Subgroups — C₂×C₇₃×#3308 #32970533

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3308	C₂	1	16	yes	maximal, direct product factor
4	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#484×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#480×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#477×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#468×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#463×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#449×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#448×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₇₃	—	2	1	no	—
18	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
25	#548×C₇₃	—	2	4	no	—
26	#548×C₇₃	C₂²	1	8	yes	complemented
27	#547×C₇₃	—	2	4	no	—
28	#547×C₇₃	C₂²	1	8	yes	complemented
29	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#124×C₇₃	—	2	1	no	—
31	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#123×C₇₃	—	2	1	no	—
33	C₂×#123×C₇₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₃	—	2	1	no	—
38	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₃	—	2	1	no	—
43	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
47	#489×C₇₃	C₂²	1	8	yes	complemented
48	#484×C₇₃	C₂²	1	8	yes	complemented
49	#480×C₇₃	C₂²	1	8	yes	complemented
50	#477×C₇₃	C₂²	1	8	yes	complemented
51	#468×C₇₃	C₂²	1	8	yes	complemented
52	#466×C₇₃	C₂²	1	8	yes	complemented
53	#463×C₇₃	C₂²	1	8	yes	complemented
54	#449×C₇₃	C₂²	1	8	yes	complemented
55	#448×C₇₃	C₂²	1	8	yes	complemented
56	#440×C₇₃	C₂²	1	8	yes	complemented
57	#435×C₇₃	C₂²	1	8	yes	complemented
58	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
59	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
60	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
62	#417×C₇₃	C₂²	1	8	yes	complemented
63	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
64	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
65	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
66	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
67	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
68	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
69	C₂×#103×C₇₃	C₂²	1	8	yes	complemented
70	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
72	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
73	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
76	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₇₃	—	2	8	no	—
78	C₂×#41×C₇₃	—	2	2	no	—
79	C₂×#41×C₇₃	—	2	4	no	—
80	C₂×#41×C₇₃	—	4	2	no	—
81	C₂×#41×C₇₃	—	4	8	no	—
82	C₂×#41×C₇₃	C₂³	1	4	yes	—
83	C₂²×Q₈×C₇₃	—	2	1	no	—
84	C₂²×Q₈×C₇₃	—	2	1	no	—
85	C₂²×Q₈×C₇₃	—	2	2	no	—
86	C₂²×Q₈×C₇₃	—	2	4	no	—
87	C₂²×Q₈×C₇₃	—	4	2	no	—
88	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
90	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₃	—	2	1	no	—
92	C₂²×D₄×C₇₃	—	2	1	no	—
93	C₂²×D₄×C₇₃	—	2	1	no	—
94	C₂²×D₄×C₇₃	—	2	1	no	—
95	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇₃	—	2	1	no	—
99	C₂³×C₄×C₇₃	—	2	1	no	—
100	C₂³×C₄×C₇₃	—	2	1	no	—
101	C₂³×C₄×C₇₃	—	2	1	no	—
