Subgroups — C₇₃×#61419 #32970823

Order 18688.

2028 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₇₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3399	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3397	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3394	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3391	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₇₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#459×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
21	C₂×#135×C₇₃	C₂²	1	2	yes	—
22	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
23	#559×C₇₃	C₂²	1	4	yes	complemented
24	#559×C₇₃	C₂²	1	2	yes	complemented
25	#559×C₇₃	C₂²	1	2	yes	complemented
26	#556×C₇₃	C₂²	1	2	yes	complemented
27	#555×C₇₃	—	2	1	no	—
28	#553×C₇₃	—	2	2	no	—
29	#550×C₇₃	C₂²	1	2	yes	complemented
30	#550×C₇₃	C₂²	1	2	yes	complemented
31	#550×C₇₃	C₂²	1	2	yes	complemented
32	#547×C₇₃	—	2	1	no	—
33	#546×C₇₃	—	2	2	no	—
34	#546×C₇₃	—	2	2	no	—
35	#540×C₇₃	—	2	2	no	—
36	#538×C₇₃	—	2	2	no	—
37	#535×C₇₃	C₂²	1	2	yes	—
38	#535×C₇₃	C₂²	1	2	yes	—
39	#533×C₇₃	C₂²	1	1	yes	characteristic
40	#532×C₇₃	—	2	1	no	—
41	#532×C₇₃	—	2	1	no	—
42	#532×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
44	#525×C₇₃	—	2	2	no	—
45	#520×C₇₃	C₂²	1	2	yes	—
46	#518×C₇₃	C₂²	1	2	yes	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	#496×C₇₃	C₂²	1	4	yes	complemented
50	#496×C₇₃	C₂²	1	4	yes	complemented
51	#496×C₇₃	C₂²	1	4	yes	complemented
52	#495×C₇₃	C₂²	1	4	yes	complemented
53	#493×C₇₃	C₂²	1	2	yes	complemented
54	#493×C₇₃	C₂²	1	4	yes	complemented
55	#492×C₇₃	C₂²	1	2	yes	complemented
56	#464×C₇₃	C₂²	1	2	yes	complemented
57	#464×C₇₃	C₂²	1	4	yes	complemented
58	#463×C₇₃	C₂²	1	2	yes	complemented
59	#463×C₇₃	C₂²	1	4	yes	complemented
60	#463×C₇₃	C₂²	1	4	yes	complemented
61	#463×C₇₃	C₂²	1	4	yes	complemented
62	#462×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#461×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#460×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#460×C₇₃	C₂²	1	4	yes	complemented
66	#459×C₇₃	C₂²	1	2	yes	—
67	#459×C₇₃	C₂²	1	2	yes	—
68	#459×C₇₃	C₂²	1	4	yes	—
69	#459×C₇₃	C₂²	1	1	yes	characteristic, complemented
70	#459×C₇₃	C₂²	1	4	yes	complemented
71	#459×C₇₃	C₂²	1	4	yes	complemented
72	#459×C₇₃	C₂²	1	4	yes	complemented
73	#446×C₇₃	C₂²	1	2	yes	complemented
74	#446×C₇₃	C₂²	1	4	yes	complemented
75	C₈×Q₈×C₇₃	C₂²	1	2	yes	complemented
76	#442×C₇₃	C₂²	1	2	yes	complemented
77	#442×C₇₃	C₂²	1	4	yes	complemented
78	#440×C₇₃	C₂²	1	4	yes	complemented
79	#440×C₇₃	C₂²	1	2	yes	complemented
80	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₇₃	C₂²	1	4	yes	complemented
82	C₄×D₈×C₇₃	C₂²	1	2	yes	complemented
83	C₄×D₈×C₇₃	C₂²	1	4	yes	complemented
84	#428×C₇₃	C₂²	1	1	yes	characteristic
85	#424×C₇₃	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
87	#418×C₇₃	C₂²	1	1	yes	characteristic
88	#417×C₇₃	C₂²	1	1	yes	characteristic
89	#416×C₇₃	C₂²	1	2	yes	—
90	C₂×#102×C₇₃	C₂²	1	2	yes	—
91	#405×C₇₃	C₂²	1	2	yes	—
