Subgroups — C₆₇×#36729 #30715980

Order 17152.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2747	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2742	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2741	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2717	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2702	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2692	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2691	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2672	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	#400×C₆₇	C₂²	1	2	yes	complemented
39	#400×C₆₇	C₂²	1	2	yes	complemented
40	#400×C₆₇	C₂²	1	2	yes	complemented
41	#399×C₆₇	C₂²	1	2	yes	—
42	#399×C₆₇	C₂²	1	2	yes	complemented
43	#398×C₆₇	C₂²	1	2	yes	complemented
44	#398×C₆₇	C₂²	1	2	yes	complemented
45	#398×C₆₇	C₂²	1	2	yes	complemented
46	#397×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	complemented
49	#397×C₆₇	C₂²	1	2	yes	complemented
50	#396×C₆₇	C₂²	1	2	yes	complemented
51	#396×C₆₇	C₂²	1	2	yes	complemented
52	#395×C₆₇	C₂²	1	2	yes	complemented
53	#395×C₆₇	C₂²	1	2	yes	complemented
54	#395×C₆₇	C₂²	1	2	yes	complemented
55	#394×C₆₇	C₂²	1	2	yes	—
56	#394×C₆₇	C₂²	1	2	yes	—
57	#394×C₆₇	C₂²	1	2	yes	—
58	#394×C₆₇	C₂²	1	2	yes	—
59	#394×C₆₇	C₂²	1	2	yes	complemented
60	#393×C₆₇	C₂²	1	2	yes	—
61	#393×C₆₇	C₂²	1	2	yes	complemented
62	#391×C₆₇	C₂²	1	2	yes	complemented
63	#390×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	complemented
65	#389×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	2	yes	complemented
75	#387×C₆₇	C₂²	1	2	yes	complemented
76	#387×C₆₇	C₂²	1	2	yes	complemented
77	#387×C₆₇	C₂²	1	2	yes	complemented
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	complemented
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	2	yes	complemented
91	#385×C₆₇	C₂²	1	2	yes	complemented
92	#380×C₆₇	C₂²	1	2	yes	—
93	#380×C₆₇	C₂²	1	2	yes	—
94	#380×C₆₇	C₂²	1	2	yes	—
95	#380×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	1	yes	characteristic
97	#380×C₆₇	C₂²	1	1	yes	characteristic
98	#380×C₆₇	C₂²	1	1	yes	characteristic
99	#380×C₆₇	C₂²	1	1	yes	characteristic
100	#380×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	2	yes	—
103	#379×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	—	2	4	no	—
115	C₂³×C₄×C₆₇	—	4	2	no	—
116	C₂³×C₄×C₆₇	—	4	2	no	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	#126×C₆₇	—	4	4	no	—
129	#124×C₆₇	—	4	4	no	—
130	#123×C₆₇	—	4	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	4	4	no	—
133	C₂²⋊Q₈×C₆₇	—	4	4	no	—
134	C₂²⋊Q₈×C₆₇	—	4	2	no	—
135	C₂²⋊Q₈×C₆₇	—	4	2	no	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	—	4	2	no	—
138	#121×C₆₇	—	4	2	no	—
139	#120×C₆₇	—	4	4	no	—
140	C₄×D₄×C₆₇	—	4	4	no	—
141	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
142	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
165	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	C₂⁴×C₆₇	—	2	2	no	—