102	C₂³×C₄×C₇₃	—	2	1	no	—
103	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×SD₁₆×C₇₃	—	2	4	no	—
106	C₂×SD₁₆×C₇₃	—	4	2	no	—
107	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
109	C₂×D₈×C₇₃	—	4	2	no	—
110	C₂×D₈×C₇₃	C₂³	1	4	yes	—
111	C₂×M₁₆×C₇₃	—	4	2	no	—
112	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
113	C₂²×C₈×C₇₃	—	4	2	no	—
114	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
119	C₄⋊Q₈×C₇₃	—	2	2	no	—
120	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
121	#124×C₇₃	—	2	8	no	—
122	#124×C₇₃	—	2	2	no	—
123	#124×C₇₃	C₂³	1	4	yes	—
124	#123×C₇₃	—	2	8	no	—
125	#123×C₇₃	—	2	8	no	—
126	C₂²⋊Q₈×C₇₃	—	2	2	no	—
127	C₂²⋊Q₈×C₇₃	—	2	8	no	—
128	C₂²⋊Q₈×C₇₃	—	2	8	no	—
129	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
130	#121×C₇₃	—	2	8	no	—
131	#121×C₇₃	—	2	2	no	—
132	#121×C₇₃	—	2	2	no	—
133	#121×C₇₃	—	2	2	no	—
134	#121×C₇₃	C₂³	1	4	yes	—
135	#121×C₇₃	C₂³	1	4	yes	—
136	#121×C₇₃	C₂³	1	4	yes	—
137	C₄×Q₈×C₇₃	—	2	2	no	—
138	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
139	C₄×D₄×C₇₃	—	2	8	no	—
140	C₄×D₄×C₇₃	—	2	2	no	—
141	C₄×D₄×C₇₃	D₄	1	4	yes	—
142	C₄×D₄×C₇₃	C₂³	1	4	yes	—
143	C₄×D₄×C₇₃	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
147	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
151	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
167	C₂×C₄²×C₇₃	—	2	1	no	—
168	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
169	#107×C₇₃	C₂³	1	4	yes	—
170	#107×C₇₃	C₂³	1	4	yes	—
171	#107×C₇₃	C₂³	1	4	yes	—
172	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
173	#103×C₇₃	C₂³	1	4	yes	—
174	#103×C₇₃	C₂³	1	4	yes	—
175	#103×C₇₃	C₂³	1	4	yes	—
176	#103×C₇₃	C₂³	1	4	yes	—
177	#103×C₇₃	C₂³	1	4	yes	—
178	#103×C₇₃	C₂³	1	4	yes	—
179	#102×C₇₃	C₂³	1	4	yes	—
180	#102×C₇₃	C₂³	1	4	yes	—
181	#102×C₇₃	C₂³	1	4	yes	—
182	#102×C₇₃	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
184	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
185	#97×C₇₃	C₂³	1	4	yes	—
186	C₂⁴×C₇₃	—	2	1	no	—
187	C₂⁴×C₇₃	—	2	1	no	—
188	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
190	#41×C₇₃	—	2	8	no	—
191	#41×C₇₃	—	4	4	no	—
192	#41×C₇₃	—	4	8	no	—
193	#41×C₇₃	—	4	32	no	—
194	C₂×Q₈×C₇₃	—	2	1	no	—
195	C₂×Q₈×C₇₃	—	2	4	no	—
196	C₂×Q₈×C₇₃	—	2	1	no	—
197	C₂×Q₈×C₇₃	—	2	4	no	—
198	C₂×Q₈×C₇₃	—	2	2	no	—
199	C₂×Q₈×C₇₃	—	2	8	no	—
200	C₂×Q₈×C₇₃	—	2	2	no	—
201	C₂×Q₈×C₇₃	—	2	2	no	—
202	C₂×Q₈×C₇₃	—	4	4	no	—
203	C₂×Q₈×C₇₃	—	4	4	no	—
204	C₂×Q₈×C₇₃	—	4	8	no	—
205	C₂×Q₈×C₇₃	—	4	4	no	—
206	C₂×Q₈×C₇₃	#41	1	4	yes	complemented
207	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₇₃	—	2	4	no	—
210	C₂×D₄×C₇₃	—	2	4	no	—
211	C₂×D₄×C₇₃	—	2	4	no	—
212	C₂×D₄×C₇₃	—	2	4	no	—
213	C₂×D₄×C₇₃	—	2	4	no	—
214	C₂×D₄×C₇₃	—	2	1	no	—
215	C₂×D₄×C₇₃	—	2	1	no	—
216	C₂×D₄×C₇₃	—	2	2	no	—
217	C₂×D₄×C₇₃	—	2	2	no	—
218	C₂×D₄×C₇₃	—	2	2	no	—
219	C₂×D₄×C₇₃	—	2	2	no	—
220	C₂×D₄×C₇₃	—	4	4	no	—
221	C₂×D₄×C₇₃	—	4	4	no	—
222	C₂×D₄×C₇₃	—	4	4	no	—
223	C₂×D₄×C₇₃	—	4	4	no	—
224	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₇₃	—	2	1	no	—
228	C₂²×C₄×C₇₃	—	2	2	no	—
