Subgroups — C₇₃×#62576 #32971980

Order 18688.

2050 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3368	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3295	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#3234	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3217	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#490×C₇₃	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₇₃	—	2	1	no	—
19	#557×C₇₃	C₂²	1	1	yes	characteristic, complemented
20	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#553×C₇₃	C₂²	1	2	yes	complemented
23	#552×C₇₃	—	2	2	no	—
24	#552×C₇₃	—	2	1	no	—
25	#552×C₇₃	C₂²	1	2	yes	complemented
26	#550×C₇₃	—	2	1	no	—
27	#550×C₇₃	C₂²	1	2	yes	—
28	#547×C₇₃	—	2	1	no	—
29	#547×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	D₄²×C₇₃	—	2	1	no	—
31	D₄²×C₇₃	—	2	2	no	—
32	D₄²×C₇₃	C₂²	1	2	yes	—
33	D₄²×C₇₃	C₂²	1	4	yes	—
34	#541×C₇₃	—	2	1	no	—
35	#539×C₇₃	—	2	2	no	—
36	#535×C₇₃	—	2	1	no	—
37	#535×C₇₃	—	2	2	no	—
38	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
39	#532×C₇₃	C₂²	1	2	yes	—
40	#532×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#127×C₇₃	C₂²	1	2	yes	—
42	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
43	#529×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	#529×C₇₃	C₂²	1	2	yes	complemented
45	C₂×#125×C₇₃	C₂²	1	2	yes	complemented
46	#520×C₇₃	—	2	1	no	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	#501×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	#501×C₇₃	C₂²	1	2	yes	complemented
50	#496×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#496×C₇₃	C₂²	1	2	yes	complemented
52	#490×C₇₃	C₂²	1	2	yes	complemented
53	#490×C₇₃	C₂²	1	2	yes	complemented
54	#490×C₇₃	C₂²	1	2	yes	complemented
55	#490×C₇₃	C₂²	1	4	yes	complemented
56	#490×C₇₃	C₂²	1	4	yes	complemented
57	#490×C₇₃	C₂²	1	1	yes	characteristic, complemented
58	#490×C₇₃	C₂²	1	2	yes	complemented
59	#489×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#486×C₇₃	C₂²	1	2	yes	complemented
61	#486×C₇₃	C₂²	1	2	yes	complemented
62	#482×C₇₃	C₂²	1	4	yes	complemented
63	#481×C₇₃	C₂²	1	4	yes	complemented
64	#480×C₇₃	C₂²	1	4	yes	complemented
65	#478×C₇₃	C₂²	1	4	yes	complemented
66	#478×C₇₃	C₂²	1	4	yes	complemented
67	#476×C₇₃	C₂²	1	2	yes	complemented
68	#474×C₇₃	C₂²	1	2	yes	complemented
69	#469×C₇₃	C₂²	1	2	yes	complemented
70	#468×C₇₃	C₂²	1	2	yes	complemented
71	#466×C₇₃	C₂²	1	4	yes	complemented
72	#465×C₇₃	C₂²	1	4	yes	complemented
73	#460×C₇₃	C₂²	1	2	yes	complemented
74	#460×C₇₃	C₂²	1	4	yes	complemented
75	#459×C₇₃	C₂²	1	2	yes	complemented
76	#459×C₇₃	C₂²	1	4	yes	complemented
77	#450×C₇₃	C₂²	1	4	yes	complemented
78	#450×C₇₃	C₂²	1	2	yes	complemented
79	#447×C₇₃	C₂²	1	4	yes	complemented
80	#447×C₇₃	C₂²	1	2	yes	complemented
81	#446×C₇₃	C₂²	1	2	yes	complemented
82	#442×C₇₃	C₂²	1	4	yes	complemented
83	#440×C₇₃	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₇₃	C₂²	1	2	yes	complemented
86	#435×C₇₃	C₂²	1	4	yes	complemented
87	C₈×D₄×C₇₃	C₂²	1	2	yes	complemented
88	#432×C₇₃	C₂²	1	2	yes	complemented
89	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
90	#418×C₇₃	C₂²	1	4	yes	complemented
91	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
92	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₇₃	—	4	8	no	—
