Subgroups — C₇₃×#62591 #32971995

Order 18688.

1726 conjugacy classes of subgroups.

The subgroup lattice has 850 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×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3364	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3331	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3330	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3327	C₂	1	4	yes	maximal, complemented
8	C₇₃×#3326	C₂	1	4	yes	maximal, complemented
9	C₇₃×#3236	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#3219	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3172	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3142	C₂	1	2	yes	maximal, complemented
16	C₇₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	#557×C₇₃	C₂²	1	1	yes	characteristic
19	#556×C₇₃	C₂²	1	2	yes	—
20	#555×C₇₃	—	2	1	no	—
21	#554×C₇₃	—	2	1	no	—
22	#554×C₇₃	C₂²	1	1	yes	characteristic
23	#554×C₇₃	C₂²	1	1	yes	characteristic
24	#553×C₇₃	—	2	2	no	—
25	#553×C₇₃	C₂²	1	2	yes	—
26	#552×C₇₃	—	2	2	no	—
27	#552×C₇₃	—	2	1	no	—
28	#552×C₇₃	C₂²	1	2	yes	—
29	#548×C₇₃	C₂²	1	4	yes	—
30	#547×C₇₃	—	2	1	no	—
31	#547×C₇₃	C₂²	1	2	yes	—
32	#547×C₇₃	C₂²	1	1	yes	characteristic
33	#542×C₇₃	—	2	2	no	—
34	#541×C₇₃	—	2	1	no	—
35	#539×C₇₃	—	2	2	no	—
36	#537×C₇₃	—	2	1	no	—
37	#533×C₇₃	C₂²	1	2	yes	—
38	#533×C₇₃	C₂²	1	1	yes	characteristic
39	#532×C₇₃	C₂²	1	2	yes	—
40	#532×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
42	#529×C₇₃	C₂²	1	1	yes	characteristic
43	#529×C₇₃	C₂²	1	2	yes	—
44	C₂×#125×C₇₃	C₂²	1	2	yes	—
45	#520×C₇₃	—	2	1	no	—
46	#520×C₇₃	—	2	1	no	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	#501×C₇₃	C₂²	1	2	yes	—
49	#501×C₇₃	C₂²	1	1	yes	characteristic
50	#497×C₇₃	C₂²	1	2	yes	—
51	#496×C₇₃	C₂²	1	1	yes	characteristic
52	#491×C₇₃	C₂²	1	2	yes	—
53	#491×C₇₃	C₂²	1	2	yes	—
54	#491×C₇₃	C₂²	1	2	yes	—
55	#490×C₇₃	C₂²	1	2	yes	—
56	#490×C₇₃	C₂²	1	1	yes	characteristic
57	#489×C₇₃	C₂²	1	1	yes	characteristic
58	#488×C₇₃	C₂²	1	4	yes	—
59	#488×C₇₃	C₂²	1	4	yes	—
60	#487×C₇₃	C₂²	1	2	yes	—
61	#487×C₇₃	C₂²	1	2	yes	—
62	#484×C₇₃	C₂²	1	4	yes	—
63	#483×C₇₃	C₂²	1	4	yes	—
64	#482×C₇₃	C₂²	1	4	yes	—
65	#479×C₇₃	C₂²	1	4	yes	—
66	#479×C₇₃	C₂²	1	4	yes	—
67	#476×C₇₃	C₂²	1	2	yes	—
68	#474×C₇₃	C₂²	1	2	yes	—
69	#470×C₇₃	C₂²	1	4	yes	—
70	#469×C₇₃	C₂²	1	2	yes	—
71	#468×C₇₃	C₂²	1	4	yes	—
72	#468×C₇₃	C₂²	1	2	yes	—
73	#464×C₇₃	C₂²	1	4	yes	—
74	#463×C₇₃	C₂²	1	4	yes	—
75	#462×C₇₃	C₂²	1	2	yes	—
76	#461×C₇₃	C₂²	1	2	yes	—
77	#452×C₇₃	C₂²	1	4	yes	—