229	C₂²×C₄×C₇₃	—	2	2	no	—
230	C₂²×C₄×C₇₃	—	2	2	no	—
231	C₂²×C₄×C₇₃	—	2	2	no	—
232	C₂²×C₄×C₇₃	—	2	4	no	—
233	C₂²×C₄×C₇₃	—	2	4	no	—
234	C₂²×C₄×C₇₃	—	2	4	no	—
235	C₂²×C₄×C₇₃	—	2	1	no	—
236	C₂²×C₄×C₇₃	—	2	1	no	—
237	C₂²×C₄×C₇₃	—	2	1	no	—
238	C₂²×C₄×C₇₃	—	2	1	no	—
239	C₂²×C₄×C₇₃	—	2	1	no	—
240	C₂²×C₄×C₇₃	—	2	4	no	—
241	C₂²×C₄×C₇₃	—	2	4	no	—
242	C₂²×C₄×C₇₃	—	4	4	no	—
243	C₂²×C₄×C₇₃	—	4	4	no	—
244	C₂²×C₄×C₇₃	—	4	4	no	—
245	C₂²×C₄×C₇₃	—	4	4	no	—
246	C₂²×C₄×C₇₃	—	4	4	no	—
247	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₇₃	—	2	8	no	—
257	SD₁₆×C₇₃	—	4	4	no	—
258	D₈×C₇₃	—	4	4	no	—
259	M₁₆×C₇₃	—	4	4	no	—
260	C₂×C₈×C₇₃	—	2	2	no	—
261	C₂×C₈×C₇₃	—	2	2	no	—
262	C₂×C₈×C₇₃	—	2	2	no	—
263	C₂×C₈×C₇₃	—	2	2	no	—
264	C₂×C₈×C₇₃	—	4	4	no	—
265	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₇₃	—	2	1	no	—
270	C₄⋊C₄×C₇₃	—	2	1	no	—
271	C₄⋊C₄×C₇₃	—	2	1	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	2	4	no	—
276	C₄⋊C₄×C₇₃	—	2	4	no	—
277	C₄⋊C₄×C₇₃	—	2	1	no	—
278	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₇₃	—	2	4	no	—
284	C₂²⋊C₄×C₇₃	—	2	4	no	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	—	2	4	no	—
288	C₂²⋊C₄×C₇₃	—	2	4	no	—
289	C₂²⋊C₄×C₇₃	—	2	4	no	—
290	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
292	C₄²×C₇₃	—	2	4	no	—
293	C₄²×C₇₃	C₂×D₄	1	2	yes	—
294	C₄²×C₇₃	C₂⁴	1	2	yes	—
295	C₂³×C₇₃	—	2	2	no	—
296	C₂³×C₇₃	—	2	2	no	—
297	C₂³×C₇₃	—	2	2	no	—
298	C₂³×C₇₃	—	2	2	no	—
299	C₂³×C₇₃	—	2	2	no	—
300	C₂³×C₇₃	—	2	2	no	—
301	C₂³×C₇₃	—	2	2	no	—
302	C₂³×C₇₃	—	4	2	no	—
303	C₂³×C₇₃	—	4	2	no	—
304	C₂³×C₇₃	—	4	2	no	—
305	C₂³×C₇₃	—	4	2	no	—
306	C₂³×C₇₃	—	4	2	no	—
307	C₂³×C₇₃	—	4	2	no	—
308	C₂³×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
309	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
310	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
311	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₇₃	—	2	4	no	—
313	Q₈×C₇₃	—	2	2	no	—
314	Q₈×C₇₃	—	2	2	no	—
315	Q₈×C₇₃	—	2	2	no	—
316	Q₈×C₇₃	—	4	8	no	—
317	Q₈×C₇₃	—	4	8	no	—
318	Q₈×C₇₃	—	4	2	no	—
319	Q₈×C₇₃	C₂×#41	1	4	yes	complemented
320	D₄×C₇₃	—	2	8	no	—
321	D₄×C₇₃	—	2	2	no	—
322	D₄×C₇₃	—	2	2	no	—
323	D₄×C₇₃	—	2	2	no	—
324	D₄×C₇₃	—	2	2	no	—
325	D₄×C₇₃	—	4	8	no	—
326	D₄×C₇₃	—	4	8	no	—
327	D₄×C₇₃	—	4	8	no	—
328	D₄×C₇₃	—	4	8	no	—
329	D₄×C₇₃	—	4	2	no	—
330	D₄×C₇₃	—	4	2	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	4	no	—
334	C₂×C₄×C₇₃	—	2	2	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	4	no	—
338	C₂×C₄×C₇₃	—	2	4	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	2	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	2	no	—
344	C₂×C₄×C₇₃	—	2	2	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	4	8	no	—
349	C₂×C₄×C₇₃	—	4	8	no	—
350	C₂×C₄×C₇₃	—	4	8	no	—
351	C₂×C₄×C₇₃	—	4	8	no	—
352	C₂×C₄×C₇₃	—	4	2	no	—
353	C₂×C₄×C₇₃	—	4	2	no	—
354	C₂×C₄×C₇₃	—	4	2	no	—
355	C₂×C₄×C₇₃	—	4	2	no	—
356	C₂×C₄×C₇₃	—	4	8	no	—
357	C₂×C₄×C₇₃	—	4	2	no	—
358	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
364	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
