Subgroups — C₆₇×#61668 #30740919

Order 17152.

2200 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3332	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3198	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3012	C₂	1	4	yes	maximal, complemented
17	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
21	#562×C₆₇	—	2	2	no	—
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	C₂²	1	2	yes	complemented
24	#550×C₆₇	—	2	1	no	—
25	#550×C₆₇	C₂²	1	2	yes	—
26	#550×C₆₇	C₂²	1	2	yes	—
27	#550×C₆₇	C₂²	1	2	yes	complemented
28	#547×C₆₇	C₂²	1	2	yes	complemented
29	#547×C₆₇	C₂²	1	2	yes	complemented
30	D₄²×C₆₇	—	2	2	no	—
31	D₄²×C₆₇	—	2	2	no	—
32	D₄²×C₆₇	C₂²	1	2	yes	—
33	D₄²×C₆₇	C₂²	1	2	yes	—
34	#540×C₆₇	—	2	2	no	—
35	#537×C₆₇	—	2	2	no	—
36	#537×C₆₇	C₂²	1	4	yes	complemented
37	#535×C₆₇	—	2	2	no	—
38	#535×C₆₇	C₂²	1	2	yes	—
39	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#532×C₆₇	—	2	1	no	—
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#127×C₆₇	—	2	1	no	—
44	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	#493×C₆₇	C₂²	1	2	yes	complemented
47	#492×C₆₇	C₂²	1	2	yes	complemented
48	#486×C₆₇	C₂²	1	2	yes	complemented
49	#486×C₆₇	C₂²	1	2	yes	complemented
50	#485×C₆₇	C₂²	1	2	yes	complemented
51	#482×C₆₇	C₂²	1	2	yes	complemented
52	#481×C₆₇	C₂²	1	4	yes	complemented
53	#480×C₆₇	C₂²	1	4	yes	complemented
54	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#469×C₆₇	C₂²	1	4	yes	complemented
59	#468×C₆₇	C₂²	1	4	yes	complemented
60	#466×C₆₇	C₂²	1	4	yes	complemented
61	#465×C₆₇	C₂²	1	4	yes	complemented
62	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#460×C₆₇	C₂²	1	2	yes	complemented
65	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#460×C₆₇	C₂²	1	2	yes	complemented
67	#459×C₆₇	C₂²	1	2	yes	complemented
68	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	2	yes	—
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	complemented
74	#449×C₆₇	C₂²	1	2	yes	—
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#449×C₆₇	C₂²	1	4	yes	complemented
77	#449×C₆₇	C₂²	1	4	yes	complemented
78	#447×C₆₇	C₂²	1	4	yes	complemented
79	#447×C₆₇	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
83	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
84	#436×C₆₇	C₂²	1	2	yes	complemented
85	#436×C₆₇	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
88	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#417×C₆₇	C₂²	1	4	yes	complemented
91	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
92	#408×C₆₇	C₂²	1	4	yes	complemented
93	H(5,𝔽₂)×C₆₇	—	4	4	no	—
94	H(5,𝔽₂)×C₆₇	—	4	4	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂²×D₄×C₆₇	—	2	2	no	—
103	C₂²×D₄×C₆₇	—	2	4	no	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	—	2	2	no	—
106	C₂²×D₄×C₆₇	—	2	1	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
111	#135×C₆₇	—	4	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×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×D₈×C₆₇	C₂³	1	2	yes	—
118	C₂×D₈×C₆₇	C₂³	1	4	yes	—
119	C₂×D₈×C₆₇	C₂³	1	4	yes	—
120	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
121	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
123	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	#127×C₆₇	—	2	2	no	—
127	#127×C₆₇	—	2	2	no	—
128	#127×C₆₇	—	2	2	no	—
129	#127×C₆₇	—	2	2	no	—