215	C₂⁴×C₆₇	—	2	2	no	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	C₂⁴×C₆₇	—	2	2	no	—
218	C₂⁴×C₆₇	—	2	2	no	—
219	C₂⁴×C₆₇	—	4	1	no	—
220	C₂⁴×C₆₇	—	4	1	no	—
221	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
222	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂×Q₈×C₆₇	—	2	2	no	—
226	C₂×Q₈×C₆₇	—	4	1	no	—
227	C₂×Q₈×C₆₇	—	4	1	no	—
228	C₂×Q₈×C₆₇	—	4	2	no	—
229	C₂×Q₈×C₆₇	—	4	2	no	—
230	C₂×Q₈×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	4	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	4	1	no	—
240	C₂×D₄×C₆₇	—	4	1	no	—
241	C₂×D₄×C₆₇	—	4	2	no	—
242	C₂×D₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	—	4	1	no	—
259	C₂²×C₄×C₆₇	—	4	1	no	—
260	C₂²×C₄×C₆₇	—	4	1	no	—
261	C₂²×C₄×C₆₇	—	4	1	no	—
262	C₂²×C₄×C₆₇	—	4	1	no	—
263	C₂²×C₄×C₆₇	—	4	1	no	—
264	C₂²×C₄×C₆₇	—	4	1	no	—
265	C₂²×C₄×C₆₇	—	4	1	no	—
266	C₂²×C₄×C₆₇	—	4	1	no	—
267	C₂²×C₄×C₆₇	—	4	1	no	—
268	C₂²×C₄×C₆₇	—	4	1	no	—
269	C₂²×C₄×C₆₇	—	4	1	no	—
270	C₂²×C₄×C₆₇	—	4	1	no	—
271	C₂²×C₄×C₆₇	—	4	1	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	16	no	—
276	C₂²×C₄×C₆₇	#41	1	4	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	4	no	—
297	C₄⋊C₄×C₆₇	—	2	4	no	—
298	C₄⋊C₄×C₆₇	—	2	4	no	—
299	C₄⋊C₄×C₆₇	—	4	2	no	—
300	C₄⋊C₄×C₆₇	—	4	2	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	1	no	—
303	C₄⋊C₄×C₆₇	—	4	1	no	—
304	C₄⋊C₄×C₆₇	—	4	1	no	—
305	C₄⋊C₄×C₆₇	—	4	1	no	—
306	C₄⋊C₄×C₆₇	—	4	2	no	—
307	C₄⋊C₄×C₆₇	—	4	2	no	—
308	C₄⋊C₄×C₆₇	—	4	2	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	2	no	—
312	C₄⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	4	2	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₂²⋊C₄×C₆₇	—	4	2	no	—
326	C₂²⋊C₄×C₆₇	—	4	2	no	—
327	C₂²⋊C₄×C₆₇	—	4	2	no	—
328	C₂²⋊C₄×C₆₇	—	4	2	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	—	4	2	no	—
331	C₂²⋊C₄×C₆₇	—	4	2	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₄²×C₆₇	—	4	2	no	—
337	C₄²×C₆₇	—	4	2	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	8	no	—
344	C₂³×C₆₇	—	2	1	no	—
345	C₂³×C₆₇	—	2	1	no	—
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	4	4	no	—
364	C₂³×C₆₇	—	4	4	no	—
365	C₂³×C₆₇	—	4	4	no	—
366	C₂³×C₆₇	—	4	4	no	—
367	C₂³×C₆₇	—	4	4	no	—
368	C₂³×C₆₇	—	4	4	no	—
369	C₂³×C₆₇	C₂×#41	1	2	yes	—
370	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
371	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
372	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
373	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
374	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
375	Q₈×C₆₇	—	8	2	no	—
376	Q₈×C₆₇	—	8	4	no	—
377	D₄×C₆₇	—	4	8	no	—
378	D₄×C₆₇	—	8	2	no	—
379	D₄×C₆₇	—	8	4	no	—
380	D₄×C₆₇	—	8	4	no	—
381	C₂×C₄×C₆₇	—	2	8	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	4	4	no	—
424	C₂×C₄×C₆₇	—	4	4	no	—
425	C₂×C₄×C₆₇	—	4	4	no	—
426	C₂×C₄×C₆₇	—	4	4	no	—
427	C₂×C₄×C₆₇	—	4	4	no	—
428	C₂×C₄×C₆₇	—	8	2	no	—
