Subgroups — C₇₃×#62560 #32971964

Order 18688.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3554	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3313	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#3302	C₂	1	2	yes	maximal, complemented
13	C₇₃×#3300	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₇₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#3223	C₂	1	2	yes	maximal, complemented
18	C₇₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#3178	C₂	1	2	yes	maximal, complemented
20	C₇₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₃×#3137	C₂	1	2	yes	maximal, complemented
22	C₇₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₇₃	—	2	2	no	—
25	#562×C₇₃	—	2	2	no	—
26	#559×C₇₃	—	2	1	no	—
27	#559×C₇₃	C₂²	1	1	yes	characteristic
28	Q₈²×C₇₃	C₂²	1	1	yes	characteristic
29	#557×C₇₃	—	2	1	no	—
30	#557×C₇₃	C₂²	1	1	yes	characteristic
31	#557×C₇₃	C₂²	1	1	yes	characteristic
32	#556×C₇₃	—	2	1	no	—
33	#556×C₇₃	C₂²	1	2	yes	—
34	#556×C₇₃	C₂²	1	1	yes	characteristic
35	#554×C₇₃	—	2	1	no	—
36	#554×C₇₃	C₂²	1	1	yes	characteristic
37	#552×C₇₃	C₂²	1	2	yes	—
38	#550×C₇₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
40	#548×C₇₃	C₂²	1	2	yes	—
41	#547×C₇₃	C₂²	1	2	yes	—
42	#544×C₇₃	C₂²	1	2	yes	—
43	#542×C₇₃	—	2	1	no	—
44	#542×C₇₃	—	2	1	no	—
45	#542×C₇₃	C₂²	1	2	yes	—
46	#541×C₇₃	—	2	2	no	—
47	#541×C₇₃	—	2	1	no	—
48	#541×C₇₃	C₂²	1	2	yes	—
49	#540×C₇₃	—	2	1	no	—
50	#539×C₇₃	—	2	2	no	—
51	#536×C₇₃	C₂²	1	2	yes	—
52	#533×C₇₃	C₂²	1	1	yes	characteristic
53	#533×C₇₃	C₂²	1	1	yes	characteristic
54	#533×C₇₃	C₂²	1	1	yes	characteristic
55	#532×C₇₃	C₂²	1	1	yes	characteristic
56	#529×C₇₃	C₂²	1	1	yes	characteristic
57	#501×C₇₃	C₂²	1	2	yes	—
58	#500×C₇₃	C₂²	1	1	yes	characteristic
59	#497×C₇₃	C₂²	1	2	yes	—
60	#494×C₇₃	C₂²	1	1	yes	characteristic
61	#491×C₇₃	C₂²	1	2	yes	—
62	#491×C₇₃	C₂²	1	2	yes	—
63	#489×C₇₃	C₂²	1	2	yes	—
64	#489×C₇₃	C₂²	1	2	yes	—
65	#488×C₇₃	C₂²	1	2	yes	—
66	#488×C₇₃	C₂²	1	2	yes	—
67	#488×C₇₃	C₂²	1	2	yes	—
68	#487×C₇₃	C₂²	1	1	yes	characteristic
69	#487×C₇₃	C₂²	1	2	yes	—
70	#487×C₇₃	C₂²	1	1	yes	characteristic
71	#487×C₇₃	C₂²	1	1	yes	characteristic
72	#487×C₇₃	C₂²	1	1	yes	characteristic
73	#486×C₇₃	C₂²	1	1	yes	characteristic
74	#486×C₇₃	C₂²	1	1	yes	characteristic
75	#485×C₇₃	C₂²	1	2	yes	—
76	#485×C₇₃	C₂²	1	2	yes	—
77	#485×C₇₃	C₂²	1	2	yes	—
78	#484×C₇₃	C₂²	1	2	yes	—
79	#482×C₇₃	C₂²	1	2	yes	—
80	#480×C₇₃	C₂²	1	2	yes	—
81	#479×C₇₃	C₂²	1	2	yes	—
82	#478×C₇₃	C₂²	1	2	yes	—
83	#477×C₇₃	C₂²	1	1	yes	characteristic
84	#477×C₇₃	C₂²	1	1	yes	characteristic
85	#477×C₇₃	C₂²	1	2	yes	—
86	#475×C₇₃	C₂²	1	1	yes	characteristic
87	#475×C₇₃	C₂²	1	1	yes	characteristic
88	#474×C₇₃	C₂²	1	2	yes	—
89	#470×C₇₃	C₂²	1	2	yes	—
90	#468×C₇₃	C₂²	1	2	yes	—
91	#467×C₇₃	C₂²	1	2	yes	—
92	#467×C₇₃	C₂²	1	1	yes	characteristic
93	#467×C₇₃	C₂²	1	1	yes	characteristic
94	#467×C₇₃	C₂²	1	1	yes	characteristic
95	#467×C₇₃	C₂²	1	1	yes	characteristic
96	#465×C₇₃	C₂²	1	2	yes	—
97	#464×C₇₃	C₂²	1	2	yes	—
98	#464×C₇₃	C₂²	1	2	yes	—
99	#462×C₇₃	C₂²	1	1	yes	characteristic
100	#462×C₇₃	C₂²	1	1	yes	characteristic
101	#462×C₇₃	C₂²	1	2	yes	—