78	#451×C₇₃	C₂²	1	2	yes	—
79	#449×C₇₃	C₂²	1	4	yes	—
80	#448×C₇₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
82	C₄×Q₁₆×C₇₃	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₇₃	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
85	C₄×D₈×C₇₃	C₂²	1	2	yes	—
86	#436×C₇₃	C₂²	1	4	yes	—
87	#436×C₇₃	C₂²	1	2	yes	—
88	#432×C₇₃	C₂²	1	1	yes	characteristic
89	#432×C₇₃	C₂²	1	2	yes	—
90	#419×C₇₃	C₂²	1	4	yes	—
91	#417×C₇₃	C₂²	1	4	yes	—
92	#417×C₇₃	C₂²	1	4	yes	—
93	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
95	C₂×#41×C₇₃	—	2	1	no	—
96	C₂×#41×C₇₃	—	2	1	no	—
97	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
98	C₂×#41×C₇₃	C₂³	1	4	yes	—
99	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
103	C₂×D₈×C₇₃	C₂³	1	2	yes	—
104	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
105	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₇₃	—	2	1	no	—
107	C₄⋊Q₈×C₇₃	—	2	1	no	—
108	C₄⋊Q₈×C₇₃	—	2	1	no	—
109	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
114	#127×C₇₃	C₂³	1	1	yes	characteristic
115	#126×C₇₃	—	2	2	no	—
116	#126×C₇₃	—	2	4	no	—
117	#126×C₇₃	—	2	2	no	—
118	#126×C₇₃	—	2	2	no	—
119	#126×C₇₃	—	2	1	no	—
120	#125×C₇₃	—	2	2	no	—
121	#125×C₇₃	—	2	2	no	—
122	#125×C₇₃	—	2	1	no	—
123	#125×C₇₃	—	2	2	no	—
124	#125×C₇₃	—	2	2	no	—
125	#125×C₇₃	—	2	2	no	—
126	#125×C₇₃	C₂³	1	2	yes	—
127	#125×C₇₃	C₂³	1	2	yes	—
128	#125×C₇₃	C₂³	1	1	yes	characteristic
129	#125×C₇₃	C₂³	1	2	yes	—
130	#124×C₇₃	—	2	4	no	—
131	#124×C₇₃	—	2	1	no	—
132	#124×C₇₃	C₂³	1	4	yes	—
133	#124×C₇₃	C₂³	1	1	yes	characteristic
134	#123×C₇₃	—	2	2	no	—
135	#123×C₇₃	—	2	1	no	—
136	#123×C₇₃	—	2	2	no	—
137	#123×C₇₃	—	2	2	no	—
138	#123×C₇₃	—	2	2	no	—
139	#123×C₇₃	—	2	4	no	—
140	C₂²⋊Q₈×C₇₃	—	2	2	no	—
141	C₂²⋊Q₈×C₇₃	—	2	1	no	—
142	C₂²⋊Q₈×C₇₃	—	2	2	no	—
143	C₂²⋊Q₈×C₇₃	—	2	1	no	—
144	C₂²⋊Q₈×C₇₃	—	2	1	no	—
145	C₂²⋊Q₈×C₇₃	—	2	2	no	—
146	C₂²⋊Q₈×C₇₃	—	2	1	no	—
147	C₂²⋊Q₈×C₇₃	—	2	4	no	—
148	C₂²⋊Q₈×C₇₃	—	2	2	no	—
149	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
150	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
152	#121×C₇₃	—	2	2	no	—
153	#121×C₇₃	—	2	4	no	—
154	#121×C₇₃	—	2	2	no	—
155	#121×C₇₃	—	2	2	no	—
156	#121×C₇₃	—	2	1	no	—
157	#121×C₇₃	—	2	2	no	—
158	#121×C₇₃	C₂³	1	1	yes	characteristic
159	#121×C₇₃	C₂³	1	2	yes	—
160	#121×C₇₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₇₃	—	2	1	no	—
162	C₄×Q₈×C₇₃	—	2	1	no	—
163	C₄×Q₈×C₇₃	—	2	2	no	—
164	C₄×Q₈×C₇₃	—	2	1	no	—
165	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₇₃	—	2	1	no	—