92	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₇₃	—	2	2	no	—
94	C₂×#41×C₇₃	—	2	2	no	—
95	C₂×#41×C₇₃	—	2	2	no	—
96	C₂×#41×C₇₃	C₂³	1	2	yes	—
97	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₇₃	—	2	1	no	—
99	C₂²×D₄×C₇₃	—	2	1	no	—
100	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇₃	—	2	1	no	—
103	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
104	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
105	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
106	#135×C₇₃	—	4	4	no	—
107	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
113	C₂×D₈×C₇₃	—	4	4	no	—
114	C₂×D₈×C₇₃	C₂³	1	2	yes	—
115	C₂×D₈×C₇₃	C₂³	1	4	yes	—
116	C₂×D₈×C₇₃	C₂³	1	4	yes	—
117	C₂×D₈×C₇₃	C₂³	1	4	yes	—
118	C₂×D₈×C₇₃	C₂³	1	2	yes	—
119	C₂×D₈×C₇₃	C₂³	1	4	yes	—
120	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
125	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	#127×C₇₃	—	2	1	no	—
127	#127×C₇₃	—	2	1	no	—
128	#127×C₇₃	C₂³	1	2	yes	—
129	#127×C₇₃	C₂³	1	2	yes	—
130	#127×C₇₃	C₂³	1	4	yes	—
131	#127×C₇₃	C₂³	1	1	yes	characteristic
132	#127×C₇₃	C₂³	1	4	yes	—
133	#126×C₇₃	—	2	4	no	—
134	#125×C₇₃	D₄	1	2	yes	—
135	#124×C₇₃	—	2	2	no	—
136	#124×C₇₃	—	2	2	no	—
137	#124×C₇₃	—	2	4	no	—
138	#124×C₇₃	C₂³	1	4	yes	—
139	#124×C₇₃	C₂³	1	4	yes	—
140	#124×C₇₃	C₂³	1	2	yes	—
141	#123×C₇₃	—	2	4	no	—
142	#123×C₇₃	—	2	4	no	—
143	#123×C₇₃	—	2	4	no	—
144	#123×C₇₃	—	2	4	no	—
145	C₂²⋊Q₈×C₇₃	—	2	2	no	—
146	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
147	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
148	#121×C₇₃	—	2	1	no	—
149	#121×C₇₃	—	2	1	no	—
150	#121×C₇₃	—	2	2	no	—
151	#121×C₇₃	—	2	2	no	—
152	#121×C₇₃	—	2	2	no	—
153	#121×C₇₃	—	2	2	no	—
154	#121×C₇₃	—	2	2	no	—
155	#121×C₇₃	—	2	2	no	—
156	#121×C₇₃	—	2	2	no	—
157	#121×C₇₃	—	2	4	no	—
158	#121×C₇₃	—	2	4	no	—
159	#121×C₇₃	—	2	4	no	—
160	#120×C₇₃	—	2	4	no	—
161	#120×C₇₃	—	2	4	no	—
162	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
167	C₄×D₄×C₇₃	—	2	1	no	—
168	C₄×D₄×C₇₃	—	2	1	no	—
169	C₄×D₄×C₇₃	—	2	2	no	—
170	C₄×D₄×C₇₃	—	2	2	no	—
171	C₄×D₄×C₇₃	—	2	4	no	—
172	C₄×D₄×C₇₃	—	2	2	no	—
173	C₄×D₄×C₇₃	—	2	2	no	—
174	C₄×D₄×C₇₃	—	2	4	no	—
175	C₄×D₄×C₇₃	—	2	1	no	—
176	C₄×D₄×C₇₃	—	2	1	no	—
177	C₄×D₄×C₇₃	—	2	1	no	—
178	C₄×D₄×C₇₃	—	2	1	no	—
179	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₇₃	C₂³	1	2	yes	—
181	C₄×D₄×C₇₃	C₂³	1	4	yes	—
182	C₄×D₄×C₇₃	C₂³	1	4	yes	—
183	C₄×D₄×C₇₃	C₂³	1	4	yes	—
184	C₄×D₄×C₇₃	C₂³	1	2	yes	—
185	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
186	#117×C₇₃	—	2	2	no	—
187	#117×C₇₃	—	2	2	no	—
188	#117×C₇₃	—	2	1	no	—
189	#117×C₇₃	C₂³	1	1	yes	characteristic
190	#117×C₇₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
195	C₂×C₄²×C₇₃	—	2	1	no	—
196	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
197	#107×C₇₃	C₂³	1	2	yes	—
198	#106×C₇₃	C₂³	1	2	yes	—
199	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
201	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
202	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
203	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
