Subgroups — C₇₃×#62556 #32971960

Order 18688.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1008 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×#3558	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3371	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3365	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3316	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3244	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×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₇₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#3136	C₂	1	2	yes	maximal, complemented
18	C₂×#488×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	#564×C₇₃	—	2	1	no	—
21	#563×C₇₃	—	2	1	no	—
22	#562×C₇₃	—	2	1	no	—
23	H(3,𝔽₄)×C₇₃	—	2	1	no	—
24	#559×C₇₃	C₂²	1	2	yes	—
25	#557×C₇₃	C₂²	1	2	yes	complemented
26	#554×C₇₃	C₂²	1	2	yes	complemented
27	#552×C₇₃	—	2	2	no	—
28	#552×C₇₃	C₂²	1	2	yes	complemented
29	#552×C₇₃	C₂²	1	2	yes	complemented
30	#548×C₇₃	C₂²	1	2	yes	—
31	#546×C₇₃	—	2	2	no	—
32	#546×C₇₃	C₂²	1	2	yes	—
33	D₄²×C₇₃	C₂²	1	2	yes	—
34	#544×C₇₃	—	2	1	no	—
35	#544×C₇₃	C₂²	1	2	yes	complemented
36	#542×C₇₃	C₂²	1	2	yes	—
37	#541×C₇₃	—	2	2	no	—
38	#541×C₇₃	C₂²	1	2	yes	complemented
39	#539×C₇₃	—	2	1	no	—
40	#538×C₇₃	—	2	2	no	—
41	#538×C₇₃	—	2	1	no	—
42	#535×C₇₃	C₂²	1	2	yes	—
43	#534×C₇₃	—	2	1	no	—
44	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#532×C₇₃	C₂²	1	1	yes	characteristic
46	#529×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
49	#501×C₇₃	C₂²	1	2	yes	complemented
50	#498×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#497×C₇₃	C₂²	1	2	yes	complemented
52	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	#490×C₇₃	C₂²	1	2	yes	—
54	#490×C₇₃	C₂²	1	2	yes	complemented
55	#489×C₇₃	C₂²	1	2	yes	complemented
56	#489×C₇₃	C₂²	1	2	yes	complemented
57	#488×C₇₃	C₂²	1	2	yes	complemented
58	#488×C₇₃	C₂²	1	2	yes	complemented
59	#488×C₇₃	C₂²	1	2	yes	complemented
60	#488×C₇₃	C₂²	1	2	yes	complemented
61	#488×C₇₃	C₂²	1	2	yes	complemented
62	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#486×C₇₃	C₂²	1	2	yes	—
64	#486×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#485×C₇₃	C₂²	1	2	yes	complemented
66	#483×C₇₃	C₂²	1	2	yes	complemented
67	#482×C₇₃	C₂²	1	2	yes	—
68	#481×C₇₃	C₂²	1	2	yes	—
69	#481×C₇₃	C₂²	1	2	yes	complemented
70	#480×C₇₃	C₂²	1	2	yes	complemented
71	#479×C₇₃	C₂²	1	2	yes	complemented
72	#478×C₇₃	C₂²	1	2	yes	complemented
73	#478×C₇₃	C₂²	1	2	yes	complemented
74	#478×C₇₃	C₂²	1	2	yes	complemented
75	#476×C₇₃	C₂²	1	2	yes	complemented
76	#475×C₇₃	C₂²	1	2	yes	complemented
77	#470×C₇₃	C₂²	1	2	yes	complemented
78	#468×C₇₃	C₂²	1	2	yes	—
79	#467×C₇₃	C₂²	1	2	yes	complemented
80	#465×C₇₃	C₂²	1	2	yes	—
81	#465×C₇₃	C₂²	1	2	yes	complemented
82	#465×C₇₃	C₂²	1	2	yes	complemented
83	#464×C₇₃	C₂²	1	2	yes	complemented
84	#464×C₇₃	C₂²	1	2	yes	complemented
85	#464×C₇₃	C₂²	1	2	yes	complemented
86	#464×C₇₃	C₂²	1	2	yes	complemented
87	#460×C₇₃	C₂²	1	2	yes	—
88	#460×C₇₃	C₂²	1	2	yes	—
89	#452×C₇₃	C₂²	1	2	yes	complemented
90	#452×C₇₃	C₂²	1	2	yes	complemented
91	#451×C₇₃	C₂²	1	2	yes	complemented
92	#450×C₇₃	C₂²	1	2	yes	—
93	#450×C₇₃	C₂²	1	2	yes	complemented
94	#450×C₇₃	C₂²	1	2	yes	complemented
95	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
97	#441×C₇₃	C₂²	1	2	yes	complemented
98	#440×C₇₃	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
103	#436×C₇₃	C₂²	1	1	yes	characteristic, complemented
104	#435×C₇₃	C₂²	1	2	yes	complemented
105	C₈×D₄×C₇₃	C₂²	1	2	yes	complemented
106	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
