Subgroups — C₆₇×#60597 #30739848

Order 17152.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3125	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3118	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3109	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3101	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#476×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2952	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂×#135×C₆₇	C₂²	1	2	yes	—
21	#556×C₆₇	—	2	1	no	—
22	#555×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	1	no	—
24	#553×C₆₇	—	2	2	no	—
25	#548×C₆₇	—	2	2	no	—
26	#547×C₆₇	—	2	1	no	—
27	#542×C₆₇	C₂²	1	4	yes	complemented
28	#537×C₆₇	C₂²	1	2	yes	—
29	#533×C₆₇	C₂²	1	2	yes	complemented
30	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#532×C₆₇	C₂²	1	2	yes	complemented
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#520×C₆₇	—	2	1	no	—
34	#520×C₆₇	C₂²	1	2	yes	—
35	#520×C₆₇	C₂²	1	1	yes	characteristic
36	#520×C₆₇	C₂²	1	1	yes	characteristic
37	#520×C₆₇	C₂²	1	2	yes	complemented
38	#518×C₆₇	—	2	1	no	—
39	#518×C₆₇	—	2	2	no	—
40	#518×C₆₇	C₂²	1	2	yes	—
41	#518×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×#41×C₆₇	—	2	1	no	—
43	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
44	C₄×#41×C₆₇	C₂²	1	2	yes	—
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	—	2	2	no	—
47	C₂×C₄×D₄×C₆₇	—	2	1	no	—
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
50	#485×C₆₇	C₂²	1	4	yes	complemented
51	#483×C₆₇	C₂²	1	4	yes	complemented
52	#482×C₆₇	C₂²	1	4	yes	complemented
53	#481×C₆₇	C₂²	1	4	yes	complemented
54	#477×C₆₇	C₂²	1	2	yes	complemented
55	#476×C₆₇	C₂²	1	2	yes	complemented
56	#476×C₆₇	C₂²	1	2	yes	complemented
57	#476×C₆₇	C₂²	1	4	yes	complemented
58	#476×C₆₇	C₂²	1	2	yes	complemented
59	#475×C₆₇	C₂²	1	2	yes	complemented
60	#474×C₆₇	C₂²	1	2	yes	complemented
61	#464×C₆₇	C₂²	1	2	yes	complemented
62	#463×C₆₇	C₂²	1	2	yes	complemented
63	#463×C₆₇	C₂²	1	4	yes	complemented
64	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#461×C₆₇	C₂²	1	2	yes	complemented
67	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	—
71	#450×C₆₇	C₂²	1	4	yes	—
72	#449×C₆₇	C₂²	1	4	yes	—
73	#447×C₆₇	C₂²	1	4	yes	—
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	#442×C₆₇	C₂²	1	4	yes	complemented
76	#441×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
81	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
82	#433×C₆₇	C₂²	1	4	yes	complemented
83	#432×C₆₇	C₂²	1	2	yes	complemented
84	#431×C₆₇	C₂²	1	2	yes	complemented
85	#428×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
87	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#417×C₆₇	C₂²	1	2	yes	—
90	#417×C₆₇	C₂²	1	2	yes	complemented
91	#416×C₆₇	C₂²	1	2	yes	complemented
92	C₂×#102×C₆₇	C₂²	1	2	yes	—
93	#408×C₆₇	C₂²	1	2	yes	—
94	#405×C₆₇	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₆₇	—	2	4	no	—
96	H(5,𝔽₂)×C₆₇	—	2	4	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₆₇	—	2	1	no	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	—	2	1	no	—
106	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
107	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	—	2	1	no	—
109	C₂³×C₄×C₆₇	—	2	2	no	—
110	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
111	#135×C₆₇	—	2	8	no	—
112	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×D₈×C₆₇	C₂³	1	4	yes	—
117	C₂×D₈×C₆₇	C₂³	1	2	yes	—
118	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