204	#103×C₇₃	C₂³	1	2	yes	—
205	#103×C₇₃	C₂³	1	2	yes	—
206	#103×C₇₃	C₂³	1	2	yes	—
207	#102×C₇₃	C₂³	1	4	yes	—
208	#102×C₇₃	C₂³	1	4	yes	—
209	#102×C₇₃	C₂³	1	2	yes	—
210	#102×C₇₃	C₂³	1	2	yes	—
211	#102×C₇₃	C₂³	1	2	yes	—
212	#102×C₇₃	C₂³	1	2	yes	—
213	#102×C₇₃	C₂³	1	2	yes	—
214	#97×C₇₃	C₂³	1	2	yes	—
215	#97×C₇₃	C₂³	1	4	yes	—
216	C₄×C₈×C₇₃	C₂³	1	2	yes	—
217	C₄×C₈×C₇₃	C₂³	1	4	yes	—
218	C₂⁴×C₇₃	—	2	2	no	—
219	C₂⁴×C₇₃	—	2	1	no	—
220	#41×C₇₃	—	2	4	no	—
221	#41×C₇₃	—	2	2	no	—
222	#41×C₇₃	—	2	2	no	—
223	#41×C₇₃	—	2	4	no	—
224	#41×C₇₃	—	8	4	no	—
225	#41×C₇₃	—	8	4	no	—
226	#41×C₇₃	—	8	4	no	—
227	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₇₃	—	2	1	no	—
232	C₂×D₄×C₇₃	—	2	2	no	—
233	C₂×D₄×C₇₃	—	2	1	no	—
234	C₂×D₄×C₇₃	—	2	2	no	—
235	C₂×D₄×C₇₃	—	2	1	no	—
236	C₂×D₄×C₇₃	—	2	2	no	—
237	C₂×D₄×C₇₃	—	2	2	no	—
238	C₂×D₄×C₇₃	—	2	4	no	—
239	C₂×D₄×C₇₃	—	2	1	no	—
240	C₂×D₄×C₇₃	—	2	4	no	—
241	C₂×D₄×C₇₃	—	2	4	no	—
242	C₂×D₄×C₇₃	—	2	4	no	—
243	C₂×D₄×C₇₃	—	2	2	no	—
244	C₂×D₄×C₇₃	—	2	2	no	—
245	C₂×D₄×C₇₃	—	2	2	no	—
246	C₂×D₄×C₇₃	—	2	4	no	—
247	C₂×D₄×C₇₃	—	2	2	no	—
248	C₂×D₄×C₇₃	—	2	4	no	—
249	C₂×D₄×C₇₃	—	8	2	no	—
250	C₂×D₄×C₇₃	—	8	2	no	—
251	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
254	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₇₃	—	2	1	no	—
256	C₂²×C₄×C₇₃	—	2	1	no	—
257	C₂²×C₄×C₇₃	—	2	1	no	—
258	C₂²×C₄×C₇₃	—	2	1	no	—
259	C₂²×C₄×C₇₃	—	2	2	no	—
260	C₂²×C₄×C₇₃	—	2	2	no	—
261	C₂²×C₄×C₇₃	—	2	4	no	—
262	C₂²×C₄×C₇₃	—	2	4	no	—
263	C₂²×C₄×C₇₃	—	2	4	no	—
264	C₂²×C₄×C₇₃	—	2	2	no	—
265	C₂²×C₄×C₇₃	—	8	2	no	—
266	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	Q₁₆×C₇₃	—	4	2	no	—
270	SD₁₆×C₇₃	—	2	8	no	—
271	SD₁₆×C₇₃	—	2	4	no	—
272	SD₁₆×C₇₃	—	4	2	no	—
273	SD₁₆×C₇₃	—	4	2	no	—
274	SD₁₆×C₇₃	—	4	4	no	—
275	D₈×C₇₃	—	2	8	no	—
276	D₈×C₇₃	—	2	4	no	—
277	D₈×C₇₃	—	4	4	no	—
278	D₈×C₇₃	—	4	4	no	—
279	D₈×C₇₃	—	4	2	no	—
280	D₈×C₇₃	—	4	4	no	—
281	M₁₆×C₇₃	—	2	2	no	—
282	M₁₆×C₇₃	#41	1	4	yes	complemented
283	C₂×C₈×C₇₃	—	2	4	no	—
284	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₇₃	—	2	1	no	—
289	C₄⋊C₄×C₇₃	—	2	4	no	—
290	C₄⋊C₄×C₇₃	—	2	1	no	—
291	C₄⋊C₄×C₇₃	—	2	1	no	—
292	C₄⋊C₄×C₇₃	—	2	1	no	—
293	C₄⋊C₄×C₇₃	—	2	1	no	—
294	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
298	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
300	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₇₃	—	2	1	no	—
304	C₂²⋊C₄×C₇₃	—	2	4	no	—
305	C₂²⋊C₄×C₇₃	—	2	4	no	—
306	C₂²⋊C₄×C₇₃	—	2	2	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	4	no	—
312	C₂²⋊C₄×C₇₃	—	2	2	no	—
313	C₂²⋊C₄×C₇₃	—	2	4	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	4	no	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
318	C₄²×C₇₃	—	2	1	no	—
319	C₄²×C₇₃	—	2	1	no	—
320	C₄²×C₇₃	—	2	1	no	—
321	C₄²×C₇₃	—	2	4	no	—
322	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
325	C₄²×C₇₃	C₂⁴	1	4	yes	—
326	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
327	C₂³×C₇₃	—	2	2	no	—
328	C₂³×C₇₃	—	2	2	no	—
329	C₂³×C₇₃	—	2	4	no	—
330	C₂³×C₇₃	—	2	1	no	—
