1	2	yes	—
749	#106	C₂³×C₇₃	1	2	yes	—
750	#106	C₂³×C₇₃	1	2	yes	—
751	#106	C₂³×C₇₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
755	#103	C₂³×C₇₃	1	2	yes	—
756	#103	C₂³×C₇₃	1	2	yes	—
757	#103	C₂³×C₇₃	1	2	yes	—
758	#103	C₂³×C₇₃	1	2	yes	—
759	#103	C₂³×C₇₃	1	2	yes	—
760	#103	C₂³×C₇₃	1	2	yes	—
761	#103	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	#102	C₂³×C₇₃	1	2	yes	—
769	#102	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	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
776	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
777	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
779	#97	C₂³×C₇₃	1	1	yes	characteristic
780	#97	C₂³×C₇₃	1	1	yes	characteristic
781	#97	C₂³×C₇₃	1	2	yes	—
782	#97	C₂³×C₇₃	1	2	yes	—
783	C₄×C₈	C₂³×C₇₃	1	2	yes	—
784	C₄×C₈	C₂³×C₇₃	1	2	yes	—
785	C₂⁴	—	2	1	no	—
786	#41	—	4	2	no	—
787	#41	—	4	2	no	—
788	#41	—	8	4	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	—	8	2	no	—
800	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
801	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
802	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
811	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
812	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
813	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
826	Q₁₆	—	4	2	no	—
827	Q₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	4	2	no	—
832	M₁₆	—	4	2	no	—
833	C₂×C₈	—	4	2	no	—
834	C₂×C₈	—	4	2	no	—
835	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
836	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
837	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
838	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	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	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
871	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
903	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
904	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
905	C₄²	C₂⁴×C₇₃	1	2	yes	—
906	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
913	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	8	2	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	1	no	—
923	Q₈	—	8	2	no	—
924	Q₈	—	8	1	no	—
925	Q₈	—	8	2	no	—
926	Q₈	—	8	1	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	2	no	—
929	D₄	—	2	2	no	—
930	D₄	—	2	2	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	2	no	—
933	D₄	—	8	1	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	2	no	—
955	C₂×C₄	—	8	2	no	—
956	C₂×C₄	—	8	1	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
961	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
963	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₈	—	2	2	no	—
970	C₈	—	2	2	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	16	2	no	—
983	C₂²	#577×C₇₃	1	2	yes	—
984	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
985	C₄	—	2	2	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	#585×C₇₃	1	2	yes	—
1002	C₂	—	2	2	no	—
1003	C₂	—	4	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₇₃×#3500	1	1	yes	characteristic
1007	C₂	C₂×#577×C₇₃	1	1	yes	characteristic
1008	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
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×#3561	C₂	semidirect
2. C₇₃×#3544	C₂	semidirect
3. C₇₃×#3376	C₂	semidirect
4. C₇₃×#3369	C₂	semidirect
5. C₇₃×#3321	C₂	semidirect
6. C₇₃×#3316	C₂	semidirect
7. C₇₃×#3312	C₂	semidirect