119	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₇	—	2	1	no	—
121	C₄⋊Q₈×C₆₇	—	2	1	no	—
122	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
125	#127×C₆₇	C₂³	1	1	yes	characteristic
126	#126×C₆₇	—	2	4	no	—
127	#125×C₆₇	—	2	2	no	—
128	#124×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	C₂³	1	2	yes	—
131	#123×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	4	no	—
138	#121×C₆₇	—	2	1	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	2	no	—
141	#121×C₆₇	C₂³	1	4	yes	—
142	C₄×Q₈×C₆₇	—	2	1	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
145	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
146	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	1	no	—
152	C₄×D₄×C₆₇	—	2	1	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	1	no	—
155	C₄×D₄×C₆₇	—	2	2	no	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	2	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	2	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	D₄	1	2	yes	—
172	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
173	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	2	yes	—
181	C₄×D₄×C₆₇	C₂³	1	2	yes	—
182	C₄×D₄×C₆₇	C₂³	1	4	yes	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	1	no	—
185	#117×C₆₇	—	2	2	no	—
186	#117×C₆₇	—	2	2	no	—
187	#117×C₆₇	—	2	1	no	—
188	#117×C₆₇	—	2	2	no	—
189	#117×C₆₇	C₂³	1	2	yes	—
190	#117×C₆₇	C₂³	1	1	yes	characteristic
191	#117×C₆₇	C₂³	1	1	yes	characteristic
192	#117×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
203	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
205	C₂×C₄²×C₆₇	—	2	2	no	—
206	C₂×C₄²×C₆₇	—	2	1	no	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	#107×C₆₇	C₂³	1	4	yes	—
210	#106×C₆₇	C₂³	1	4	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	#106×C₆₇	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	4	yes	—
219	#103×C₆₇	C₂³	1	4	yes	—
220	#103×C₆₇	C₂³	1	2	yes	—
221	#103×C₆₇	C₂³	1	2	yes	—
222	#102×C₆₇	C₂³	1	4	yes	—
223	#102×C₆₇	C₂³	1	4	yes	—
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	4	yes	—
226	#102×C₆₇	C₂³	1	2	yes	—
227	#102×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	#97×C₆₇	C₂³	1	4	yes	—
231	C₄×C₈×C₆₇	C₂³	1	4	yes	—
232	C₂⁴×C₆₇	—	2	2	no	—
233	C₂⁴×C₆₇	—	2	1	no	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	2	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	—	2	2	no	—
240	#41×C₆₇	—	2	4	no	—
241	#41×C₆₇	—	2	4	no	—
242	#41×C₆₇	—	8	4	no	—
243	#41×C₆₇	#41	1	4	yes	complemented
244	C₂×Q₈×C₆₇	—	2	2	no	—
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	8	2	no	—
247	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₆₇	—	2	16	no	—
251	C₂×D₄×C₆₇	—	2	8	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	1	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	1	no	—
260	C₂×D₄×C₆₇	—	2	1	no	—
261	C₂×D₄×C₆₇	—	2	1	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₆₇	#41	1	4	yes	complemented
266	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	1	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	1	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	1	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	8	2	no	—
284	C₂²×C₄×C₆₇	—	8	4	no	—
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	Q₁₆×C₆₇	—	2	4	no	—
292	SD₁₆×C₆₇	—	2	4	no	—
293	SD₁₆×C₆₇	—	2	4	no	—
294	SD₁₆×C₆₇	—	2	8	no	—
295	D₈×C₆₇	—	2	4	no	—
296	D₈×C₆₇	—	2	8	no	—
297	M₁₆×C₆₇	—	2	4	no	—
298	C₂×C₈×C₆₇	—	2	4	no	—
299	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