96	C₂×#41×C₇₃	—	2	2	no	—
97	C₂×#41×C₇₃	—	2	1	no	—
98	C₂×#41×C₇₃	—	2	2	no	—
99	C₂×#41×C₇₃	—	2	1	no	—
100	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₇₃	—	2	4	no	—
102	C₂²×D₄×C₇₃	—	2	2	no	—
103	C₂²×D₄×C₇₃	—	2	2	no	—
104	C₂²×D₄×C₇₃	—	2	1	no	—
105	C₂²×D₄×C₇₃	—	2	2	no	—
106	C₂²×D₄×C₇₃	—	2	1	no	—
107	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
111	C₂×D₈×C₇₃	C₂³	1	2	yes	—
112	C₂×D₈×C₇₃	C₂³	1	4	yes	—
113	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
114	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₇₃	—	2	1	no	—
116	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
119	#127×C₇₃	—	2	2	no	—
120	#127×C₇₃	—	2	1	no	—
121	#127×C₇₃	—	2	1	no	—
122	#127×C₇₃	—	2	2	no	—
123	#127×C₇₃	C₂³	1	2	yes	—
124	#127×C₇₃	C₂³	1	4	yes	—
125	#127×C₇₃	C₂³	1	2	yes	—
126	#127×C₇₃	C₂³	1	1	yes	characteristic
127	#126×C₇₃	—	2	2	no	—
128	#126×C₇₃	—	2	2	no	—
129	#126×C₇₃	—	2	2	no	—
130	#126×C₇₃	—	2	1	no	—
131	#125×C₇₃	—	2	2	no	—
132	#125×C₇₃	—	2	2	no	—
133	#125×C₇₃	—	2	1	no	—
134	#125×C₇₃	—	2	2	no	—
135	#125×C₇₃	—	2	2	no	—
136	#125×C₇₃	C₂³	1	2	yes	—
137	#125×C₇₃	C₂³	1	2	yes	—
138	#125×C₇₃	C₂³	1	1	yes	characteristic
139	#125×C₇₃	C₂³	1	2	yes	—
140	#124×C₇₃	—	2	2	no	—
141	#124×C₇₃	—	2	1	no	—
142	#124×C₇₃	C₂³	1	1	yes	characteristic
143	#123×C₇₃	—	2	2	no	—
144	#123×C₇₃	—	2	1	no	—
145	#123×C₇₃	—	2	2	no	—
146	#123×C₇₃	—	2	2	no	—
147	#123×C₇₃	—	2	2	no	—
148	C₂²⋊Q₈×C₇₃	—	2	1	no	—
149	C₂²⋊Q₈×C₇₃	—	2	1	no	—
150	C₂²⋊Q₈×C₇₃	—	2	1	no	—
151	C₂²⋊Q₈×C₇₃	—	2	2	no	—
152	C₂²⋊Q₈×C₇₃	—	2	1	no	—
153	C₂²⋊Q₈×C₇₃	—	2	2	no	—
154	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
156	#121×C₇₃	—	2	2	no	—
157	#121×C₇₃	—	2	2	no	—
158	#121×C₇₃	—	2	1	no	—
159	#121×C₇₃	—	2	2	no	—
160	#121×C₇₃	—	2	4	no	—
161	#121×C₇₃	—	2	2	no	—
162	#121×C₇₃	—	2	4	no	—
163	#121×C₇₃	C₂³	1	2	yes	—
164	#121×C₇₃	C₂³	1	1	yes	characteristic
165	#121×C₇₃	C₂³	1	4	yes	—
166	#121×C₇₃	C₂³	1	2	yes	—
167	#120×C₇₃	—	2	4	no	—
168	#120×C₇₃	—	2	4	no	—
169	#120×C₇₃	—	2	4	no	—
170	C₄×Q₈×C₇₃	—	2	1	no	—
171	C₄×Q₈×C₇₃	—	2	1	no	—
172	C₄×Q₈×C₇₃	—	2	1	no	—
173	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₇₃	—	2	1	no	—
178	C₄×D₄×C₇₃	—	2	2	no	—
179	C₄×D₄×C₇₃	—	2	1	no	—
180	C₄×D₄×C₇₃	—	2	2	no	—
181	C₄×D₄×C₇₃	—	2	1	no	—
182	C₄×D₄×C₇₃	—	2	2	no	—
183	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₇₃	D₄	1	2	yes	—
185	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₇₃	C₂³	1	2	yes	—
187	C₄×D₄×C₇₃	C₂³	1	4	yes	—
188	C₄×D₄×C₇₃	C₂³	1	2	yes	—
189	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₇₃	C₂³	1	2	yes	—
191	#117×C₇₃	—	2	2	no	—
192	#117×C₇₃	—	2	1	no	—
193	#117×C₇₃	—	2	2	no	—
194	#117×C₇₃	D₄	1	1	yes	characteristic
195	#117×C₇₃	D₄	1	2	yes	—
196	#117×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
204	#107×C₇₃	C₂³	1	2	yes	—
205	#107×C₇₃	C₂³	1	4	yes	—
206	#106×C₇₃	C₂³	1	2	yes	—
207	#106×C₇₃	C₂³	1	4	yes	—
208	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
210	#103×C₇₃	C₂³	1	2	yes	—
211	#102×C₇₃	C₂³	1	2	yes	—
212	#102×C₇₃	C₂³	1	2	yes	—
213	#102×C₇₃	C₂³	1	4	yes	—
214	#102×C₇₃	C₂³	1	4	yes	—
215	#102×C₇₃	C₂³	1	4	yes	—
216	#102×C₇₃	C₂³	1	4	yes	—
217	#102×C₇₃	C₂³	1	4	yes	—
218	#102×C₇₃	C₂³	1	4	yes	—
219	#102×C₇₃	C₂³	1	4	yes	—
220	#102×C₇₃	C₂³	1	4	yes	—