130	#127×C₆₇	—	2	1	no	—
131	#127×C₆₇	—	2	1	no	—
132	#127×C₆₇	D₄	1	1	yes	characteristic
133	#127×C₆₇	C₂³	1	2	yes	—
134	#127×C₆₇	C₂³	1	1	yes	characteristic
135	#127×C₆₇	C₂³	1	2	yes	—
136	#125×C₆₇	—	2	2	no	—
137	#125×C₆₇	—	2	1	no	—
138	#124×C₆₇	—	2	2	no	—
139	#124×C₆₇	—	2	1	no	—
140	#124×C₆₇	D₄	1	2	yes	—
141	#123×C₆₇	—	2	4	no	—
142	#123×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	4	no	—
144	C₂²⋊Q₈×C₆₇	—	2	1	no	—
145	C₂²⋊Q₈×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	—	2	4	no	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
149	#121×C₆₇	—	2	4	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	2	no	—
152	#121×C₆₇	—	2	4	no	—
153	#121×C₆₇	—	2	1	no	—
154	#121×C₆₇	—	2	2	no	—
155	#121×C₆₇	—	2	2	no	—
156	#121×C₆₇	—	2	4	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	D₄	1	2	yes	—
160	#121×C₆₇	D₄	1	2	yes	—
161	#121×C₆₇	C₂³	1	2	yes	—
162	#121×C₆₇	C₂³	1	4	yes	—
163	#121×C₆₇	C₂³	1	4	yes	—
164	#121×C₆₇	C₂³	1	4	yes	—
165	#120×C₆₇	—	2	4	no	—
166	#120×C₆₇	—	2	4	no	—
167	#120×C₆₇	—	2	4	no	—
168	C₄×Q₈×C₆₇	—	2	1	no	—
169	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
170	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	1	no	—
174	C₄×D₄×C₆₇	—	2	1	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	2	no	—
177	C₄×D₄×C₆₇	—	2	2	no	—
178	C₄×D₄×C₆₇	—	2	1	no	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₆₇	C₂³	1	2	yes	—
183	C₄×D₄×C₆₇	C₂³	1	2	yes	—
184	#117×C₆₇	—	2	1	no	—
185	#117×C₆₇	—	2	1	no	—
186	#117×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
189	C₂×C₄²×C₆₇	—	2	1	no	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	#107×C₆₇	C₂³	1	2	yes	—
192	#107×C₆₇	C₂³	1	2	yes	—
193	#106×C₆₇	C₂³	1	2	yes	—
194	#106×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
199	#103×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	2	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₄×C₈×C₆₇	C₂³	1	2	yes	—
216	C₄×C₈×C₆₇	C₂³	1	2	yes	—
217	C₂⁴×C₆₇	—	2	4	no	—
218	C₂⁴×C₆₇	—	2	2	no	—
219	#41×C₆₇	—	2	2	no	—
220	#41×C₆₇	—	2	2	no	—
221	#41×C₆₇	—	2	8	no	—
222	#41×C₆₇	—	4	2	no	—
223	#41×C₆₇	—	4	2	no	—
224	#41×C₆₇	—	4	4	no	—
225	#41×C₆₇	—	4	8	no	—
226	#41×C₆₇	—	4	4	no	—
227	#41×C₆₇	—	4	4	no	—
228	#41×C₆₇	—	8	2	no	—
229	#41×C₆₇	—	8	4	no	—
230	C₂×Q₈×C₆₇	—	2	1	no	—
231	C₂×Q₈×C₆₇	—	2	1	no	—
232	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂×D₄×C₆₇	—	2	1	no	—
236	C₂×D₄×C₆₇	—	2	8	no	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	4	4	no	—
252	C₂×D₄×C₆₇	—	4	2	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	8	no	—
255	C₂×D₄×C₆₇	—	4	16	no	—
256	C₂×D₄×C₆₇	—	8	2	no	—
257	C₂×D₄×C₆₇	—	8	2	no	—
258	C₂×D₄×C₆₇	—	8	4	no	—
259	C₂×D₄×C₆₇	—	8	4	no	—
260	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
263	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	1	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
278	Q₁₆×C₆₇	—	2	4	no	—
279	SD₁₆×C₆₇	—	2	4	no	—
280	SD₁₆×C₆₇	—	2	4	no	—
281	SD₁₆×C₆₇	—	4	4	no	—
282	SD₁₆×C₆₇	—	4	4	no	—
283	D₈×C₆₇	—	2	4	no	—
284	D₈×C₆₇	—	4	4	no	—
285	D₈×C₆₇	—	4	4	no	—
286	M₁₆×C₆₇	—	4	4	no	—
287	C₂×C₈×C₆₇	—	4	4	no	—
288	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
289	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
290	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