171	C₄×D₄×C₇₃	—	2	2	no	—
172	C₄×D₄×C₇₃	—	2	1	no	—
173	C₄×D₄×C₇₃	—	2	4	no	—
174	C₄×D₄×C₇₃	—	2	2	no	—
175	C₄×D₄×C₇₃	—	2	2	no	—
176	C₄×D₄×C₇₃	—	2	2	no	—
177	C₄×D₄×C₇₃	—	2	1	no	—
178	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₇₃	D₄	1	2	yes	—
180	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₇₃	C₂³	1	2	yes	—
182	C₄×D₄×C₇₃	C₂³	1	2	yes	—
183	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₇₃	C₂³	1	2	yes	—
185	#117×C₇₃	—	2	2	no	—
186	#117×C₇₃	—	2	2	no	—
187	#117×C₇₃	—	2	2	no	—
188	#117×C₇₃	—	2	1	no	—
189	#117×C₇₃	—	2	2	no	—
190	#117×C₇₃	D₄	1	1	yes	characteristic
191	#117×C₇₃	D₄	1	2	yes	—
192	#117×C₇₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
203	#107×C₇₃	C₂³	1	2	yes	—
204	#107×C₇₃	C₂³	1	4	yes	—
205	#106×C₇₃	C₂³	1	2	yes	—
206	#106×C₇₃	C₂³	1	4	yes	—
207	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
208	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
209	#103×C₇₃	C₂³	1	4	yes	—
210	#103×C₇₃	C₂³	1	4	yes	—
211	#103×C₇₃	C₂³	1	4	yes	—
212	#103×C₇₃	C₂³	1	4	yes	—
213	#103×C₇₃	C₂³	1	4	yes	—
214	#103×C₇₃	C₂³	1	4	yes	—
215	#103×C₇₃	C₂³	1	2	yes	—
216	#102×C₇₃	C₂³	1	2	yes	—
217	#102×C₇₃	C₂³	1	2	yes	—
218	#102×C₇₃	C₂³	1	4	yes	—
219	#102×C₇₃	C₂³	1	4	yes	—
220	#102×C₇₃	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
223	#97×C₇₃	C₂³	1	1	yes	characteristic
224	#97×C₇₃	C₂³	1	2	yes	—
225	#97×C₇₃	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₇₃	C₂³	1	2	yes	—
227	C₄×C₈×C₇₃	C₂³	1	4	yes	—
228	#41×C₇₃	—	4	2	no	—
229	#41×C₇₃	—	4	4	no	—
230	#41×C₇₃	—	4	4	no	—
231	#41×C₇₃	—	4	4	no	—
232	#41×C₇₃	—	4	4	no	—
233	C₂×Q₈×C₇₃	—	2	1	no	—
234	C₂×Q₈×C₇₃	—	2	1	no	—
235	C₂×Q₈×C₇₃	—	2	1	no	—
236	C₂×Q₈×C₇₃	—	2	2	no	—
237	C₂×Q₈×C₇₃	—	4	4	no	—
238	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
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	1	no	—
244	C₂×D₄×C₇₃	—	2	4	no	—
245	C₂×D₄×C₇₃	—	2	1	no	—
246	C₂×D₄×C₇₃	—	2	1	no	—
247	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	—	2	2	no	—
252	C₂²×C₄×C₇₃	—	2	2	no	—
253	C₂²×C₄×C₇₃	—	2	2	no	—
254	C₂²×C₄×C₇₃	—	2	2	no	—
255	C₂²×C₄×C₇₃	—	2	1	no	—
256	C₂²×C₄×C₇₃	—	2	2	no	—
257	C₂²×C₄×C₇₃	—	2	4	no	—
258	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₇₃	—	4	4	no	—
265	SD₁₆×C₇₃	—	4	2	no	—
266	SD₁₆×C₇₃	—	4	4	no	—
267	D₈×C₇₃	—	4	2	no	—
268	M₁₆×C₇₃	—	4	2	no	—
269	M₁₆×C₇₃	—	4	4	no	—
270	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
272	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₇₃	—	2	2	no	—