102	#462×C₇₃	C₂²	1	2	yes	—
103	#460×C₇₃	C₂²	1	1	yes	characteristic
104	#460×C₇₃	C₂²	1	1	yes	characteristic
105	#452×C₇₃	C₂²	1	2	yes	—
106	#452×C₇₃	C₂²	1	2	yes	—
107	#452×C₇₃	C₂²	1	2	yes	—
108	#452×C₇₃	C₂²	1	2	yes	—
109	#451×C₇₃	C₂²	1	2	yes	—
110	#451×C₇₃	C₂²	1	2	yes	—
111	#446×C₇₃	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
113	#441×C₇₃	C₂²	1	2	yes	—
114	#440×C₇₃	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
121	#436×C₇₃	C₂²	1	1	yes	characteristic
122	#435×C₇₃	C₂²	1	2	yes	—
123	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₇₃	C₂²	1	2	yes	—
125	#433×C₇₃	C₂²	1	2	yes	—
126	#432×C₇₃	C₂²	1	1	yes	characteristic
127	#419×C₇₃	C₂²	1	2	yes	—
128	#417×C₇₃	C₂²	1	2	yes	—
129	#416×C₇₃	C₂²	1	2	yes	—
130	#416×C₇₃	C₂²	1	2	yes	—
131	#416×C₇₃	C₂²	1	2	yes	—
132	C₂×#103×C₇₃	C₂²	1	2	yes	—
133	#405×C₇₃	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₃	C₂³	1	2	yes	—
136	C₂×#41×C₇₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
150	C₄⋊Q₈×C₇₃	—	2	1	no	—
151	C₄⋊Q₈×C₇₃	—	2	2	no	—
152	C₄⋊Q₈×C₇₃	—	2	1	no	—
153	C₄⋊Q₈×C₇₃	—	2	1	no	—
154	C₄⋊Q₈×C₇₃	—	2	2	no	—
155	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
164	#127×C₇₃	—	2	1	no	—
165	#127×C₇₃	C₂³	1	1	yes	characteristic
166	#126×C₇₃	—	2	2	no	—
167	#126×C₇₃	—	2	2	no	—
168	#126×C₇₃	—	2	2	no	—
169	#126×C₇₃	—	2	2	no	—
170	#126×C₇₃	—	2	2	no	—
171	#126×C₇₃	—	2	2	no	—
172	#126×C₇₃	—	2	2	no	—
173	#126×C₇₃	D₄	1	2	yes	—
174	#125×C₇₃	—	2	2	no	—
175	#125×C₇₃	—	2	1	no	—
176	#125×C₇₃	—	2	2	no	—
177	#125×C₇₃	—	2	2	no	—
178	#125×C₇₃	—	2	2	no	—
179	#125×C₇₃	—	2	1	no	—
180	#125×C₇₃	—	2	2	no	—
181	#125×C₇₃	—	2	2	no	—
182	#125×C₇₃	—	2	1	no	—
183	#125×C₇₃	—	2	1	no	—
184	#125×C₇₃	D₄	1	1	yes	characteristic
185	#125×C₇₃	C₂³	1	2	yes	—
186	#125×C₇₃	C₂³	1	2	yes	—
187	#124×C₇₃	—	2	1	no	—
188	#124×C₇₃	—	2	1	no	—
189	#124×C₇₃	—	2	2	no	—
190	#124×C₇₃	—	2	2	no	—
191	#124×C₇₃	—	2	2	no	—
192	#124×C₇₃	D₄	1	1	yes	characteristic
193	#124×C₇₃	C₂³	1	2	yes	—
194	#124×C₇₃	C₂³	1	2	yes	—
195	#123×C₇₃	—	2	2	no	—
196	#123×C₇₃	—	2	2	no	—
197	#123×C₇₃	—	2	2	no	—
198	#123×C₇₃	—	2	2	no	—
199	#123×C₇₃	—	2	2	no	—
200	#123×C₇₃	—	2	2	no	—
201	#123×C₇₃	—	2	2	no	—
202	#123×C₇₃	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₇₃	—	2	1	no	—
204	C₂²⋊Q₈×C₇₃	—	2	1	no	—
205	C₂²⋊Q₈×C₇₃	—	2	1	no	—
206	C₂²⋊Q₈×C₇₃	—	2	1	no	—
207	C₂²⋊Q₈×C₇₃	—	2	2	no	—
208	C₂²⋊Q₈×C₇₃	—	2	2	no	—
209	C₂²⋊Q₈×C₇₃	—	2	2	no	—
210	C₂²⋊Q₈×C₇₃	—	2	2	no	—
211	C₂²⋊Q₈×C₇₃	—	2	2	no	—
212	C₂²⋊Q₈×C₇₃	—	2	2	no	—
213	C₂²⋊Q₈×C₇₃	—	2	2	no	—
214	C₂²⋊Q₈×C₇₃	—	2	2	no	—
215	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
216	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
223	#121×C₇₃	—	2	2	no	—
224	#121×C₇₃	—	2	2	no	—
225	#121×C₇₃	—	2	1	no	—
226	#121×C₇₃	—	2	1	no	—
227	#121×C₇₃	—	2	2	no	—
228	#121×C₇₃	D₄	1	1	yes	characteristic
229	#121×C₇₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₇₃	—	2	1	no	—
231	C₄×Q₈×C₇₃	—	2	1	no	—
232	C₄×Q₈×C₇₃	—	2	2	no	—
233	C₄×Q₈×C₇₃	—	2	1	no	—
234	C₄×Q₈×C₇₃	—	2	1	no	—
235	C₄×Q₈×C₇₃	—	2	1	no	—
236	C₄×Q₈×C₇₃	—	2	1	no	—
237	C₄×Q₈×C₇₃	—	2	1	no	—
238	C₄×Q₈×C₇₃	—	2	1	no	—