291	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₆₇	—	2	1	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	1	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	1	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
319	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
320	C₄²×C₆₇	—	2	1	no	—
321	C₄²×C₆₇	—	2	1	no	—
322	C₄²×C₆₇	—	2	1	no	—
323	C₄²×C₆₇	—	2	2	no	—
324	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂³×C₆₇	—	2	1	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	4	no	—
331	C₂³×C₆₇	—	4	8	no	—
332	C₂³×C₆₇	—	4	4	no	—
333	C₂³×C₆₇	—	8	2	no	—
334	C₂³×C₆₇	—	8	4	no	—
335	C₂³×C₆₇	—	8	2	no	—
336	C₂³×C₆₇	—	8	4	no	—
337	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
339	Q₈×C₆₇	—	2	1	no	—
340	Q₈×C₆₇	—	2	2	no	—
341	Q₈×C₆₇	—	2	2	no	—
342	Q₈×C₆₇	—	4	2	no	—
343	Q₈×C₆₇	—	4	2	no	—
344	Q₈×C₆₇	—	8	1	no	—
345	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
346	D₄×C₆₇	—	2	4	no	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	2	4	no	—
349	D₄×C₆₇	—	2	1	no	—
350	D₄×C₆₇	—	2	2	no	—
351	D₄×C₆₇	—	2	2	no	—
352	D₄×C₆₇	—	2	4	no	—
353	D₄×C₆₇	—	2	4	no	—
354	D₄×C₆₇	—	4	2	no	—
355	D₄×C₆₇	—	4	4	no	—
356	D₄×C₆₇	—	4	8	no	—
357	D₄×C₆₇	—	4	8	no	—
358	D₄×C₆₇	—	4	4	no	—
359	D₄×C₆₇	—	4	4	no	—
360	D₄×C₆₇	—	4	2	no	—
361	D₄×C₆₇	—	4	4	no	—
362	D₄×C₆₇	—	8	2	no	—
363	D₄×C₆₇	—	8	2	no	—
364	D₄×C₆₇	—	8	1	no	—
365	D₄×C₆₇	—	8	4	no	—
366	D₄×C₆₇	—	8	4	no	—
367	D₄×C₆₇	—	8	4	no	—
368	D₄×C₆₇	—	8	2	no	—
369	D₄×C₆₇	—	8	4	no	—
370	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	4	no	—
376	C₂×C₄×C₆₇	—	2	4	no	—
377	C₂×C₄×C₆₇	—	2	1	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	4	8	no	—
385	C₂×C₄×C₆₇	—	4	2	no	—
386	C₂×C₄×C₆₇	—	4	4	no	—
387	C₂×C₄×C₆₇	—	4	2	no	—
388	C₂×C₄×C₆₇	—	8	4	no	—
389	C₂×C₄×C₆₇	—	8	4	no	—
390	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
394	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
397	C₈×C₆₇	—	2	2	no	—
398	C₈×C₆₇	—	2	2	no	—
399	C₈×C₆₇	—	2	2	no	—
400	C₈×C₆₇	—	2	2	no	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	2	1	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	1	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	—	4	1	no	—
410	C₂²×C₆₇	—	4	4	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	4	no	—
414	C₂²×C₆₇	—	4	4	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	16	8	no	—
417	C₂²×C₆₇	—	16	4	no	—
418	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₆₇	—	2	1	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	4	no	—
422	C₄×C₆₇	—	2	1	no	—
423	C₄×C₆₇	—	2	1	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	1	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	#576	1	2	yes	—
430	C₄×C₆₇	#577	1	2	yes	—
431	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	#61668	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₆₇	—	4	4	no	—
435	C₂×C₆₇	—	4	1	no	—
436	C₂×C₆₇	—	4	2	no	—
437	C₂×C₆₇	—	8	2	no	—
438	C₂×C₆₇	—	8	4	no	—
439	C₂×C₆₇	#3484	1	1	yes	characteristic
440	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
441	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
442	#3548	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#3333	C₂×C₆₇	1	2	yes	complemented
445	#3332	C₂×C₆₇	1	2	yes	complemented
446	#3295	C₂×C₆₇	1	2	yes	complemented
447	#3294	C₂×C₆₇	1	2	yes	complemented
448	#3287	C₂×C₆₇	1	2	yes	complemented