274	C₄⋊C₄×C₇₃	—	2	2	no	—
275	C₄⋊C₄×C₇₃	—	2	1	no	—
276	C₄⋊C₄×C₇₃	—	2	1	no	—
277	C₄⋊C₄×C₇₃	—	2	2	no	—
278	C₄⋊C₄×C₇₃	—	2	2	no	—
279	C₄⋊C₄×C₇₃	—	2	2	no	—
280	C₄⋊C₄×C₇₃	—	2	1	no	—
281	C₄⋊C₄×C₇₃	—	2	4	no	—
282	C₄⋊C₄×C₇₃	—	2	2	no	—
283	C₄⋊C₄×C₇₃	—	2	2	no	—
284	C₄⋊C₄×C₇₃	—	2	2	no	—
285	C₄⋊C₄×C₇₃	—	2	2	no	—
286	C₄⋊C₄×C₇₃	—	2	2	no	—
287	C₄⋊C₄×C₇₃	—	2	2	no	—
288	C₄⋊C₄×C₇₃	—	2	2	no	—
289	C₄⋊C₄×C₇₃	—	2	1	no	—
290	C₄⋊C₄×C₇₃	—	2	1	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	1	no	—
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	1	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₇₃	—	2	2	no	—
306	C₂²⋊C₄×C₇₃	—	2	4	no	—
307	C₂²⋊C₄×C₇₃	—	2	2	no	—
308	C₂²⋊C₄×C₇₃	—	2	1	no	—
309	C₂²⋊C₄×C₇₃	—	2	1	no	—
310	C₂²⋊C₄×C₇₃	—	2	4	no	—
311	C₂²⋊C₄×C₇₃	—	2	1	no	—
312	C₂²⋊C₄×C₇₃	—	2	1	no	—
313	C₂²⋊C₄×C₇₃	—	2	2	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
322	C₄²×C₇₃	—	2	4	no	—
323	C₄²×C₇₃	—	2	2	no	—
324	C₄²×C₇₃	—	2	2	no	—
325	C₄²×C₇₃	—	2	1	no	—
326	C₄²×C₇₃	C₂×D₄	1	2	yes	—
327	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇₃	C₂×D₄	1	2	yes	—
330	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₇₃	C₂⁴	1	2	yes	—
332	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₇₃	—	2	1	no	—
334	C₂³×C₇₃	—	2	2	no	—
335	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
336	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₇₃	—	2	2	no	—
338	Q₈×C₇₃	—	2	2	no	—
339	Q₈×C₇₃	—	2	4	no	—
340	Q₈×C₇₃	—	2	4	no	—
341	Q₈×C₇₃	—	4	2	no	—
342	Q₈×C₇₃	—	4	2	no	—
343	Q₈×C₇₃	—	8	1	no	—
344	Q₈×C₇₃	—	8	2	no	—
345	D₄×C₇₃	—	2	2	no	—
346	D₄×C₇₃	—	2	2	no	—
347	D₄×C₇₃	—	2	2	no	—
348	D₄×C₇₃	—	2	2	no	—
349	D₄×C₇₃	—	4	2	no	—
350	D₄×C₇₃	—	4	2	no	—
351	D₄×C₇₃	—	4	2	no	—
352	D₄×C₇₃	—	4	4	no	—
353	D₄×C₇₃	—	4	4	no	—
354	D₄×C₇₃	—	8	1	no	—
355	D₄×C₇₃	—	8	4	no	—
356	C₂×C₄×C₇₃	—	2	2	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	4	no	—
359	C₂×C₄×C₇₃	—	2	1	no	—
360	C₂×C₄×C₇₃	—	2	2	no	—
361	C₂×C₄×C₇₃	—	2	2	no	—
362	C₂×C₄×C₇₃	—	2	2	no	—
363	C₂×C₄×C₇₃	—	2	4	no	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	1	no	—
366	C₂×C₄×C₇₃	—	4	2	no	—
367	C₂×C₄×C₇₃	—	4	1	no	—
368	C₂×C₄×C₇₃	—	4	2	no	—
369	C₂×C₄×C₇₃	—	4	4	no	—
370	C₂×C₄×C₇₃	—	4	2	no	—
371	C₂×C₄×C₇₃	—	4	4	no	—
372	C₂×C₄×C₇₃	—	8	2	no	—
373	C₂×C₄×C₇₃	—	8	4	no	—
374	C₂×C₄×C₇₃	—	8	2	no	—
375	C₂×C₄×C₇₃	—	8	2	no	—
376	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
385	C₈×C₇₃	—	2	2	no	—
386	C₈×C₇₃	—	2	2	no	—
387	C₈×C₇₃	—	2	4	no	—
388	C₂²×C₇₃	—	2	2	no	—
389	C₂²×C₇₃	—	2	1	no	—