300	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
301	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	1	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	4	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	1	no	—
311	C₄⋊C₄×C₆₇	—	2	1	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	4	no	—
314	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
316	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	2	no	—
326	C₂²⋊C₄×C₆₇	—	2	1	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	2	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₄²×C₆₇	—	2	1	no	—
340	C₄²×C₆₇	—	2	1	no	—
341	C₄²×C₆₇	—	2	2	no	—
342	C₄²×C₆₇	—	2	2	no	—
343	C₄²×C₆₇	—	2	1	no	—
344	C₄²×C₆₇	—	2	4	no	—
345	C₄²×C₆₇	C₂×D₄	1	2	yes	—
346	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₆₇	C₂×D₄	1	2	yes	—
349	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₄²×C₆₇	C₂⁴	1	2	yes	—
352	C₂³×C₆₇	—	2	8	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	4	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	8	1	no	—
358	C₂³×C₆₇	—	8	2	no	—
359	C₂³×C₆₇	—	8	1	no	—
360	C₂³×C₆₇	—	8	2	no	—
361	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
362	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₆₇	—	2	2	no	—
364	Q₈×C₆₇	—	2	1	no	—
365	Q₈×C₆₇	—	2	2	no	—
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	4	4	no	—
368	Q₈×C₆₇	—	8	2	no	—
369	Q₈×C₆₇	C₂×#41	1	2	yes	—
370	D₄×C₆₇	—	2	8	no	—
371	D₄×C₆₇	—	2	8	no	—
372	D₄×C₆₇	—	2	4	no	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	2	4	no	—
376	D₄×C₆₇	—	2	2	no	—
377	D₄×C₆₇	—	2	1	no	—
378	D₄×C₆₇	—	2	2	no	—
379	D₄×C₆₇	—	2	2	no	—
380	D₄×C₆₇	—	4	2	no	—
381	D₄×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	4	2	no	—
383	D₄×C₆₇	—	8	4	no	—
384	D₄×C₆₇	C₂×#41	1	2	yes	—
385	D₄×C₆₇	C₂×#41	1	4	yes	—
386	C₂×C₄×C₆₇	—	2	8	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	4	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	4	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	4	no	—
398	C₂×C₄×C₆₇	—	4	1	no	—
399	C₂×C₄×C₆₇	—	4	2	no	—
400	C₂×C₄×C₆₇	—	4	4	no	—
401	C₂×C₄×C₆₇	—	4	4	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	8	2	no	—
404	C₂×C₄×C₆₇	—	8	1	no	—
405	C₂×C₄×C₆₇	—	8	2	no	—
406	C₂×C₄×C₆₇	—	8	2	no	—
407	C₂×C₄×C₆₇	—	8	2	no	—
408	C₂×C₄×C₆₇	—	8	4	no	—
409	C₂×C₄×C₆₇	—	8	1	no	—
410	C₂×C₄×C₆₇	—	8	2	no	—
411	C₂×C₄×C₆₇	—	8	2	no	—
412	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
421	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
422	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
423	C₈×C₆₇	—	2	2	no	—
424	C₈×C₆₇	—	2	2	no	—
425	C₈×C₆₇	—	2	4	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	1	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	2	2	no	—
430	C₂²×C₆₇	—	2	4	no	—
431	C₂²×C₆₇	—	2	2	no	—
432	C₂²×C₆₇	—	2	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	1	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	2	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	8	4	no	—
441	C₂²×C₆₇	—	8	8	no	—
442	C₂²×C₆₇	#525	1	2	yes	—
443	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
444	C₄×C₆₇	—	2	1	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	1	no	—
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	1	no	—
451	C₄×C₆₇	—	4	1	no	—
452	C₄×C₆₇	—	4	4	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	1	no	—
456	C₄×C₆₇	#525	1	2	yes	—
457	C₄×C₆₇	#577	1	2	yes	—
458	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
459	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