331	C₂³×C₇₃	—	4	2	no	—
332	C₂³×C₇₃	—	4	4	no	—
333	C₂³×C₇₃	—	8	1	no	—
334	C₂³×C₇₃	—	8	1	no	—
335	C₂³×C₇₃	—	8	2	no	—
336	C₂³×C₇₃	—	8	2	no	—
337	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₇₃	—	2	4	no	—
339	Q₈×C₇₃	—	2	1	no	—
340	Q₈×C₇₃	—	2	2	no	—
341	Q₈×C₇₃	—	2	2	no	—
342	Q₈×C₇₃	—	2	1	no	—
343	Q₈×C₇₃	—	4	2	no	—
344	D₄×C₇₃	—	2	2	no	—
345	D₄×C₇₃	—	2	1	no	—
346	D₄×C₇₃	—	2	2	no	—
347	D₄×C₇₃	—	2	4	no	—
348	D₄×C₇₃	—	2	2	no	—
349	D₄×C₇₃	—	2	4	no	—
350	D₄×C₇₃	—	2	2	no	—
351	D₄×C₇₃	—	2	1	no	—
352	D₄×C₇₃	—	4	4	no	—
353	D₄×C₇₃	—	4	2	no	—
354	D₄×C₇₃	—	4	4	no	—
355	D₄×C₇₃	—	4	2	no	—
356	D₄×C₇₃	—	4	4	no	—
357	D₄×C₇₃	—	4	4	no	—
358	D₄×C₇₃	—	4	2	no	—
359	D₄×C₇₃	—	8	1	no	—
360	D₄×C₇₃	—	8	4	no	—
361	D₄×C₇₃	—	8	2	no	—
362	D₄×C₇₃	—	8	2	no	—
363	D₄×C₇₃	—	8	4	no	—
364	D₄×C₇₃	—	8	4	no	—
365	D₄×C₇₃	—	8	4	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	1	no	—
368	C₂×C₄×C₇₃	—	2	2	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	1	no	—
371	C₂×C₄×C₇₃	—	2	2	no	—
372	C₂×C₄×C₇₃	—	4	1	no	—
373	C₂×C₄×C₇₃	—	4	2	no	—
374	C₂×C₄×C₇₃	—	4	2	no	—
375	C₂×C₄×C₇₃	—	4	4	no	—
376	C₂×C₄×C₇₃	—	4	4	no	—
377	C₂×C₄×C₇₃	—	4	2	no	—
378	C₂×C₄×C₇₃	—	8	2	no	—
379	C₂×C₄×C₇₃	—	8	4	no	—
380	C₂×C₄×C₇₃	—	8	4	no	—
381	C₂×C₄×C₇₃	—	8	4	no	—
382	C₂×C₄×C₇₃	—	8	1	no	—
383	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
391	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
392	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₇₃	—	2	2	no	—
394	C₈×C₇₃	—	2	2	no	—
395	C₈×C₇₃	—	2	2	no	—
396	C₈×C₇₃	C₂×#41	1	4	yes	—
397	C₂²×C₇₃	—	2	1	no	—
398	C₂²×C₇₃	—	2	1	no	—
399	C₂²×C₇₃	—	4	1	no	—
400	C₂²×C₇₃	—	4	4	no	—
401	C₂²×C₇₃	—	4	2	no	—
402	C₂²×C₇₃	—	4	2	no	—
403	C₂²×C₇₃	—	4	2	no	—
404	C₂²×C₇₃	—	4	1	no	—
405	C₂²×C₇₃	—	4	2	no	—
406	C₂²×C₇₃	—	4	4	no	—
407	C₂²×C₇₃	—	4	2	no	—
408	C₂²×C₇₃	—	4	1	no	—
409	C₂²×C₇₃	—	4	2	no	—
410	C₂²×C₇₃	—	4	4	no	—
411	C₂²×C₇₃	—	8	4	no	—
412	C₂²×C₇₃	—	16	4	no	—
413	C₂²×C₇₃	#550	1	2	yes	—
414	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₇₃	—	2	1	no	—
416	C₄×C₇₃	—	2	1	no	—
417	C₄×C₇₃	—	2	4	no	—
418	C₄×C₇₃	—	2	1	no	—
419	C₄×C₇₃	—	2	4	no	—
420	C₄×C₇₃	—	4	1	no	—
421	C₄×C₇₃	—	4	1	no	—
422	C₄×C₇₃	—	4	2	no	—
423	C₄×C₇₃	—	4	1	no	—
424	C₄×C₇₃	—	4	2	no	—
425	C₄×C₇₃	#550	1	2	yes	—
426	C₄×C₇₃	#576	1	2	yes	—
427	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
428	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	#61419	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂×C₇₃	—	2	2	no	—
431	C₂×C₇₃	—	8	1	no	—
432	C₂×C₇₃	—	8	2	no	—
433	C₂×C₇₃	—	8	2	no	—
434	C₂×C₇₃	—	8	4	no	—
435	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
436	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
437	C₂×C₇₃	#3585	1	1	yes	characteristic
438	#3508	C₂×C₇₃	1	1	yes	characteristic, complemented
439	#3506	C₂×C₇₃	1	1	yes	characteristic, complemented
440	#3403	C₂×C₇₃	1	4	yes	complemented
441	#3399	C₂×C₇₃	1	2	yes	complemented
442	#3399	C₂×C₇₃	1	4	yes	complemented
443	#3397	C₂×C₇₃	1	2	yes	complemented
444	#3394	C₂×C₇₃	1	2	yes	complemented