390	C₂²×C₇₃	—	2	1	no	—
391	C₂²×C₇₃	—	2	2	no	—
392	C₂²×C₇₃	—	2	1	no	—
393	C₂²×C₇₃	—	2	2	no	—
394	C₂²×C₇₃	—	4	1	no	—
395	C₂²×C₇₃	—	4	2	no	—
396	C₂²×C₇₃	—	4	2	no	—
397	C₂²×C₇₃	—	4	1	no	—
398	C₂²×C₇₃	—	4	2	no	—
399	C₂²×C₇₃	—	4	1	no	—
400	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₇₃	—	2	1	no	—
402	C₄×C₇₃	—	2	2	no	—
403	C₄×C₇₃	—	2	1	no	—
404	C₄×C₇₃	—	2	2	no	—
405	C₄×C₇₃	—	2	1	no	—
406	C₄×C₇₃	—	2	1	no	—
407	C₄×C₇₃	—	2	2	no	—
408	C₄×C₇₃	—	4	1	no	—
409	C₄×C₇₃	—	4	2	no	—
410	C₄×C₇₃	—	4	4	no	—
411	C₄×C₇₃	—	4	1	no	—
412	C₄×C₇₃	—	4	1	no	—
413	C₄×C₇₃	—	4	2	no	—
414	C₄×C₇₃	—	4	2	no	—
415	C₄×C₇₃	#575	1	2	yes	—
416	C₄×C₇₃	#585	1	2	yes	—
417	#62591	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂×C₇₃	—	4	2	no	—
419	C₂×C₇₃	—	4	1	no	—
420	C₂×C₇₃	—	8	1	no	—
421	C₂×C₇₃	—	8	2	no	—
422	C₂×C₇₃	#3500	1	1	yes	characteristic
423	C₂×C₇₃	C₂×#575	1	1	yes	characteristic
424	C₂×C₇₃	#3586	1	1	yes	characteristic
425	#3515	C₂×C₇₃	1	1	yes	characteristic, complemented
426	#3511	C₂×C₇₃	1	1	yes	characteristic, complemented
427	#3364	C₂×C₇₃	1	2	yes	complemented
428	#3360	C₂×C₇₃	1	2	yes	complemented
429	#3331	C₂×C₇₃	1	2	yes	complemented
430	#3330	C₂×C₇₃	1	2	yes	complemented
431	#3327	C₂×C₇₃	1	4	yes	complemented
432	#3326	C₂×C₇₃	1	4	yes	complemented
433	#3236	C₂×C₇₃	1	2	yes	complemented
434	#3235	C₂×C₇₃	1	1	yes	characteristic, complemented
435	#3219	C₂×C₇₃	1	2	yes	complemented
436	#3218	C₂×C₇₃	1	1	yes	characteristic, complemented
437	#3172	C₂×C₇₃	1	2	yes	complemented
438	#3171	C₂×C₇₃	1	1	yes	characteristic, complemented
439	#3142	C₂×C₇₃	1	2	yes	complemented
440	#3139	C₂×C₇₃	1	1	yes	characteristic, complemented
441	#2971	C₂×C₇₃	1	1	yes	characteristic, complemented
442	C₇₃	#62591	1	1	yes	characteristic, direct product factor, Sylow
443	#557	C₂²×C₇₃	1	1	yes	characteristic
444	#556	C₂²×C₇₃	1	2	yes	—
445	#555	—	2	1	no	—
446	#554	—	2	1	no	—
447	#554	C₂²×C₇₃	1	1	yes	characteristic
448	#554	C₂²×C₇₃	1	1	yes	characteristic
449	#553	—	2	2	no	—
450	#553	C₂²×C₇₃	1	2	yes	—
451	#552	—	2	2	no	—
452	#552	—	2	1	no	—
453	#552	C₂²×C₇₃	1	2	yes	—
454	#548	C₂²×C₇₃	1	4	yes	—
455	#547	—	2	1	no	—
456	#547	C₂²×C₇₃	1	2	yes	—
457	#547	C₂²×C₇₃	1	1	yes	characteristic
458	#542	—	2	2	no	—
459	#541	—	2	1	no	—
460	#539	—	2	2	no	—
461	#537	—	2	1	no	—
462	#533	C₂²×C₇₃	1	2	yes	—
463	#533	C₂²×C₇₃	1	1	yes	characteristic
464	#532	C₂²×C₇₃	1	2	yes	—
465	#532	C₂²×C₇₃	1	1	yes	characteristic
466	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
467	#529	C₂²×C₇₃	1	1	yes	characteristic