449	#3284	C₂×C₆₇	1	2	yes	complemented
450	#3274	C₂×C₆₇	1	2	yes	complemented
451	#3272	C₂×C₆₇	1	2	yes	complemented
452	#3208	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#3205	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#3198	C₂×C₆₇	1	4	yes	complemented
455	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#3012	C₂×C₆₇	1	4	yes	complemented
458	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
459	C₆₇	#61668	1	1	yes	characteristic, direct product factor, Sylow
460	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
461	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
462	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
463	#562	—	2	2	no	—
464	#554	—	2	1	no	—
465	#554	C₂²×C₆₇	1	2	yes	complemented
466	#550	—	2	1	no	—
467	#550	C₂²×C₆₇	1	2	yes	—
468	#550	C₂²×C₆₇	1	2	yes	—
469	#550	C₂²×C₆₇	1	2	yes	complemented
470	#547	C₂²×C₆₇	1	2	yes	complemented
471	#547	C₂²×C₆₇	1	2	yes	complemented
472	D₄²	—	2	2	no	—
473	D₄²	—	2	2	no	—
474	D₄²	C₂²×C₆₇	1	2	yes	—
475	D₄²	C₂²×C₆₇	1	2	yes	—
476	#540	—	2	2	no	—
477	#537	—	2	2	no	—
478	#537	C₂²×C₆₇	1	4	yes	complemented
479	#535	—	2	2	no	—
480	#535	C₂²×C₆₇	1	2	yes	—
481	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#532	—	2	1	no	—
483	#532	C₂²×C₆₇	1	1	yes	characteristic
484	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	C₂×#127	—	2	1	no	—
486	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
487	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
488	#493	C₂²×C₆₇	1	2	yes	complemented
489	#492	C₂²×C₆₇	1	2	yes	complemented
490	#486	C₂²×C₆₇	1	2	yes	complemented
491	#486	C₂²×C₆₇	1	2	yes	complemented
492	#485	C₂²×C₆₇	1	2	yes	complemented
493	#482	C₂²×C₆₇	1	2	yes	complemented
494	#481	C₂²×C₆₇	1	4	yes	complemented
495	#480	C₂²×C₆₇	1	4	yes	complemented
496	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	#469	C₂²×C₆₇	1	4	yes	complemented
501	#468	C₂²×C₆₇	1	4	yes	complemented
502	#466	C₂²×C₆₇	1	4	yes	complemented
503	#465	C₂²×C₆₇	1	4	yes	complemented
504	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
506	#460	C₂²×C₆₇	1	2	yes	complemented
507	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	#460	C₂²×C₆₇	1	2	yes	complemented
509	#459	C₂²×C₆₇	1	2	yes	complemented
510	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	#459	C₂²×C₆₇	1	2	yes	complemented
512	#452	C₂²×C₆₇	1	2	yes	—
513	#452	C₂²×C₆₇	1	4	yes	complemented
514	#450	C₂²×C₆₇	1	4	yes	complemented
515	#450	C₂²×C₆₇	1	4	yes	complemented
516	#449	C₂²×C₆₇	1	2	yes	—
517	#449	C₂²×C₆₇	1	4	yes	complemented
518	#449	C₂²×C₆₇	1	4	yes	complemented
519	#449	C₂²×C₆₇	1	4	yes	complemented
520	#447	C₂²×C₆₇	1	4	yes	complemented
521	#447	C₂²×C₆₇	1	4	yes	complemented
522	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
523	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
524	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
525	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
526	#436	C₂²×C₆₇	1	2	yes	complemented
527	#436	C₂²×C₆₇	1	2	yes	complemented
528	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
529	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
530	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
532	#417	C₂²×C₆₇	1	4	yes	complemented
533	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