239	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₇₃	—	2	1	no	—
248	C₄×D₄×C₇₃	—	2	1	no	—
249	C₄×D₄×C₇₃	—	2	1	no	—
250	C₄×D₄×C₇₃	—	2	1	no	—
251	C₄×D₄×C₇₃	—	2	2	no	—
252	C₄×D₄×C₇₃	—	2	1	no	—
253	C₄×D₄×C₇₃	—	2	1	no	—
254	C₄×D₄×C₇₃	C₂³	1	2	yes	—
255	C₄×D₄×C₇₃	C₂³	1	2	yes	—
256	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
257	#117×C₇₃	—	2	1	no	—
258	#117×C₇₃	—	2	1	no	—
259	#117×C₇₃	—	2	2	no	—
260	#117×C₇₃	C₂³	1	2	yes	—
261	#117×C₇₃	C₂³	1	2	yes	—
262	#117×C₇₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
264	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
265	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
266	#107×C₇₃	C₂³	1	1	yes	characteristic
267	#107×C₇₃	C₂³	1	1	yes	characteristic
268	#107×C₇₃	C₂³	1	1	yes	characteristic
269	#107×C₇₃	C₂³	1	1	yes	characteristic
270	#107×C₇₃	C₂³	1	2	yes	—
271	#107×C₇₃	C₂³	1	2	yes	—
272	#106×C₇₃	C₂³	1	2	yes	—
273	#106×C₇₃	C₂³	1	2	yes	—
274	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
278	#103×C₇₃	C₂³	1	1	yes	characteristic
279	#103×C₇₃	C₂³	1	2	yes	—
280	#103×C₇₃	C₂³	1	2	yes	—
281	#103×C₇₃	C₂³	1	2	yes	—
282	#103×C₇₃	C₂³	1	1	yes	characteristic
283	#103×C₇₃	C₂³	1	2	yes	—
284	#103×C₇₃	C₂³	1	2	yes	—
285	#103×C₇₃	C₂³	1	2	yes	—
286	#103×C₇₃	C₂³	1	2	yes	—
287	#103×C₇₃	C₂³	1	1	yes	characteristic
288	#103×C₇₃	C₂³	1	2	yes	—
289	#103×C₇₃	C₂³	1	1	yes	characteristic
290	#103×C₇₃	C₂³	1	2	yes	—
291	#103×C₇₃	C₂³	1	2	yes	—
292	#103×C₇₃	C₂³	1	1	yes	characteristic
293	#103×C₇₃	C₂³	1	1	yes	characteristic
294	#103×C₇₃	C₂³	1	1	yes	characteristic
295	#103×C₇₃	C₂³	1	1	yes	characteristic
296	#102×C₇₃	C₂³	1	2	yes	—
297	#102×C₇₃	C₂³	1	2	yes	—
298	#102×C₇₃	C₂³	1	2	yes	—
299	#102×C₇₃	C₂³	1	2	yes	—
300	#102×C₇₃	C₂³	1	2	yes	—
301	#102×C₇₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
305	#97×C₇₃	C₂³	1	2	yes	—
306	#97×C₇₃	C₂³	1	2	yes	—
307	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₃	C₂³	1	2	yes	—
312	#41×C₇₃	—	4	2	no	—
313	#41×C₇₃	—	4	2	no	—
314	#41×C₇₃	—	4	2	no	—
315	#41×C₇₃	—	4	2	no	—
316	C₂×Q₈×C₇₃	—	2	1	no	—
317	C₂×Q₈×C₇₃	—	2	1	no	—
318	C₂×Q₈×C₇₃	—	2	1	no	—
319	C₂×Q₈×C₇₃	—	2	1	no	—
320	C₂×Q₈×C₇₃	—	2	2	no	—
321	C₂×Q₈×C₇₃	—	2	2	no	—
322	C₂×Q₈×C₇₃	—	4	2	no	—
323	C₂×Q₈×C₇₃	—	4	2	no	—
324	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₇₃	—	2	2	no	—
331	C₂×D₄×C₇₃	—	2	2	no	—
332	C₂×D₄×C₇₃	—	2	2	no	—
333	C₂×D₄×C₇₃	—	2	1	no	—
334	C₂×D₄×C₇₃	—	2	1	no	—
335	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
347	Q₁₆×C₇₃	—	4	2	no	—
348	Q₁₆×C₇₃	—	4	1	no	—
349	Q₁₆×C₇₃	—	4	1	no	—
350	Q₁₆×C₇₃	—	4	1	no	—
351	Q₁₆×C₇₃	—	4	1	no	—
352	Q₁₆×C₇₃	—	4	2	no	—
353	SD₁₆×C₇₃	—	4	2	no	—
354	SD₁₆×C₇₃	—	4	2	no	—
355	M₁₆×C₇₃	—	4	2	no	—
356	C₂×C₈×C₇₃	—	4	2	no	—
357	C₂×C₈×C₇₃	—	4	1	no	—
358	C₂×C₈×C₇₃	—	4	1	no	—
359	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₇₃	—	2	1	no	—
366	C₄⋊C₄×C₇₃	—	2	2	no	—
367	C₄⋊C₄×C₇₃	—	2	2	no	—
368	C₄⋊C₄×C₇₃	—	2	2	no	—
369	C₄⋊C₄×C₇₃	—	2	1	no	—
370	C₄⋊C₄×C₇₃	—	2	1	no	—
371	C₄⋊C₄×C₇₃	—	2	1	no	—
372	C₄⋊C₄×C₇₃	—	2	2	no	—
373	C₄⋊C₄×C₇₃	—	2	1	no	—
374	C₄⋊C₄×C₇₃	—	2	1	no	—
375	C₄⋊C₄×C₇₃	—	2	1	no	—
376	C₄⋊C₄×C₇₃	—	2	1	no	—
377	C₄⋊C₄×C₇₃	—	2	1	no	—