365	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
366	C₈×C₇₃	—	2	2	no	—
367	C₈×C₇₃	—	2	2	no	—
368	C₈×C₇₃	—	2	2	no	—
369	C₈×C₇₃	—	2	2	no	—
370	C₂²×C₇₃	—	2	2	no	—
371	C₂²×C₇₃	—	2	8	no	—
372	C₂²×C₇₃	—	2	2	no	—
373	C₂²×C₇₃	—	2	2	no	—
374	C₂²×C₇₃	—	2	2	no	—
375	C₂²×C₇₃	—	2	2	no	—
376	C₂²×C₇₃	—	4	4	no	—
377	C₂²×C₇₃	—	4	2	no	—
378	C₂²×C₇₃	—	4	2	no	—
379	C₂²×C₇₃	—	4	2	no	—
380	C₂²×C₇₃	—	4	2	no	—
381	C₂²×C₇₃	—	4	2	no	—
382	C₂²×C₇₃	—	4	2	no	—
383	C₂²×C₇₃	—	8	4	no	—
384	C₂²×C₇₃	—	8	4	no	—
385	C₂²×C₇₃	#546	1	2	yes	—
386	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
387	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
388	C₂²×C₇₃	#578	1	2	yes	—
389	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
390	C₄×C₇₃	—	2	2	no	—
391	C₄×C₇₃	—	2	2	no	—
392	C₄×C₇₃	—	2	4	no	—
393	C₄×C₇₃	—	2	2	no	—
394	C₄×C₇₃	—	2	2	no	—
395	C₄×C₇₃	—	4	2	no	—
396	C₄×C₇₃	—	4	2	no	—
397	C₄×C₇₃	—	4	2	no	—
398	C₄×C₇₃	—	4	2	no	—
399	C₄×C₇₃	—	4	2	no	—
400	C₄×C₇₃	#546	1	2	yes	—
401	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
402	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×#3308	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₇₃	—	2	4	no	—
405	C₂×C₇₃	—	4	2	no	—
406	C₂×C₇₃	—	8	2	no	—
407	C₂×C₇₃	—	8	2	no	—
408	C₂×C₇₃	#3308	1	4	yes	direct product factor
409	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
410	C₂×C₇₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
412	C₂×#548	C₂×C₇₃	1	1	yes	characteristic, complemented
413	C₂×#547	C₂×C₇₃	1	1	yes	characteristic, complemented
414	#3308	C₂×C₇₃	1	16	yes	direct product factor
415	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
416	C₂×#484	C₂×C₇₃	1	1	yes	characteristic, complemented
417	C₂×#480	C₂×C₇₃	1	1	yes	characteristic, complemented
418	C₂×#477	C₂×C₇₃	1	1	yes	characteristic, complemented
419	C₂×#468	C₂×C₇₃	1	1	yes	characteristic, complemented
420	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
421	C₂×#463	C₂×C₇₃	1	1	yes	characteristic, complemented
422	C₂×#449	C₂×C₇₃	1	1	yes	characteristic, complemented
423	C₂×#448	C₂×C₇₃	1	1	yes	characteristic, complemented
424	C₂×#440	C₂×C₇₃	1	1	yes	characteristic, complemented
425	C₂×#435	C₂×C₇₃	1	1	yes	characteristic, complemented
426	C₂×#417	C₂×C₇₃	1	1	yes	characteristic, complemented
427	C₂²×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
428	C₇₃	C₂×#3308	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²×#41	—	2	1	no	—
430	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
431	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
432	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
433	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
434	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
435	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
436	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
437	#548	—	2	4	no	—
438	#548	C₂²×C₇₃	1	8	yes	complemented
439	#547	—	2	4	no	—
440	#547	C₂²×C₇₃	1	8	yes	complemented
441	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
442	C₂×#124	—	2	1	no	—