107	#433×C₇₃	C₂²	1	2	yes	complemented
108	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
109	#418×C₇₃	C₂²	1	2	yes	complemented
110	#417×C₇₃	C₂²	1	2	yes	complemented
111	#416×C₇₃	C₂²	1	2	yes	complemented
112	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
115	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
116	C₂×#102×C₇₃	C₂²	1	2	yes	complemented
117	#405×C₇₃	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₇₃	—	2	1	no	—
120	C₂×#41×C₇₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₇₃	—	2	2	no	—
123	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₇₃	—	2	2	no	—
136	C₄⋊Q₈×C₇₃	—	2	2	no	—
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	C₂³	1	2	yes	—
142	#127×C₇₃	C₂³	1	1	yes	characteristic
143	#126×C₇₃	—	2	2	no	—
144	#126×C₇₃	—	2	2	no	—
145	#126×C₇₃	—	2	2	no	—
146	#126×C₇₃	—	2	2	no	—
147	#126×C₇₃	—	2	2	no	—
148	#126×C₇₃	D₄	1	2	yes	—
149	#125×C₇₃	—	2	2	no	—
150	#125×C₇₃	—	2	2	no	—
151	#125×C₇₃	—	2	2	no	—
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	1	no	—
158	#125×C₇₃	—	2	1	no	—
159	#125×C₇₃	—	2	1	no	—
160	#125×C₇₃	D₄	1	1	yes	characteristic
161	#125×C₇₃	C₂³	1	2	yes	—
162	#125×C₇₃	C₂³	1	2	yes	—
163	#125×C₇₃	C₂³	1	2	yes	—
164	#124×C₇₃	—	2	2	no	—
165	#124×C₇₃	—	2	2	no	—
166	#124×C₇₃	—	2	2	no	—
167	#124×C₇₃	—	2	1	no	—
168	#124×C₇₃	—	2	1	no	—
169	#124×C₇₃	—	2	1	no	—
170	#124×C₇₃	D₄	1	1	yes	characteristic
171	#124×C₇₃	C₂³	1	2	yes	—
172	#124×C₇₃	C₂³	1	2	yes	—
173	#124×C₇₃	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
181	C₂²⋊Q₈×C₇₃	—	2	1	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	—	2	2	no	—
186	C₂²⋊Q₈×C₇₃	—	2	2	no	—
187	C₂²⋊Q₈×C₇₃	—	2	2	no	—
188	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
193	#121×C₇₃	—	2	2	no	—
194	#121×C₇₃	—	2	1	no	—
195	#121×C₇₃	—	2	2	no	—
196	#121×C₇₃	—	2	2	no	—
197	#121×C₇₃	—	2	2	no	—
198	#121×C₇₃	—	2	2	no	—
199	#121×C₇₃	D₄	1	1	yes	characteristic
200	#121×C₇₃	C₂³	1	2	yes	—
201	#121×C₇₃	C₂³	1	2	yes	—
202	#120×C₇₃	—	2	2	no	—
203	#120×C₇₃	—	2	2	no	—
204	#120×C₇₃	—	2	2	no	—
205	#120×C₇₃	—	2	2	no	—
206	#120×C₇₃	—	2	2	no	—
207	C₄×Q₈×C₇₃	—	2	2	no	—
208	C₄×Q₈×C₇₃	—	2	1	no	—
209	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₇₃	—	2	2	no	—
215	C₄×D₄×C₇₃	—	2	2	no	—
216	C₄×D₄×C₇₃	—	2	2	no	—
217	C₄×D₄×C₇₃	—	2	1	no	—
218	C₄×D₄×C₇₃	C₂³	1	2	yes	—
219	C₄×D₄×C₇₃	C₂³	1	2	yes	—
220	C₄×D₄×C₇₃	C₂³	1	2	yes	—
221	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
222	#117×C₇₃	—	2	1	no	—
223	#117×C₇₃	—	2	2	no	—
224	#117×C₇₃	—	2	2	no	—
225	#117×C₇₃	C₂³	1	2	yes	—
226	#117×C₇₃	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
228	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
234	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	#107×C₇₃	C₂³	1	2	yes	—
237	#107×C₇₃	C₂³	1	2	yes	—
238	#106×C₇₃	C₂³	1	2	yes	—
239	#106×C₇₃	C₂³	1	2	yes	—
240	#106×C₇₃	C₂³	1	2	yes	—
241	#106×C₇₃	C₂³	1	2	yes	—
242	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
243	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
245	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
246	#103×C₇₃	C₂³	1	2	yes	—
247	#103×C₇₃	C₂³	1	2	yes	—
248	#103×C₇₃	C₂³	1	2	yes	—
249	#103×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	#102×C₇₃	C₂³	1	2	yes	—
255	#102×C₇₃	C₂³	1	2	yes	—
256	#102×C₇₃	C₂³	1	2	yes	—
257	#102×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	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
267	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
268	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
269	#97×C₇₃	C₂³	1	2	yes	—
270	#97×C₇₃	C₂³	1	2	yes	—