460	#60597	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₆₇	—	2	2	no	—
462	C₂×C₆₇	—	4	2	no	—
463	C₂×C₆₇	—	4	4	no	—
464	C₂×C₆₇	—	4	2	no	—
465	C₂×C₆₇	—	8	2	no	—
466	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
467	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
468	C₂×C₆₇	#3585	1	1	yes	characteristic
469	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₄×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#3125	C₂×C₆₇	1	4	yes	complemented
472	#3118	C₂×C₆₇	1	4	yes	complemented
473	#3116	C₂×C₆₇	1	2	yes	complemented
474	#3109	C₂×C₆₇	1	2	yes	complemented
475	#3106	C₂×C₆₇	1	2	yes	complemented
476	#3101	C₂×C₆₇	1	2	yes	complemented
477	#3099	C₂×C₆₇	1	2	yes	complemented
478	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
479	C₂×#476	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#3012	C₂×C₆₇	1	2	yes	complemented
483	#2952	C₂×C₆₇	1	2	yes	complemented
484	#2946	C₂×C₆₇	1	2	yes	complemented
485	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
486	C₆₇	#60597	1	1	yes	characteristic, direct product factor, Sylow
487	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
489	C₂×#135	C₂²×C₆₇	1	2	yes	—
490	#556	—	2	1	no	—
491	#555	—	2	1	no	—
492	#554	—	2	1	no	—
493	#553	—	2	2	no	—
494	#548	—	2	2	no	—
495	#547	—	2	1	no	—
496	#542	C₂²×C₆₇	1	4	yes	complemented
497	#537	C₂²×C₆₇	1	2	yes	—
498	#533	C₂²×C₆₇	1	2	yes	complemented
499	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	#532	C₂²×C₆₇	1	2	yes	complemented
501	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
502	#520	—	2	1	no	—
503	#520	C₂²×C₆₇	1	2	yes	—
504	#520	C₂²×C₆₇	1	1	yes	characteristic
505	#520	C₂²×C₆₇	1	1	yes	characteristic
506	#520	C₂²×C₆₇	1	2	yes	complemented
507	#518	—	2	1	no	—
508	#518	—	2	2	no	—
509	#518	C₂²×C₆₇	1	2	yes	—
510	#518	C₂²×C₆₇	1	1	yes	characteristic
511	C₄×#41	—	2	1	no	—
512	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
513	C₄×#41	C₂²×C₆₇	1	2	yes	—
514	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
515	C₂×C₄×D₄	—	2	2	no	—
516	C₂×C₄×D₄	—	2	1	no	—
517	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
518	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
519	#485	C₂²×C₆₇	1	4	yes	complemented
520	#483	C₂²×C₆₇	1	4	yes	complemented
521	#482	C₂²×C₆₇	1	4	yes	complemented
522	#481	C₂²×C₆₇	1	4	yes	complemented
523	#477	C₂²×C₆₇	1	2	yes	complemented
524	#476	C₂²×C₆₇	1	2	yes	complemented
525	#476	C₂²×C₆₇	1	2	yes	complemented
526	#476	C₂²×C₆₇	1	2	yes	complemented
527	#476	C₂²×C₆₇	1	4	yes	complemented
528	#475	C₂²×C₆₇	1	2	yes	complemented
529	#474	C₂²×C₆₇	1	2	yes	complemented
530	#464	C₂²×C₆₇	1	2	yes	complemented
531	#463	C₂²×C₆₇	1	2	yes	complemented
532	#463	C₂²×C₆₇	1	4	yes	complemented
533	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
535	#461	C₂²×C₆₇	1	2	yes	complemented
536	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	#459	C₂²×C₆₇	1	2	yes	complemented
538	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	#452	C₂²×C₆₇	1	4	yes	—
540	#450	C₂²×C₆₇	1	4	yes	—
541	#449	C₂²×C₆₇	1	4	yes	—
542	#447	C₂²×C₆₇	1	4	yes	—
543	#442	C₂²×C₆₇	1	4	yes	complemented
544	#442	C₂²×C₆₇	1	4	yes	complemented
545	#441	C₂²×C₆₇	1	4	yes	complemented
546	#440	C₂²×C₆₇	1	4	yes	complemented
547	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
548	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
549	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
550	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