445	#3391	C₂×C₇₃	1	2	yes	complemented
446	#3155	C₂×C₇₃	1	2	yes	complemented
447	#3151	C₂×C₇₃	1	1	yes	characteristic, complemented
448	#3045	C₂×C₇₃	1	2	yes	complemented
449	#3041	C₂×C₇₃	1	2	yes	complemented
450	#3035	C₂×C₇₃	1	1	yes	characteristic, complemented
451	C₂×#459	C₂×C₇₃	1	1	yes	characteristic, complemented
452	#2962	C₂×C₇₃	1	1	yes	characteristic, complemented
453	#2946	C₂×C₇₃	1	2	yes	complemented
454	C₄×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic, complemented
455	C₇₃	#61419	1	1	yes	characteristic, direct product factor, Sylow
456	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
457	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
458	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
459	C₂×#135	C₂²×C₇₃	1	2	yes	—
460	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
461	#559	C₂²×C₇₃	1	2	yes	complemented
462	#559	C₂²×C₇₃	1	4	yes	complemented
463	#559	C₂²×C₇₃	1	2	yes	complemented
464	#556	C₂²×C₇₃	1	2	yes	complemented
465	#555	—	2	1	no	—
466	#553	—	2	2	no	—
467	#550	C₂²×C₇₃	1	2	yes	complemented
468	#550	C₂²×C₇₃	1	2	yes	complemented
469	#550	C₂²×C₇₃	1	2	yes	complemented
470	#547	—	2	1	no	—
471	#546	—	2	2	no	—
472	#546	—	2	2	no	—
473	#540	—	2	2	no	—
474	#538	—	2	2	no	—
475	#535	C₂²×C₇₃	1	2	yes	—
476	#535	C₂²×C₇₃	1	2	yes	—
477	#533	C₂²×C₇₃	1	1	yes	characteristic
478	#532	—	2	1	no	—
479	#532	—	2	1	no	—
480	#532	C₂²×C₇₃	1	1	yes	characteristic
481	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
482	#525	—	2	2	no	—
483	#520	C₂²×C₇₃	1	2	yes	—
484	#518	C₂²×C₇₃	1	2	yes	—
485	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
486	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
487	#496	C₂²×C₇₃	1	4	yes	complemented
488	#496	C₂²×C₇₃	1	4	yes	complemented
489	#496	C₂²×C₇₃	1	4	yes	complemented
490	#495	C₂²×C₇₃	1	4	yes	complemented
491	#493	C₂²×C₇₃	1	2	yes	complemented
492	#493	C₂²×C₇₃	1	4	yes	complemented
493	#492	C₂²×C₇₃	1	2	yes	complemented
494	#464	C₂²×C₇₃	1	4	yes	complemented
495	#464	C₂²×C₇₃	1	2	yes	complemented
496	#463	C₂²×C₇₃	1	4	yes	complemented
497	#463	C₂²×C₇₃	1	4	yes	complemented
498	#463	C₂²×C₇₃	1	2	yes	complemented
499	#463	C₂²×C₇₃	1	4	yes	complemented
500	#462	C₂²×C₇₃	1	1	yes	characteristic, complemented
501	#461	C₂²×C₇₃	1	1	yes	characteristic, complemented
502	#460	C₂²×C₇₃	1	4	yes	complemented
503	#460	C₂²×C₇₃	1	1	yes	characteristic, complemented
504	#459	C₂²×C₇₃	1	2	yes	—
505	#459	C₂²×C₇₃	1	2	yes	—
506	#459	C₂²×C₇₃	1	4	yes	—
507	#459	C₂²×C₇₃	1	1	yes	characteristic, complemented
508	#459	C₂²×C₇₃	1	4	yes	complemented
509	#459	C₂²×C₇₃	1	4	yes	complemented
510	#459	C₂²×C₇₃	1	4	yes	complemented
511	#446	C₂²×C₇₃	1	2	yes	complemented
512	#446	C₂²×C₇₃	1	4	yes	complemented
513	C₈×Q₈	C₂²×C₇₃	1	2	yes	complemented
514	#442	C₂²×C₇₃	1	2	yes	complemented
515	#442	C₂²×C₇₃	1	4	yes	complemented
516	#440	C₂²×C₇₃	1	4	yes	complemented
517	#440	C₂²×C₇₃	1	2	yes	complemented
518	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₇₃	1	4	yes	complemented
520	C₄×D₈	C₂²×C₇₃	1	2	yes	complemented