221	#102×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
223	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
224	#97×C₇₃	C₂³	1	1	yes	characteristic
225	#97×C₇₃	C₂³	1	2	yes	—
226	#97×C₇₃	C₂³	1	4	yes	—
227	#97×C₇₃	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₇₃	C₂³	1	2	yes	—
229	C₂⁴×C₇₃	—	2	2	no	—
230	C₂⁴×C₇₃	—	2	4	no	—
231	#41×C₇₃	—	2	4	no	—
232	#41×C₇₃	—	4	8	no	—
233	#41×C₇₃	—	4	4	no	—
234	#41×C₇₃	—	4	8	no	—
235	#41×C₇₃	—	4	4	no	—
236	C₂×Q₈×C₇₃	—	2	1	no	—
237	C₂×Q₈×C₇₃	—	2	1	no	—
238	C₂×Q₈×C₇₃	—	2	1	no	—
239	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₇₃	—	2	2	no	—
242	C₂×D₄×C₇₃	—	2	2	no	—
243	C₂×D₄×C₇₃	—	2	4	no	—
244	C₂×D₄×C₇₃	—	2	1	no	—
245	C₂×D₄×C₇₃	—	2	1	no	—
246	C₂×D₄×C₇₃	—	2	2	no	—
247	C₂×D₄×C₇₃	—	2	4	no	—
248	C₂×D₄×C₇₃	—	2	2	no	—
249	C₂×D₄×C₇₃	—	2	2	no	—
250	C₂×D₄×C₇₃	—	2	1	no	—
251	C₂×D₄×C₇₃	—	2	2	no	—
252	C₂×D₄×C₇₃	—	2	4	no	—
253	C₂×D₄×C₇₃	—	2	4	no	—
254	C₂×D₄×C₇₃	—	2	2	no	—
255	C₂×D₄×C₇₃	—	4	4	no	—
256	C₂×D₄×C₇₃	—	4	4	no	—
257	C₂×D₄×C₇₃	—	4	4	no	—
258	C₂×D₄×C₇₃	—	4	8	no	—
259	C₂×D₄×C₇₃	—	4	4	no	—
260	C₂×D₄×C₇₃	—	4	16	no	—
261	C₂×D₄×C₇₃	—	4	8	no	—
262	C₂×D₄×C₇₃	—	8	4	no	—
263	C₂×D₄×C₇₃	—	8	2	no	—
264	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
268	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₃	—	2	2	no	—
270	C₂²×C₄×C₇₃	—	2	2	no	—
271	C₂²×C₄×C₇₃	—	2	1	no	—
272	C₂²×C₄×C₇₃	—	2	4	no	—
273	C₂²×C₄×C₇₃	—	2	2	no	—
274	C₂²×C₄×C₇₃	—	2	2	no	—
275	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	SD₁₆×C₇₃	—	4	4	no	—
282	SD₁₆×C₇₃	—	4	2	no	—
283	D₈×C₇₃	—	4	4	no	—
284	D₈×C₇₃	—	4	2	no	—
285	M₁₆×C₇₃	—	4	2	no	—
286	C₂×C₈×C₇₃	—	4	4	no	—
287	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
289	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
290	C₄⋊C₄×C₇₃	—	2	2	no	—
291	C₄⋊C₄×C₇₃	—	2	1	no	—
292	C₄⋊C₄×C₇₃	—	2	1	no	—
293	C₄⋊C₄×C₇₃	—	2	2	no	—
294	C₄⋊C₄×C₇₃	—	2	1	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	—	2	2	no	—
297	C₄⋊C₄×C₇₃	—	2	2	no	—
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	—	2	2	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	1	no	—
302	C₄⋊C₄×C₇₃	—	2	2	no	—
303	C₄⋊C₄×C₇₃	—	2	1	no	—
304	C₄⋊C₄×C₇₃	—	2	1	no	—
305	C₄⋊C₄×C₇₃	—	2	1	no	—
306	C₄⋊C₄×C₇₃	—	2	2	no	—
307	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	1	no	—
319	C₂²⋊C₄×C₇₃	—	2	1	no	—
320	C₂²⋊C₄×C₇₃	—	2	1	no	—
321	C₂²⋊C₄×C₇₃	—	2	1	no	—
322	C₂²⋊C₄×C₇₃	—	2	2	no	—
323	C₂²⋊C₄×C₇₃	—	2	2	no	—
324	C₂²⋊C₄×C₇₃	—	2	4	no	—
325	C₂²⋊C₄×C₇₃	—	2	4	no	—
326	C₂²⋊C₄×C₇₃	—	2	2	no	—
327	C₂²⋊C₄×C₇₃	—	2	2	no	—
328	C₂²⋊C₄×C₇₃	—	2	1	no	—
329	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
332	C₄²×C₇₃	—	2	2	no	—
333	C₄²×C₇₃	—	2	2	no	—
334	C₄²×C₇₃	—	2	1	no	—
335	C₄²×C₇₃	C₂×D₄	1	2	yes	—
336	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇₃	C₂×D₄	1	2	yes	—
339	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₇₃	C₂⁴	1	2	yes	—
342	C₂³×C₇₃	—	2	1	no	—
343	C₂³×C₇₃	—	2	4	no	—
344	C₂³×C₇₃	—	2	2	no	—
345	C₂³×C₇₃	—	4	4	no	—
346	C₂³×C₇₃	—	4	8	no	—
347	C₂³×C₇₃	—	8	4	no	—
348	C₂³×C₇₃	—	8	2	no	—
349	C₂³×C₇₃	—	8	4	no	—
350	C₂³×C₇₃	—	8	2	no	—
351	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
353	Q₈×C₇₃	—	2	2	no	—
354	Q₈×C₇₃	—	2	2	no	—
355	Q₈×C₇₃	—	4	2	no	—
356	Q₈×C₇₃	—	4	2	no	—
357	Q₈×C₇₃	—	8	1	no	—
358	D₄×C₇₃	—	2	4	no	—