468	#529	C₂²×C₇₃	1	2	yes	—
469	C₂×#125	C₂²×C₇₃	1	2	yes	—
470	#520	—	2	1	no	—
471	#520	—	2	1	no	—
472	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
473	#501	C₂²×C₇₃	1	1	yes	characteristic
474	#501	C₂²×C₇₃	1	2	yes	—
475	#497	C₂²×C₇₃	1	2	yes	—
476	#496	C₂²×C₇₃	1	1	yes	characteristic
477	#491	C₂²×C₇₃	1	2	yes	—
478	#491	C₂²×C₇₃	1	2	yes	—
479	#491	C₂²×C₇₃	1	2	yes	—
480	#490	C₂²×C₇₃	1	1	yes	characteristic
481	#490	C₂²×C₇₃	1	2	yes	—
482	#489	C₂²×C₇₃	1	1	yes	characteristic
483	#488	C₂²×C₇₃	1	4	yes	—
484	#488	C₂²×C₇₃	1	4	yes	—
485	#487	C₂²×C₇₃	1	2	yes	—
486	#487	C₂²×C₇₃	1	2	yes	—
487	#484	C₂²×C₇₃	1	4	yes	—
488	#483	C₂²×C₇₃	1	4	yes	—
489	#482	C₂²×C₇₃	1	4	yes	—
490	#479	C₂²×C₇₃	1	4	yes	—
491	#479	C₂²×C₇₃	1	4	yes	—
492	#476	C₂²×C₇₃	1	2	yes	—
493	#474	C₂²×C₇₃	1	2	yes	—
494	#470	C₂²×C₇₃	1	4	yes	—
495	#469	C₂²×C₇₃	1	2	yes	—
496	#468	C₂²×C₇₃	1	4	yes	—
497	#468	C₂²×C₇₃	1	2	yes	—
498	#464	C₂²×C₇₃	1	4	yes	—
499	#463	C₂²×C₇₃	1	4	yes	—
500	#462	C₂²×C₇₃	1	2	yes	—
501	#461	C₂²×C₇₃	1	2	yes	—
502	#452	C₂²×C₇₃	1	4	yes	—
503	#451	C₂²×C₇₃	1	2	yes	—
504	#449	C₂²×C₇₃	1	4	yes	—
505	#448	C₂²×C₇₃	1	2	yes	—
506	C₈×Q₈	C₂²×C₇₃	1	2	yes	—
507	C₄×Q₁₆	C₂²×C₇₃	1	4	yes	—
508	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
509	C₄×SD₁₆	C₂²×C₇₃	1	4	yes	—
510	C₄×D₈	C₂²×C₇₃	1	2	yes	—
511	#436	C₂²×C₇₃	1	2	yes	—
512	#436	C₂²×C₇₃	1	4	yes	—
513	#432	C₂²×C₇₃	1	1	yes	characteristic
514	#432	C₂²×C₇₃	1	2	yes	—
515	#419	C₂²×C₇₃	1	4	yes	—
516	#417	C₂²×C₇₃	1	4	yes	—
517	#417	C₂²×C₇₃	1	4	yes	—
518	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
519	C₄×M₁₆	C₂²×C₇₃	1	2	yes	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	2	1	no	—
522	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
523	C₂×#41	C₂³×C₇₃	1	4	yes	—
524	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
525	C₂×Q₁₆	C₂³×C₇₃	1	4	yes	—
526	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
527	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
528	C₂×D₈	C₂³×C₇₃	1	2	yes	—
529	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
530	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
539	#127	C₂³×C₇₃	1	1	yes	characteristic
540	#126	—	2	2	no	—
541	#126	—	2	4	no	—
542	#126	—	2	2	no	—
543	#126	—	2	2	no	—
544	#126	—	2	1	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	C₂³×C₇₃	1	1	yes	characteristic
552	#125	C₂³×C₇₃	1	2	yes	—
553	#125	C₂³×C₇₃	1	2	yes	—
554	#125	C₂³×C₇₃	1	2	yes	—
555	#124	—	2	4	no	—
556	#124	—	2	1	no	—
557	#124	C₂³×C₇₃	1	1	yes	characteristic