429	C₂×C₄×C₆₇	—	8	2	no	—
430	C₂×C₄×C₆₇	—	8	2	no	—
431	C₂×C₄×C₆₇	—	8	2	no	—
432	C₂×C₄×C₆₇	—	8	4	no	—
433	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
434	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
435	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	2	no	—
447	C₂²×C₆₇	—	2	2	no	—
448	C₂²×C₆₇	—	2	2	no	—
449	C₂²×C₆₇	—	4	16	no	—
450	C₂²×C₆₇	—	4	1	no	—
451	C₂²×C₆₇	—	4	1	no	—
452	C₂²×C₆₇	—	4	1	no	—
453	C₂²×C₆₇	—	4	1	no	—
454	C₂²×C₆₇	—	4	1	no	—
455	C₂²×C₆₇	—	4	1	no	—
456	C₂²×C₆₇	—	4	1	no	—
457	C₂²×C₆₇	—	4	1	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	#542	1	4	yes	—
466	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
473	C₄×C₆₇	—	2	2	no	—
474	C₄×C₆₇	—	2	2	no	—
475	C₄×C₆₇	—	2	2	no	—
476	C₄×C₆₇	—	2	2	no	—
477	C₄×C₆₇	—	4	2	no	—
478	C₄×C₆₇	—	4	2	no	—
479	C₄×C₆₇	—	4	2	no	—
480	C₄×C₆₇	—	4	2	no	—
481	C₄×C₆₇	—	4	2	no	—
482	C₄×C₆₇	—	4	2	no	—
483	C₄×C₆₇	—	4	2	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	—	4	2	no	—
486	C₄×C₆₇	—	4	2	no	—
487	C₄×C₆₇	—	4	2	no	—
488	#36729	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
489	C₂×C₆₇	—	2	4	no	—
490	C₂×C₆₇	—	4	2	no	—
491	C₂×C₆₇	—	4	2	no	—
492	C₂×C₆₇	—	8	2	no	—
493	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
494	C₂×C₆₇	#3490	1	1	yes	characteristic
495	C₂×C₆₇	#3492	1	1	yes	characteristic
496	C₂×C₆₇	#3536	1	1	yes	characteristic
497	C₂×C₆₇	#3536	1	1	yes	characteristic
498	C₂×C₆₇	#3537	1	1	yes	characteristic
499	C₂×C₆₇	#3538	1	1	yes	characteristic
500	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
501	#2847	C₂×C₆₇	1	1	yes	characteristic
502	#2747	C₂×C₆₇	1	2	yes	complemented
503	#2742	C₂×C₆₇	1	2	yes	complemented
504	#2741	C₂×C₆₇	1	2	yes	complemented
505	#2717	C₂×C₆₇	1	2	yes	complemented
506	#2702	C₂×C₆₇	1	2	yes	complemented
507	#2692	C₂×C₆₇	1	2	yes	complemented
508	#2691	C₂×C₆₇	1	2	yes	complemented
509	#2672	C₂×C₆₇	1	2	yes	complemented
510	#2659	C₂×C₆₇	1	1	yes	characteristic, complemented
511	#2639	C₂×C₆₇	1	1	yes	characteristic, complemented
512	#2481	C₂×C₆₇	1	2	yes	complemented
513	#2472	C₂×C₆₇	1	2	yes	complemented
514	#2449	C₂×C₆₇	1	2	yes	complemented
515	#2418	C₂×C₆₇	1	2	yes	complemented
516	#2329	C₂×C₆₇	1	1	yes	characteristic, complemented
517	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
518	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
519	C₆₇	#36729	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
522	C₂×#124	C₂²×C₆₇	1	2	yes	—
523	C₂×#123	C₂²×C₆₇	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
528	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
529	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
530	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
531	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
532	C₂×#120	C₂²×C₆₇	1	2	yes	—
533	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
534	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