551	#433	C₂²×C₆₇	1	4	yes	complemented
552	#432	C₂²×C₆₇	1	2	yes	complemented
553	#431	C₂²×C₆₇	1	2	yes	complemented
554	#428	C₂²×C₆₇	1	2	yes	complemented
555	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
556	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
557	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	#417	C₂²×C₆₇	1	2	yes	—
559	#417	C₂²×C₆₇	1	2	yes	complemented
560	#416	C₂²×C₆₇	1	2	yes	complemented
561	C₂×#102	C₂²×C₆₇	1	2	yes	—
562	#408	C₂²×C₆₇	1	2	yes	—
563	#405	C₂²×C₆₇	1	2	yes	complemented
564	H(5,𝔽₂)	—	2	4	no	—
565	H(5,𝔽₂)	—	2	4	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	C₂³×C₆₇	1	2	yes	—
569	C₂×#41	C₂³×C₆₇	1	2	yes	—
570	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	—	2	1	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
576	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	—	2	1	no	—
578	C₂³×C₄	—	2	2	no	—
579	AGL(1,ℤ/8)	—	2	8	no	—
580	#135	—	2	8	no	—
581	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
584	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
585	C₂×D₈	C₂³×C₆₇	1	2	yes	—
586	C₂×D₈	C₂³×C₆₇	1	4	yes	—
587	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
588	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	—	2	1	no	—
591	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
593	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
594	#127	C₂³×C₆₇	1	1	yes	characteristic
595	#126	—	2	4	no	—
596	#125	—	2	2	no	—
597	#124	—	2	4	no	—
598	#124	—	2	2	no	—
599	#124	C₂³×C₆₇	1	2	yes	—
600	#123	—	2	4	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	4	no	—
604	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	C₂³×C₆₇	1	4	yes	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
614	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
617	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	D₄×C₆₇	1	2	yes	—
641	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
642	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
643	C₄×D₄	D₄×C₆₇	1	2	yes	—
644	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₄×D₄	C₂³×C₆₇	1	2	yes	—
646	C₄×D₄	C₂³×C₆₇	1	2	yes	—
647	C₄×D₄	C₂³×C₆₇	1	2	yes	—
648	C₄×D₄	C₂³×C₆₇	1	2	yes	—
649	C₄×D₄	C₂³×C₆₇	1	2	yes	—
650	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₆₇	1	4	yes	—
652	#117	—	2	2	no	—
653	#117	—	2	1	no	—
654	#117	—	2	2	no	—
655	#117	—	2	2	no	—
656	#117	—	2	1	no	—
657	#117	—	2	2	no	—
658	#117	C₂³×C₆₇	1	1	yes	characteristic
659	#117	C₂³×C₆₇	1	2	yes	—
660	#117	C₂³×C₆₇	1	1	yes	characteristic
661	#117	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	2	no	—
671	C₂×C₂²⋊C₄	—	2	2	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
678	#107	C₂³×C₆₇	1	4	yes	—
679	#106	C₂³×C₆₇	1	4	yes	—
680	#106	C₂³×C₆₇	1	4	yes	—
681	#106	C₂³×C₆₇	1	4	yes	—
682	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
683	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
684	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
685	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
686	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
687	#103	C₂³×C₆₇	1	2	yes	—
688	#103	C₂³×C₆₇	1	2	yes	—
689	#103	C₂³×C₆₇	1	4	yes	—
690	#103	C₂³×C₆₇	1	4	yes	—
691	#102	C₂³×C₆₇	1	4	yes	—
692	#102	C₂³×C₆₇	1	4	yes	—
693	#102	C₂³×C₆₇	1	2	yes	—
694	#102	C₂³×C₆₇	1	2	yes	—
695	#102	C₂³×C₆₇	1	4	yes	—
696	#102	C₂³×C₆₇	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
698	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
699	#97	C₂³×C₆₇	1	4	yes	—