443	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
444	C₂×#123	—	2	1	no	—
445	C₂×#123	—	2	1	no	—
446	C₂×C₂²⋊Q₈	—	2	1	no	—
447	C₂×C₂²⋊Q₈	—	2	1	no	—
448	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
449	C₂×#121	—	2	1	no	—
450	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
451	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
452	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
453	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
454	C₂×C₄×D₄	—	2	1	no	—
455	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
459	#489	C₂²×C₇₃	1	8	yes	complemented
460	#484	C₂²×C₇₃	1	8	yes	complemented
461	#480	C₂²×C₇₃	1	8	yes	complemented
462	#477	C₂²×C₇₃	1	8	yes	complemented
463	#468	C₂²×C₇₃	1	8	yes	complemented
464	#466	C₂²×C₇₃	1	8	yes	complemented
465	#463	C₂²×C₇₃	1	8	yes	complemented
466	#449	C₂²×C₇₃	1	8	yes	complemented
467	#448	C₂²×C₇₃	1	8	yes	complemented
468	#440	C₂²×C₇₃	1	8	yes	complemented
469	#435	C₂²×C₇₃	1	8	yes	complemented
470	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
471	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
472	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
473	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
474	#417	C₂²×C₇₃	1	8	yes	complemented
475	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
476	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
477	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
478	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
479	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
480	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
481	C₂×#103	C₂²×C₇₃	1	8	yes	complemented
482	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
484	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
485	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
488	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
489	C₂×#41	—	2	8	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	4	no	—
492	C₂×#41	—	4	2	no	—
493	C₂×#41	—	4	8	no	—
494	C₂×#41	C₂³×C₇₃	1	4	yes	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	—	2	2	no	—
498	C₂²×Q₈	—	2	4	no	—
499	C₂²×Q₈	—	4	2	no	—
500	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
502	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
508	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
517	C₂×SD₁₆	—	2	4	no	—
518	C₂×SD₁₆	—	4	2	no	—
519	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
521	C₂×D₈	—	4	2	no	—
522	C₂×D₈	C₂³×C₇₃	1	4	yes	—
523	C₂×M₁₆	—	4	2	no	—
524	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
525	C₂²×C₈	—	4	2	no	—
526	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
533	#124	—	2	8	no	—
534	#124	—	2	2	no	—
535	#124	C₂³×C₇₃	1	4	yes	—
536	#123	—	2	8	no	—
537	#123	—	2	8	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	8	no	—
540	C₂²⋊Q₈	—	2	8	no	—
541	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	—
542	#121	—	2	8	no	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	C₂³×C₇₃	1	4	yes	—
547	#121	C₂³×C₇₃	1	4	yes	—
548	#121	C₂³×C₇₃	1	4	yes	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