535	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
536	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
537	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
538	#400	C₂²×C₆₇	1	2	yes	complemented
539	#400	C₂²×C₆₇	1	2	yes	complemented
540	#400	C₂²×C₆₇	1	2	yes	complemented
541	#399	C₂²×C₆₇	1	2	yes	—
542	#399	C₂²×C₆₇	1	2	yes	complemented
543	#398	C₂²×C₆₇	1	2	yes	complemented
544	#398	C₂²×C₆₇	1	2	yes	complemented
545	#398	C₂²×C₆₇	1	2	yes	complemented
546	#397	C₂²×C₆₇	1	2	yes	—
547	#397	C₂²×C₆₇	1	2	yes	—
548	#397	C₂²×C₆₇	1	2	yes	complemented
549	#397	C₂²×C₆₇	1	2	yes	complemented
550	#396	C₂²×C₆₇	1	2	yes	complemented
551	#396	C₂²×C₆₇	1	2	yes	complemented
552	#395	C₂²×C₆₇	1	2	yes	complemented
553	#395	C₂²×C₆₇	1	2	yes	complemented
554	#395	C₂²×C₆₇	1	2	yes	complemented
555	#394	C₂²×C₆₇	1	2	yes	—
556	#394	C₂²×C₆₇	1	2	yes	—
557	#394	C₂²×C₆₇	1	2	yes	—
558	#394	C₂²×C₆₇	1	2	yes	—
559	#394	C₂²×C₆₇	1	2	yes	complemented
560	#393	C₂²×C₆₇	1	2	yes	—
561	#393	C₂²×C₆₇	1	2	yes	complemented
562	#391	C₂²×C₆₇	1	2	yes	complemented
563	#390	C₂²×C₆₇	1	2	yes	—
564	#389	C₂²×C₆₇	1	2	yes	complemented
565	#389	C₂²×C₆₇	1	2	yes	complemented
566	#388	C₂²×C₆₇	1	2	yes	—
567	#388	C₂²×C₆₇	1	2	yes	—
568	#388	C₂²×C₆₇	1	2	yes	—
569	#388	C₂²×C₆₇	1	2	yes	—
570	#388	C₂²×C₆₇	1	2	yes	complemented
571	#388	C₂²×C₆₇	1	2	yes	complemented
572	#387	C₂²×C₆₇	1	2	yes	complemented
573	#387	C₂²×C₆₇	1	2	yes	complemented
574	#387	C₂²×C₆₇	1	2	yes	complemented
575	#387	C₂²×C₆₇	1	2	yes	complemented
576	#387	C₂²×C₆₇	1	2	yes	complemented
577	#387	C₂²×C₆₇	1	2	yes	complemented
578	#386	C₂²×C₆₇	1	2	yes	—
579	#386	C₂²×C₆₇	1	2	yes	—
580	#386	C₂²×C₆₇	1	2	yes	—
581	#386	C₂²×C₆₇	1	2	yes	—
582	#386	C₂²×C₆₇	1	2	yes	—
583	#386	C₂²×C₆₇	1	2	yes	—
584	#386	C₂²×C₆₇	1	2	yes	—
585	#386	C₂²×C₆₇	1	2	yes	complemented
586	#385	C₂²×C₆₇	1	2	yes	—
587	#385	C₂²×C₆₇	1	2	yes	—
588	#385	C₂²×C₆₇	1	2	yes	—
589	#385	C₂²×C₆₇	1	2	yes	—
590	#385	C₂²×C₆₇	1	2	yes	complemented
591	#385	C₂²×C₆₇	1	2	yes	complemented
592	#380	C₂²×C₆₇	1	1	yes	characteristic
593	#380	C₂²×C₆₇	1	1	yes	characteristic
594	#380	C₂²×C₆₇	1	1	yes	characteristic
595	#380	C₂²×C₆₇	1	1	yes	characteristic
596	#380	C₂²×C₆₇	1	1	yes	characteristic
597	#380	C₂²×C₆₇	1	1	yes	characteristic
598	#380	C₂²×C₆₇	1	2	yes	—
599	#380	C₂²×C₆₇	1	2	yes	—
600	#380	C₂²×C₆₇	1	2	yes	—
601	#380	C₂²×C₆₇	1	2	yes	—
602	#380	C₂²×C₆₇	1	2	yes	—
603	#379	C₂²×C₆₇	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
605	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
607	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
610	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
611	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
612	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
613	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂³×C₄	—	2	4	no	—
615	C₂³×C₄	—	4	2	no	—
616	C₂³×C₄	—	4	2	no	—
617	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