558	#124	C₂³×C₇₃	1	4	yes	—
559	#123	—	2	2	no	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
575	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	—
577	#121	—	2	2	no	—
578	#121	—	2	4	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	#121	C₂³×C₇₃	1	2	yes	—
584	#121	C₂³×C₇₃	1	1	yes	characteristic
585	#121	C₂³×C₇₃	1	2	yes	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
594	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
604	C₄×D₄	D₄×C₇₃	1	2	yes	—
605	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₇₃	1	2	yes	—
607	C₄×D₄	C₂³×C₇₃	1	2	yes	—
608	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₇₃	1	2	yes	—
610	#117	—	2	2	no	—
611	#117	—	2	2	no	—
612	#117	—	2	2	no	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	D₄×C₇₃	1	1	yes	characteristic
616	#117	D₄×C₇₃	1	2	yes	—
617	#117	C₂³×C₇₃	1	2	yes	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	2	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
628	#107	C₂³×C₇₃	1	2	yes	—
629	#107	C₂³×C₇₃	1	4	yes	—
630	#106	C₂³×C₇₃	1	2	yes	—
631	#106	C₂³×C₇₃	1	4	yes	—
632	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
633	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
634	#103	C₂³×C₇₃	1	4	yes	—
635	#103	C₂³×C₇₃	1	4	yes	—
636	#103	C₂³×C₇₃	1	4	yes	—
637	#103	C₂³×C₇₃	1	4	yes	—
638	#103	C₂³×C₇₃	1	4	yes	—
639	#103	C₂³×C₇₃	1	4	yes	—
640	#103	C₂³×C₇₃	1	2	yes	—
641	#102	C₂³×C₇₃	1	2	yes	—
642	#102	C₂³×C₇₃	1	2	yes	—
643	#102	C₂³×C₇₃	1	4	yes	—
644	#102	C₂³×C₇₃	1	4	yes	—
645	#102	C₂³×C₇₃	1	2	yes	—
646	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
647	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
648	#97	C₂³×C₇₃	1	1	yes	characteristic
649	#97	C₂³×C₇₃	1	2	yes	—
650	#97	C₂³×C₇₃	1	1	yes	characteristic
651	C₄×C₈	C₂³×C₇₃	1	2	yes	—
652	C₄×C₈	C₂³×C₇₃	1	4	yes	—
653	#41	—	4	2	no	—
654	#41	—	4	4	no	—
655	#41	—	4	4	no	—
656	#41	—	4	4	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
665	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
673	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
674	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
675	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
689	Q₁₆	—	4	4	no	—
690	SD₁₆	—	4	2	no	—
691	SD₁₆	—	4	4	no	—
692	D₈	—	4	2	no	—
693	M₁₆	—	4	2	no	—
694	M₁₆	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
697	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	1	no	—
751	C₄²	C₂×D₄×C₇₃	1	2	yes	—
752	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₇₃	1	2	yes	—