521	C₄×D₈	C₂²×C₇₃	1	4	yes	complemented
522	#428	C₂²×C₇₃	1	1	yes	characteristic
523	#424	C₂²×C₇₃	1	2	yes	—
524	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
525	#418	C₂²×C₇₃	1	1	yes	characteristic
526	#417	C₂²×C₇₃	1	1	yes	characteristic
527	#416	C₂²×C₇₃	1	2	yes	—
528	C₂×#102	C₂²×C₇₃	1	2	yes	—
529	#405	C₂²×C₇₃	1	2	yes	—
530	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
535	C₂×#41	C₂³×C₇₃	1	2	yes	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
540	C₂³×C₄	—	2	1	no	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	AGL(1,ℤ/8)	—	2	4	no	—
543	AGL(1,ℤ/8)	—	4	4	no	—
544	#135	—	4	4	no	—
545	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
551	C₂×D₈	—	4	4	no	—
552	C₂×D₈	C₂³×C₇₃	1	2	yes	—
553	C₂×D₈	C₂³×C₇₃	1	4	yes	—
554	C₂×D₈	C₂³×C₇₃	1	4	yes	—
555	C₂×D₈	C₂³×C₇₃	1	4	yes	—
556	C₂×D₈	C₂³×C₇₃	1	2	yes	—
557	C₂×D₈	C₂³×C₇₃	1	4	yes	—
558	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
559	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
561	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
562	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
564	#127	—	2	1	no	—
565	#127	—	2	1	no	—
566	#127	C₂³×C₇₃	1	2	yes	—
567	#127	C₂³×C₇₃	1	2	yes	—
568	#127	C₂³×C₇₃	1	1	yes	characteristic
569	#127	C₂³×C₇₃	1	4	yes	—
570	#127	C₂³×C₇₃	1	4	yes	—
571	#126	—	2	4	no	—
572	#125	D₄×C₇₃	1	2	yes	—
573	#124	—	2	2	no	—
574	#124	—	2	2	no	—
575	#124	—	2	4	no	—
576	#124	C₂³×C₇₃	1	2	yes	—
577	#124	C₂³×C₇₃	1	4	yes	—
578	#124	C₂³×C₇₃	1	4	yes	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
585	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#120	—	2	4	no	—
599	#120	—	2	4	no	—
600	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
603	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	C₂³×C₇₃	1	2	yes	—
618	C₄×D₄	C₂³×C₇₃	1	2	yes	—
619	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₇₃	1	4	yes	—
622	C₄×D₄	C₂³×C₇₃	1	4	yes	—
623	C₄×D₄	C₂³×C₇₃	1	4	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₇₃	1	1	yes	characteristic
628	#117	C₂³×C₇₃	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
635	#107	C₂³×C₇₃	1	2	yes	—
636	#106	C₂³×C₇₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
639	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
641	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
642	#103	C₂³×C₇₃	1	2	yes	—
643	#103	C₂³×C₇₃	1	2	yes	—
644	#103	C₂³×C₇₃	1	2	yes	—
645	#102	C₂³×C₇₃	1	4	yes	—
646	#102	C₂³×C₇₃	1	4	yes	—
647	#102	C₂³×C₇₃	1	2	yes	—
648	#102	C₂³×C₇₃	1	2	yes	—
649	#102	C₂³×C₇₃	1	2	yes	—
650	#102	C₂³×C₇₃	1	2	yes	—
651	#102	C₂³×C₇₃	1	2	yes	—
652	#97	C₂³×C₇₃	1	2	yes	—
653	#97	C₂³×C₇₃	1	4	yes	—
654	C₄×C₈	C₂³×C₇₃	1	2	yes	—
655	C₄×C₈	C₂³×C₇₃	1	4	yes	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	2	1	no	—
658	#41	—	2	2	no	—
659	#41	—	2	4	no	—
660	#41	—	2	2	no	—
661	#41	—	2	4	no	—
662	#41	—	8	4	no	—
663	#41	—	8	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
666	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	8	2	no	—
688	C₂×D₄	—	8	2	no	—