271	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₇₃	C₂³	1	2	yes	—
276	C₂⁴×C₇₃	—	2	1	no	—
277	C₂⁴×C₇₃	—	2	2	no	—
278	#41×C₇₃	—	4	2	no	—
279	#41×C₇₃	—	4	2	no	—
280	#41×C₇₃	—	8	2	no	—
281	C₂×Q₈×C₇₃	—	2	1	no	—
282	C₂×Q₈×C₇₃	—	2	2	no	—
283	C₂×Q₈×C₇₃	—	2	1	no	—
284	C₂×Q₈×C₇₃	—	2	1	no	—
285	C₂×Q₈×C₇₃	—	4	1	no	—
286	C₂×Q₈×C₇₃	—	4	1	no	—
287	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
289	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₇₃	—	2	2	no	—
291	C₂×D₄×C₇₃	—	2	2	no	—
292	C₂×D₄×C₇₃	—	2	2	no	—
293	C₂×D₄×C₇₃	—	2	2	no	—
294	C₂×D₄×C₇₃	—	2	1	no	—
295	C₂×D₄×C₇₃	—	2	1	no	—
296	C₂×D₄×C₇₃	—	2	1	no	—
297	C₂×D₄×C₇₃	—	2	2	no	—
298	C₂×D₄×C₇₃	—	2	2	no	—
299	C₂×D₄×C₇₃	—	4	1	no	—
300	C₂×D₄×C₇₃	—	4	1	no	—
301	C₂×D₄×C₇₃	—	4	2	no	—
302	C₂×D₄×C₇₃	—	4	2	no	—
303	C₂×D₄×C₇₃	—	8	4	no	—
304	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₇₃	—	2	1	no	—
309	C₂²×C₄×C₇₃	—	2	1	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	2	no	—
314	C₂²×C₄×C₇₃	—	2	2	no	—
315	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
319	Q₁₆×C₇₃	—	4	2	no	—
320	Q₁₆×C₇₃	—	4	2	no	—
321	SD₁₆×C₇₃	—	4	2	no	—
322	SD₁₆×C₇₃	—	4	2	no	—
323	SD₁₆×C₇₃	—	4	2	no	—
324	SD₁₆×C₇₃	—	4	2	no	—
325	M₁₆×C₇₃	—	4	2	no	—
326	C₂×C₈×C₇₃	—	4	1	no	—
327	C₂×C₈×C₇₃	—	4	2	no	—
328	C₂×C₈×C₇₃	—	4	1	no	—
329	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
330	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₇₃	—	2	2	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	1	no	—
340	C₄⋊C₄×C₇₃	—	2	2	no	—
341	C₄⋊C₄×C₇₃	—	2	1	no	—
342	C₄⋊C₄×C₇₃	—	2	1	no	—
343	C₄⋊C₄×C₇₃	—	2	2	no	—
344	C₄⋊C₄×C₇₃	—	2	2	no	—
345	C₄⋊C₄×C₇₃	—	2	2	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	2	no	—
352	C₄⋊C₄×C₇₃	—	2	1	no	—
353	C₄⋊C₄×C₇₃	—	2	2	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	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
362	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
367	C₂²⋊C₄×C₇₃	—	2	2	no	—
368	C₂²⋊C₄×C₇₃	—	2	2	no	—
369	C₂²⋊C₄×C₇₃	—	2	2	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	2	no	—
381	C₂²⋊C₄×C₇₃	—	2	2	no	—
382	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
387	C₄²×C₇₃	—	2	2	no	—
388	C₄²×C₇₃	—	2	2	no	—
389	C₄²×C₇₃	—	2	2	no	—
390	C₄²×C₇₃	—	2	2	no	—
391	C₄²×C₇₃	—	2	2	no	—
392	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
396	C₄²×C₇₃	C₂⁴	1	2	yes	—
397	C₂³×C₇₃	—	2	2	no	—
398	C₂³×C₇₃	—	2	2	no	—
399	C₂³×C₇₃	—	4	2	no	—
400	C₂³×C₇₃	—	8	1	no	—
401	C₂³×C₇₃	—	8	2	no	—
402	C₂³×C₇₃	—	8	2	no	—
403	C₂³×C₇₃	—	8	1	no	—
404	C₂³×C₇₃	—	8	2	no	—
405	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
406	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
407	Q₈×C₇₃	—	2	2	no	—
408	Q₈×C₇₃	—	2	2	no	—
409	Q₈×C₇₃	—	2	2	no	—
410	Q₈×C₇₃	—	2	2	no	—
411	Q₈×C₇₃	—	4	1	no	—
412	Q₈×C₇₃	—	8	1	no	—
413	Q₈×C₇₃	—	8	2	no	—
414	Q₈×C₇₃	—	8	1	no	—
415	Q₈×C₇₃	—	8	1	no	—
416	D₄×C₇₃	—	2	4	no	—
417	D₄×C₇₃	—	2	2	no	—
418	D₄×C₇₃	—	2	2	no	—
419	D₄×C₇₃	—	2	2	no	—
420	D₄×C₇₃	—	2	2	no	—
421	D₄×C₇₃	—	4	1	no	—
422	D₄×C₇₃	—	4	4	no	—
423	D₄×C₇₃	—	8	1	no	—
424	D₄×C₇₃	—	8	2	no	—
425	D₄×C₇₃	—	8	2	no	—
426	D₄×C₇₃	—	8	1	no	—
427	D₄×C₇₃	—	8	2	no	—
428	D₄×C₇₃	—	8	1	no	—
429	D₄×C₇₃	—	8	2	no	—
430	D₄×C₇₃	—	8	2	no	—
431	C₂×C₄×C₇₃	—	2	2	no	—
432	C₂×C₄×C₇₃	—	2	1	no	—
433	C₂×C₄×C₇₃	—	2	1	no	—
434	C₂×C₄×C₇₃	—	2	2	no	—
435	C₂×C₄×C₇₃	—	2	2	no	—
436	C₂×C₄×C₇₃	—	2	2	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	2	no	—
442	C₂×C₄×C₇₃	—	4	1	no	—
443	C₂×C₄×C₇₃	—	4	2	no	—
444	C₂×C₄×C₇₃	—	8	2	no	—
445	C₂×C₄×C₇₃	—	8	2	no	—
446	C₂×C₄×C₇₃	—	8	2	no	—
447	C₂×C₄×C₇₃	—	8	1	no	—
448	C₂×C₄×C₇₃	—	8	2	no	—
449	C₂×C₄×C₇₃	—	8	1	no	—