378	C₄⋊C₄×C₇₃	—	2	1	no	—
379	C₄⋊C₄×C₇₃	—	2	1	no	—
380	C₄⋊C₄×C₇₃	—	2	1	no	—
381	C₄⋊C₄×C₇₃	—	2	2	no	—
382	C₄⋊C₄×C₇₃	—	2	2	no	—
383	C₄⋊C₄×C₇₃	—	2	2	no	—
384	C₄⋊C₄×C₇₃	—	2	2	no	—
385	C₄⋊C₄×C₇₃	—	2	2	no	—
386	C₄⋊C₄×C₇₃	—	2	1	no	—
387	C₄⋊C₄×C₇₃	—	2	1	no	—
388	C₄⋊C₄×C₇₃	—	2	2	no	—
389	C₄⋊C₄×C₇₃	—	2	2	no	—
390	C₄⋊C₄×C₇₃	—	2	1	no	—
391	C₄⋊C₄×C₇₃	—	2	2	no	—
392	C₄⋊C₄×C₇₃	—	2	1	no	—
393	C₄⋊C₄×C₇₃	—	2	1	no	—
394	C₄⋊C₄×C₇₃	—	2	1	no	—
395	C₄⋊C₄×C₇₃	—	2	2	no	—
396	C₄⋊C₄×C₇₃	—	2	2	no	—
397	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₇₃	—	2	1	no	—
410	C₂²⋊C₄×C₇₃	—	2	1	no	—
411	C₂²⋊C₄×C₇₃	—	2	1	no	—
412	C₂²⋊C₄×C₇₃	—	2	1	no	—
413	C₂²⋊C₄×C₇₃	—	2	2	no	—
414	C₂²⋊C₄×C₇₃	—	2	2	no	—
415	C₂²⋊C₄×C₇₃	—	2	2	no	—
416	C₂²⋊C₄×C₇₃	—	2	2	no	—
417	C₂²⋊C₄×C₇₃	—	2	2	no	—
418	C₂²⋊C₄×C₇₃	—	2	2	no	—
419	C₂²⋊C₄×C₇₃	—	2	2	no	—
420	C₂²⋊C₄×C₇₃	—	2	2	no	—
421	C₂²⋊C₄×C₇₃	—	2	2	no	—
422	C₂²⋊C₄×C₇₃	—	2	2	no	—
423	C₂²⋊C₄×C₇₃	—	2	2	no	—
424	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
429	C₄²×C₇₃	—	2	2	no	—
430	C₄²×C₇₃	—	2	1	no	—
431	C₄²×C₇₃	—	2	1	no	—
432	C₄²×C₇₃	—	2	1	no	—
433	C₄²×C₇₃	—	2	1	no	—
434	C₄²×C₇₃	—	2	2	no	—
435	C₄²×C₇₃	—	2	2	no	—
436	C₄²×C₇₃	—	2	2	no	—
437	C₄²×C₇₃	—	2	2	no	—
438	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₇₃	C₂⁴	1	2	yes	—
443	C₂³×C₇₃	—	2	2	no	—
444	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
445	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
446	Q₈×C₇₃	—	2	2	no	—
447	Q₈×C₇₃	—	2	1	no	—
448	Q₈×C₇₃	—	2	1	no	—
449	Q₈×C₇₃	—	2	1	no	—
450	Q₈×C₇₃	—	2	1	no	—
451	Q₈×C₇₃	—	2	1	no	—
452	Q₈×C₇₃	—	2	1	no	—
453	Q₈×C₇₃	—	2	2	no	—
454	Q₈×C₇₃	—	2	2	no	—
455	Q₈×C₇₃	—	2	1	no	—
456	Q₈×C₇₃	—	2	1	no	—
457	Q₈×C₇₃	—	4	2	no	—
458	Q₈×C₇₃	—	8	1	no	—
459	Q₈×C₇₃	—	8	1	no	—
460	Q₈×C₇₃	—	8	1	no	—
461	Q₈×C₇₃	—	8	2	no	—
462	Q₈×C₇₃	—	8	2	no	—
463	D₄×C₇₃	—	2	2	no	—
464	D₄×C₇₃	—	2	2	no	—
465	D₄×C₇₃	—	2	2	no	—
466	D₄×C₇₃	—	4	2	no	—
467	D₄×C₇₃	—	4	2	no	—
468	D₄×C₇₃	—	8	1	no	—
469	D₄×C₇₃	—	8	2	no	—
470	D₄×C₇₃	—	8	2	no	—
471	D₄×C₇₃	—	8	2	no	—
472	C₂×C₄×C₇₃	—	2	2	no	—
473	C₂×C₄×C₇₃	—	2	2	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	1	no	—
476	C₂×C₄×C₇₃	—	2	2	no	—
477	C₂×C₄×C₇₃	—	2	1	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	2	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	1	no	—
482	C₂×C₄×C₇₃	—	2	2	no	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	2	1	no	—
485	C₂×C₄×C₇₃	—	2	2	no	—
486	C₂×C₄×C₇₃	—	2	1	no	—
487	C₂×C₄×C₇₃	—	2	1	no	—
488	C₂×C₄×C₇₃	—	4	1	no	—
489	C₂×C₄×C₇₃	—	8	2	no	—
490	C₂×C₄×C₇₃	—	8	2	no	—
491	C₂×C₄×C₇₃	—	8	2	no	—
492	C₂×C₄×C₇₃	—	8	2	no	—
493	C₂×C₄×C₇₃	—	8	2	no	—
494	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
503	C₈×C₇₃	—	2	1	no	—
504	C₈×C₇₃	—	2	1	no	—
505	C₈×C₇₃	—	2	2	no	—
506	C₈×C₇₃	—	2	1	no	—
507	C₈×C₇₃	—	2	1	no	—
508	C₈×C₇₃	—	2	2	no	—
509	C₂²×C₇₃	—	2	1	no	—
510	C₂²×C₇₃	—	2	2	no	—
511	C₂²×C₇₃	—	2	2	no	—
512	C₂²×C₇₃	—	2	1	no	—
513	C₂²×C₇₃	—	2	1	no	—
514	C₂²×C₇₃	—	2	2	no	—
515	C₂²×C₇₃	—	4	2	no	—
516	C₂²×C₇₃	—	4	2	no	—
517	C₂²×C₇₃	—	4	2	no	—
518	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₇₃	—	2	1	no	—
520	C₄×C₇₃	—	2	1	no	—