689	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
690	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
691	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
692	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	8	2	no	—
704	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
707	Q₁₆	—	4	2	no	—
708	SD₁₆	—	2	8	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	4	2	no	—
711	SD₁₆	—	4	2	no	—
712	SD₁₆	—	4	4	no	—
713	D₈	—	2	8	no	—
714	D₈	—	2	4	no	—
715	D₈	—	4	4	no	—
716	D₈	—	4	4	no	—
717	D₈	—	4	2	no	—
718	D₈	—	4	4	no	—
719	M₁₆	—	2	2	no	—
720	M₁₆	#41×C₇₃	1	4	yes	complemented
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
723	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
724	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
725	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
736	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	4	no	—
760	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₇₃	1	4	yes	—
764	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	2	no	—
774	C₂³	—	8	2	no	—
775	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	1	no	—
781	Q₈	—	4	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	2	no	—
798	D₄	—	8	2	no	—
799	D₄	—	8	4	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	1	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	—	8	1	no	—
821	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
823	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
828	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
829	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
830	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	C₂×#41×C₇₃	1	4	yes	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	8	4	no	—
850	C₂²	—	16	4	no	—
851	C₂²	#550×C₇₃	1	2	yes	—
852	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	#550×C₇₃	1	2	yes	—
864	C₄	#576×C₇₃	1	2	yes	—
865	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
866	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	4	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	2	no	—
872	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
873	C₂	C₂×#576×C₇₃	1	1	yes	characteristic
874	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 ◁ #533×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3508	C₂	semidirect
2. C₇₃×#3506	C₂	semidirect
3. C₇₃×#3403	C₂	semidirect
4. C₇₃×#3399	C₂	semidirect
5. C₇₃×#3399	C₂	semidirect
6. C₇₃×#3397	C₂	semidirect
7. C₇₃×#3394	C₂	semidirect
8. C₇₃×#3391	C₂	semidirect
9. C₇₃×#3155	C₂	semidirect
10. C₇₃×#3151	C₂	semidirect
11. C₇₃×#3045	C₂	semidirect
12. C₇₃×#3041	C₂	semidirect
13. C₇₃×#3035	C₂	semidirect
14. C₂×#459×C₇₃	C₂	semidirect
15. C₇₃×#2962	C₂	semidirect
16. C₇₃×#2946	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₇₃	C₂	semidirect
23. #559×C₇₃	C₂²	semidirect
24. #559×C₇₃	C₂²	semidirect
25. #559×C₇₃	C₂²	semidirect
26. #556×C₇₃	C₂²	semidirect
29. #550×C₇₃	C₂²	semidirect
30. #550×C₇₃	C₂²	semidirect
31. #550×C₇₃	C₂²	semidirect
49. #496×C₇₃	C₂²	semidirect
50. #496×C₇₃	C₂²	semidirect