359	D₄×C₇₃	—	2	2	no	—
360	D₄×C₇₃	—	2	4	no	—
361	D₄×C₇₃	—	2	2	no	—
362	D₄×C₇₃	—	2	4	no	—
363	D₄×C₇₃	—	2	2	no	—
364	D₄×C₇₃	—	4	4	no	—
365	D₄×C₇₃	—	4	2	no	—
366	D₄×C₇₃	—	4	8	no	—
367	D₄×C₇₃	—	4	2	no	—
368	D₄×C₇₃	—	4	4	no	—
369	D₄×C₇₃	—	4	4	no	—
370	D₄×C₇₃	—	4	8	no	—
371	D₄×C₇₃	—	4	4	no	—
372	D₄×C₇₃	—	4	4	no	—
373	D₄×C₇₃	—	8	4	no	—
374	D₄×C₇₃	—	8	2	no	—
375	D₄×C₇₃	—	8	4	no	—
376	D₄×C₇₃	—	8	2	no	—
377	D₄×C₇₃	—	8	1	no	—
378	D₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
379	C₂×C₄×C₇₃	—	2	4	no	—
380	C₂×C₄×C₇₃	—	2	2	no	—
381	C₂×C₄×C₇₃	—	2	4	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	2	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	1	no	—
389	C₂×C₄×C₇₃	—	4	2	no	—
390	C₂×C₄×C₇₃	—	4	1	no	—
391	C₂×C₄×C₇₃	—	4	8	no	—
392	C₂×C₄×C₇₃	—	4	4	no	—
393	C₂×C₄×C₇₃	—	4	4	no	—
394	C₂×C₄×C₇₃	—	4	2	no	—
395	C₂×C₄×C₇₃	—	8	2	no	—
396	C₂×C₄×C₇₃	—	8	2	no	—
397	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₇₃	—	2	2	no	—
407	C₈×C₇₃	—	2	4	no	—
408	C₈×C₇₃	—	2	2	no	—
409	C₂²×C₇₃	—	2	2	no	—
410	C₂²×C₇₃	—	2	2	no	—
411	C₂²×C₇₃	—	2	1	no	—
412	C₂²×C₇₃	—	2	1	no	—
413	C₂²×C₇₃	—	2	1	no	—
414	C₂²×C₇₃	—	4	1	no	—
415	C₂²×C₇₃	—	4	2	no	—
416	C₂²×C₇₃	—	4	4	no	—
417	C₂²×C₇₃	—	4	2	no	—
418	C₂²×C₇₃	—	4	4	no	—
419	C₂²×C₇₃	—	4	1	no	—
420	C₂²×C₇₃	—	4	4	no	—
421	C₂²×C₇₃	—	4	2	no	—
422	C₂²×C₇₃	—	4	1	no	—
423	C₂²×C₇₃	—	16	8	no	—
424	C₂²×C₇₃	—	16	4	no	—
425	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
426	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₇₃	—	2	1	no	—
428	C₄×C₇₃	—	2	2	no	—
429	C₄×C₇₃	—	2	1	no	—
430	C₄×C₇₃	—	2	2	no	—
431	C₄×C₇₃	—	2	1	no	—
432	C₄×C₇₃	—	2	1	no	—
433	C₄×C₇₃	—	2	2	no	—
434	C₄×C₇₃	—	4	1	no	—
435	C₄×C₇₃	—	4	2	no	—
436	C₄×C₇₃	—	4	1	no	—
437	C₄×C₇₃	—	4	1	no	—
438	C₄×C₇₃	—	4	2	no	—
439	C₄×C₇₃	—	4	2	no	—
440	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
441	C₄×C₇₃	#585	1	2	yes	—
442	#62576	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₂×C₇₃	—	2	4	no	—
444	C₂×C₇₃	—	4	1	no	—
445	C₂×C₇₃	—	8	1	no	—
446	C₂×C₇₃	—	8	2	no	—
447	C₂×C₇₃	—	8	4	no	—
448	C₂×C₇₃	#3500	1	1	yes	characteristic
449	C₂×C₇₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
450	C₂×C₇₃	#3585	1	1	yes	characteristic
451	#3515	C₂×C₇₃	1	1	yes	characteristic, complemented
452	#3498	C₂×C₇₃	1	1	yes	characteristic, complemented
453	#3368	C₂×C₇₃	1	2	yes	complemented
454	#3366	C₂×C₇₃	1	2	yes	complemented
455	#3318	C₂×C₇₃	1	4	yes	complemented
456	#3310	C₂×C₇₃	1	4	yes	complemented
457	#3295	C₂×C₇₃	1	2	yes	complemented
458	#3294	C₂×C₇₃	1	2	yes	complemented
459	#3235	C₂×C₇₃	1	1	yes	characteristic, complemented
460	#3234	C₂×C₇₃	1	2	yes	complemented
461	#3217	C₂×C₇₃	1	1	yes	characteristic, complemented
462	#3217	C₂×C₇₃	1	2	yes	complemented
463	#3180	C₂×C₇₃	1	2	yes	complemented
464	#3171	C₂×C₇₃	1	1	yes	characteristic, complemented
465	#3138	C₂×C₇₃	1	1	yes	characteristic, complemented
466	C₂×#490	C₂×C₇₃	1	2	yes	complemented
467	#2970	C₂×C₇₃	1	1	yes	characteristic, complemented
468	C₇₃	#62576	1	1	yes	characteristic, direct product factor, Sylow
469	C₂×H(5,𝔽₂)	—	2	1	no	—
470	#557	C₂²×C₇₃	1	1	yes	characteristic, complemented
471	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
472	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