534	#408	C₂²×C₆₇	1	4	yes	complemented
535	H(5,𝔽₂)	—	4	4	no	—
536	H(5,𝔽₂)	—	4	4	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×#41	C₂³×C₆₇	1	4	yes	—
542	C₂×#41	C₂³×C₆₇	1	4	yes	—
543	C₂×#41	C₂³×C₆₇	1	2	yes	—
544	C₂²×D₄	—	2	2	no	—
545	C₂²×D₄	—	2	4	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
551	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
552	AGL(1,ℤ/8)	—	4	8	no	—
553	#135	—	4	8	no	—
554	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
559	C₂×D₈	C₂³×C₆₇	1	2	yes	—
560	C₂×D₈	C₂³×C₆₇	1	4	yes	—
561	C₂×D₈	C₂³×C₆₇	1	4	yes	—
562	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
563	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
564	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
568	#127	—	2	2	no	—
569	#127	—	2	2	no	—
570	#127	—	2	2	no	—
571	#127	—	2	2	no	—
572	#127	—	2	1	no	—
573	#127	—	2	1	no	—
574	#127	D₄×C₆₇	1	1	yes	characteristic
575	#127	C₂³×C₆₇	1	2	yes	—
576	#127	C₂³×C₆₇	1	2	yes	—
577	#127	C₂³×C₆₇	1	1	yes	characteristic
578	#125	—	2	2	no	—
579	#125	—	2	1	no	—
580	#124	—	2	2	no	—
581	#124	—	2	1	no	—
582	#124	D₄×C₆₇	1	2	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
591	#121	—	2	4	no	—
592	#121	—	2	4	no	—
593	#121	—	2	2	no	—
594	#121	—	2	4	no	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	4	no	—
599	#121	—	2	4	no	—
600	#121	—	2	4	no	—
601	#121	D₄×C₆₇	1	2	yes	—
602	#121	D₄×C₆₇	1	2	yes	—
603	#121	C₂³×C₆₇	1	2	yes	—
604	#121	C₂³×C₆₇	1	4	yes	—
605	#121	C₂³×C₆₇	1	4	yes	—
606	#121	C₂³×C₆₇	1	4	yes	—
607	#120	—	2	4	no	—
608	#120	—	2	4	no	—
609	#120	—	2	4	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₆₇	1	2	yes	—
624	C₄×D₄	C₂³×C₆₇	1	2	yes	—
625	C₄×D₄	C₂³×C₆₇	1	2	yes	—
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	C₂³×C₆₇	1	1	yes	characteristic
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
633	#107	C₂³×C₆₇	1	2	yes	—
634	#107	C₂³×C₆₇	1	2	yes	—
635	#106	C₂³×C₆₇	1	2	yes	—
636	#106	C₂³×C₆₇	1	2	yes	—
637	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
639	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
641	#103	C₂³×C₆₇	1	2	yes	—
642	#103	C₂³×C₆₇	1	2	yes	—
643	#103	C₂³×C₆₇	1	2	yes	—
644	#103	C₂³×C₆₇	1	2	yes	—
645	#102	C₂³×C₆₇	1	2	yes	—
646	#102	C₂³×C₆₇	1	2	yes	—
647	#102	C₂³×C₆₇	1	4	yes	—
648	#102	C₂³×C₆₇	1	4	yes	—
649	#102	C₂³×C₆₇	1	4	yes	—
650	#102	C₂³×C₆₇	1	4	yes	—
651	#102	C₂³×C₆₇	1	2	yes	—
652	#102	C₂³×C₆₇	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
655	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
656	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
657	C₄×C₈	C₂³×C₆₇	1	2	yes	—
658	C₄×C₈	C₂³×C₆₇	1	2	yes	—
659	C₂⁴	—	2	4	no	—
660	C₂⁴	—	2	2	no	—
661	#41	—	2	2	no	—
662	#41	—	2	2	no	—
663	#41	—	2	8	no	—
664	#41	—	4	2	no	—
665	#41	—	4	2	no	—
666	#41	—	4	4	no	—
667	#41	—	4	8	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	8	2	no	—
671	#41	—	8	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	—	4	16	no	—
698	C₂×D₄	—	8	2	no	—
699	C₂×D₄	—	8	2	no	—
700	C₂×D₄	—	8	4	no	—
701	C₂×D₄	—	8	4	no	—
702	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
705	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
706	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
707	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
720	Q₁₆	—	2	4	no	—
721	SD₁₆	—	2	4	no	—