450	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
459	C₈×C₇₃	—	2	1	no	—
460	C₈×C₇₃	—	2	1	no	—
461	C₈×C₇₃	—	2	1	no	—
462	C₈×C₇₃	—	2	1	no	—
463	C₈×C₇₃	—	2	2	no	—
464	C₈×C₇₃	—	2	2	no	—
465	C₂²×C₇₃	—	2	1	no	—
466	C₂²×C₇₃	—	2	1	no	—
467	C₂²×C₇₃	—	2	2	no	—
468	C₂²×C₇₃	—	2	2	no	—
469	C₂²×C₇₃	—	2	2	no	—
470	C₂²×C₇₃	—	4	2	no	—
471	C₂²×C₇₃	—	4	2	no	—
472	C₂²×C₇₃	—	4	2	no	—
473	C₂²×C₇₃	—	4	2	no	—
474	C₂²×C₇₃	—	4	2	no	—
475	C₂²×C₇₃	—	4	2	no	—
476	C₂²×C₇₃	—	16	2	no	—
477	C₂²×C₇₃	—	16	4	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	2	no	—
489	C₄×C₇₃	—	4	2	no	—
490	C₄×C₇₃	—	4	2	no	—
491	C₄×C₇₃	—	4	2	no	—
492	C₄×C₇₃	—	4	2	no	—
493	C₄×C₇₃	—	4	2	no	—
494	C₄×C₇₃	#585	1	1	yes	characteristic
495	C₄×C₇₃	#585	1	1	yes	characteristic
496	#62556	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂×C₇₃	—	2	2	no	—
498	C₂×C₇₃	—	4	2	no	—
499	C₂×C₇₃	—	8	2	no	—
500	C₂×C₇₃	—	8	2	no	—
501	C₂×C₇₃	#3500	1	1	yes	characteristic
502	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
503	C₂×C₇₃	#3584	1	1	yes	characteristic
504	#3563	C₂×C₇₃	1	1	yes	characteristic, complemented
505	#3558	C₂×C₇₃	1	1	yes	characteristic
506	#3371	C₂×C₇₃	1	2	yes	complemented
507	#3365	C₂×C₇₃	1	2	yes	complemented
508	#3323	C₂×C₇₃	1	2	yes	complemented
509	#3316	C₂×C₇₃	1	2	yes	complemented
510	#3310	C₂×C₇₃	1	2	yes	complemented
511	#3300	C₂×C₇₃	1	2	yes	complemented
512	#3296	C₂×C₇₃	1	2	yes	complemented
513	#3295	C₂×C₇₃	1	2	yes	complemented
514	#3244	C₂×C₇₃	1	2	yes	complemented
515	#3234	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#3222	C₂×C₇₃	1	2	yes	complemented
517	#3215	C₂×C₇₃	1	1	yes	characteristic, complemented
518	#3178	C₂×C₇₃	1	2	yes	complemented
519	#3167	C₂×C₇₃	1	1	yes	characteristic, complemented
520	#3136	C₂×C₇₃	1	2	yes	complemented
521	C₂×#488	C₂×C₇₃	1	1	yes	characteristic, complemented
522	#2966	C₂×C₇₃	1	1	yes	characteristic, complemented
523	C₇₃	#62556	1	1	yes	characteristic, direct product factor, Sylow
524	#564	—	2	1	no	—
525	#563	—	2	1	no	—
526	#562	—	2	1	no	—
527	H(3,𝔽₄)	—	2	1	no	—
528	#559	C₂²×C₇₃	1	2	yes	—
529	#557	C₂²×C₇₃	1	2	yes	complemented
530	#554	C₂²×C₇₃	1	2	yes	complemented
531	#552	—	2	2	no	—
532	#552	C₂²×C₇₃	1	2	yes	complemented
533	#552	C₂²×C₇₃	1	2	yes	complemented
534	#548	C₂²×C₇₃	1	2	yes	—
535	#546	—	2	2	no	—
536	#546	C₂²×C₇₃	1	2	yes	—
537	D₄²	C₂²×C₇₃	1	2	yes	—
538	#544	—	2	1	no	—
539	#544	C₂²×C₇₃	1	2	yes	complemented
540	#542	C₂²×C₇₃	1	2	yes	—
541	#541	—	2	2	no	—
542	#541	C₂²×C₇₃	1	2	yes	complemented
543	#539	—	2	1	no	—
544	#538	—	2	2	no	—
545	#538	—	2	1	no	—
546	#535	C₂²×C₇₃	1	2	yes	—
547	#534	—	2	1	no	—
548	#533	C₂²×C₇₃	1	1	yes	characteristic, complemented
549	#532	C₂²×C₇₃	1	1	yes	characteristic
550	#529	C₂²×C₇₃	1	1	yes	characteristic
551	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic, complemented
552	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
553	#501	C₂²×C₇₃	1	2	yes	complemented
554	#498	C₂²×C₇₃	1	1	yes	characteristic, complemented
555	#497	C₂²×C₇₃	1	2	yes	complemented
556	#492	C₂²×C₇₃	1	1	yes	characteristic, complemented
557	#490	C₂²×C₇₃	1	2	yes	—
558	#490	C₂²×C₇₃	1	2	yes	complemented
559	#489	C₂²×C₇₃	1	2	yes	complemented
560	#489	C₂²×C₇₃	1	2	yes	complemented
561	#488	C₂²×C₇₃	1	2	yes	complemented
562	#488	C₂²×C₇₃	1	2	yes	complemented
563	#488	C₂²×C₇₃	1	2	yes	complemented
564	#488	C₂²×C₇₃	1	2	yes	complemented
565	#488	C₂²×C₇₃	1	2	yes	complemented
566	#487	C₂²×C₇₃	1	1	yes	characteristic, complemented
567	#486	C₂²×C₇₃	1	2	yes	—
568	#486	C₂²×C₇₃	1	1	yes	characteristic, complemented
569	#485	C₂²×C₇₃	1	2	yes	complemented