627	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
628	#126	—	4	4	no	—
629	#124	—	4	4	no	—
630	#123	—	4	4	no	—
631	C₂²⋊Q₈	—	2	4	no	—
632	C₂²⋊Q₈	—	4	4	no	—
633	C₂²⋊Q₈	—	4	4	no	—
634	C₂²⋊Q₈	—	4	2	no	—
635	C₂²⋊Q₈	—	4	2	no	—
636	#121	—	2	4	no	—
637	#121	—	4	2	no	—
638	#121	—	4	2	no	—
639	#120	—	4	4	no	—
640	C₄×D₄	—	4	4	no	—
641	C₂×C₄⋊C₄	—	4	2	no	—
642	C₂×C₄⋊C₄	—	4	2	no	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	—	4	2	no	—
665	C₂×C₂²⋊C₄	—	4	2	no	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	2	yes	—
698	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	2	yes	—
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	2	no	—
717	C₂⁴	—	2	2	no	—
718	C₂⁴	—	2	2	no	—
719	C₂⁴	—	4	1	no	—
720	C₂⁴	—	4	1	no	—
721	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
722	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	4	1	no	—
727	C₂×Q₈	—	4	1	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×Q₈	—	4	2	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	16	no	—
776	C₂²×C₄	#41×C₆₇	1	4	yes	—
777	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	—	4	1	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	4	no	—
869	C₂³	C₂×#41×C₆₇	1	2	yes	—
870	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
871	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
872	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
873	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
874	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
875	Q₈	—	8	2	no	—
876	Q₈	—	8	4	no	—
877	D₄	—	4	8	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	4	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
934	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
935	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
936	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	16	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	#542×C₆₇	1	4	yes	—
966	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
967	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
968	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
969	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
970	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
971	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
972	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	—	4	2	no	—
991	C₂	—	8	2	no	—
992	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
993	C₂	C₆₇×#3490	1	1	yes	characteristic
994	C₂	C₆₇×#3492	1	1	yes	characteristic
995	C₂	C₆₇×#3536	1	1	yes	characteristic
996	C₂	C₆₇×#3536	1	1	yes	characteristic
997	C₂	C₆₇×#3537	1	1	yes	characteristic
998	C₂	C₆₇×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2848	C₂	semidirect
3. C₆₇×#2747	C₂	semidirect
4. C₆₇×#2742	C₂	semidirect
5. C₆₇×#2741	C₂	semidirect
6. C₆₇×#2717	C₂	semidirect
7. C₆₇×#2702	C₂	semidirect
8. C₆₇×#2692	C₂	semidirect
9. C₆₇×#2691	C₂	semidirect
10. C₆₇×#2672	C₂	semidirect