722	SD₁₆	—	2	4	no	—
723	SD₁₆	—	4	4	no	—
724	SD₁₆	—	4	4	no	—
725	D₈	—	2	4	no	—
726	D₈	—	4	4	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	4	4	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
731	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
732	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
733	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
745	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
761	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	2	no	—
766	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
768	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
770	C₂³	—	2	1	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	4	no	—
773	C₂³	—	4	8	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	4	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	4	no	—
779	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	2	no	—
786	Q₈	—	8	1	no	—
787	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
788	D₄	—	2	4	no	—
789	D₄	—	2	4	no	—
790	D₄	—	2	4	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	8	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	1	no	—
807	D₄	—	8	4	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	4	no	—
812	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
836	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
838	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	4	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	16	8	no	—
859	C₂²	—	16	4	no	—
860	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	4	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	#576×C₆₇	1	2	yes	—
872	C₄	#577×C₆₇	1	2	yes	—
873	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
874	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
875	C₂	—	4	1	no	—
876	C₂	—	4	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	8	4	no	—
879	C₂	—	8	2	no	—
880	C₂	C₆₇×#3484	1	1	yes	characteristic
881	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
882	C₂	C₂×#577×C₆₇	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3548	C₂	semidirect
2. C₆₇×#3498	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3332	C₂	semidirect
5. C₆₇×#3295	C₂	semidirect
6. C₆₇×#3294	C₂	semidirect
7. C₆₇×#3287	C₂	semidirect
8. C₆₇×#3284	C₂	semidirect
9. C₆₇×#3274	C₂	semidirect
10. C₆₇×#3272	C₂	semidirect
11. C₆₇×#3208	C₂	semidirect
12. C₆₇×#3205	C₂	semidirect
13. C₆₇×#3198	C₂	semidirect
14. C₆₇×#3107	C₂	semidirect
15. C₆₇×#3106	C₂	semidirect
16. C₆₇×#3012	C₂	semidirect
17. C₆₇×#2979	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
23. #554×C₆₇	C₂²	semidirect
27. #550×C₆₇	C₂²	semidirect
28. #547×C₆₇	C₂²	semidirect
29. #547×C₆₇	C₂²	semidirect
36. #537×C₆₇	C₂²	semidirect
39. #533×C₆₇	C₂²	semidirect
42. #532×C₆₇	C₂²	semidirect
46. #493×C₆₇	C₂²	semidirect
47. #492×C₆₇	C₂²	semidirect
48. #486×C₆₇	C₂²	semidirect
49. #486×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #482×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
53. #480×C₆₇	C₂²	semidirect
54. #477×C₆₇	C₂²	semidirect
55. #476×C₆₇	C₂²	semidirect
56. #475×C₆₇	C₂²	semidirect
57. #474×C₆₇	C₂²	semidirect
58. #469×C₆₇	C₂²	semidirect
59. #468×C₆₇	C₂²	semidirect
60. #466×C₆₇	C₂²	semidirect
61. #465×C₆₇	C₂²	semidirect
62. #462×C₆₇	C₂²	semidirect
63. #461×C₆₇	C₂²	semidirect