570	#483	C₂²×C₇₃	1	2	yes	complemented
571	#482	C₂²×C₇₃	1	2	yes	—
572	#481	C₂²×C₇₃	1	2	yes	—
573	#481	C₂²×C₇₃	1	2	yes	complemented
574	#480	C₂²×C₇₃	1	2	yes	complemented
575	#479	C₂²×C₇₃	1	2	yes	complemented
576	#478	C₂²×C₇₃	1	2	yes	complemented
577	#478	C₂²×C₇₃	1	2	yes	complemented
578	#478	C₂²×C₇₃	1	2	yes	complemented
579	#476	C₂²×C₇₃	1	2	yes	complemented
580	#475	C₂²×C₇₃	1	2	yes	complemented
581	#470	C₂²×C₇₃	1	2	yes	complemented
582	#468	C₂²×C₇₃	1	2	yes	—
583	#467	C₂²×C₇₃	1	2	yes	complemented
584	#465	C₂²×C₇₃	1	2	yes	—
585	#465	C₂²×C₇₃	1	2	yes	complemented
586	#465	C₂²×C₇₃	1	2	yes	complemented
587	#464	C₂²×C₇₃	1	2	yes	complemented
588	#464	C₂²×C₇₃	1	2	yes	complemented
589	#464	C₂²×C₇₃	1	2	yes	complemented
590	#464	C₂²×C₇₃	1	2	yes	complemented
591	#460	C₂²×C₇₃	1	2	yes	—
592	#460	C₂²×C₇₃	1	2	yes	—
593	#452	C₂²×C₇₃	1	2	yes	complemented
594	#452	C₂²×C₇₃	1	2	yes	complemented
595	#451	C₂²×C₇₃	1	2	yes	complemented
596	#450	C₂²×C₇₃	1	2	yes	—
597	#450	C₂²×C₇₃	1	2	yes	complemented
598	#450	C₂²×C₇₃	1	2	yes	complemented
599	#446	C₂²×C₇₃	1	1	yes	characteristic, complemented
600	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
601	#441	C₂²×C₇₃	1	2	yes	complemented
602	#440	C₂²×C₇₃	1	2	yes	complemented
603	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
604	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
605	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
606	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
607	#436	C₂²×C₇₃	1	1	yes	characteristic, complemented
608	#435	C₂²×C₇₃	1	2	yes	complemented
609	C₈×D₄	C₂²×C₇₃	1	2	yes	complemented
610	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
611	#433	C₂²×C₇₃	1	2	yes	complemented
612	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
613	#418	C₂²×C₇₃	1	2	yes	complemented
614	#417	C₂²×C₇₃	1	2	yes	complemented
615	#416	C₂²×C₇₃	1	2	yes	complemented
616	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
617	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
618	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
619	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
620	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
621	#405	C₂²×C₇₃	1	2	yes	complemented
622	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
623	C₂×#41	—	2	1	no	—
624	C₂×#41	C₂³×C₇₃	1	2	yes	—
625	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
626	C₂²×D₄	—	2	2	no	—
627	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
629	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
631	C₂×SD₁₆	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×M₁₆	C₂³×C₇₃	1	2	yes	—
636	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
638	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
645	#127	C₂³×C₇₃	1	1	yes	characteristic
646	#127	C₂³×C₇₃	1	2	yes	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	D₄×C₇₃	1	2	yes	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	—	2	1	no	—
663	#125	—	2	1	no	—
664	#125	D₄×C₇₃	1	1	yes	characteristic
665	#125	C₂³×C₇₃	1	2	yes	—
666	#125	C₂³×C₇₃	1	2	yes	—
667	#125	C₂³×C₇₃	1	2	yes	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	—	2	1	no	—
673	#124	—	2	1	no	—
674	#124	D₄×C₇₃	1	1	yes	characteristic
675	#124	C₂³×C₇₃	1	2	yes	—
676	#124	C₂³×C₇₃	1	2	yes	—
677	#124	C₂³×C₇₃	1	2	yes	—
678	#123	—	2	2	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	D₄×C₇₃	1	2	yes	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
697	#121	—	2	2	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	D₄×C₇₃	1	1	yes	characteristic
704	#121	C₂³×C₇₃	1	2	yes	—
705	#121	C₂³×C₇₃	1	2	yes	—
706	#120	—	2	2	no	—