473	#553	C₂²×C₇₃	1	2	yes	complemented
474	#552	—	2	2	no	—
475	#552	—	2	1	no	—
476	#552	C₂²×C₇₃	1	2	yes	complemented
477	#550	—	2	1	no	—
478	#550	C₂²×C₇₃	1	2	yes	—
479	#547	—	2	1	no	—
480	#547	C₂²×C₇₃	1	1	yes	characteristic, complemented
481	D₄²	—	2	1	no	—
482	D₄²	—	2	2	no	—
483	D₄²	C₂²×C₇₃	1	2	yes	—
484	D₄²	C₂²×C₇₃	1	4	yes	—
485	#541	—	2	1	no	—
486	#539	—	2	2	no	—
487	#535	—	2	1	no	—
488	#535	—	2	2	no	—
489	#533	C₂²×C₇₃	1	1	yes	characteristic, complemented
490	#532	C₂²×C₇₃	1	1	yes	characteristic
491	#532	C₂²×C₇₃	1	2	yes	—
492	C₂×#127	C₂²×C₇₃	1	2	yes	—
493	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
494	#529	C₂²×C₇₃	1	1	yes	characteristic, complemented
495	#529	C₂²×C₇₃	1	2	yes	complemented
496	C₂×#125	C₂²×C₇₃	1	2	yes	complemented
497	#520	—	2	1	no	—
498	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
499	#501	C₂²×C₇₃	1	1	yes	characteristic, complemented
500	#501	C₂²×C₇₃	1	2	yes	complemented
501	#496	C₂²×C₇₃	1	1	yes	characteristic, complemented
502	#496	C₂²×C₇₃	1	2	yes	complemented
503	#490	C₂²×C₇₃	1	4	yes	complemented
504	#490	C₂²×C₇₃	1	4	yes	complemented
505	#490	C₂²×C₇₃	1	1	yes	characteristic, complemented
506	#490	C₂²×C₇₃	1	2	yes	complemented
507	#490	C₂²×C₇₃	1	2	yes	complemented
508	#490	C₂²×C₇₃	1	2	yes	complemented
509	#490	C₂²×C₇₃	1	2	yes	complemented
510	#489	C₂²×C₇₃	1	1	yes	characteristic, complemented
511	#486	C₂²×C₇₃	1	2	yes	complemented
512	#486	C₂²×C₇₃	1	2	yes	complemented
513	#482	C₂²×C₇₃	1	4	yes	complemented
514	#481	C₂²×C₇₃	1	4	yes	complemented
515	#480	C₂²×C₇₃	1	4	yes	complemented
516	#478	C₂²×C₇₃	1	4	yes	complemented
517	#478	C₂²×C₇₃	1	4	yes	complemented
518	#476	C₂²×C₇₃	1	2	yes	complemented
519	#474	C₂²×C₇₃	1	2	yes	complemented
520	#469	C₂²×C₇₃	1	2	yes	complemented
521	#468	C₂²×C₇₃	1	2	yes	complemented
522	#466	C₂²×C₇₃	1	4	yes	complemented
523	#465	C₂²×C₇₃	1	4	yes	complemented
524	#460	C₂²×C₇₃	1	2	yes	complemented
525	#460	C₂²×C₇₃	1	4	yes	complemented
526	#459	C₂²×C₇₃	1	2	yes	complemented
527	#459	C₂²×C₇₃	1	4	yes	complemented
528	#450	C₂²×C₇₃	1	4	yes	complemented
529	#450	C₂²×C₇₃	1	2	yes	complemented
530	#447	C₂²×C₇₃	1	4	yes	complemented
531	#447	C₂²×C₇₃	1	2	yes	complemented
532	#446	C₂²×C₇₃	1	2	yes	complemented
533	#442	C₂²×C₇₃	1	4	yes	complemented
534	#440	C₂²×C₇₃	1	4	yes	complemented
535	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
536	C₄×D₈	C₂²×C₇₃	1	2	yes	complemented
537	#435	C₂²×C₇₃	1	4	yes	complemented
538	C₈×D₄	C₂²×C₇₃	1	2	yes	complemented
539	#432	C₂²×C₇₃	1	2	yes	complemented
540	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
541	#418	C₂²×C₇₃	1	4	yes	complemented
542	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
543	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
544	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
545	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
546	H(5,𝔽₂)	—	4	8	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
552	C₂²×D₄	—	2	4	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	2	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	2	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
559	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
561	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
562	C₂×D₈	C₂³×C₇₃	1	2	yes	—