755	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₇₃	1	2	yes	—
757	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
758	C₂³	—	2	1	no	—
759	C₂³	—	2	2	no	—
760	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
761	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	2	4	no	—
766	Q₈	—	4	2	no	—
767	Q₈	—	4	2	no	—
768	Q₈	—	8	2	no	—
769	Q₈	—	8	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	8	4	no	—
780	D₄	—	8	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	2	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
809	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
810	C₈	—	2	2	no	—
811	C₈	—	2	2	no	—
812	C₈	—	2	4	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
826	C₄	—	2	2	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	#575×C₇₃	1	2	yes	—
841	C₄	#585×C₇₃	1	2	yes	—
842	C₂	—	4	1	no	—
843	C₂	—	4	2	no	—
844	C₂	—	8	2	no	—
845	C₂	—	8	1	no	—
846	C₂	C₇₃×#3500	1	1	yes	characteristic
847	C₂	C₂×#575×C₇₃	1	1	yes	characteristic
848	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ 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×#3511	C₂	semidirect
3. C₇₃×#3364	C₂	semidirect
4. C₇₃×#3360	C₂	semidirect
5. C₇₃×#3331	C₂	semidirect
6. C₇₃×#3330	C₂	semidirect
7. C₇₃×#3327	C₂	semidirect
8. C₇₃×#3326	C₂	semidirect
9. C₇₃×#3236	C₂	semidirect
10. C₇₃×#3235	C₂	semidirect
11. C₇₃×#3219	C₂	semidirect
12. C₇₃×#3218	C₂	semidirect
13. C₇₃×#3172	C₂	semidirect
14. C₇₃×#3171	C₂	semidirect
15. C₇₃×#3142	C₂	semidirect
16. C₇₃×#3139	C₂	semidirect
17. C₇₃×#2971	C₂	semidirect
417. #62591	C₇₃	direct (N × H)
425. #3515	C₂×C₇₃	semidirect
426. #3511	C₂×C₇₃	semidirect
427. #3364	C₂×C₇₃	semidirect
428. #3360	C₂×C₇₃	semidirect
429. #3331	C₂×C₇₃	semidirect
430. #3330	C₂×C₇₃	semidirect
431. #3327	C₂×C₇₃	semidirect
432. #3326	C₂×C₇₃	semidirect
433. #3236	C₂×C₇₃	semidirect
434. #3235	C₂×C₇₃	semidirect
435. #3219	C₂×C₇₃	semidirect
436. #3218	C₂×C₇₃	semidirect
437. #3172	C₂×C₇₃	semidirect
438. #3171	C₂×C₇₃	semidirect
439. #3142	C₂×C₇₃	semidirect
440. #3139	C₂×C₇₃	semidirect
441. #2971	C₂×C₇₃	semidirect
442. C₇₃	#62591	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×#3515	2
C₇₃×#3511	2
C₇₃×#3364	2
C₇₃×#3360	2
C₇₃×#3331	2
C₇₃×#3330	2
C₇₃×#3327	2
C₇₃×#3326	2
C₇₃×#3236	2
C₇₃×#3235	2
C₇₃×#3219	2
C₇₃×#3218	2
C₇₃×#3172	2
C₇₃×#3171	2
C₇₃×#3142	2
C₇₃×#3139	2
C₇₃×#2971	2
#62591	73

Subgroups — C73×#62591 #32971995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62591 #32971995