707	#120	—	2	2	no	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	#120	—	2	2	no	—
711	C₄×Q₈	—	2	2	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
714	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
715	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
716	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	C₂³×C₇₃	1	2	yes	—
723	C₄×D₄	C₂³×C₇₃	1	2	yes	—
724	C₄×D₄	C₂³×C₇₃	1	2	yes	—
725	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
726	#117	—	2	1	no	—
727	#117	—	2	2	no	—
728	#117	—	2	2	no	—
729	#117	C₂³×C₇₃	1	2	yes	—
730	#117	C₂³×C₇₃	1	2	yes	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	—	2	1	no	—
733	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
736	C₂×C₂²⋊C₄	—	2	1	no	—
737	C₂×C₂²⋊C₄	—	2	1	no	—
738	C₂×C₂²⋊C₄	—	2	2	no	—
739	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
740	#107	C₂³×C₇₃	1	2	yes	—
741	#107	C₂³×C₇₃	1	2	yes	—
742	#106	C₂³×C₇₃	1	2	yes	—
743	#106	C₂³×C₇₃	1	2	yes	—
744	#106	C₂³×C₇₃	1	2	yes	—
745	#106	C₂³×C₇₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
747	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
748	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
750	#103	C₂³×C₇₃	1	2	yes	—
751	#103	C₂³×C₇₃	1	2	yes	—
752	#103	C₂³×C₇₃	1	2	yes	—
753	#103	C₂³×C₇₃	1	2	yes	—
754	#103	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	#102	C₂³×C₇₃	1	2	yes	—
759	#102	C₂³×C₇₃	1	2	yes	—
760	#102	C₂³×C₇₃	1	2	yes	—
761	#102	C₂³×C₇₃	1	2	yes	—
762	#102	C₂³×C₇₃	1	2	yes	—
763	#102	C₂³×C₇₃	1	2	yes	—
764	#102	C₂³×C₇₃	1	2	yes	—
765	#102	C₂³×C₇₃	1	2	yes	—
766	#102	C₂³×C₇₃	1	2	yes	—
767	#102	C₂³×C₇₃	1	2	yes	—
768	#102	C₂³×C₇₃	1	2	yes	—
769	#102	C₂³×C₇₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
773	#97	C₂³×C₇₃	1	2	yes	—
774	#97	C₂³×C₇₃	1	2	yes	—
775	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
776	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
777	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₇₃	1	2	yes	—
780	C₂⁴	—	2	1	no	—
781	C₂⁴	—	2	2	no	—
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	—	8	2	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	4	1	no	—
790	C₂×Q₈	—	4	1	no	—
791	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	4	1	no	—
804	C₂×D₄	—	4	1	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	8	4	no	—
808	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
809	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
810	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
811	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
823	Q₁₆	—	4	2	no	—
824	Q₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	M₁₆	—	4	2	no	—
830	C₂×C₈	—	4	1	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	—	4	1	no	—
833	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
834	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
835	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
836	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
837	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
838	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	1	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	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
866	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
867	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	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	2	no	—
886	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
897	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
898	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
899	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