563	C₂×D₈	C₂³×C₇₃	1	4	yes	—
564	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
565	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
570	#127	—	2	2	no	—
571	#127	—	2	1	no	—
572	#127	—	2	1	no	—
573	#127	—	2	2	no	—
574	#127	C₂³×C₇₃	1	1	yes	characteristic
575	#127	C₂³×C₇₃	1	2	yes	—
576	#127	C₂³×C₇₃	1	2	yes	—
577	#127	C₂³×C₇₃	1	4	yes	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#126	—	2	1	no	—
582	#125	—	2	2	no	—
583	#125	—	2	2	no	—
584	#125	—	2	1	no	—
585	#125	—	2	2	no	—
586	#125	—	2	2	no	—
587	#125	C₂³×C₇₃	1	1	yes	characteristic
588	#125	C₂³×C₇₃	1	2	yes	—
589	#125	C₂³×C₇₃	1	2	yes	—
590	#125	C₂³×C₇₃	1	2	yes	—
591	#124	—	2	2	no	—
592	#124	—	2	1	no	—
593	#124	C₂³×C₇₃	1	1	yes	characteristic
594	#123	—	2	2	no	—
595	#123	—	2	1	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	4	no	—
612	#121	—	2	2	no	—
613	#121	—	2	4	no	—
614	#121	C₂³×C₇₃	1	2	yes	—
615	#121	C₂³×C₇₃	1	1	yes	characteristic
616	#121	C₂³×C₇₃	1	4	yes	—
617	#121	C₂³×C₇₃	1	2	yes	—
618	#120	—	2	4	no	—
619	#120	—	2	4	no	—
620	#120	—	2	4	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
625	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
626	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
627	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
635	C₄×D₄	D₄×C₇₃	1	2	yes	—
636	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₇₃	1	2	yes	—
638	C₄×D₄	C₂³×C₇₃	1	2	yes	—
639	C₄×D₄	C₂³×C₇₃	1	4	yes	—
640	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
641	C₄×D₄	C₂³×C₇₃	1	2	yes	—
642	#117	—	2	2	no	—
643	#117	—	2	1	no	—
644	#117	—	2	2	no	—
645	#117	D₄×C₇₃	1	1	yes	characteristic
646	#117	D₄×C₇₃	1	2	yes	—
647	#117	C₂³×C₇₃	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	2	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
655	#107	C₂³×C₇₃	1	2	yes	—
656	#107	C₂³×C₇₃	1	4	yes	—
657	#106	C₂³×C₇₃	1	2	yes	—
658	#106	C₂³×C₇₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
661	#103	C₂³×C₇₃	1	2	yes	—
662	#102	C₂³×C₇₃	1	2	yes	—
663	#102	C₂³×C₇₃	1	2	yes	—
664	#102	C₂³×C₇₃	1	4	yes	—
665	#102	C₂³×C₇₃	1	4	yes	—
666	#102	C₂³×C₇₃	1	4	yes	—
667	#102	C₂³×C₇₃	1	4	yes	—
668	#102	C₂³×C₇₃	1	4	yes	—
669	#102	C₂³×C₇₃	1	4	yes	—
670	#102	C₂³×C₇₃	1	4	yes	—
671	#102	C₂³×C₇₃	1	4	yes	—
672	#102	C₂³×C₇₃	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
675	#97	C₂³×C₇₃	1	1	yes	characteristic
676	#97	C₂³×C₇₃	1	2	yes	—
677	#97	C₂³×C₇₃	1	4	yes	—
678	#97	C₂³×C₇₃	1	1	yes	characteristic
679	C₄×C₈	C₂³×C₇₃	1	2	yes	—
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	4	8	no	—
684	#41	—	4	4	no	—
685	#41	—	4	8	no	—
686	#41	—	4	4	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	4	8	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	16	no	—
712	C₂×D₄	—	4	8	no	—
713	C₂×D₄	—	8	4	no	—
714	C₂×D₄	—	8	2	no	—
715	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
716	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
717	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
718	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
719	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
727	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
732	SD₁₆	—	4	4	no	—
733	SD₁₆	—	4	2	no	—
734	D₈	—	4	4	no	—
735	D₈	—	4	2	no	—
736	M₁₆	—	4	2	no	—
737	C₂×C₈	—	4	4	no	—