700	C₄×C₈	C₂³×C₆₇	1	4	yes	—
701	C₂⁴	—	2	2	no	—
702	C₂⁴	—	2	1	no	—
703	#41	—	2	8	no	—
704	#41	—	2	4	no	—
705	#41	—	2	4	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	2	2	no	—
709	#41	—	2	4	no	—
710	#41	—	2	4	no	—
711	#41	—	8	4	no	—
712	#41	#41×C₆₇	1	4	yes	complemented
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	8	2	no	—
716	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
717	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
718	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₂×D₄	—	2	16	no	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
733	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₂×D₄	#41×C₆₇	1	4	yes	complemented
735	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	1	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	4	no	—
752	C₂²×C₄	—	8	2	no	—
753	C₂²×C₄	—	8	4	no	—
754	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	Q₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	2	8	no	—
764	D₈	—	2	4	no	—
765	D₈	—	2	8	no	—
766	M₁₆	—	2	4	no	—
767	C₂×C₈	—	2	4	no	—
768	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
769	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
770	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
786	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
790	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	4	no	—
814	C₄²	C₂×D₄×C₆₇	1	2	yes	—
815	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
817	C₄²	C₂×D₄×C₆₇	1	2	yes	—
818	C₄²	C₂⁴×C₆₇	1	2	yes	—
819	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
821	C₂³	—	2	8	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	8	1	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	1	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
831	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	8	2	no	—
838	Q₈	C₂×#41×C₆₇	1	2	yes	—
839	D₄	—	2	8	no	—
840	D₄	—	2	8	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	4	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	1	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	2	no	—
852	D₄	—	8	4	no	—
853	D₄	C₂×#41×C₆₇	1	2	yes	—
854	D₄	C₂×#41×C₆₇	1	4	yes	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
883	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
889	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
890	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
891	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	4	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	#525×C₆₇	1	2	yes	—
912	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	4	no	—
924	C₄	—	4	2	no	—
925	C₄	#525×C₆₇	1	2	yes	—
926	C₄	#577×C₆₇	1	2	yes	—
927	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
928	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
935	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
936	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3511	C₂	semidirect
2. C₄×H(5,𝔽₂)×C₆₇	C₂	semidirect
3. C₆₇×#3125	C₂	semidirect
4. C₆₇×#3118	C₂	semidirect
5. C₆₇×#3116	C₂	semidirect
6. C₆₇×#3109	C₂	semidirect
7. C₆₇×#3106	C₂	semidirect
8. C₆₇×#3101	C₂	semidirect
9. C₆₇×#3099	C₂	semidirect
10. C₆₇×#3079	C₂	semidirect
11. C₂×#476×C₆₇	C₂	semidirect
12. C₆₇×#3036	C₂	semidirect
13. C₆₇×#3035	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₆₇×#2952	C₂	semidirect
16. C₆₇×#2946	C₂	semidirect
17. C₆₇×#2925	C₂	semidirect
27. #542×C₆₇	C₂²	semidirect
29. #533×C₆₇	C₂²	semidirect
30. #532×C₆₇	C₂²	semidirect
31. #532×C₆₇	C₂²	semidirect
32. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
37. #520×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #483×C₆₇	C₂²	semidirect
52. #482×C₆₇	C₂²	semidirect
53. #481×C₆₇	C₂²	semidirect
54. #477×C₆₇	C₂²	semidirect
55. #476×C₆₇	C₂²	semidirect
56. #476×C₆₇	C₂²	semidirect
57. #476×C₆₇	C₂²	semidirect
58. #476×C₆₇	C₂²	semidirect
59. #475×C₆₇	C₂²	semidirect
60. #474×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #463×C₆₇	C₂²	semidirect
64. #462×C₆₇	C₂²	semidirect
65. #461×C₆₇	C₂²	semidirect
66. #461×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. #442×C₆₇	C₂²	semidirect
76. #441×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
81. C₄×D₈×C₆₇	C₂²	semidirect
82. #433×C₆₇	C₂²	semidirect
83. #432×C₆₇	C₂²	semidirect
84. #431×C₆₇	C₂²	semidirect
85. #428×C₆₇	C₂²	semidirect
86. C₂×#106×C₆₇	C₂²	semidirect
87. #423×C₆₇	C₂²	semidirect
88. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
90. #417×C₆₇	C₂²	semidirect
91. #416×C₆₇	C₂²	semidirect
94. #405×C₆₇	C₂²	semidirect
243. #41×C₆₇	#41	semidirect
265. C₂×D₄×C₆₇	#41	semidirect
460. #60597	C₆₇	direct (N × H)
469. #3511	C₂×C₆₇	semidirect
470. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
471. #3125	C₂×C₆₇	semidirect
472. #3118	C₂×C₆₇	semidirect
473. #3116	C₂×C₆₇	semidirect
474. #3109	C₂×C₆₇	semidirect
475. #3106	C₂×C₆₇	semidirect
476. #3101	C₂×C₆₇	semidirect
477. #3099	C₂×C₆₇	semidirect
478. #3079	C₂×C₆₇	semidirect
479. C₂×#476	C₂×C₆₇	semidirect
480. #3036	C₂×C₆₇	semidirect
481. #3035	C₂×C₆₇	semidirect
482. #3012	C₂×C₆₇	semidirect
483. #2952	C₂×C₆₇	semidirect
484. #2946	C₂×C₆₇	semidirect
485. #2925	C₂×C₆₇	semidirect
486. C₆₇	#60597	direct (N × H)
496. #542	C₂²×C₆₇	semidirect
498. #533	C₂²×C₆₇	semidirect
499. #532	C₂²×C₆₇	semidirect
500. #532	C₂²×C₆₇	semidirect
501. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
506. #520	C₂²×C₆₇	semidirect
519. #485	C₂²×C₆₇	semidirect
520. #483	C₂²×C₆₇	semidirect
521. #482	C₂²×C₆₇	semidirect
522. #481	C₂²×C₆₇	semidirect
523. #477	C₂²×C₆₇	semidirect
524. #476	C₂²×C₆₇	semidirect
525. #476	C₂²×C₆₇	semidirect
526. #476	C₂²×C₆₇	semidirect
527. #476	C₂²×C₆₇	semidirect
528. #475	C₂²×C₆₇	semidirect
529. #474	C₂²×C₆₇	semidirect
530. #464	C₂²×C₆₇	semidirect
531. #463	C₂²×C₆₇	semidirect
532. #463	C₂²×C₆₇	semidirect
533. #462	C₂²×C₆₇	semidirect
534. #461	C₂²×C₆₇	semidirect
535. #461	C₂²×C₆₇	semidirect
536. #460	C₂²×C₆₇	semidirect
537. #459	C₂²×C₆₇	semidirect
538. #459	C₂²×C₆₇	semidirect
543. #442	C₂²×C₆₇	semidirect
544. #442	C₂²×C₆₇	semidirect
545. #441	C₂²×C₆₇	semidirect
546. #440	C₂²×C₆₇	semidirect
547. C₄×SD₁₆	C₂²×C₆₇	semidirect
548. C₄×SD₁₆	C₂²×C₆₇	semidirect
549. C₄×SD₁₆	C₂²×C₆₇	semidirect
550. C₄×D₈	C₂²×C₆₇	semidirect
551. #433	C₂²×C₆₇	semidirect
552. #432	C₂²×C₆₇	semidirect
553. #431	C₂²×C₆₇	semidirect
554. #428	C₂²×C₆₇	semidirect
555. C₂×#106	C₂²×C₆₇	semidirect
556. #423	C₂²×C₆₇	semidirect
557. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
559. #417	C₂²×C₆₇	semidirect
560. #416	C₂²×C₆₇	semidirect
563. #405	C₂²×C₆₇	semidirect
712. #41	#41×C₆₇	semidirect
734. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₄×H(5,𝔽₂)×C₆₇	2
C₆₇×#3125	2
C₆₇×#3118	2
C₆₇×#3116	2
C₆₇×#3109	2
C₆₇×#3106	2
C₆₇×#3101	2
C₆₇×#3099	2
C₆₇×#3079	2
C₂×#476×C₆₇	2
C₆₇×#3036	2
C₆₇×#3035	2
C₆₇×#3012	2
C₆₇×#2952	2
C₆₇×#2946	2
C₆₇×#2925	2
#60597	67

Subgroups — C67×#60597 #30739848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60597 #30739848