521	C₄×C₇₃	—	2	2	no	—
522	C₄×C₇₃	—	2	1	no	—
523	C₄×C₇₃	—	2	2	no	—
524	C₄×C₇₃	—	2	1	no	—
525	C₄×C₇₃	—	2	2	no	—
526	C₄×C₇₃	—	4	1	no	—
527	C₄×C₇₃	—	4	1	no	—
528	C₄×C₇₃	—	4	2	no	—
529	C₄×C₇₃	—	4	1	no	—
530	C₄×C₇₃	—	4	1	no	—
531	C₄×C₇₃	—	4	1	no	—
532	C₄×C₇₃	—	4	2	no	—
533	C₄×C₇₃	—	4	1	no	—
534	C₄×C₇₃	—	4	1	no	—
535	C₄×C₇₃	—	4	1	no	—
536	C₄×C₇₃	—	4	2	no	—
537	C₄×C₇₃	#578	1	2	yes	—
538	C₄×C₇₃	#585	1	1	yes	characteristic
539	C₄×C₇₃	#585	1	1	yes	characteristic
540	#62560	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
541	C₂×C₇₃	—	4	1	no	—
542	C₂×C₇₃	—	4	2	no	—
543	C₂×C₇₃	—	8	2	no	—
544	C₂×C₇₃	#3500	1	1	yes	characteristic
545	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
546	C₂×C₇₃	#3584	1	1	yes	characteristic
547	#3555	C₂×C₇₃	1	1	yes	characteristic, complemented
548	#3554	C₂×C₇₃	1	1	yes	characteristic
549	#3375	C₂×C₇₃	1	1	yes	characteristic, complemented
550	#3374	C₂×C₇₃	1	1	yes	characteristic, complemented
551	#3365	C₂×C₇₃	1	1	yes	characteristic, complemented
552	#3363	C₂×C₇₃	1	1	yes	characteristic, complemented
553	#3333	C₂×C₇₃	1	1	yes	characteristic, complemented
554	#3328	C₂×C₇₃	1	1	yes	characteristic, complemented
555	#3315	C₂×C₇₃	1	2	yes	complemented
556	#3313	C₂×C₇₃	1	2	yes	complemented
557	#3304	C₂×C₇₃	1	1	yes	characteristic, complemented
558	#3302	C₂×C₇₃	1	2	yes	complemented
559	#3300	C₂×C₇₃	1	2	yes	complemented
560	#3299	C₂×C₇₃	1	1	yes	characteristic, complemented
561	#3243	C₂×C₇₃	1	2	yes	complemented
562	#3237	C₂×C₇₃	1	1	yes	characteristic, complemented
563	#3223	C₂×C₇₃	1	2	yes	complemented
564	#3216	C₂×C₇₃	1	1	yes	characteristic, complemented
565	#3178	C₂×C₇₃	1	2	yes	complemented
566	#3170	C₂×C₇₃	1	1	yes	characteristic, complemented
567	#3137	C₂×C₇₃	1	2	yes	complemented
568	#3131	C₂×C₇₃	1	1	yes	characteristic, complemented
569	#2966	C₂×C₇₃	1	1	yes	characteristic, complemented
570	C₇₃	#62560	1	1	yes	characteristic, direct product factor, Sylow
571	#563	—	2	2	no	—
572	#562	—	2	2	no	—
573	#559	—	2	1	no	—
574	#559	C₂²×C₇₃	1	1	yes	characteristic
575	Q₈²	C₂²×C₇₃	1	1	yes	characteristic
576	#557	—	2	1	no	—
577	#557	C₂²×C₇₃	1	1	yes	characteristic
578	#557	C₂²×C₇₃	1	1	yes	characteristic
579	#556	—	2	1	no	—
580	#556	C₂²×C₇₃	1	1	yes	characteristic
581	#556	C₂²×C₇₃	1	2	yes	—
582	#554	—	2	1	no	—
583	#554	C₂²×C₇₃	1	1	yes	characteristic
584	#552	C₂²×C₇₃	1	2	yes	—
585	#550	C₂²×C₇₃	1	1	yes	characteristic
586	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
587	#548	C₂²×C₇₃	1	2	yes	—
588	#547	C₂²×C₇₃	1	2	yes	—
589	#544	C₂²×C₇₃	1	2	yes	—
590	#542	—	2	1	no	—
591	#542	—	2	1	no	—
592	#542	C₂²×C₇₃	1	2	yes	—
593	#541	—	2	2	no	—
594	#541	—	2	1	no	—
595	#541	C₂²×C₇₃	1	2	yes	—
596	#540	—	2	1	no	—
597	#539	—	2	2	no	—
598	#536	C₂²×C₇₃	1	2	yes	—
599	#533	C₂²×C₇₃	1	1	yes	characteristic
600	#533	C₂²×C₇₃	1	1	yes	characteristic
601	#533	C₂²×C₇₃	1	1	yes	characteristic
602	#532	C₂²×C₇₃	1	1	yes	characteristic
603	#529	C₂²×C₇₃	1	1	yes	characteristic
604	#501	C₂²×C₇₃	1	2	yes	—
605	#500	C₂²×C₇₃	1	1	yes	characteristic
606	#497	C₂²×C₇₃	1	2	yes	—
607	#494	C₂²×C₇₃	1	1	yes	characteristic
608	#491	C₂²×C₇₃	1	2	yes	—