738	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
739	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
740	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
760	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
781	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	1	no	—
786	C₄²	C₂×D₄×C₇₃	1	2	yes	—
787	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
789	C₄²	C₂×D₄×C₇₃	1	2	yes	—
790	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
791	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
792	C₄²	C₂⁴×C₇₃	1	2	yes	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	4	8	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	2	no	—
800	C₂³	—	8	4	no	—
801	C₂³	—	8	2	no	—
802	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
803	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	—	8	1	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	8	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	4	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	1	no	—
829	D₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
856	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
857	C₈	—	2	2	no	—
858	C₈	—	2	4	no	—
859	C₈	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	16	8	no	—
875	C₂²	—	16	4	no	—
876	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	4	yes	—
877	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
892	C₄	#585×C₇₃	1	2	yes	—
893	C₂	—	2	4	no	—
894	C₂	—	4	1	no	—
895	C₂	—	8	2	no	—
896	C₂	—	8	4	no	—
897	C₂	—	8	1	no	—
898	C₂	C₇₃×#3500	1	1	yes	characteristic
899	C₂	C₂²×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
900	C₂	C₇₃×#3585	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 ◁ C₄×#41×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3515	C₂	semidirect
2. C₇₃×#3498	C₂	semidirect
3. C₇₃×#3368	C₂	semidirect
4. C₇₃×#3366	C₂	semidirect
5. C₇₃×#3318	C₂	semidirect
6. C₇₃×#3310	C₂	semidirect
7. C₇₃×#3295	C₂	semidirect
8. C₇₃×#3294	C₂	semidirect
9. C₇₃×#3235	C₂	semidirect
10. C₇₃×#3234	C₂	semidirect
11. C₇₃×#3217	C₂	semidirect
12. C₇₃×#3217	C₂	semidirect
13. C₇₃×#3180	C₂	semidirect
14. C₇₃×#3171	C₂	semidirect
15. C₇₃×#3138	C₂	semidirect
16. C₂×#490×C₇₃	C₂	semidirect
17. C₇₃×#2970	C₂	semidirect
19. #557×C₇₃	C₂²	semidirect
20. #554×C₇₃	C₂²	semidirect
21. #554×C₇₃	C₂²	semidirect
22. #553×C₇₃	C₂²	semidirect
25. #552×C₇₃	C₂²	semidirect
29. #547×C₇₃	C₂²	semidirect
38. #533×C₇₃	C₂²	semidirect
43. #529×C₇₃	C₂²	semidirect
44. #529×C₇₃	C₂²	semidirect
45. C₂×#125×C₇₃	C₂²	semidirect
48. #501×C₇₃	C₂²	semidirect
49. #501×C₇₃	C₂²	semidirect
50. #496×C₇₃	C₂²	semidirect
51. #496×C₇₃	C₂²	semidirect
52. #490×C₇₃	C₂²	semidirect
53. #490×C₇₃	C₂²	semidirect
54. #490×C₇₃	C₂²	semidirect
55. #490×C₇₃	C₂²	semidirect
56. #490×C₇₃	C₂²	semidirect
57. #490×C₇₃	C₂²	semidirect
58. #490×C₇₃	C₂²	semidirect
59. #489×C₇₃	C₂²	semidirect
60. #486×C₇₃	C₂²	semidirect
61. #486×C₇₃	C₂²	semidirect
62. #482×C₇₃	C₂²	semidirect
63. #481×C₇₃	C₂²	semidirect
64. #480×C₇₃	C₂²	semidirect
65. #478×C₇₃	C₂²	semidirect
66. #478×C₇₃	C₂²	semidirect
67. #476×C₇₃	C₂²	semidirect
68. #474×C₇₃	C₂²	semidirect
69. #469×C₇₃	C₂²	semidirect
70. #468×C₇₃	C₂²	semidirect
71. #466×C₇₃	C₂²	semidirect
72. #465×C₇₃	C₂²	semidirect