8. C₇₃×#3306	C₂	semidirect
9. C₇₃×#3298	C₂	semidirect
10. C₇₃×#3296	C₂	semidirect
11. C₇₃×#3244	C₂	semidirect
12. C₇₃×#3229	C₂	semidirect
13. C₇₃×#3225	C₂	semidirect
14. C₇₃×#3211	C₂	semidirect
15. C₇₃×#3181	C₂	semidirect
16. C₇₃×#3173	C₂	semidirect
17. C₇₃×#3137	C₂	semidirect
18. C₂×#489×C₇₃	C₂	semidirect
19. C₇₃×#2968	C₂	semidirect
23. Q₈²×C₇₃	C₂²	semidirect
25. #555×C₇₃	C₂²	semidirect
26. #554×C₇₃	C₂²	semidirect
27. #554×C₇₃	C₂²	semidirect
37. #544×C₇₃	C₂²	semidirect
42. #542×C₇₃	C₂²	semidirect
51. #501×C₇₃	C₂²	semidirect
52. #498×C₇₃	C₂²	semidirect
53. #497×C₇₃	C₂²	semidirect
55. #491×C₇₃	C₂²	semidirect
56. #491×C₇₃	C₂²	semidirect
62. #489×C₇₃	C₂²	semidirect
65. #487×C₇₃	C₂²	semidirect
66. #487×C₇₃	C₂²	semidirect
67. #485×C₇₃	C₂²	semidirect
70. #483×C₇₃	C₂²	semidirect
73. #479×C₇₃	C₂²	semidirect
76. #475×C₇₃	C₂²	semidirect
77. #475×C₇₃	C₂²	semidirect
78. #475×C₇₃	C₂²	semidirect
79. #470×C₇₃	C₂²	semidirect
84. #465×C₇₃	C₂²	semidirect
89. #462×C₇₃	C₂²	semidirect
90. #461×C₇₃	C₂²	semidirect
93. #451×C₇₃	C₂²	semidirect
97. #448×C₇₃	C₂²	semidirect
99. #446×C₇₃	C₂²	semidirect
101. #441×C₇₃	C₂²	semidirect
102. #441×C₇₃	C₂²	semidirect
103. #440×C₇₃	C₂²	semidirect
105. C₄×SD₁₆×C₇₃	C₂²	semidirect
107. #435×C₇₃	C₂²	semidirect
109. #433×C₇₃	C₂²	semidirect
111. #419×C₇₃	C₂²	semidirect
115. C₂×#103×C₇₃	C₂²	semidirect
117. #405×C₇₃	C₂²	semidirect
497. #62603	C₇₃	direct (N × H)
505. #3561	C₂×C₇₃	semidirect
506. #3544	C₂×C₇₃	semidirect
507. #3376	C₂×C₇₃	semidirect
508. #3369	C₂×C₇₃	semidirect
509. #3321	C₂×C₇₃	semidirect
510. #3316	C₂×C₇₃	semidirect
511. #3312	C₂×C₇₃	semidirect
512. #3306	C₂×C₇₃	semidirect
513. #3298	C₂×C₇₃	semidirect
514. #3296	C₂×C₇₃	semidirect
515. #3244	C₂×C₇₃	semidirect
516. #3229	C₂×C₇₃	semidirect
517. #3225	C₂×C₇₃	semidirect
518. #3211	C₂×C₇₃	semidirect
519. #3181	C₂×C₇₃	semidirect
520. #3173	C₂×C₇₃	semidirect
521. #3137	C₂×C₇₃	semidirect
522. C₂×#489	C₂×C₇₃	semidirect
523. #2968	C₂×C₇₃	semidirect
524. C₇₃	#62603	direct (N × H)
528. Q₈²	C₂²×C₇₃	semidirect
530. #555	C₂²×C₇₃	semidirect
531. #554	C₂²×C₇₃	semidirect
532. #554	C₂²×C₇₃	semidirect
542. #544	C₂²×C₇₃	semidirect
547. #542	C₂²×C₇₃	semidirect
556. #501	C₂²×C₇₃	semidirect
557. #498	C₂²×C₇₃	semidirect
558. #497	C₂²×C₇₃	semidirect
560. #491	C₂²×C₇₃	semidirect
561. #491	C₂²×C₇₃	semidirect
567. #489	C₂²×C₇₃	semidirect
570. #487	C₂²×C₇₃	semidirect
571. #487	C₂²×C₇₃	semidirect
572. #485	C₂²×C₇₃	semidirect
575. #483	C₂²×C₇₃	semidirect
578. #479	C₂²×C₇₃	semidirect
581. #475	C₂²×C₇₃	semidirect
582. #475	C₂²×C₇₃	semidirect
583. #475	C₂²×C₇₃	semidirect
584. #470	C₂²×C₇₃	semidirect
589. #465	C₂²×C₇₃	semidirect
594. #462	C₂²×C₇₃	semidirect
595. #461	C₂²×C₇₃	semidirect
598. #451	C₂²×C₇₃	semidirect
602. #448	C₂²×C₇₃	semidirect
604. #446	C₂²×C₇₃	semidirect
606. #441	C₂²×C₇₃	semidirect
607. #441	C₂²×C₇₃	semidirect
608. #440	C₂²×C₇₃	semidirect
610. C₄×SD₁₆	C₂²×C₇₃	semidirect
612. #435	C₂²×C₇₃	semidirect
614. #433	C₂²×C₇₃	semidirect
616. #419	C₂²×C₇₃	semidirect
620. C₂×#103	C₂²×C₇₃	semidirect
622. #405	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×#3561	2
C₇₃×#3544	2
C₇₃×#3376	2
C₇₃×#3369	2
C₇₃×#3321	2
C₇₃×#3316	2
C₇₃×#3312	2
C₇₃×#3306	2
C₇₃×#3298	2
C₇₃×#3296	2
C₇₃×#3244	2
C₇₃×#3229	2
C₇₃×#3225	2
C₇₃×#3211	2
C₇₃×#3181	2
C₇₃×#3173	2
C₇₃×#3137	2
C₂×#489×C₇₃	2
C₇₃×#2968	2
#62603	73

Subgroups — C73×#62603 #32972007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62603 #32972007