11. C₆₇×#2659	C₂	semidirect
12. C₆₇×#2639	C₂	semidirect
13. C₆₇×#2481	C₂	semidirect
14. C₆₇×#2472	C₂	semidirect
15. C₆₇×#2449	C₂	semidirect
16. C₆₇×#2418	C₂	semidirect
17. C₆₇×#2329	C₂	semidirect
18. C₆₇×#2325	C₂	semidirect
19. C₂×#380×C₆₇	C₂	semidirect
21. C₂×#126×C₆₇	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
38. #400×C₆₇	C₂²	semidirect
39. #400×C₆₇	C₂²	semidirect
40. #400×C₆₇	C₂²	semidirect
42. #399×C₆₇	C₂²	semidirect
43. #398×C₆₇	C₂²	semidirect
44. #398×C₆₇	C₂²	semidirect
45. #398×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #396×C₆₇	C₂²	semidirect
51. #396×C₆₇	C₂²	semidirect
52. #395×C₆₇	C₂²	semidirect
53. #395×C₆₇	C₂²	semidirect
54. #395×C₆₇	C₂²	semidirect
59. #394×C₆₇	C₂²	semidirect
61. #393×C₆₇	C₂²	semidirect
62. #391×C₆₇	C₂²	semidirect
64. #389×C₆₇	C₂²	semidirect
65. #389×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
77. #387×C₆₇	C₂²	semidirect
85. #386×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
488. #36729	C₆₇	direct (N × H)
500. #2848	C₂×C₆₇	semidirect
502. #2747	C₂×C₆₇	semidirect
503. #2742	C₂×C₆₇	semidirect
504. #2741	C₂×C₆₇	semidirect
505. #2717	C₂×C₆₇	semidirect
506. #2702	C₂×C₆₇	semidirect
507. #2692	C₂×C₆₇	semidirect
508. #2691	C₂×C₆₇	semidirect
509. #2672	C₂×C₆₇	semidirect
510. #2659	C₂×C₆₇	semidirect
511. #2639	C₂×C₆₇	semidirect
512. #2481	C₂×C₆₇	semidirect
513. #2472	C₂×C₆₇	semidirect
514. #2449	C₂×C₆₇	semidirect
515. #2418	C₂×C₆₇	semidirect
516. #2329	C₂×C₆₇	semidirect
517. #2325	C₂×C₆₇	semidirect
518. C₂×#380	C₂×C₆₇	semidirect
519. C₆₇	#36729	direct (N × H)
521. C₂×#126	C₂²×C₆₇	semidirect
528. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
538. #400	C₂²×C₆₇	semidirect
539. #400	C₂²×C₆₇	semidirect
540. #400	C₂²×C₆₇	semidirect
542. #399	C₂²×C₆₇	semidirect
543. #398	C₂²×C₆₇	semidirect
544. #398	C₂²×C₆₇	semidirect
545. #398	C₂²×C₆₇	semidirect
548. #397	C₂²×C₆₇	semidirect
549. #397	C₂²×C₆₇	semidirect
550. #396	C₂²×C₆₇	semidirect
551. #396	C₂²×C₆₇	semidirect
552. #395	C₂²×C₆₇	semidirect
553. #395	C₂²×C₆₇	semidirect
554. #395	C₂²×C₆₇	semidirect
559. #394	C₂²×C₆₇	semidirect
561. #393	C₂²×C₆₇	semidirect
562. #391	C₂²×C₆₇	semidirect
564. #389	C₂²×C₆₇	semidirect
565. #389	C₂²×C₆₇	semidirect
570. #388	C₂²×C₆₇	semidirect
571. #388	C₂²×C₆₇	semidirect
572. #387	C₂²×C₆₇	semidirect
573. #387	C₂²×C₆₇	semidirect
574. #387	C₂²×C₆₇	semidirect
575. #387	C₂²×C₆₇	semidirect
576. #387	C₂²×C₆₇	semidirect
577. #387	C₂²×C₆₇	semidirect
585. #386	C₂²×C₆₇	semidirect
590. #385	C₂²×C₆₇	semidirect
591. #385	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2747	2
C₆₇×#2742	2
C₆₇×#2741	2
C₆₇×#2717	2
C₆₇×#2702	2
C₆₇×#2692	2
C₆₇×#2691	2
C₆₇×#2672	2
C₆₇×#2659	2
C₆₇×#2639	2
C₆₇×#2481	2
C₆₇×#2472	2
C₆₇×#2449	2
C₆₇×#2418	2
C₆₇×#2329	2
C₆₇×#2325	2
C₂×#380×C₆₇	2
#36729	67

Subgroups — C67×#36729 #30715980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36729 #30715980