73. #460×C₇₃	C₂²	semidirect
74. #460×C₇₃	C₂²	semidirect
75. #459×C₇₃	C₂²	semidirect
76. #459×C₇₃	C₂²	semidirect
77. #450×C₇₃	C₂²	semidirect
78. #450×C₇₃	C₂²	semidirect
79. #447×C₇₃	C₂²	semidirect
80. #447×C₇₃	C₂²	semidirect
81. #446×C₇₃	C₂²	semidirect
82. #442×C₇₃	C₂²	semidirect
83. #440×C₇₃	C₂²	semidirect
84. C₄×SD₁₆×C₇₃	C₂²	semidirect
85. C₄×D₈×C₇₃	C₂²	semidirect
86. #435×C₇₃	C₂²	semidirect
87. C₈×D₄×C₇₃	C₂²	semidirect
88. #432×C₇₃	C₂²	semidirect
89. #432×C₇₃	C₂²	semidirect
90. #418×C₇₃	C₂²	semidirect
91. C₂×#102×C₇₃	C₂²	semidirect
92. C₂×#102×C₇₃	C₂²	semidirect
93. C₄×M₁₆×C₇₃	C₂²	semidirect
94. C₂×#97×C₇₃	C₂²	semidirect
442. #62576	C₇₃	direct (N × H)
451. #3515	C₂×C₇₃	semidirect
452. #3498	C₂×C₇₃	semidirect
453. #3368	C₂×C₇₃	semidirect
454. #3366	C₂×C₇₃	semidirect
455. #3318	C₂×C₇₃	semidirect
456. #3310	C₂×C₇₃	semidirect
457. #3295	C₂×C₇₃	semidirect
458. #3294	C₂×C₇₃	semidirect
459. #3235	C₂×C₇₃	semidirect
460. #3234	C₂×C₇₃	semidirect
461. #3217	C₂×C₇₃	semidirect
462. #3217	C₂×C₇₃	semidirect
463. #3180	C₂×C₇₃	semidirect
464. #3171	C₂×C₇₃	semidirect
465. #3138	C₂×C₇₃	semidirect
466. C₂×#490	C₂×C₇₃	semidirect
467. #2970	C₂×C₇₃	semidirect
468. C₇₃	#62576	direct (N × H)
470. #557	C₂²×C₇₃	semidirect
471. #554	C₂²×C₇₃	semidirect
472. #554	C₂²×C₇₃	semidirect
473. #553	C₂²×C₇₃	semidirect
476. #552	C₂²×C₇₃	semidirect
480. #547	C₂²×C₇₃	semidirect
489. #533	C₂²×C₇₃	semidirect
494. #529	C₂²×C₇₃	semidirect
495. #529	C₂²×C₇₃	semidirect
496. C₂×#125	C₂²×C₇₃	semidirect
499. #501	C₂²×C₇₃	semidirect
500. #501	C₂²×C₇₃	semidirect
501. #496	C₂²×C₇₃	semidirect
502. #496	C₂²×C₇₃	semidirect
503. #490	C₂²×C₇₃	semidirect
504. #490	C₂²×C₇₃	semidirect
505. #490	C₂²×C₇₃	semidirect
506. #490	C₂²×C₇₃	semidirect
507. #490	C₂²×C₇₃	semidirect
508. #490	C₂²×C₇₃	semidirect
509. #490	C₂²×C₇₃	semidirect
510. #489	C₂²×C₇₃	semidirect
511. #486	C₂²×C₇₃	semidirect
512. #486	C₂²×C₇₃	semidirect
513. #482	C₂²×C₇₃	semidirect
514. #481	C₂²×C₇₃	semidirect
515. #480	C₂²×C₇₃	semidirect
516. #478	C₂²×C₇₃	semidirect
517. #478	C₂²×C₇₃	semidirect
518. #476	C₂²×C₇₃	semidirect
519. #474	C₂²×C₇₃	semidirect
520. #469	C₂²×C₇₃	semidirect
521. #468	C₂²×C₇₃	semidirect
522. #466	C₂²×C₇₃	semidirect
523. #465	C₂²×C₇₃	semidirect
524. #460	C₂²×C₇₃	semidirect
525. #460	C₂²×C₇₃	semidirect
526. #459	C₂²×C₇₃	semidirect
527. #459	C₂²×C₇₃	semidirect
528. #450	C₂²×C₇₃	semidirect
529. #450	C₂²×C₇₃	semidirect
530. #447	C₂²×C₇₃	semidirect
531. #447	C₂²×C₇₃	semidirect
532. #446	C₂²×C₇₃	semidirect
533. #442	C₂²×C₇₃	semidirect
534. #440	C₂²×C₇₃	semidirect
535. C₄×SD₁₆	C₂²×C₇₃	semidirect
536. C₄×D₈	C₂²×C₇₃	semidirect
537. #435	C₂²×C₇₃	semidirect
538. C₈×D₄	C₂²×C₇₃	semidirect
539. #432	C₂²×C₇₃	semidirect
540. #432	C₂²×C₇₃	semidirect
541. #418	C₂²×C₇₃	semidirect
542. C₂×#102	C₂²×C₇₃	semidirect
543. C₂×#102	C₂²×C₇₃	semidirect
544. C₄×M₁₆	C₂²×C₇₃	semidirect
545. C₂×#97	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×#3515	2
C₇₃×#3498	2
C₇₃×#3368	2
C₇₃×#3366	2
C₇₃×#3318	2
C₇₃×#3310	2
C₇₃×#3295	2
C₇₃×#3294	2
C₇₃×#3235	2
C₇₃×#3234	2
C₇₃×#3217	2
C₇₃×#3180	2
C₇₃×#3171	2
C₇₃×#3138	2
C₂×#490×C₇₃	2
C₇₃×#2970	2
#62576	73

Subgroups — C73×#62576 #32971980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62576 #32971980