51. #496×C₇₃	C₂²	semidirect
52. #495×C₇₃	C₂²	semidirect
53. #493×C₇₃	C₂²	semidirect
54. #493×C₇₃	C₂²	semidirect
55. #492×C₇₃	C₂²	semidirect
56. #464×C₇₃	C₂²	semidirect
57. #464×C₇₃	C₂²	semidirect
58. #463×C₇₃	C₂²	semidirect
59. #463×C₇₃	C₂²	semidirect
60. #463×C₇₃	C₂²	semidirect
61. #463×C₇₃	C₂²	semidirect
62. #462×C₇₃	C₂²	semidirect
63. #461×C₇₃	C₂²	semidirect
64. #460×C₇₃	C₂²	semidirect
65. #460×C₇₃	C₂²	semidirect
69. #459×C₇₃	C₂²	semidirect
70. #459×C₇₃	C₂²	semidirect
71. #459×C₇₃	C₂²	semidirect
72. #459×C₇₃	C₂²	semidirect
73. #446×C₇₃	C₂²	semidirect
74. #446×C₇₃	C₂²	semidirect
75. C₈×Q₈×C₇₃	C₂²	semidirect
76. #442×C₇₃	C₂²	semidirect
77. #442×C₇₃	C₂²	semidirect
78. #440×C₇₃	C₂²	semidirect
79. #440×C₇₃	C₂²	semidirect
80. C₄×SD₁₆×C₇₃	C₂²	semidirect
81. C₄×SD₁₆×C₇₃	C₂²	semidirect
82. C₄×D₈×C₇₃	C₂²	semidirect
83. C₄×D₈×C₇₃	C₂²	semidirect
282. M₁₆×C₇₃	#41	semidirect
429. #61419	C₇₃	direct (N × H)
438. #3508	C₂×C₇₃	semidirect
439. #3506	C₂×C₇₃	semidirect
440. #3403	C₂×C₇₃	semidirect
441. #3399	C₂×C₇₃	semidirect
442. #3399	C₂×C₇₃	semidirect
443. #3397	C₂×C₇₃	semidirect
444. #3394	C₂×C₇₃	semidirect
445. #3391	C₂×C₇₃	semidirect
446. #3155	C₂×C₇₃	semidirect
447. #3151	C₂×C₇₃	semidirect
448. #3045	C₂×C₇₃	semidirect
449. #3041	C₂×C₇₃	semidirect
450. #3035	C₂×C₇₃	semidirect
451. C₂×#459	C₂×C₇₃	semidirect
452. #2962	C₂×C₇₃	semidirect
453. #2946	C₂×C₇₃	semidirect
454. C₄×AGL(1,ℤ/8)	C₂×C₇₃	semidirect
455. C₇₃	#61419	direct (N × H)
461. #559	C₂²×C₇₃	semidirect
462. #559	C₂²×C₇₃	semidirect
463. #559	C₂²×C₇₃	semidirect
464. #556	C₂²×C₇₃	semidirect
467. #550	C₂²×C₇₃	semidirect
468. #550	C₂²×C₇₃	semidirect
469. #550	C₂²×C₇₃	semidirect
487. #496	C₂²×C₇₃	semidirect
488. #496	C₂²×C₇₃	semidirect
489. #496	C₂²×C₇₃	semidirect
490. #495	C₂²×C₇₃	semidirect
491. #493	C₂²×C₇₃	semidirect
492. #493	C₂²×C₇₃	semidirect
493. #492	C₂²×C₇₃	semidirect
494. #464	C₂²×C₇₃	semidirect
495. #464	C₂²×C₇₃	semidirect
496. #463	C₂²×C₇₃	semidirect
497. #463	C₂²×C₇₃	semidirect
498. #463	C₂²×C₇₃	semidirect
499. #463	C₂²×C₇₃	semidirect
500. #462	C₂²×C₇₃	semidirect
501. #461	C₂²×C₇₃	semidirect
502. #460	C₂²×C₇₃	semidirect
503. #460	C₂²×C₇₃	semidirect
507. #459	C₂²×C₇₃	semidirect
508. #459	C₂²×C₇₃	semidirect
509. #459	C₂²×C₇₃	semidirect
510. #459	C₂²×C₇₃	semidirect
511. #446	C₂²×C₇₃	semidirect
512. #446	C₂²×C₇₃	semidirect
513. C₈×Q₈	C₂²×C₇₃	semidirect
514. #442	C₂²×C₇₃	semidirect
515. #442	C₂²×C₇₃	semidirect
516. #440	C₂²×C₇₃	semidirect
517. #440	C₂²×C₇₃	semidirect
518. C₄×SD₁₆	C₂²×C₇₃	semidirect
519. C₄×SD₁₆	C₂²×C₇₃	semidirect
520. C₄×D₈	C₂²×C₇₃	semidirect
521. C₄×D₈	C₂²×C₇₃	semidirect
720. M₁₆	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3508	2
C₇₃×#3506	2
C₇₃×#3403	2
C₇₃×#3399	2
C₇₃×#3397	2
C₇₃×#3394	2
C₇₃×#3391	2
C₇₃×#3155	2
C₇₃×#3151	2
C₇₃×#3045	2
C₇₃×#3041	2
C₇₃×#3035	2
C₂×#459×C₇₃	2
C₇₃×#2962	2
C₇₃×#2946	2
C₄×AGL(1,ℤ/8)×C₇₃	2
#61419	73

Subgroups — C73×#61419 #32970823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#61419 #32970823