609	#491	C₂²×C₇₃	1	2	yes	—
610	#489	C₂²×C₇₃	1	2	yes	—
611	#489	C₂²×C₇₃	1	2	yes	—
612	#488	C₂²×C₇₃	1	2	yes	—
613	#488	C₂²×C₇₃	1	2	yes	—
614	#488	C₂²×C₇₃	1	2	yes	—
615	#487	C₂²×C₇₃	1	1	yes	characteristic
616	#487	C₂²×C₇₃	1	1	yes	characteristic
617	#487	C₂²×C₇₃	1	2	yes	—
618	#487	C₂²×C₇₃	1	1	yes	characteristic
619	#487	C₂²×C₇₃	1	1	yes	characteristic
620	#486	C₂²×C₇₃	1	1	yes	characteristic
621	#486	C₂²×C₇₃	1	1	yes	characteristic
622	#485	C₂²×C₇₃	1	2	yes	—
623	#485	C₂²×C₇₃	1	2	yes	—
624	#485	C₂²×C₇₃	1	2	yes	—
625	#484	C₂²×C₇₃	1	2	yes	—
626	#482	C₂²×C₇₃	1	2	yes	—
627	#480	C₂²×C₇₃	1	2	yes	—
628	#479	C₂²×C₇₃	1	2	yes	—
629	#478	C₂²×C₇₃	1	2	yes	—
630	#477	C₂²×C₇₃	1	1	yes	characteristic
631	#477	C₂²×C₇₃	1	2	yes	—
632	#477	C₂²×C₇₃	1	1	yes	characteristic
633	#475	C₂²×C₇₃	1	1	yes	characteristic
634	#475	C₂²×C₇₃	1	1	yes	characteristic
635	#474	C₂²×C₇₃	1	2	yes	—
636	#470	C₂²×C₇₃	1	2	yes	—
637	#468	C₂²×C₇₃	1	2	yes	—
638	#467	C₂²×C₇₃	1	1	yes	characteristic
639	#467	C₂²×C₇₃	1	1	yes	characteristic
640	#467	C₂²×C₇₃	1	1	yes	characteristic
641	#467	C₂²×C₇₃	1	1	yes	characteristic
642	#467	C₂²×C₇₃	1	2	yes	—
643	#465	C₂²×C₇₃	1	2	yes	—
644	#464	C₂²×C₇₃	1	2	yes	—
645	#464	C₂²×C₇₃	1	2	yes	—
646	#462	C₂²×C₇₃	1	1	yes	characteristic
647	#462	C₂²×C₇₃	1	2	yes	—
648	#462	C₂²×C₇₃	1	1	yes	characteristic
649	#462	C₂²×C₇₃	1	2	yes	—
650	#460	C₂²×C₇₃	1	1	yes	characteristic
651	#460	C₂²×C₇₃	1	1	yes	characteristic
652	#452	C₂²×C₇₃	1	2	yes	—
653	#452	C₂²×C₇₃	1	2	yes	—
654	#452	C₂²×C₇₃	1	2	yes	—
655	#452	C₂²×C₇₃	1	2	yes	—
656	#451	C₂²×C₇₃	1	2	yes	—
657	#451	C₂²×C₇₃	1	2	yes	—
658	#446	C₂²×C₇₃	1	1	yes	characteristic
659	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic
660	#441	C₂²×C₇₃	1	2	yes	—
661	#440	C₂²×C₇₃	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
668	#436	C₂²×C₇₃	1	1	yes	characteristic
669	#435	C₂²×C₇₃	1	2	yes	—
670	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic
671	C₈×D₄	C₂²×C₇₃	1	2	yes	—
672	#433	C₂²×C₇₃	1	2	yes	—
673	#432	C₂²×C₇₃	1	1	yes	characteristic
674	#419	C₂²×C₇₃	1	2	yes	—
675	#417	C₂²×C₇₃	1	2	yes	—
676	#416	C₂²×C₇₃	1	2	yes	—
677	#416	C₂²×C₇₃	1	2	yes	—
678	#416	C₂²×C₇₃	1	2	yes	—
679	C₂×#103	C₂²×C₇₃	1	2	yes	—
680	#405	C₂²×C₇₃	1	2	yes	—
681	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
682	C₂×#41	C₂³×C₇₃	1	2	yes	—
683	C₂×#41	C₂³×C₇₃	1	2	yes	—
684	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
686	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
687	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
688	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
689	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
693	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
694	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
695	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
696	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
711	#127	—	2	1	no	—
712	#127	C₂³×C₇₃	1	1	yes	characteristic
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	D₄×C₇₃	1	2	yes	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	D₄×C₇₃	1	1	yes	characteristic
732	#125	C₂³×C₇₃	1	2	yes	—