900	C₄²	C₂⁴×C₇₃	1	2	yes	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	4	2	no	—
904	C₂³	—	8	1	no	—
905	C₂³	—	8	2	no	—
906	C₂³	—	8	2	no	—
907	C₂³	—	8	1	no	—
908	C₂³	—	8	2	no	—
909	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
910	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	2	2	no	—
914	Q₈	—	2	2	no	—
915	Q₈	—	4	1	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	1	no	—
918	Q₈	—	8	1	no	—
919	Q₈	—	8	2	no	—
920	D₄	—	2	4	no	—
921	D₄	—	2	2	no	—
922	D₄	—	2	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	4	1	no	—
926	D₄	—	4	4	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	1	no	—
929	D₄	—	8	2	no	—
930	D₄	—	8	1	no	—
931	D₄	—	8	1	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	D₄	—	8	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	1	no	—
952	C₂×C₄	—	8	1	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
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	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
962	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
963	C₈	—	2	1	no	—
964	C₈	—	2	1	no	—
965	C₈	—	2	1	no	—
966	C₈	—	2	1	no	—
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	16	2	no	—
981	C₂²	—	16	4	no	—
982	C₂²	#577×C₇₃	1	2	yes	—
983	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
984	C₄	—	2	2	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	#585×C₇₃	1	1	yes	characteristic
999	C₄	#585×C₇₃	1	1	yes	characteristic
1000	C₂	—	2	2	no	—
1001	C₂	—	4	2	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₇₃×#3500	1	1	yes	characteristic
1005	C₂	C₂×#577×C₇₃	1	1	yes	characteristic
1006	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×#3558	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×#3371	C₂	semidirect
4. C₇₃×#3365	C₂	semidirect
5. C₇₃×#3323	C₂	semidirect
6. C₇₃×#3316	C₂	semidirect
7. C₇₃×#3310	C₂	semidirect
8. C₇₃×#3300	C₂	semidirect
9. C₇₃×#3296	C₂	semidirect
10. C₇₃×#3295	C₂	semidirect
11. C₇₃×#3244	C₂	semidirect
12. C₇₃×#3234	C₂	semidirect
13. C₇₃×#3222	C₂	semidirect
14. C₇₃×#3215	C₂	semidirect
15. C₇₃×#3178	C₂	semidirect
16. C₇₃×#3167	C₂	semidirect
17. C₇₃×#3136	C₂	semidirect
18. C₂×#488×C₇₃	C₂	semidirect
19. C₇₃×#2966	C₂	semidirect
25. #557×C₇₃	C₂²	semidirect
26. #554×C₇₃	C₂²	semidirect
28. #552×C₇₃	C₂²	semidirect
29. #552×C₇₃	C₂²	semidirect
35. #544×C₇₃	C₂²	semidirect
38. #541×C₇₃	C₂²	semidirect
44. #533×C₇₃	C₂²	semidirect
47. C₂×#125×C₇₃	C₂²	semidirect
49. #501×C₇₃	C₂²	semidirect
50. #498×C₇₃	C₂²	semidirect
51. #497×C₇₃	C₂²	semidirect
52. #492×C₇₃	C₂²	semidirect
54. #490×C₇₃	C₂²	semidirect
55. #489×C₇₃	C₂²	semidirect
56. #489×C₇₃	C₂²	semidirect
57. #488×C₇₃	C₂²	semidirect
58. #488×C₇₃	C₂²	semidirect
59. #488×C₇₃	C₂²	semidirect
60. #488×C₇₃	C₂²	semidirect
61. #488×C₇₃	C₂²	semidirect
62. #487×C₇₃	C₂²	semidirect
64. #486×C₇₃	C₂²	semidirect
65. #485×C₇₃	C₂²	semidirect
66. #483×C₇₃	C₂²	semidirect
69. #481×C₇₃	C₂²	semidirect
70. #480×C₇₃	C₂²	semidirect
71. #479×C₇₃	C₂²	semidirect
72. #478×C₇₃	C₂²	semidirect
73. #478×C₇₃	C₂²	semidirect
74. #478×C₇₃	C₂²	semidirect
75. #476×C₇₃	C₂²	semidirect
76. #475×C₇₃	C₂²	semidirect
77. #470×C₇₃	C₂²	semidirect
79. #467×C₇₃	C₂²	semidirect
81. #465×C₇₃	C₂²	semidirect
82. #465×C₇₃	C₂²	semidirect
83. #464×C₇₃	C₂²	semidirect
84. #464×C₇₃	C₂²	semidirect
85. #464×C₇₃	C₂²	semidirect
86. #464×C₇₃	C₂²	semidirect
89. #452×C₇₃	C₂²	semidirect
90. #452×C₇₃	C₂²	semidirect
91. #451×C₇₃	C₂²	semidirect
93. #450×C₇₃	C₂²	semidirect
94. #450×C₇₃	C₂²	semidirect
95. #446×C₇₃	C₂²	semidirect
96. C₈×Q₈×C₇₃	C₂²	semidirect