551	C₄×D₄	—	2	8	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	D₄×C₇₃	1	4	yes	—
554	C₄×D₄	C₂³×C₇₃	1	4	yes	—
555	C₄×D₄	C₂³×C₇₃	1	4	yes	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
581	#107	C₂³×C₇₃	1	4	yes	—
582	#107	C₂³×C₇₃	1	4	yes	—
583	#107	C₂³×C₇₃	1	4	yes	—
584	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
585	#103	C₂³×C₇₃	1	4	yes	—
586	#103	C₂³×C₇₃	1	4	yes	—
587	#103	C₂³×C₇₃	1	4	yes	—
588	#103	C₂³×C₇₃	1	4	yes	—
589	#103	C₂³×C₇₃	1	4	yes	—
590	#103	C₂³×C₇₃	1	4	yes	—
591	#102	C₂³×C₇₃	1	4	yes	—
592	#102	C₂³×C₇₃	1	4	yes	—
593	#102	C₂³×C₇₃	1	4	yes	—
594	#102	C₂³×C₇₃	1	4	yes	—
595	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
596	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
597	#97	C₂³×C₇₃	1	4	yes	—
598	C₂⁴	—	2	1	no	—
599	C₂⁴	—	2	1	no	—
600	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
601	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
602	#41	—	2	8	no	—
603	#41	—	4	4	no	—
604	#41	—	4	8	no	—
605	#41	—	4	32	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	8	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	4	4	no	—
615	C₂×Q₈	—	4	4	no	—
616	C₂×Q₈	—	4	8	no	—
617	C₂×Q₈	—	4	4	no	—
618	C₂×Q₈	#41×C₇₃	1	4	yes	complemented
619	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
637	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
638	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	4	4	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	4	no	—
659	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
664	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
668	SD₁₆	—	2	8	no	—
669	SD₁₆	—	4	4	no	—
670	D₈	—	4	4	no	—
671	M₁₆	—	4	4	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	4	4	no	—
677	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
678	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
679	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
680	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
703	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
704	C₄²	—	2	4	no	—
705	C₄²	C₂×D₄×C₇₃	1	2	yes	—
706	C₄²	C₂⁴×C₇₃	1	2	yes	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
721	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
722	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
723	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	8	no	—
729	Q₈	—	4	8	no	—
730	Q₈	—	4	2	no	—
731	Q₈	C₂×#41×C₇₃	1	4	yes	complemented
732	D₄	—	2	8	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
774	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
775	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
776	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
777	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	8	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	8	4	no	—
796	C₂²	—	8	4	no	—
797	C₂²	#546×C₇₃	1	2	yes	—
798	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	4	yes	—
799	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
800	C₂²	#578×C₇₃	1	2	yes	—