64. #460×C₆₇	C₂²	semidirect
65. #460×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #459×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #450×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #449×C₆₇	C₂²	semidirect
77. #449×C₆₇	C₂²	semidirect
78. #447×C₆₇	C₂²	semidirect
79. #447×C₆₇	C₂²	semidirect
80. C₄×Q₁₆×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
82. C₄×SD₁₆×C₆₇	C₂²	semidirect
83. C₄×D₈×C₆₇	C₂²	semidirect
84. #436×C₆₇	C₂²	semidirect
85. #436×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. C₈×D₄×C₆₇	C₂²	semidirect
88. #431×C₆₇	C₂²	semidirect
89. #431×C₆₇	C₂²	semidirect
90. #417×C₆₇	C₂²	semidirect
91. C₂×#102×C₆₇	C₂²	semidirect
92. #408×C₆₇	C₂²	semidirect
433. #61668	C₆₇	direct (N × H)
442. #3548	C₂×C₆₇	semidirect
443. #3498	C₂×C₆₇	semidirect
444. #3333	C₂×C₆₇	semidirect
445. #3332	C₂×C₆₇	semidirect
446. #3295	C₂×C₆₇	semidirect
447. #3294	C₂×C₆₇	semidirect
448. #3287	C₂×C₆₇	semidirect
449. #3284	C₂×C₆₇	semidirect
450. #3274	C₂×C₆₇	semidirect
451. #3272	C₂×C₆₇	semidirect
452. #3208	C₂×C₆₇	semidirect
453. #3205	C₂×C₆₇	semidirect
454. #3198	C₂×C₆₇	semidirect
455. #3107	C₂×C₆₇	semidirect
456. #3106	C₂×C₆₇	semidirect
457. #3012	C₂×C₆₇	semidirect
458. #2979	C₂×C₆₇	semidirect
459. C₆₇	#61668	direct (N × H)
461. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
462. C₂×#135	C₂²×C₆₇	semidirect
465. #554	C₂²×C₆₇	semidirect
469. #550	C₂²×C₆₇	semidirect
470. #547	C₂²×C₆₇	semidirect
471. #547	C₂²×C₆₇	semidirect
478. #537	C₂²×C₆₇	semidirect
481. #533	C₂²×C₆₇	semidirect
484. #532	C₂²×C₆₇	semidirect
488. #493	C₂²×C₆₇	semidirect
489. #492	C₂²×C₆₇	semidirect
490. #486	C₂²×C₆₇	semidirect
491. #486	C₂²×C₆₇	semidirect
492. #485	C₂²×C₆₇	semidirect
493. #482	C₂²×C₆₇	semidirect
494. #481	C₂²×C₆₇	semidirect
495. #480	C₂²×C₆₇	semidirect
496. #477	C₂²×C₆₇	semidirect
497. #476	C₂²×C₆₇	semidirect
498. #475	C₂²×C₆₇	semidirect
499. #474	C₂²×C₆₇	semidirect
500. #469	C₂²×C₆₇	semidirect
501. #468	C₂²×C₆₇	semidirect
502. #466	C₂²×C₆₇	semidirect
503. #465	C₂²×C₆₇	semidirect
504. #462	C₂²×C₆₇	semidirect
505. #461	C₂²×C₆₇	semidirect
506. #460	C₂²×C₆₇	semidirect
507. #460	C₂²×C₆₇	semidirect
508. #460	C₂²×C₆₇	semidirect
509. #459	C₂²×C₆₇	semidirect
510. #459	C₂²×C₆₇	semidirect
511. #459	C₂²×C₆₇	semidirect
513. #452	C₂²×C₆₇	semidirect
514. #450	C₂²×C₆₇	semidirect
515. #450	C₂²×C₆₇	semidirect
517. #449	C₂²×C₆₇	semidirect
518. #449	C₂²×C₆₇	semidirect
519. #449	C₂²×C₆₇	semidirect
520. #447	C₂²×C₆₇	semidirect
521. #447	C₂²×C₆₇	semidirect
522. C₄×Q₁₆	C₂²×C₆₇	semidirect
523. C₄×SD₁₆	C₂²×C₆₇	semidirect
524. C₄×SD₁₆	C₂²×C₆₇	semidirect
525. C₄×D₈	C₂²×C₆₇	semidirect
526. #436	C₂²×C₆₇	semidirect
527. #436	C₂²×C₆₇	semidirect
528. C₈×D₄	C₂²×C₆₇	semidirect
529. C₈×D₄	C₂²×C₆₇	semidirect
530. #431	C₂²×C₆₇	semidirect
531. #431	C₂²×C₆₇	semidirect
532. #417	C₂²×C₆₇	semidirect
533. C₂×#102	C₂²×C₆₇	semidirect
534. #408	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×#3548	2
C₆₇×#3498	2
C₆₇×#3333	2
C₆₇×#3332	2
C₆₇×#3295	2
C₆₇×#3294	2
C₆₇×#3287	2
C₆₇×#3284	2
C₆₇×#3274	2
C₆₇×#3272	2
C₆₇×#3208	2
C₆₇×#3205	2
C₆₇×#3198	2
C₆₇×#3107	2
C₆₇×#3106	2
C₆₇×#3012	2
C₆₇×#2979	2
#61668	67

Subgroups — C67×#61668 #30740919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61668 #30740919