733	#125	C₂³×C₇₃	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	D₄×C₇₃	1	1	yes	characteristic
740	#124	C₂³×C₇₃	1	2	yes	—
741	#124	C₂³×C₇₃	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	D₄×C₇₃	1	2	yes	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	D₄×C₇₃	1	1	yes	characteristic
776	#121	C₂³×C₇₃	1	2	yes	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
791	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
792	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	C₂³×C₇₃	1	2	yes	—
802	C₄×D₄	C₂³×C₇₃	1	2	yes	—
803	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	C₂³×C₇₃	1	2	yes	—
808	#117	C₂³×C₇₃	1	2	yes	—
809	#117	C₂³×C₇₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
812	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
813	#107	C₂³×C₇₃	1	1	yes	characteristic
814	#107	C₂³×C₇₃	1	1	yes	characteristic
815	#107	C₂³×C₇₃	1	1	yes	characteristic
816	#107	C₂³×C₇₃	1	1	yes	characteristic
817	#107	C₂³×C₇₃	1	2	yes	—
818	#107	C₂³×C₇₃	1	2	yes	—
819	#106	C₂³×C₇₃	1	2	yes	—
820	#106	C₂³×C₇₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
824	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
825	#103	C₂³×C₇₃	1	1	yes	characteristic
826	#103	C₂³×C₇₃	1	2	yes	—
827	#103	C₂³×C₇₃	1	2	yes	—
828	#103	C₂³×C₇₃	1	2	yes	—
829	#103	C₂³×C₇₃	1	1	yes	characteristic
830	#103	C₂³×C₇₃	1	2	yes	—
831	#103	C₂³×C₇₃	1	2	yes	—
832	#103	C₂³×C₇₃	1	2	yes	—
833	#103	C₂³×C₇₃	1	2	yes	—
834	#103	C₂³×C₇₃	1	1	yes	characteristic
835	#103	C₂³×C₇₃	1	2	yes	—
836	#103	C₂³×C₇₃	1	1	yes	characteristic
837	#103	C₂³×C₇₃	1	2	yes	—
838	#103	C₂³×C₇₃	1	2	yes	—
839	#103	C₂³×C₇₃	1	1	yes	characteristic
840	#103	C₂³×C₇₃	1	1	yes	characteristic
841	#103	C₂³×C₇₃	1	1	yes	characteristic
842	#103	C₂³×C₇₃	1	1	yes	characteristic
843	#102	C₂³×C₇₃	1	2	yes	—
844	#102	C₂³×C₇₃	1	2	yes	—
845	#102	C₂³×C₇₃	1	2	yes	—
846	#102	C₂³×C₇₃	1	2	yes	—
847	#102	C₂³×C₇₃	1	2	yes	—
848	#102	C₂³×C₇₃	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
852	#97	C₂³×C₇₃	1	2	yes	—
853	#97	C₂³×C₇₃	1	2	yes	—
854	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
856	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
857	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
858	C₄×C₈	C₂³×C₇₃	1	2	yes	—
859	#41	—	4	2	no	—
860	#41	—	4	2	no	—
861	#41	—	4	2	no	—
862	#41	—	4	2	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	4	2	no	—
870	C₂×Q₈	—	4	2	no	—
871	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
872	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
874	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
875	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
883	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
884	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
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	C₂×D₄×C₇₃	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
894	Q₁₆	—	4	2	no	—
895	Q₁₆	—	4	1	no	—
896	Q₁₆	—	4	1	no	—
897	Q₁₆	—	4	1	no	—
898	Q₁₆	—	4	1	no	—
899	Q₁₆	—	4	2	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	2	no	—
902	M₁₆	—	4	2	no	—
903	C₂×C₈	—	4	2	no	—
904	C₂×C₈	—	4	1	no	—