97. #441×C₇₃	C₂²	semidirect
98. #440×C₇₃	C₂²	semidirect
99. C₄×Q₁₆×C₇₃	C₂²	semidirect
100. C₄×SD₁₆×C₇₃	C₂²	semidirect
101. C₄×SD₁₆×C₇₃	C₂²	semidirect
102. C₄×SD₁₆×C₇₃	C₂²	semidirect
103. #436×C₇₃	C₂²	semidirect
104. #435×C₇₃	C₂²	semidirect
105. C₈×D₄×C₇₃	C₂²	semidirect
106. C₈×D₄×C₇₃	C₂²	semidirect
107. #433×C₇₃	C₂²	semidirect
108. #432×C₇₃	C₂²	semidirect
109. #418×C₇₃	C₂²	semidirect
110. #417×C₇₃	C₂²	semidirect
111. #416×C₇₃	C₂²	semidirect
112. C₂×#103×C₇₃	C₂²	semidirect
113. C₂×#103×C₇₃	C₂²	semidirect
116. C₂×#102×C₇₃	C₂²	semidirect
117. #405×C₇₃	C₂²	semidirect
118. C₂×C₄×C₈×C₇₃	C₂²	semidirect
496. #62556	C₇₃	direct (N × H)
504. #3563	C₂×C₇₃	semidirect
506. #3371	C₂×C₇₃	semidirect
507. #3365	C₂×C₇₃	semidirect
508. #3323	C₂×C₇₃	semidirect
509. #3316	C₂×C₇₃	semidirect
510. #3310	C₂×C₇₃	semidirect
511. #3300	C₂×C₇₃	semidirect
512. #3296	C₂×C₇₃	semidirect
513. #3295	C₂×C₇₃	semidirect
514. #3244	C₂×C₇₃	semidirect
515. #3234	C₂×C₇₃	semidirect
516. #3222	C₂×C₇₃	semidirect
517. #3215	C₂×C₇₃	semidirect
518. #3178	C₂×C₇₃	semidirect
519. #3167	C₂×C₇₃	semidirect
520. #3136	C₂×C₇₃	semidirect
521. C₂×#488	C₂×C₇₃	semidirect
522. #2966	C₂×C₇₃	semidirect
523. C₇₃	#62556	direct (N × H)
529. #557	C₂²×C₇₃	semidirect
530. #554	C₂²×C₇₃	semidirect
532. #552	C₂²×C₇₃	semidirect
533. #552	C₂²×C₇₃	semidirect
539. #544	C₂²×C₇₃	semidirect
542. #541	C₂²×C₇₃	semidirect
548. #533	C₂²×C₇₃	semidirect
551. C₂×#125	C₂²×C₇₃	semidirect
553. #501	C₂²×C₇₃	semidirect
554. #498	C₂²×C₇₃	semidirect
555. #497	C₂²×C₇₃	semidirect
556. #492	C₂²×C₇₃	semidirect
558. #490	C₂²×C₇₃	semidirect
559. #489	C₂²×C₇₃	semidirect
560. #489	C₂²×C₇₃	semidirect
561. #488	C₂²×C₇₃	semidirect
562. #488	C₂²×C₇₃	semidirect
563. #488	C₂²×C₇₃	semidirect
564. #488	C₂²×C₇₃	semidirect
565. #488	C₂²×C₇₃	semidirect
566. #487	C₂²×C₇₃	semidirect
568. #486	C₂²×C₇₃	semidirect
569. #485	C₂²×C₇₃	semidirect
570. #483	C₂²×C₇₃	semidirect
573. #481	C₂²×C₇₃	semidirect
574. #480	C₂²×C₇₃	semidirect
575. #479	C₂²×C₇₃	semidirect
576. #478	C₂²×C₇₃	semidirect
577. #478	C₂²×C₇₃	semidirect
578. #478	C₂²×C₇₃	semidirect
579. #476	C₂²×C₇₃	semidirect
580. #475	C₂²×C₇₃	semidirect
581. #470	C₂²×C₇₃	semidirect
583. #467	C₂²×C₇₃	semidirect
585. #465	C₂²×C₇₃	semidirect
586. #465	C₂²×C₇₃	semidirect
587. #464	C₂²×C₇₃	semidirect
588. #464	C₂²×C₇₃	semidirect
589. #464	C₂²×C₇₃	semidirect
590. #464	C₂²×C₇₃	semidirect
593. #452	C₂²×C₇₃	semidirect
594. #452	C₂²×C₇₃	semidirect
595. #451	C₂²×C₇₃	semidirect
597. #450	C₂²×C₇₃	semidirect
598. #450	C₂²×C₇₃	semidirect
599. #446	C₂²×C₇₃	semidirect
600. C₈×Q₈	C₂²×C₇₃	semidirect
601. #441	C₂²×C₇₃	semidirect
602. #440	C₂²×C₇₃	semidirect
603. C₄×Q₁₆	C₂²×C₇₃	semidirect
604. C₄×SD₁₆	C₂²×C₇₃	semidirect
605. C₄×SD₁₆	C₂²×C₇₃	semidirect
606. C₄×SD₁₆	C₂²×C₇₃	semidirect
607. #436	C₂²×C₇₃	semidirect
608. #435	C₂²×C₇₃	semidirect
609. C₈×D₄	C₂²×C₇₃	semidirect
610. C₈×D₄	C₂²×C₇₃	semidirect
611. #433	C₂²×C₇₃	semidirect
612. #432	C₂²×C₇₃	semidirect
613. #418	C₂²×C₇₃	semidirect
614. #417	C₂²×C₇₃	semidirect
615. #416	C₂²×C₇₃	semidirect
616. C₂×#103	C₂²×C₇₃	semidirect
617. C₂×#103	C₂²×C₇₃	semidirect
620. C₂×#102	C₂²×C₇₃	semidirect
621. #405	C₂²×C₇₃	semidirect
622. C₂×C₄×C₈	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×#3558	2
C₇₃×#3371	2
C₇₃×#3365	2
C₇₃×#3323	2
C₇₃×#3316	2
C₇₃×#3310	2
C₇₃×#3300	2
C₇₃×#3296	2
C₇₃×#3295	2
C₇₃×#3244	2
C₇₃×#3234	2
C₇₃×#3222	2
C₇₃×#3215	2
C₇₃×#3178	2
C₇₃×#3167	2
C₇₃×#3136	2
C₂×#488×C₇₃	2
C₇₃×#2966	2
#62556	73

Subgroups — C73×#62556 #32971960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62556 #32971960