801	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	4	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	#546×C₇₃	1	2	yes	—
813	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
814	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
815	C₂	—	2	4	no	—
816	C₂	—	4	2	no	—
817	C₂	—	8	2	no	—
818	C₂	—	8	2	no	—
819	C₂	C₇₃×#3308	1	4	yes	direct product factor
820	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
821	C₂	C₂²×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
822	C₂	C₂×#578×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#548×C₇₃	C₂	semidirect
2. C₂×#547×C₇₃	C₂	semidirect
3. C₇₃×#3308	C₂	direct (N × H)
4. C₂×#489×C₇₃	C₂	semidirect
5. C₂×#484×C₇₃	C₂	semidirect
6. C₂×#480×C₇₃	C₂	semidirect
7. C₂×#477×C₇₃	C₂	semidirect
8. C₂×#468×C₇₃	C₂	semidirect
9. C₂×#466×C₇₃	C₂	semidirect
10. C₂×#463×C₇₃	C₂	semidirect
11. C₂×#449×C₇₃	C₂	semidirect
12. C₂×#448×C₇₃	C₂	semidirect
13. C₂×#440×C₇₃	C₂	semidirect
14. C₂×#435×C₇₃	C₂	semidirect
15. C₂×#417×C₇₃	C₂	semidirect
16. C₂²×#103×C₇₃	C₂	semidirect
26. #548×C₇₃	C₂²	semidirect
28. #547×C₇₃	C₂²	semidirect
47. #489×C₇₃	C₂²	semidirect
48. #484×C₇₃	C₂²	semidirect
49. #480×C₇₃	C₂²	semidirect
50. #477×C₇₃	C₂²	semidirect
51. #468×C₇₃	C₂²	semidirect
52. #466×C₇₃	C₂²	semidirect
53. #463×C₇₃	C₂²	semidirect
54. #449×C₇₃	C₂²	semidirect
55. #448×C₇₃	C₂²	semidirect
56. #440×C₇₃	C₂²	semidirect
57. #435×C₇₃	C₂²	semidirect
62. #417×C₇₃	C₂²	semidirect
69. C₂×#103×C₇₃	C₂²	semidirect
206. C₂×Q₈×C₇₃	#41	semidirect
319. Q₈×C₇₃	C₂×#41	semidirect
403. C₂×#3308	C₇₃	direct (N × H)
408. C₂×C₇₃	#3308	direct (N × H)
412. C₂×#548	C₂×C₇₃	semidirect
413. C₂×#547	C₂×C₇₃	semidirect
414. #3308	C₂×C₇₃	direct (N × H)
415. C₂×#489	C₂×C₇₃	semidirect
416. C₂×#484	C₂×C₇₃	semidirect
417. C₂×#480	C₂×C₇₃	semidirect
418. C₂×#477	C₂×C₇₃	semidirect
419. C₂×#468	C₂×C₇₃	semidirect
420. C₂×#466	C₂×C₇₃	semidirect
421. C₂×#463	C₂×C₇₃	semidirect
422. C₂×#449	C₂×C₇₃	semidirect
423. C₂×#448	C₂×C₇₃	semidirect
424. C₂×#440	C₂×C₇₃	semidirect
425. C₂×#435	C₂×C₇₃	semidirect
426. C₂×#417	C₂×C₇₃	semidirect
427. C₂²×#103	C₂×C₇₃	semidirect
428. C₇₃	C₂×#3308	direct (N × H)
438. #548	C₂²×C₇₃	semidirect
440. #547	C₂²×C₇₃	semidirect
459. #489	C₂²×C₇₃	semidirect
460. #484	C₂²×C₇₃	semidirect
461. #480	C₂²×C₇₃	semidirect
462. #477	C₂²×C₇₃	semidirect
463. #468	C₂²×C₇₃	semidirect
464. #466	C₂²×C₇₃	semidirect
465. #463	C₂²×C₇₃	semidirect
466. #449	C₂²×C₇₃	semidirect
467. #448	C₂²×C₇₃	semidirect
468. #440	C₂²×C₇₃	semidirect
469. #435	C₂²×C₇₃	semidirect
474. #417	C₂²×C₇₃	semidirect
481. C₂×#103	C₂²×C₇₃	semidirect
618. C₂×Q₈	#41×C₇₃	semidirect
731. Q₈	C₂×#41×C₇₃	semidirect
819. C₂	C₇₃×#3308	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#548×C₇₃	2
C₂×#547×C₇₃	2
C₇₃×#3308	2
C₂×#489×C₇₃	2
C₂×#484×C₇₃	2
C₂×#480×C₇₃	2
C₂×#477×C₇₃	2
C₂×#468×C₇₃	2
C₂×#466×C₇₃	2
C₂×#463×C₇₃	2
C₂×#449×C₇₃	2
C₂×#448×C₇₃	2
C₂×#440×C₇₃	2
C₂×#435×C₇₃	2
C₂×#417×C₇₃	2
C₂²×#103×C₇₃	2
C₂×#3308	73

Subgroups — C2×C73×#3308 #32970533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3308 #32970533