905	C₂×C₈	—	4	1	no	—
906	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
911	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
947	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
986	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
987	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
988	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
989	C₄²	C₂⁴×C₇₃	1	2	yes	—
990	C₂³	—	2	2	no	—
991	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
992	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	—	8	1	no	—
1007	Q₈	—	8	1	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	—	8	2	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	8	1	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	8	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1043	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1049	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	2	2	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	#578×C₇₃	1	2	yes	—
1085	C₄	#585×C₇₃	1	1	yes	characteristic
1086	C₄	#585×C₇₃	1	1	yes	characteristic
1087	C₂	—	4	2	no	—
1088	C₂	—	4	1	no	—
1089	C₂	—	8	2	no	—
1090	C₂	C₇₃×#3500	1	1	yes	characteristic
1091	C₂	C₂×#578×C₇₃	1	1	yes	characteristic
1092	C₂	C₇₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₇₃×#3554	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×#3555	C₂	semidirect
3. C₇₃×#3375	C₂	semidirect
4. C₇₃×#3374	C₂	semidirect
5. C₇₃×#3365	C₂	semidirect
6. C₇₃×#3363	C₂	semidirect
7. C₇₃×#3333	C₂	semidirect
8. C₇₃×#3328	C₂	semidirect
9. C₇₃×#3315	C₂	semidirect
10. C₇₃×#3313	C₂	semidirect
11. C₇₃×#3304	C₂	semidirect
12. C₇₃×#3302	C₂	semidirect
13. C₇₃×#3300	C₂	semidirect
14. C₇₃×#3299	C₂	semidirect
15. C₇₃×#3243	C₂	semidirect
16. C₇₃×#3237	C₂	semidirect
17. C₇₃×#3223	C₂	semidirect
18. C₇₃×#3216	C₂	semidirect
19. C₇₃×#3178	C₂	semidirect
20. C₇₃×#3170	C₂	semidirect
21. C₇₃×#3137	C₂	semidirect
22. C₇₃×#3131	C₂	semidirect
23. C₇₃×#2966	C₂	semidirect
540. #62560	C₇₃	direct (N × H)
547. #3555	C₂×C₇₃	semidirect
549. #3375	C₂×C₇₃	semidirect
550. #3374	C₂×C₇₃	semidirect
551. #3365	C₂×C₇₃	semidirect
552. #3363	C₂×C₇₃	semidirect
553. #3333	C₂×C₇₃	semidirect
554. #3328	C₂×C₇₃	semidirect
555. #3315	C₂×C₇₃	semidirect
556. #3313	C₂×C₇₃	semidirect
557. #3304	C₂×C₇₃	semidirect
558. #3302	C₂×C₇₃	semidirect
559. #3300	C₂×C₇₃	semidirect
560. #3299	C₂×C₇₃	semidirect
561. #3243	C₂×C₇₃	semidirect
562. #3237	C₂×C₇₃	semidirect
563. #3223	C₂×C₇₃	semidirect
564. #3216	C₂×C₇₃	semidirect
565. #3178	C₂×C₇₃	semidirect
566. #3170	C₂×C₇₃	semidirect
567. #3137	C₂×C₇₃	semidirect
568. #3131	C₂×C₇₃	semidirect
569. #2966	C₂×C₇₃	semidirect
570. C₇₃	#62560	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3555	2
C₇₃×#3554	2
C₇₃×#3375	2
C₇₃×#3374	2
C₇₃×#3365	2
C₇₃×#3363	2
C₇₃×#3333	2
C₇₃×#3328	2
C₇₃×#3315	2
C₇₃×#3313	2
C₇₃×#3304	2
C₇₃×#3302	2
C₇₃×#3300	2
C₇₃×#3299	2
C₇₃×#3243	2
C₇₃×#3237	2
C₇₃×#3223	2
C₇₃×#3216	2
C₇₃×#3178	2
C₇₃×#3170	2
C₇₃×#3137	2
C₇₃×#3131	2
C₇₃×#2966	2
#62560	73

Subgroups — C73×#62560 #32971964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62560 #32971964